Lipid Nanoparticle Database towards structure-function modeling and data-driven design for nucleic acid delivery

Domain: neuroscience
Published: 2026-01-28
Editorial outcome: major_revision

Abstract
Lipid nanoparticles (LNPs) are the leading nonviral nucleic acid delivery technology, but LNP structure-function data remains fragmented and non-standardized. Unlike protein engineering which is anchored by the centralized Protein Data Bank, the LNP field lacks a unified repository for systematic analysis. To address this, we develop Lipid Nanoparticle Database (LNPDB) (https://lnpdb.molcube.com), an integrated database and web tool that consolidates structural and functional data for 19,528 LNPs. LNPDB standardizes LNP featurization by encoding lipid composition, experimental methods, and functional results, and generates CHARMM force field files for constituent lipids to enable molecular dynamics simulations. LNPDB also supports future data contributions for continued growth. We examine the utility of LNPDB through two applications: advancing our deep learning model for predicting LNP delivery performance, and simulating bilayer dynamics to identify structural features – bilayer stability and critical packing parameter – that correlate with LNP delivery performance. Altogether, LNPDB provides the digital framework for LNP modeling and data-driven rational design.

Introduction
Lipid nanoparticles (LNPs) have emerged as the leading nonviral nucleic acid delivery technology across a variety of applications, including genome editing and protein replacement therapies for genetic diseases, and vaccines for infectious diseases and cancer1. In recent years, mRNA delivered via LNPs has been essential in combating serious infection and the spread of COVID-192. While LNP delivery systems have demonstrated therapeutic efficacy, the way in which LNP structural composition affects functional delivery of nucleic acids is incompletely understood. Greater understanding of the structure-function relationship of LNPs has the potential to facilitate the development of the next-generation of rationally-designed nanomedicines3.

LNPs for nucleic acid delivery commonly consist of four lipid components4. The primary component is the ionizable cationic lipid, which complexes with the negatively charged nucleic acid and facilitates endosomal escape5. The other components include the helper lipid, cholesterol, and polyethylene glycol (PEG) lipid4. Extensive in vitro and in vivo screening over decades has revealed that varying both the type and ratios of these four lipid components significantly affects LNP delivery performance5–11. Yet, the resulting data from these screens have remained dispersed across studies without standardized formatting, limiting systematic analysis.

This challenge of fragmented data in the LNP field differs from the data infrastructure in protein engineering, where the recent success of deep learning models like AlphaFold12,13 was made possible by the Protein Data Bank (PDB), a centralized repository that compiles over 200,000 protein structures derived from decades of structural biology experiments. The PDB-to-AlphaFold paradigm underscores the foundational role of large, high-quality datasets in enabling deep learning breakthroughs in the biosciences14. However, in contrast to protein engineering, the lipid-based nanomedicine field lacks a unified repository for LNP structure-function data, presenting a barrier to machine learning and predictive modeling.

In recent years, there have been efforts to incorporate machine learning into the screening of mRNA LNPs. One prior study used classifier models trained on 584 LNPs with different ionizable lipids to predict delivery efficacy15. Another study developed a graph neural network model, AGILE, trained on 1200 LNPs with different ionizable lipids to predict efficacy16. Most recently, a group introduced a message-passing neural network architecture, LiON, trained on 8727 LNPs to engineer new best-in-class ionizable lipids17. All of these methods, including a recent effort to synchronize data across studies18, reflect important first steps in bringing machine learning to lipid nanomedicine; however, there are areas for improvement. First, the datasets used to train these models are limited in size and scope, and offer no way to incorporate future LNP data, restricting their long-term utility. Second, these approaches have focused primarily on ionizable lipid design, overlooking the established contributions of helper lipid9,11, cholesterol10, and PEG lipid19,20 compositions and ratios to performance. Third, these studies have relied on representing ionizable lipids as two-dimensional static graphs as input features for model learning, neglecting potentially important three-dimensional conformational and dynamic features. Current experimental techniques like small-angle X-ray scattering (SAXS)21,22 and cryogenic electron microscopy (cryo-EM)22,23 are low-throughput, low-resolution, and cost-prohibitive, which makes it challenging to obtain the three-dimensional structural data on lipids needed for modeling.

Towards addressing these limitations to advance data-driven rational design for nucleic acid delivery, here we develop Lipid Nanoparticle Database (LNPDB) (https://lnpdb.molcube.com). LNPDB is an integrated database and web tool that compiles structure-function data for 19,528 LNP formulations, representing 12,845 unique ionizable lipids across 42 publications (as of August 2025). LNPDB standardizes the featurization of LNPs by encoding their lipid composition, experimental methods, and functional results. LNPDB allows users to systematically search and filter the database. Future user contributions are also supported, enabling LNPDB to expand over time as new data are deposited. Additionally, LNPDB provides CHARMM24 force field topology and parameter files for all constituent lipids, allowing all-atom molecular dynamics (MD) simulations to generate three-dimensional, time-resolved lipid data that can enhance predictive modeling. For rational LNP design, MD simulations offer a new modality to generate dynamic structural data for lipids not readily accessible with current experimental methods.

In this paper, we introduce the curated dataset currently available in LNPDB and outline the functionality of the accompanying web tool. We next examine two applications of LNPDB towards learning structure-function relationships of LNPs. First, we improve our deep learning model LiON for predicting LNP delivery performance. Second, we simulate bilayer dynamics for select LNP formulations and find that two structural features—bilayer stability and critical packing parameter (CPP) of the ionizable lipid—are associated with LNP delivery performance. Recent studies25–27 in LNP design have used MD to study mRNA LNP behavior, specifically to investigate pH-sensitive structural transitions; however, our study is the first to leverage features extracted from MD simulations to predict LNP performance, providing a physics-based, data-efficient alternative to traditional deep learning models that rely on two-dimensional static chemical structures. Altogether, this work develops LNPDB as a tool to advance LNP modeling and data-driven rational design for nucleic acid delivery.

Results
LNPDB is an interactive LNP structure-function data repository
The basis of LNPDB is structure-function data for 19,528 LNP formulations for nucleic acid delivery, representing 12,845 unique ionizable lipids across 42 publications6,7,11,15–17,28–63. Additionally, 269 commercially available ionizable lipids are provided (Fig. 1a, Supplementary Fig. 1, and Supplementary Table 1). LNPDB standardizes an encoding strategy for LNPs based on three general classes of features: composition, performance, and simulation (Fig. 1b). Composition features include lipid types and ratios, along with the ionizable lipid-to-nucleic acid ratio. Lipid type is represented by name and SMILES (Simplified Molecular Input Line Entry System64) strings, including parsed head-linker-tail substructures for ionizable lipids, as well as separate representations for their +1e protonated states. Experimental features include methods (e.g., mixing, delivery target, route of administration, batching, cargo type, readout technique) and functional results. Simulation features include CHARMM24 force field topology and parameter files for lipids comprising each LNP formulation, supporting all-atom MD simulations.

We have developed a web tool for LNPDB available at https://lnpdb.molcube.com. The interactive website allows users to view and search the database (Fig. 1c). Users can search for specific LNPs by LNP properties such as library source, atomic characteristics of ionizable lipids, types of helper lipid, cholesterol, and PEG lipid, molar ratio ranges, and experimental properties. Alternatively, users can search for LNPs by ionizable lipid structure or sub-structure, either by selecting from a list of head, linker, and tail groups, or by using a chemical structure drawing sketch tool. The search functionality built into LNPDB allows researchers to systematically analyze the current LNP landscape and identify any underexplored regions of chemical space for potential lipid innovation. Additionally, researchers can deposit their own LNP structure-function data using the standardized template provided on the website. This helps ensure that LNPDB grows over time as the LNP field evolves.

To visualize the diversity of LNPs and ionizable lipids present in LNPDB, representative embeddings were created using UMAP (see “Methods”). The resulting LNP and ionizable lipid landscapes demonstrate clustering patterns that largely correspond to library (i.e., publication) source, suggesting that the individual 42 studies included in LNPDB tend to explore distinct, non-overlapping regions of lipid design space (Fig. 2a). This is reinforced by our finding that within-library LNP pairs exhibit significantly higher similarity than across-library pairs (Supplementary Fig. 2a), and a UMAP of LNP fingerprints from our deep learning model LiON (as discussed below) similarly yields library-specific clusters, albeit with less pronounced separation (Supplementary Fig. 2b).

Beyond global diversity patterns, LNPDB features diverse compositional and experimental features. As shown in Fig. 2b, the molecular weight of the 12,845 unique ionizable lipids ranges from 201.31 to 3984.45, with a mean of 864.24±393.12. The number of nitrogens present in each ionizable lipid ranges from 1 to 17, with a mean of 2.54±1.41. There are 12,000 ionizable lipids with only tertiary nitrogen(s); 6437 with both tertiary and secondary nitrogens; 299 with tertiary, secondary, and primary nitrogens; 677 with only secondary nitrogen(s); and 8 with both secondary and primary nitrogens.

As for the other components besides the ionizable lipid, among the 19,528 LNP formulations, the ionizable lipid-to-nucleic acid mass ratio is most often set to 10, with a range from 0.86 to 44.58 and mean of 10.78±4.45 (Fig. 2c). The distribution of helper lipid type consists of DOPE (47.7%), DSPC (28.3%), DOTAP (12.6%), none (2.9%), MDOA (2.9%), DDAB (1.8%), 14:0 PA (1.8%), and 18:0 PG (1.8%). The distribution of PEG lipid type consists of DMG-PEG2000 (57.1%), DMPE-PEG2000 (32.4%), unreported (9.2%), none (0.9%), DSG-PEG2000 (0.1%), ALC-0159 (0.1%), DMG-C-PEG2000 (0.1%), C8-Ceramide-PEG2000 (0.1%), C16-Ceramide-PEG2000 (0.1%), DSPE-PEG2000 (0.1%), DMG-PEG5000 (0.01%), DPG-PEG2000 (0.01%), DPG-PEG5000 (0.01%), DSG-PEG5000 (0.01%), DOG-PEG2000 (0.01%), and DOG-PEG5000 (0.01%).

For experimental features, the distribution of nucleic acid cargo consists of mRNA (74.7%), siRNA (19.2%), and pDNA (6.1%) (Fig. 2d and Supplementary Fig. 1b). With respect to the type of cargo encoded by the nucleic acid, the distribution consists of firefly luciferase (90.9%), DNA barcode (3.4%), peptide barcode (2.1%), human erythropoietin (1.4%), Factor VII (0.6%), green fluorescent protein (0.6%), and renilla luciferase (0.3%). The primary delivery target involves in vitro (78.4%), lung epithelium (9.6%), liver (4.6%), muscle (2.5%), spleen (1.3%), multiorgan (1.0%), heart (0.5%), lung (0.5%), and kidney (0.5%). For the preparation method, 93.8% of LNPs were hand mixed; the remaining 6.2% were prepared via microfluidics. The readout methods report luminescence (75.2%), discretized luminescence (15.7%), protein abundance (3.9%), cellular uptake (2.5%), editing efficiency (0.7%), LRP6 knockdown (0.6%), diameter (0.5%), zeta potential (0.5%), and percent hemolysis (0.5%). Luminescence measurements quantify LNP delivery performance by reporting the level of nucleic acid transfection in target in vitro or in vivo systems. Additional summary statistics are shown in Supplementary Fig. 1.

LNPDB facilitates an improved deep learning model for predicting LNP delivery performance
In a prior study17, we introduced lipid optimization using neural networks (LiON), a deep learning model for learning ionizable lipid design towards predicting LNP delivery efficacy. LiON uses deep message-passing neural networks (D-MPNNs)65 to learn representations of ionizable lipid structure, while additional formulation details such as component ratios and experimental context are appended as auxiliary features to guide prediction.

The dataset used to train this original version of LiON involved 8727 LNP formulations17. Building on this foundation, LNPDB expands the dataset more than two fold by incorporating an additional 10,801 LNP formulations, bringing the total to 19,528. Beyond scale, LNPDB captures a more diverse and descriptive set of features for each formulation. The newly added formulations broaden the diversity of ionizable lipids and also place greater emphasis on varying the types and ratios of the other three LNP components. Moreover, as detailed in the next subsection, unlike the original dataset for LiON, LNPDB includes MD-ready CHARMM force field files for all constituent lipids, introducing a new, physics-based modeling modality altogether for assessing LNP structure-function relationships.

Given that a more robust and diverse dataset can enhance model generalization, we first revisited our deep learning framework LiON to evaluate how training on LNPDB impacts predictive performance compared to the original dataset. To compare model performance, we trained LiON on both the original dataset and LNPDB using a 70–15–15% train-validation-test split, partitioned with respect to amine identity (see “Methods”). Similar to a prior study17, we evaluated model performance as measured by the correlation between predicted and experimental delivery values. Test datasets shared between the original data and LNPDB were evaluated. The results demonstrate that LiON achieves modestly improved predictive performance for 5 out of the 7 test datasets when trained on the larger LNPDB dataset (Fig. 3a and Supplementary 3a). Overlap between LiON-learned embeddings for the original and LNPDB-added data indicates shared structure-function patterns and densely covered feature space (Supplementary Fig. 4). Moreover, despite limitations of integrating data from multiple studies as discussed in Methods, LiON models trained across datasets achieved higher predictive performance than those trained on single datasets (Supplementary Fig. 5), suggesting that training across multiple studies in LNPDB enabled LiON to learn more generalizable structure-function relationships.

With our improved LiON model trained on LNPDB, we next sought to compare the predictive performance of our model with another published LNP deep learning model, AGILE16. We find that LiON trained on LNPDB achieves significantly better predictive performance compared to AGILE for the 4 held-out test sets evaluated across different delivery targets (Fig. 3b and Supplementary Fig. 3b). Model performance was assessed using five train/validation splits with a fixed held-out test set, with mean correlation coefficients and standard deviations reported across folds. LiON trained on LNPDB has 16-fold more training data compared to AGILE, potentially enabling it to learn a broader range of structure-function relationships and generalize better to unseen data. Altogether, LNPDB supports an improved deep learning model for predicting LNP delivery performance. Importantly, LNPDB establishes a framework of training data for the continued development of next-generation deep learning models for LNP design. Moreover, given that our results demonstrates significant variation in model accuracy across libraries, future research can leverage the training data of LNPDB to design alternative models that may be better suited for the specific LNP design strategy (e.g., helper lipid optimization) or delivery target (e.g., in vivo muscle) under investigation.

LNPDB facilitates MD simulations to uncover LNP structure-function relationships
By providing CHARMM force field topology and parameter files for each lipid in 19,528 LNP formulations, LNPDB supports all-atom MD simulations of the full dataset, as well as any new formulations constructed from its constituent lipids. LNPDB represents a substantial advancement over existing CHARMM-GUI resources, which were limited to ionizable lipids comprising only 6 different head group types and 5 different tail group types66. Moreover, new lipids uploaded to LNPDB will be automatically parametrized for MD simulation as well.

MD offers a complementary alternative to machine learning models for understanding the structure-function relationships of LNPs, differing not only in the type of data produced but also in the way the data is generated. MD simulations yield three-dimensional, temporal structural information for all constituent lipids—not just the ionizable lipid—capturing both type and ratio. For small organic molecules such as those comprising LNPs, the conformational dynamics and interactions with neighboring molecules may play an outsized role in function, making MD especially informative. The importance of MD is amplified by the limited accessibility of three-dimensional structural data for lipids, as the experimental techniques SAXS21,22 and cryo-EM22,23 are low-throughput, low-resolution, and cost-prohibitive. Furthermore, unlike machine learning approaches, MD does not require training data, which is particularly valuable given that, as shown in Fig. 2a, most new ionizable lipids lie outside the distribution of previously characterized structures, potentially limiting machine learning generalization.

To demonstrate how LNPDB can be used to facilitate MD simulations, we simulated the bilayer equilibration process for a subset of LNP formulations and extracted structural features to assess correlation with experimental transfection (Fig. 4a). This use case represents just one of many potential simulation strategies enabled by the database (see “Discussion”). We used the CHARMM force field files of lipids in LNPDB to model representative bilayers for select LNP formulations (Supplementary Table 2). Each leaflet contained approximately 100 lipids. PEG lipids were excluded from our analyses, as they are typically shed prior to endosomal escape19,67,68, the key bottleneck for effective delivery69, and the physiological context that we aim to model here.

For a given LNP formulation, two bilayer conditions were simulated: fully-neutral ionizable lipids and half-neutral, half-protonated ionizable lipids. These conditions represent, respectively, the neutral pH prior to cellular uptake and the early endosome environment (pH ~ 6.5) where roughly 50% of ionizable lipids would be protonated, assuming a pKa of 6.570. All-atom simulations (N=134; 77 fully-neutral, 57 half-protonated) were run using OpenMM71 for 1.5 µs to allow for bilayer equilibration, which we observe occurring before 1 µs (Supplementary Fig. 6; see “Methods”). Any bilayer that did not remain intact—namely, through ionizable lipids escaping from the membrane—was terminated early. Additional details on simulation conditions are provided in Supplementary Table 2.

Snapshots of the final frame and density profiles of select LNP bilayer systems are shown in Fig. 4b. In all systems, protonated ionizable lipids are generally oriented with their head groups exposed at the membrane–water interface, whereas neutral ionizable lipids exhibited more variable behaviors—some remained at the surface (Fig. 4b center), while others were buried within the hydrophobic core (Fig. 4b left). We observed that certain simulated bilayers from the LM_2019 LNP library7 were unstable, with ionizable lipids dissociating from the membrane over the course of the simulation (Fig. 4b, right). Notably, we find that simulated bilayer stability is positively associated with experimental transfection, indicating in silico membrane behavior could be a useful screening criterion for the delivery potential of candidate LNPs (Fig. 4c).

Next, we aimed to analyze the simulated bilayers for additional structural features that may correlate with experimental delivery efficacy. One structural feature that we sought to quantify was CPP, which has been used to relate lipid shape to phase behavior and is hypothesized to influence endosomal escape efficiency22,25,26,69. We computed CPP values averaged across ionizable lipids for each LNP bilayer according to two different approaches: one based on volume (CPP_V) and the other based on radii of gyration (CPP_Rg) (Fig. 4d; see “Methods”). CPP values < 1 indicate a cone shape (i.e., narrower at the hydrophobic tail region buried in the membrane than at the hydrophilic head group exposed to the aqueous interface). CPP values close to 1 indicate a cylindrical shape. CPP values > 1 indicate an inverted cone shape, which has been implicated in promoting an inverse hexagonal (H_II) phase, promoting membrane fusion and endosomal escape22,69. Our CPP values derived from MD simulations demonstrate comparable relative differences consistent with experimental measurements72 for two ionizable lipids (Supplementary Fig. 7), with neutral forms having higher CPP values than their protonated counterparts (Supplementary Figs. 7 and 8), a finding which aligns with prior SAXS experiments26.

We next analyzed the subset of N=34 different LNP formulations from the LM_2019 library7 that formed stable bilayers during the simulations to assess if their ionizable lipid CPP values correlate with experimental delivery performance. We find that ionizable lipid CPP significantly predicts LNP performance. For protonated ionizable lipids, the CPP approach based on volume yields a Pearson correlation of 0.530 with delivery performance. This association strengthened when stratified by amine group: amine 12 (r=0.761), amine 2 (r=0.798), amine 3 (r=0.501) (Fig. 4e top). The alternative CPP approach based on radii of gyration of the protonated ionizable lipids also shows a robust (r=0.546) correlation with performance, with similarly improved associations when analyzed by amine group: amine 12 (r=0.745), amine 2 (r=0.760), amine 3 (r=0.420) (Fig. 4f top). Compared to protonated ionizable lipids, neutral ionizable lipids in fully-neutral systems demonstrate comparably strong correlations between CPP and delivery performance (Fig. 4e–f bottom). For both CPP approaches, we also find that the significant correlation with performance holds when analyzing neutral ionizable lipids in the half-protonated systems (Supplementary Fig. 9). Moreover, when we focused our analyses on the subset of LNPs with mean CPP values greater than 1—corresponding theoretically to a transition to negative curvature—the correlative performance improved for both the CPP_V method (protonated: overall r=0.723; neutral: overall r=0.680) and CPP_Rg method (protonated: overall r=0.621; neutral: overall r=0.646) (Supplementary Fig. 10). Some correlations for amine 3 did not reach statistical significance, likely due to its limited representation of LNPs with CPP > 1. Importantly, overall, these MD-derived correlations with experimental delivery are greater than those of the LiON deep learning model for the LM_2019 fully held-out test set (r=0.104) (Fig. 3b), underscoring the potential of MD as an alternative data-efficient modality for uncovering structure-function relationships. Moreover, we assessed whether the inclusion of PEG lipid or reducing the temperature to 298 K in simulations affected CPP and found no significant effect (Supplementary Fig. 11).

Next, we measured additional structural features of the simulated bilayers: membrane thickness, torque density, and compressibility (see “Methods”). Torque density values of the fully-neutral systems are positively associated with delivery performance (r=0.461); however, high variance in this metric limits the strength of this conclusion. The remaining features for the simulated LNP formulations did not have any significant correlations with performance (Supplementary Fig. 12). Interestingly, CPP variance also significantly predicts delivery performance, suggesting that greater ionizable lipid polymorphism could allow for more effective delivery, potentially due to increased capacity to accommodate more inverse-conical lipid geometries (Supplementary Fig. 13).

Methods
Data collection
To collect the data for the 19,528 LNPs featured in this initial version of LNPDB, we followed the same method as introduced in our prior study17. In summary, publications were selected from the literature based on the presence of large screening datasets, primarily focused on ionizable lipids, to allow for meaningful within-dataset comparisons. Additional publications were selected to broaden the representation of helper lipids, cholesterols, and PEG lipids. SMILES were created for each lipid for each publication. Functional data—most commonly delivery performance—were extracted from published heatmaps and bar plots by digitizing the figures and interpolating values based on either the color scale (heatmaps) or bar height (bar plots) as defined in the accompanying legends. Because delivery values are often reported on different scales across studies and modalities, for each publication and for each delivery context (e.g., in vivo or in vitro within the same publication), functional delivery data were standardized to have a mean 0 and a standard deviation 1. When raw luminescence values spanned several orders of magnitude, they were first log-transformed prior to standardization. Predictive performance results were separated by publication, as data points were treated as directly comparable within individual screens, but not necessarily across different screens or assay modalities. Moreover, standardization was applied to prevent overemphasis of any single dataset. The deep learning models used in this study do train across datasets to maximize the diversity of trainable data, though we recognize that the ability of data from one study to inform structure-function relationships in another is limited by inherent differences in experimental protocols, measurement modalities, and assay sensitivities across studies that may introduce systematic biases. LNPDB introduces experimental condition variables (e.g., solvents, dose) towards bridging studies, but these additions can only partially mitigate the systematic differences across laboratories and experimental setups (see “Discussion”).

A total of 269 ionizable lipids from the commercial supplier BroadPharm were also included in LNPDB, representing the full set available on the vendor’s website as of June 1, 2024.

Featurization
LNPDB standardizes an encoding strategy for LNPs based on three general classes of features: composition, performance, and simulation. Additional organizational descriptors include LNP ID, experiment ID, formulation ID, publication link, and publication PubMed ID.

Composition features include ionizable lipid name, ionizable lipid SMILES, ionizable lipid amine name, ionizable lipid amine SMILES, ionizable lipid linker name, ionizable lipid linker SMILES, ionizable lipid tail 1 name, ionizable lipid tail 1 SMILES, ionizable lipid tail 2 name, ionizable lipid tail 2 SMILES, ionizable lipid tail 3 name, ionizable lipid tail 3 SMILES, ionizable lipid tail 4 name, ionizable lipid tail 4 SMILES, ionizable lipid molar ratio, ionizable lipid-to-nucleic acid mass ratio, helper lipid name, helper lipid SMILES, helper lipid molar ratio, cholesterol name, cholesterol SMILES, cholesterol molar ratio, PEG lipid name, PEG lipid SMILES, PEG lipid molar ratio, fifth component lipid name, fifth component lipid SMILES, fifth component molar ratio, aqueous buffer, and dialysis buffer.

Experimental features include mixing preparation method, model (i.e., in vitro or in vivo), model system (e.g., HeLa), model target (e.g., lung), route of administration, cargo, cargo type (i.e., encoded protein), nucleic acid dose, readout method, batching approach, and readout value (i.e., most commonly a measure of delivery performance).

For simulation features, CHARMM topology and parameter files for all lipid components were generated (see “All-atom molecular dynamics simulations”). Ionizable lipids were modeled in both neutral and +1e protonated states. A majority of LNPs (13,097) in LNPDB include ionizable lipids that have more than one nitrogen, often with several plausible protonation sites. For simplicity, LNPDB assigns one representative +1e protonated state per ionizable lipid. To select the nitrogen for protonation for each ionizable lipid, the following rule-based decision tree was applied. If the lipid contained only a single nitrogen, that nitrogen was protonated. If multiple nitrogens were present, the nitrogen with the highest priority was protonated based on the following hierarchy: tertiary amine, secondary amine, primary amine, imidazole, pyridine, tertiary aromatic amine, secondary aromatic amine, and primary aromatic amine. Groups comprising amide or sulfonamide structures and quaternary nitrogens were excluded. If multiple candidates of the same class were found, the nitrogen closest to the molecular periphery of the ionizable lipid head—defined as having the greatest graph eccentricity (i.e., the longest existing graph distance to a terminal atom)—was selected. For specific cases within the KZ_2016 dataset involving ionizable lipids with tail amines, the most centrally-located candidate (i.e., the lowest average squared distance to all other atoms) was chosen. Once selected, the nitrogen was protonated by assigning a +1 formal charge and adjusting the SMILES accordingly. Future research is warranted to explore more accurate, dynamic protonation conditions76.

All-atom MD simulations
The CHARMM topology and parameter files for all lipid components were generated as follows: ionizable lipids were modeled in both neutral and +1e protonated states, with parameters assigned manually via CHARMM force field analogy mapping and supplemented by the CGenFF workflow77. We used the standard CHARMM force field definitions78 for helper lipids, cholesterol, and PEG lipids.

Similar to the CHARMM-GUI Membrane Builder that supports diverse lipid types66,79, LNPDB uses the latest version of the CHARMM C36 additive force field parameters. The CHARMM force field77 is designed to allow a modular, building-block approach to create force fields for molecules composed of components (blocks) similar to the ones already parametrized. Many topologies and parameters of lipids and carbohydrates in the latest version of the CHARMM C36 force field were generated using this building-block approach; and the generated force fields were further validated by comparing simulations with experimental data. Accordingly, we used a similar building-block approach for the ionizable lipids in LNPDB. We have not yet seen abnormal all-atom simulation behavior (e.g., lipid flip-flop); however, further force field optimization is recommended for specific ionizable lipids if abnormal behavior is observed.

All bilayer systems were assembled using the standalone MolCube Membrane Builder—a commercial software application analogous to the CHARMM-GUI Membrane Builder tool80—in membrane-only mode using approximately 100 lipids per leaflet and solvated with TIP3P water81 and 0.15 M NaCl.

Following the six-step equilibration procedure outlined in the CHARMM-GUI Membrane Builder protocol80,82, NVT (constant particle number, volume, and temperature) simulations were conducted at 310 K (i.e., temperature of cells treated with LNPs) with strong harmonic positional restraints on lipid heavy atoms and dihedral restraints on ionizable head groups. The restraint force constants were gradually reduced to zero over the six equilibration steps for gradual membrane relaxation. Subsequently, unrestrained NPT (constant particle number, pressure, and temperature) production runs were conducted at 310 K and 1 bar for 1.5 µs using OpenMM with a 4 fs timestep enabled by hydrogen-mass repartitioning (HMR)83,84. Temperature was maintained via a Langevin thermostat (collision frequency 1 ps⁻¹) and pressure via a semi-isotropic Monte Carlo barostat (coupling interval 0.4 ps)85,86. Bonds involving hydrogen were constrained with SHAKE87; van der Waals interactions were force-switched off between 10–12 Å88, and long-range electrostatics were treated by the Particle-Mesh Ewald method with a 12 Å real-space cutoff89. For ten bilayer systems, we additionally assessed whether the inclusion of PEG lipid or setting the temperature to 298 K (i.e., temperature of LNP synthesis) in simulations affected CPP and found no significant effect (Supplementary Fig. 11). Information for each simulation system is summarized in Supplementary Table 2. Note that the protonated systems have larger system sizes along the z-axis than their neutral counterparts because the protonated systems require more bulk region to fully solvate the system.

We ran all MD simulations on 48 NVIDIA RTX A5000 GPUs in parallel. Across the neutral systems, the average throughput was 363.86±14.93 ns/day; across the protonated systems, it was 319.11±11.65 ns/day. For the LM_2019 bilayers with a run duration of 1.5 μs, this corresponds to 4.1 days per neutral system and 4.7 days per protonated system. The full LM_2019 simulation batch, run on 48 GPUs (one per simulation), completed in about 10 days. Subsequent CPP calculations for all systems, executed on 384 CPU cores in parallel, finished in 5 h, with comparable compute times for CPP_V and CPP_Rg.

Web tool
LNPDB has been developed as a RESTful application built on Django REST Framework and React, with a PostgreSQL backend, together with RDKit for native chemical structure storage and search. Lipid molecules are represented as molecular graphs and indexed via RDKit fingerprints, enabling fast SQL-level structure and substructure queries. User contributions are handled through a CSV upload portal requiring citation metadata. Each submission triggers curator review; data are validated, standardized, and then ingested into PostgreSQL. Approved entries become searchable and visible in all table views and interactive plots via the same API, ensuring seamless integration of new LNP formulations.

UMAP visualization
UMAP visualizations were created of the high-dimensional embedding landscapes of LNPs and ionizable lipids (Fig. 2a). The embedding landscape for ionizable lipids is represented by the top ten principal components (PCs) of Morgan fingerprints90 (1024 bits, radius of 3) and the top ten PCs of Mordred descriptors91. The embedding landscape for LNPs is represented by the same axes as those for ionizable lipids, plus additional dimensions for molar ratios and the top five Morgan fingerprint PCs and top five Mordred descriptor PCs for helper lipids. UMAP visualizations were also created of the 300-dimensional embedding landscape (i.e., fingerprints) from the LiON model of LNP formulations (Supplementary Figs. 2b and 4a). Fingerprints were extracted from the penultimate linear layer of the LiON model’s feedforward neural network trained on LNPDB.

Deep learning models
As shown in Fig. 3a, we evaluated the predictive performance of LiON (lipid optimization using neural networks)17, which is based on the message-passing neural network architecture of chemprop65. To compare models trained on LNPDB versus the original dataset from our prior study, we computed Spearman correlation values between predicted and experimental delivery outcomes. This evaluation was performed on held-out test sets using a 70–15–15% train-validation-test split by amine, consistent with the approach used in our prior study17. Datasets shared between LNPDB and the original dataset are compared.

As shown in Fig. 3b, we evaluated the predictive performance of LiON trained on LNPDB compared to another deep learning model, AGILE16. To perform this analysis, each of the four datasets was fully held out as an external test set. For each held-out set, models were trained using five cross-validation folds with 80%-20% train-test splits on the remaining data. Spearman correlation values between predicted and experimental delivery performance for each fully held-out dataset were computed. For LiON trained on LNPDB, holding out an entire dataset reduced the training sample size. In contrast, AGILE maintained its original training size of 1200 LNPs, as the held-out datasets did not overlap with its training data. To run the AGILE model, the GitHub repository provided in the study was referenced, and the HeLa transfection data was used for training16.

LNP formulations selected for MD simulations
To assess whether MD simulations could provide meaningful correlations with experimental delivery performance (Fig. 4b–e), we selected N=54 LNP formulations from a prior study (LM_2019) in LNPDB, which introduced an isocyanide-mediated three-component reaction approach for ionizable lipids7. For the sake of modeling, we randomly selected to model the subset of LM_2019 LNPs that contain ionizable lipids with amines A12, A2, or A3; isocyanides Iso5 or Iso9; and any alkyl ketone7. PEG lipids were excluded from simulations, as they are typically shed prior to endosomal escape68, the key bottleneck for effective delivery69, and the physiological context that we aimed to model. This subset, drawn from a single combinatorial ionizable lipid library, was chosen as a representative example of systematic lipid library design commonly employed in the field, while keeping the scope feasible within computational limits.

Additional simulations were conducted for illustrative purposes (Figs. 1b and 4a, b) that contain PEG lipid or the common control ionizable lipids of DLin-MC3-DMA, SM-102, and ALC-0315. Details of all bilayer simulations analyzed in this study are provided in Supplementary Table 2.

Density profiles
To quantify the spatial distribution of lipid components along the membrane normal (z-axis) as shown in Fig. 4b, density profiles were computed from the final 500 ns of each 1.5 μs MD trajectory. At each frame, atomic coordinates were re-centered to have the membrane center of mass be at z = 0. For each lipid molecule, a single representative atom was used to track z-position over time: the hydroxyl oxygen for cholesterol, the phosphorus atom for helper lipids, and the nitrogen atom on the ionizable head group for ionizable lipids. These atom positions were binned along the z-axis to generate one-dimensional density histograms for each lipid type. The profiles were averaged across frames and normalized by bin width to obtain continuous density distributions, reflecting the vertical organization of each component within the bilayer.

Computing CPP using volume (CPP_V)
To quantify ionizable lipid shape, we computed CPP values. For a given stable LNP bilayer simulation, we analyzed each timestep among the final 500 ns of the 1.5 μs trajectory. For each ionizable lipid, atom subsets corresponding to the head group and tail were defined. For the LM_20197 LNP bilayers, atoms in the amine and isocyanide groups—both found to be generally positioned at the membrane–water interface—were assigned to the head group; all other atoms (i.e., alkyl ketones) were assigned to the tail group. In line with its conventional formula25,92, we calculated CPP based on volume as follows:

CPP_V = V / (a_0 * l_c) (1)

where V is the volume formed by the ionizable lipid, a_0 is the surface area of the head group at the water–membrane interface, and l_c is the average distance between the head group and tail ends (Fig. 4d). The head group area a_0 was computed as the cross-sectional area of the circle formed in the membrane plane.

a_0 = π * r_head^2 (2)

where r_head is the head group radius, calculated as half the maximum pairwise distance between head atoms in the membrane plane. The tail radius r_tail was computed similarly using terminal tail atoms. The lipid volume V was estimated by modeling the molecule as a truncated cone.

V = 1/3 * π * l_c * (r_head^2 + r_head * r_tail + r_tail^2) (3)

These geometrical parameters were computed frame-by-frame for each ionizable lipid molecule across the trajectory to calculate mean CPP_V values. Standard error of the mean (SEM) was also calculated. We observe that CPP_V values exhibit greater variability across lipids and timesteps compared to CPP_Rg. To focus on uncertainty in the central tendency of CPP across lipid molecules, SEM was used in place of standard deviation for CPP_V plots.

Lipids with CPP_V > 1 exhibit an inverse cone shape, favoring negative curvature, whereas those with CPP_V < 1 exhibit a cone shape, favoring positive curvature.

Computing CPP using radii of gyration (CPP_Rg)
We also quantified CPP for ionizable lipids using an approach based on radii of gyration, CPP_Rg. We similarly analyzed the final 500 ns of each 1.5 μs trajectory of stable bilayers. For each ionizable lipid, atom subsets corresponding to the head group and tail were defined, and their centers of mass, R_head_COM and R_tail_COM were computed at every frame.

R_mid_COM = 1/2 * (R_head_COM + R_tail_COM) (4)

from all atomic coordinates. We then translated each lipid to the origin by subtracting the midpoint. The orientation vector was computed as

v = R_head_COM - R_tail_COM (5)

and aligned to the membrane normal z^ = [0, 0, 1] by rotating the coordinate set through the angle between v and z^. With all lipids consistently oriented, the radius of gyration in the xy plane was computed as

R_g = sqrt(1/M * sum(m_i * (x_i^2 + y_i^2))) (6)

where m_i and (x_i, y_i) are the mass and coordinates of atom i, and M = sum(m_i). We recorded the average R_g values for tail and head atoms across all frames—denoted R_g_tail and R_g_head—and computed CPP_Rg as

CPP_Rg = R_g_tail / R_g_head (7)

Lipids with CPP_Rg > 1 exhibit an inverse cone shape favoring negative curvature, whereas those with CPP_Rg < 1 exhibit a cone shape favoring positive curvature. Standard deviation was directly computed from the distribution of CPP_Rg values over the analysis window (single-block averaging).

Membrane thickness, torque density, compressibility
The bilayer thickness (d_B) is defined as the instantaneous difference between the average z-coordinates of phosphate atoms in the upper and lower leaflets:

d_B(t) = <z_P,upper(t)> - <z_P,lower(t)> (8)

We averaged d_B(t) over the final 500 ns of each 1.5 μs trajectory to yield a single representative d_B per system.

Monolayer torque density (τ_mean) was calculated from the first moment of the lateral pressure profile p(z) = p_T(z) - p_N(z), where

p_T(z) = (p_xx(z) + p_yy(z)) / 2, p_N(z) = p_zz(z) (9)

Pressure profiles (0.2 Å bins) were integrated to give leaflet torques:

τ_upper = integral_0^{Lz/2} z * p(z) dz, τ_lower = integral_{-Lz/2}^0 z * p(z) dz (10)

and averaged as

τ_mean = (τ_upper + τ_lower) / 2 (11)

Pressure and torque calculations were performed on velocity- and position-recoupled trajectories over the final 500 ns to ensure full equilibration. As context, for a stress-free symmetric bilayer, the monolayer torque density (τ_mean) is related to the bending modulus (k_c) and spontaneous curvature (c_0) as τ_mean = k_c * c_0. A monolayer with positive curvature is convex to the head group side, while negative curvature is concave66.

The area compressibility modulus K_A was determined from fluctuations in the instantaneous projected bilayer area A(t):

K_A = (k_B * T * <A>) / <(A(t) - <A>)^2> (12)

where k_B is the Boltzmann constant, T the simulation temperature (310 K). Standard deviation was directly calculated from the distribution of A(t) values over the same 500 ns analysis block.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This is a timely and important contribution to the lipid nanoparticle (LNP) studies. The construction of the database and integration with molecular dynamics simulations will greatly enhance the ability to design LNPs using a combination of deep learning and physical models. The study is well thought out and will have a major impact on the community. The initial tests already supported the value of the expanded data set (compared to previous work) and the promise of the physically motivated parameters/features. I strongly support the publication of this work in Nat. Commun.\nI have only a number of minor questions.\n1. For the experimental conditions, it would be interesting to allow the inclusion of additional experimental parameters, such as solution conditions (e.g., buffer).\n2. Providing the force field parameters for new lipid formulations would be extremely useful. On the other hand, it is also important to provide some estimate for the confidence of these parameters, so that the users are aware of potential limitations, or are encouraged to further refine the parameters. Pointing this out explicitly will be important, especially to less experienced users.\n3. The CPP appears to be less predictive for \"amine3\". Any possible rationales?\n4. How is the torque density related to spontaneous curvature, which is often discussed in the lipid phase/mechanics literature?", "reviewer_2": "This study employed web-based tools and computational methods to collect structure-function data for 17,116 LNP formulations primarily from 28 publications, integrating them into the LNP database (LNPDB). The study improves their previously developed deep learning model for predicting LNP delivery efficiency, and also employ molecular modeling tool to examine the relationship between molecular structure and function for 114 LNP formulations using the CHARMM all-atom force field. However, regarding the recommendation for publication of this work, I have several concerns that need to be addressed before proceeding:\n1. Data Collection Section: While we acknowledge the authors' focus on the ionizable lipid level, resulting in 10,524 uniquely structured ionizable lipids, and their collection of helper lipids, cholesterol, and PEG lipids from the 28 publications (recognizing their established importance for LNP in vivo activity), the statistical presentation of these auxiliary components in the manuscript appears weakened. Notably, only cholesterol used in classic LNP formulations is specifically mentioned. We are aware that numerous experimental studies have investigated different sterol types (cholesterol, sitosterol, etc.) and PEG lipids (e.g., ALC-0159 used in Covid-19 vaccines). It seems a significant amount of this data is currently missing from the database and requires further incorporation.\n2. Data Sharing and Quality: The study mentions that users can download the experimental data they collected. However, the provided link does not enable a one-click download of the raw data for all LNP formulations. Instead, it only offers an interface for other user groups to upload their experimental data. It is necessary to share all raw data for these LNP formulations, as the quality of data is crucial for model construction. This would significantly advance structure-function research on LNP and has the potential to become as popular as databases like the PDB in the future.\n3. Literature Screening Strategy: The literature screening strategy and search keywords should be detailed in the Methods section. The current set of 28 publications clearly does not cover all reported LNP experimental results. Some relevant literature appears to have been excluded, and the reasons for this exclusion need to be clarified.\n4. Deep Learning Model Improvement: The authors report significantly improved prediction accuracy for LNP delivery efficiency using their deep learning model, attributed to the expanded dataset (nearly doubled in size). However, the underlying reasons for this improvement are not explained beyond citing the larger number and increased structural diversity of the dataset. A more thorough explanation is needed.\n5. Molecular Dynamics (MD) Simulation Selection: The database contains 17,116 LNP formulations, yet MD simulations were performed on only 114 of them. The rationale and criteria for selecting these specific representative formulations are not elaborated upon in the Methods section. The representativeness of this subset for the entire database warrants further discussion.\n6. LNP Spherical Model: The study has proposed several models for LNP, with the most prevalent and widely accepted being core-shell structure-like spherical models. The shell layer primarily consists of monolayers, bilayers, or mixtures of both. However, this study only performed self-assembly simulations of the LNP bilayer by removing nucleic acid molecules and PEGylated lipid molecules. This lacks simulation of the complete structure of the LNP formulation. Therefore, the related descriptions and results concerning the LNP formulation require further revision.\n7. MD Simulation Temperature: The bilayer structure indeed plays a central role in the proposed LNP structural models, and this study primarily simulates the bilayer assembly process for selected LNP formulations. The Methods section states that simulations were conducted at 310 K. However, this temperature differs from the 298 K typically used for in vitro LNP self-assembly. The justification for using 310 K requires further explanation and the related results require further revision.\n8. Critical Packing Parameter (CPP) Correlation: The CPP, previously used to correlate lipid shape with phase behavior, was calculated for ionizable lipids in 34 LNP formulations using both volume and radius of gyration methods in this study. Its correlation with delivery performance yielded intriguing results. For instance, lines 321-339 state: \"Interestingly, compared to protonated ionizable lipids, neutral ionizable lipids in fully-neutral systems demonstrate slightly stronger correlations between CPP and delivery performance.\" The reasons behind this observation deserve further exploration. Furthermore, could the type of nucleic acid cargo (mRNA, siRNA, pDNA) interacting with these lipids influence the CPP values and their correlation with performance?\n9. Protonation Site Assignment: In the Methods section (lines 476-490 / 492-496), the authors describe a set of rules used to determine the protonation site(s) for each ionizable lipid, followed by charge assignment for protonation. However, this study seems to have considered only a single protonation site (+1e charge). This approach is clearly suitable for classic ionizable lipids containing only a single tertiary amine (e.g., MC3, SM102). Yet, when an ionizable lipid possesses multiple nitrogen atoms (the study notes the number of N atoms per lipid ranges from 1 to 17), meaning multiple potential protonation sites exist, the applicability and validity of the current method and its results need careful assessment.", "reviewer_3": "Summary of the Work:\nThe manuscript introduces LNPDB, a comprehensive and centralized structure-function database for lipid nanoparticles (LNPs) designed for nucleic acid delivery. The database integrates extensive structural and functional data for 17,116 LNP formulations, standardizing their featurization and providing resources for computational simulations through CHARMM force field files. The authors demonstrate the utility of LNPDB through two applications: (1) enhancement of the LiON deep learning model for predicting LNP performance, and (2) molecular dynamics (MD) simulations that identify structural features correlated with delivery performance. This work significantly advances data-driven approaches in nucleic acid delivery research, providing critical resources analogous to the Protein Data Bank in protein science.\nThis is a highly impactful, timely, and rigorously conducted study. The authors present a substantial advancement for the field of lipid nanomedicine, addressing a critical gap by providing a standardized, accessible, and expandable platform for systematic analysis and rational design. The integration of molecular dynamics simulations adds valuable dimensionality to the predictive modeling capabilities, providing insights that static structural representations cannot offer.\nRevision Suggestions:\n1) The authors should explicitly discuss their specific methods for data harmonization and standardization across the diverse experimental conditions included in LNPDB. Given the dataset encompasses varying experimental parameters such as distinct cell lines, diverse target organs, lipid compositions and molar ratios, differing lipid-to-nucleic acid ratios, dosage variations, and varying reporting formats for luminescence measurements (including units and normalization methods), a detailed explanation of how these factors are systematically standardized or normalized is necessary. Clearly articulating this process will enhance understanding of the dataset’s consistency, reliability, and suitability for predictive modeling and comparative analyses across different studies.\n2) The authors should refer to the article (https://doi.org/10.1021/acsabm.4c01716) as this study explicitly investigates the impact of various lipid compositions, including helper lipids, cholesterol, and PEG-lipids, on LNP performance. The manuscript should clearly delineate how LNPDB advances or expands upon such existing work.\n3) The dataset described in the manuscript (as shown in Fig. 2b-c) exhibits significant imbalance. Specifically, despite featuring over 10,000 distinct ionizable lipids, the distribution is heavily skewed: most ionizable lipids contain only up to four nitrogen atoms (despite a range of 1–17 nitrogen atoms), approximately 50% of ionizable lipids have tail lengths concentrated at 18 or 19 carbons (despite a broader range of 3–37 carbons), and most formulations use an ionizable lipid-to-nucleic acid ratio of about 10. Additionally, only seven helper lipid types are represented, with nearly half (45.7%) being DOPE, followed by DSPC (26.9%) and DOTAP (14.4%), leaving minimal representation (<5%) for other types such as MDOA, DDAB, 14:0 PA, and 18:0 PG. The dataset is similarly limited for PEG-lipids, predominantly including only DMG-PEG2000 and DMPE-PEG2000. Given these substantial imbalances, the authors need to thoroughly discuss potential impacts on predictive accuracy, model generalizability, and potential biases introduced by such imbalances. They should explicitly address how these limitations might influence the reliability of data-driven models trained on this dataset and provide a justification or rationale for how the current dataset can still effectively support accurate and generalizable modeling efforts.\n4) Although the authors have visually demonstrated diversity using UMAP embeddings (Fig. 2a), the overlaps visible between data points from different sources suggest that additional quantitative measures, such as Tanimoto similarity scores or cluster purity metrics, would be beneficial. Providing such quantitative analyses would strengthen the authors' claims about the distinctiveness of LNP formulations sourced from different studies.\n5) The authors have employed Spearman correlation coefficient as their primary evaluation metric (Fig. 3a-b). Given that Spearman correlation assesses rank correlation rather than absolute predictive accuracy, it might not fully capture predictive performance, particularly in practical applications where precise quantitative predictions are essential. The authors should consider or discuss the applicability and advantages of additional metrics such as Pearson correlation, mean absolute error (MAE), root mean squared error (RMSE), or even classification-based metrics if delivery outcomes could be discretized. Justifying the choice of Spearman correlation and/or demonstrating the robustness of their model across these alternative metrics would significantly enhance the manuscript."}, "author_response": "Point-by-point response for consideration at Nature Communications\nReviewer #1:\nOur Overall Response:\nWe appreciate the reviewer’s valuable feedback. We believe the insightful points have enriched the\nquality of our manuscript. Shown below are our point-by-point responses. Any new text added to the\nrevised manuscript is shown in red.\nReviewer #1 Point #1\nFor the experimental conditions, it would be interesting to allow the inclusion of additional\nexperimental parameters, such as solution conditions (e.g., buffer).\nOur Response to Reviewer #1 Point #1\nWe thank the reviewer for motivating us to include additional experimental parameters in\nLNPDB. We agree features related to solution conditions are useful.\n- Accordingly, we have added the new columns Aqueous_buffer (e.g., acetate) and\nDialysis_buffer (e.g., PBS) for all LNPs in LNPDB. In the Featurization subsection of\nMethods, we hence now also mention “aqueous buffer” and “dialysis buffer” in line 514.\n- As for another useful experimental parameter, we have added the column\nDose_ug_nucleicacid to document the dose of nucleic acid administered in micrograms. In\nthe Featurization subsection of Methods, we hence now also mention “nucleic acid dose” in\nline 518.\n- Moreover, Fig. S1b shown below now includes pie charts depicting diversity of these\nbuffers.\nFig. S1: Additional summary statistics for LNP data in LNPDB. a Number of LNP formulations and unique ionizable\nlipids for each of the 42 libraries available in LNPDB. There are an additional 269 unique ionizable lipids from\nBroadPharm (not shown) available in LNPDB. b Additional summary statistics of properties by aqueous buffer, dialysis\nbuffer, preparation method, batching method, cargo type, route of administration, and delivery target type. Distributions of\nexperiment value z-scores for each library are plotted. Experiment values not denoting delivery performance were omitted\nfrom this analysis. All boxplots have a box that signifies the interquartile range (IQR; 25th percentile to 75th percentile), a\ncenter bar that denotes the median, whiskers that extend up to 1.5 × IQR, and a notch that extends 1.58 × IQR/√n,\nwhere n is the sample size for that condition, to estimate the 95% confidence interval. Source data are provided as a\nSource data file.\n- Although not directly related to this point, in response to Reviewer #2 Point #1, we have\nalso significantly expanded LNPDB to better capture the LNP design space, notably\nexpanding diversity in the components besides the ionizable lipid. This has led to marked\nincreases in the overall quantity and diversity of LNPs in LNPDB. The revised database has\nincreased…\no from 17,116 to 19,528 LNPs\no from 10,524 to 12,845 unique ionizable lipids, and\no from 28 to 42 publications\n- Two of these new publications include fifth components (i.e., another lipid component\nbesides ionizable, helper, cholesterol, and PEG). Therefore, we have also added new\nexperimental columns to account for fifth components: fifthcomponent_name,\nfifthcomponent_SMILES, fifthcomponent_molratio.\n- Thus, both the number of columns (i.e., features) and rows (i.e., LNPs) have been\nexpanded. All figures are thus updated to reflect this new larger version of LNPDB.\nReviewer #1 Point #2\nProviding the force field parameters for new lipid formulations would be extremely useful. On the\nother hand, it is also important to provide some estimate for the confidence of these parameters, so\nthat the users are aware of potential limitations, or are encouraged to further refine the parameters.\nPointing this out explicitly will be important, especially to less experienced users.\nOur Response to Reviewer #1 Point #2\nWe appreciate this suggestion to comment on the confidence of these CHARMM force field\nparameters. Although this manuscript reflects the first instance of parametrizing thousands of\nionizable lipids pertinent to lipid nanoparticle nucleic acid delivery, prior studies provide an\nimportant foundation of evaluating the confidence of the CHARMM force field for lipids. We\nagree it is useful to provide more context and cite these relevant studies.\n- Accordingly, in lines 546-555 of Methods, we have added the following sentences, which\nreferences important studies for more background about the CHARMM lipid force field.\nMoreover, in these sentences, we encourage further optimization of parameters as needed\n(e.g., if inaccurate lipid flip-flop behavior is observed).\n“Similar to the CHARMM-GUI Membrane Builder that supports diverse lipid types51,62,\nLNPDB uses the latest version of the CHARMM C36 additive force field parameters. The\nCHARMM force field60 is designed to allow a modular, building-block approach to create\nforce fields for molecules composed of components (blocks) similar to the ones already\nparametrized. Many topologies and parameters of lipids and carbohydrates in the latest\nversion of the CHARMM C36 force field were generated using this building-block approach;\nand the generated force fields were further validated by comparing simulations with\nexperimental data. Accordingly, we used a similar building-block approach for the ionizable\nlipids in LNPDB. We have not yet seen abnormal all-atom simulation behavior (e.g., lipid\nflip-flop); however, further force field optimization is recommended for specific ionizable\nlipids if abnormal behavior is observed.”\nReviewer #1 Point #3\nThe CPP appears to be less predictive for \"amine3\". Any possible rationales?\nOur Response to Reviewer #1 Point #3\nWe agree that further investigation of the CPP results is useful; indeed, this comment\nmotivated additional analyses that we believe strengthen this section.\nFirst, rather than assuming the relationship between delivery efficacy and ionizable lipid\nCPP to be linear across the entire range of CPP values, we also focused in on only the\nsubset of LNPs with mean CPP > 1. This threshold corresponds theoretically to the onset of\nnegative curvature and thus may represent a minimum CPP required to achieve the\nfavorable geometry (with head groups localized to leaflet at aqueous interface) for delivery.\nAs we now demonstrate in Fig. S9 shown below, when we focused our correlation analyses\non the subset of LNPs with mean CPP > 1, the correlative performance improved\nsubstantially for both the CPP and CPP methods. We thank the reviewer for motivating\nV Rg\nthis additional analysis.\nFig. S9: Correlation between CPP of neutral ionizable lipids and experimental delivery performance for the LNPs\nfrom LM_2019 which formed stable, equilibrated bilayers with CPP > 1. Similar analysis to Figs. 4e-f, S5 but with\ncorrelation only computed for LNPs whose ionizable lipids have mean CPP > 1, indicating an inverse conical shape\nconducive to hexagonal phase formation. This CPP > 1 thresholding improves correlative performance. CPP values\ncomputed using a CPP = V/(a l ) and b CPP = Rg /Rg . Pearson r and p values are noted for the overall trend as\nV 0c Rg tail head\nwell as for each ionizable lipid amine group (A12, A2, A3), which are also represented by point color. Points denote mean\nvalues, and error bars denote +/- SEM for CPP and standard deviation for CPP . Source data are provided as a Source\nV Rg\ndata file.\n- Moreover, whereas amine 3 previously appeared to have lower correlative performance, in this\nnew analysis its correlations are comparable to those of the other two amines. Some of its\ncorrelations do remain weaker, however, likely due to the limited number of amine 3 LNPs with\nCPP > 1. Thus, we have added the following sentence in lines 359-360.\n“Some correlations for amine 3 did not reach statistical significance, likely due to its limited\nrepresentation of LNPs with CPP > 1.”\nReviewer #1 Point #4\nHow is the torque density related to spontaneous curvature, which is often discussed in the lipid\nphase/mechanics literature?\nOur Response to Reviewer #1 Point #4\nWe agree additional clarification on how torque density relates to spontaneous curvature is\nhelpful.\n- In lines 731-734, we have added the following sentence. Note that our definition of torque\ndensity in this manuscript is the same as that of Park et al., J. Chem. Inf. Model. (2021),\nwhich we now cite here.\n“As context, for a stress-free symmetric bilayer, the monolayer torque density (𝜏) is related\nto the bending modulus (𝑘 ) and spontaneous curvature (𝑐 ) as 𝜏 = 𝑘 𝑐 . A monolayer with\n𝑐 0 𝑐 0\npositive curvature is convex to the head group side, while negative curvature is concave51.”\nReviewer #2:\nOur Overall Response:\nWe appreciate the review for the thoughtful and constructive feedback. The points provided have\nmotivated revisions which have significantly strengthened the manuscript. Shown below are our point-\nby-point responses. Any new text added to the revised manuscript is shown in red.\nReviewer #2 Point #1\nData Collection Section: While we acknowledge the authors' focus on the ionizable lipid level,\nresulting in 10,524 uniquely structured ionizable lipids, and their collection of helper lipids, cholesterol,\nand PEG lipids from the 28 publications (recognizing their established importance for LNP in vivo\nactivity), the statistical presentation of these auxiliary components in the manuscript appears\nweakened. Notably, only cholesterol used in classic LNP formulations is specifically mentioned. We\nare aware that numerous experimental studies have investigated different sterol types (cholesterol,\nsitosterol, etc.) and PEG lipids (e.g., ALC-0159 used in Covid-19 vaccines). It seems a significant\namount of this data is currently missing from the database and requires further incorporation.\nOur Response to Reviewer #2 Point #1\nWe thank the reviewer for this suggestion to expand LNPDB to more fully encompass the\nfield’s chemical diversity, especially among the lipid components beyond ionizable lipids.\n- Accordingly, we have added new datasets to LNPDB to better capture diversity across all\ncomponents. Additionally, we have included two publications describing five-component\nformulations (i.e., those that add a lipid beyond the ionizable, helper, cholesterol, and PEG\ncomponents), as these are becoming more prevalent in the field. Moreover, following our\ninitial submission, recently published studies evaluating new ionizable lipid libraries have\nalso been added to LNPDB. Altogether, our new version of LNPDB included in this revised\nmanuscript has increased…\no from 17,116 to 19,528 LNPs\no from 10,524 to 12,845 unique ionizable lipids, and\no from 28 to 42 publications\n- Here is a more detailed breakdown of the 14 specific publications added to LNPDB. Note\nthat this information is also reflected in the updated Fig. 2, Table S1, and Fig. S1.\no Study evaluating from Moderna evaluating SM-102 and 9 other ionizable lipids. This\nstudy was added due to the clinical significance of SM-102 for the field.\n SS_2018 (https://doi.org/10.1016/j.ymthe.2018.03.010)\no Study evaluating different cholesterols. This study was added to increase chemical\ndiversity of cholesterols.\n SP_2020 (https://www.nature.com/articles/s41467-020-14527-2)\no Studies evaluating different PEG lipids. These studies were added to increase chemical\ndiversity of PEG lipids.\n LL_2025 (https://doi.org/10.1039/D5NR00433K)\n LX_2025 (https://doi.org/10.1016/j.jconrel.2025.01.071)\no Studies evaluating different fifth component LNP formulations. These studies were\nadded to introduce fifth-component design LNPs into LNPDB.\n SB_2024 (https://doi.org/10.1016/j.bioactmat.2024.05.012)\n SY_2025 (https://doi.org/10.1002/adhm.202403366):\no Studies evaluating new ionizable lipid libraries. These recent studies were added to\nfurther increase ionizable lipid diversity.\n JL_2024\n(https://jnanobiotechnology.biomedcentral.com/articles/10.1186/s12951-024-\n02919-1)\n LX_2024_2 (https://pubs.acs.org/doi/10.1021/jacs.4c10265)\n LX_2024_3 (https://www.nature.com/articles/s41565-024-01747-6)\n SW_2024\n(https://www.sciencedirect.com/science/article/abs/pii/S0168365924007016)\n XH_2024_2 (https://www.nature.com/articles/s41551-024-01267-7)\n AP_2025 (https://www.nature.com/articles/s42004-025-01516-z)\n SX_2025 (https://www.nature.com/articles/s41551-025-01480-y)\n XH_2025 (https://www.biorxiv.org/content/10.1101/2025.02.25.640222v1)\n- Because new datasets have been added, LNPDB now has more rows (i.e., LNP\nformulations). Additionally, we have added more columns (i.e., features) to LNPDB to better\nrepresent each LNP. These new columns include Aqueous_buffer, Dialysis_buffer,\nfifthcomponent_name, fifthcomponent_SMILES, fifthcomponent_molratio,\nDose_ug_nucleicacid.\n- The revised Figs. 2, S1 are shown below.\nFig. 2: LNPDB includes diverse LNP data from 19,528 formulations across 42 studies. a UMAP visualizations of the\nhigh-dimensional embedding landscapes of LNP formulations (left) and unique ionizable lipids (right) compiled in LNPDB,\ncolored according to originating study. b Summary statistics of ionizable lipids by molecular weight, number of nitrogens,\nand nitrogen substitution class. c Summary statistics of ionizable lipid (IL)-to-nucleic acid mass ratio, helper lipid type, and\nPEG lipid type. d Summary statistics of experimental properties by cargo, delivery target, and readout method. Additional\nsummary statistics are shown in Fig. S1. Source data are provided as a Source data file.\nFig. S1: Additional summary statistics for LNP data in LNPDB. a Number of LNP formulations and unique ionizable\nlipids for each of the 42 libraries available in LNPDB. There 269 additional unique ionizable lipids from BroadPharm (not\nshown) available in LNPDB. b Additional summary statistics of properties by aqueous buffer, dialysis buffer, preparation\nmethod, batching method, cargo type, route of administration, and delivery target type. Distributions of experiment value\nz-scores for each library are plotted. Experiment values not denoting delivery performance were omitted from this\nanalysis. All boxplots have a box that signifies the interquartile range (IQR; 25th percentile to 75th percentile), a center bar\nthat denotes the median, whiskers that extend up to 1.5 × IQR, and a notch that extends 1.58 × IQR/√n, where n is the\nsample size for that condition, to estimate the 95% confidence interval. Source data are provided as a Source data file.\nReviewer #2 Point #2\nData Sharing and Quality: The study mentions that users can download the experimental data they\ncollected. However, the provided link does not enable a one-click download of the raw data for all\nLNP formulations. Instead, it only offers an interface for other user groups to upload their\nexperimental data. It is necessary to share all raw data for these LNP formulations, as the quality of\ndata is crucial for model construction. This would significantly advance structure-function research on\nLNP and has the potential to become as popular as databases like the PDB in the future.\nOur Response to Reviewer #2 Point #2\nWe thank the reviewer for this point. Although we had the raw data of the entire LNPDB on our\nGitHub repo for download, we agree it is helpful to also include on our LNPDB website\n(https://lnpdb.molcube.com/).\n- Accordingly, we have added the feature to download the entire LNPDB as a single .csv file\non our LNPDB website here: https://lnpdb.molcube.com/downloads\nReviewer #2 Point #3\nLiterature Screening Strategy: The literature screening strategy and search keywords should be\ndetailed in the Methods section. The current set of 28 publications clearly does not cover all reported\nLNP experimental results. Some relevant literature appears to have been excluded, and the reasons\nfor this exclusion need to be clarified.\nOur Response to Reviewer #2 Point #3\nWe thank the reviewer for recommending additional clarification here. We hope to see further\nexpansion of LNPDB through the community contribution.\n- To better clarify our literature screening strategy for the 42 publications in the expanded\nLNPDB, we have added the following sentences in lines 483-486 of Methods.\n“In summary, publications were selected from the literature based on the presence of large\nscreening datasets, primarily focused on ionizable lipids, to allow for meaningful within-\ndataset comparisons. Additional publications were selected to broaden representation of\nhelper lipids, cholesterols, and PEG lipids.”\nReviewer #2 Point #4\nDeep Learning Model Improvement: The authors report significantly improved prediction accuracy for\nLNP delivery efficiency using their deep learning model, attributed to the expanded dataset (nearly\ndoubled in size). However, the underlying reasons for this improvement are not explained beyond\nciting the larger number and increased structural diversity of the dataset. A more thorough\nexplanation is needed.\nOur Response to Reviewer #2 Point #4\nWe thank the reviewer for inviting additional explanation here.\n- Towards interpreting the impact of including the additional data from LNPDB in our LiON\ndeep learning model, we have now created Fig. S4 shown below. In Fig. S4a, we visualize\nthe LiON-learned LNP fingerprints (i.e., 300-dimensional encodings from the penultimate\nlinear layer of the LiON model’s feedforward neural network trained on LNPDB), coloring\npoints by data source (original dataset vs. the data newly included in LNPDB). The two\nsources are clearly mixed in the embedding space, indicating that new entries populate\ndata neighborhoods already represented by the original set. In Fig. S4b, we further\ncompare cosine-similarity distributions and observe substantial cross-source similarity,\nconsistent with increased local density. Together, these observations suggest that the\nadded data improve coverage of the structure-function manifold, providing a plausible basis\nfor the observed accuracy gains.\nFig. S4: Expanded data of LNPDB blends with original data in LNP embedding space learned by LiON. a\nAnalogous to Fig. S2b but colored by whether the training data were sourced from the original dataset (“Original”) or data\nnewly included in LNPDB (“LNPDB additional”). Note that LNPDB altogether contains the data of both “Original” and\n“LNPDB additional”. The LiON fingerprints of these two groups are interspersed, suggesting shared structure–function\npatterns and that the additional data densifies the representation space. b Analogous to Fig. S2a, displaying probability\ndistributions of cosine similarities in LiON embedding space for the top 50 nearest neighbors for each LNP, computed\nseparately within the original dataset and across the original dataset and data newly included in LNPDB. The presence of\nsome high pairwise similarities across the original dataset and the data newly included in LNPDB similarly reinforce the\nsuitability of using the combined dataset to learn shared structure-function relationships. Moreover, LNPs in the expanded\ndataset that are relatively dissimilar to those of the original dataset broaden the chemical design space, potentially\nenabling exploration and learning in under-sampled regions. Source data are provided as a Source data file.\n- Accordingly, we have added the following sentence in lines 242-244 in Results.\n“Overlap between LiON-learned embeddings for the original and LNPDB-added data\nindicates shared structure–function patterns and a more densely covered feature space\n(Fig. S4).”\n- We have also added the following sentence in lines 596-598 in Methods to explain how the\nfingerprints were computed.\n“UMAP visualizations were also created of the 300-dimensional embedding landscape (i.e.,\nfingerprints) from LiON model of LNP formulations (Figs. S2b, S4a). Fingerprints were\nextracted from the penultimate linear layer of the LiON model’s feedforward neural network\ntrained on LNPDB.”\n- Lastly, although not directly related, this comment overall motivated us to include language\nmore explicitly emphasizing how future research should explore alternative deep learning\nmodels tailored to the design strategy or delivery target under investigation. We do not\npresent the machine learning and MD models presented as final, globally optimized\nsolutions; instead, we position LNPDB as the core dataset for developing and\nbenchmarking such models. We hope future research is now equipped to build new\nmachine learning and MD approaches based on the data of LNPDB. Accordingly, we have\nadded the following sentences in lines 254-259 in Results.\n“Importantly, LNPDB establishes a framework of training data for the continued\ndevelopment of next-generation deep learning models for LNP design. Moreover, given our\nresults demonstrate significant variation in model accuracy across libraries, future research\ncan leverage the training data of LNPDB to design alternative models that may be better\nsuited for the specific LNP design strategy (e.g., helper lipid optimization) or delivery target\n(e.g., in vivo muscle) under investigation.”\nReviewer #2 Point #5\nMolecular Dynamics (MD) Simulation Selection: The database contains 17,116 LNP formulations,\nyet MD simulations were performed on only 114 of them. The rationale and criteria for selecting these\nspecific representative formulations are not elaborated upon in the Methods section. The\nrepresentativeness of this subset for the entire database warrants further discussion.\nOur Response to Reviewer #2 Point #5\nWe agree further discussion here is helpful. We now have provided additional reasoning to\nexplain the selection strategy. Note that practical limits of computational time for these all-atom\nMD simulations were also considered.\n- As shown in lines 627-629 of Methods, we now state the following.\n“This subset, drawn from a single combinatorial ionizable lipid library, was chosen as a\nrepresentative example of systematic lipid library design commonly employed in the field,\nwhile keeping the scope feasible within computational limits.”\n- Moreover, we consider our prior sentences in Discussion emphasizing the use of coarse-\ngrained efforts to improve the scalability of MD simulations are particularly pertinent in this\ncontext, as they acknowledge future work should build on this study. Accordingly, we have\namplified this section with this additional sentence in lines 465-468, emphasizing how\nfuture research could expand these efforts by simulating additional libraries to capture a\nbroader range of LNP design strategies.\n“To support MD simulations with larger system sizes, longer time scales, and the inclusion\nof nucleic acids, we plan to incorporate Martini 3 coarse-grained lipid and nucleic acid\nparameters58 in future versions of LNPDB. This will facilitate efficient simulations for many\nmore LNPs to further explore structure-function relationships.”\nReviewer #2 Point #6\nLNP Spherical Model: The study has proposed several models for LNP, with the most prevalent and\nwidely accepted being core-shell structure-like spherical models. The shell layer primarily consists of\nmonolayers, bilayers, or mixtures of both. However, this study only performed self-assembly\nsimulations of the LNP bilayer by removing nucleic acid molecules and PEGylated lipid molecules.\nThis lacks simulation of the complete structure of the LNP formulation. Therefore, the related\ndescriptions and results concerning the LNP formulation require further revision.\nOur Response to Reviewer #2 Point #6\nWe thank the reviewer for inviting additional explanation regarding our modeling choices.\n- First, this manuscript is principally intended to advance a digital framework for LNPs that\nincorporates both machine learning and molecular dynamics (MD). We acknowledge that\nthese MD bilayer models require simplifying assumptions and are not assumed to\nrepresent exhaustive or fully accurate experimental LNP structures. Nevertheless, the\nresults demonstrate that the models can provide meaningful and statistically significant\ncorrelations with experimental performance, underscoring their utility despite these\nsimplifications.\n- For the MD modeling strategy presented in this manuscript, we decided to model a small\nportion (i.e., the outermost leaflets of the LNP facing the environments such as solution,\n,\nplasma membranes, and endosomal membranes) of what the reviewer describes as the\ncore-shell structure-like spherical model. Other MD work too has modeled and analyzed\nonly a portion of LNPs (Tesei et al., PNAS, 2024). As mentioned in our response to\nReviewer #2 Point #5, practical computational limits prevent full-LNP all-atom MD\nsimulations; it is challenging to model and simulate the entire LNP using all-atom models\ndue to the system size and simulation time. This is why, as we mention in Discussion, our\nfuture research will explore coarse-grained models that enable larger-scale simulations.\nLastly, when predicting delivery performance in silico, smaller-scale models can be\nadvantageous because they enable faster and more efficient simulations. Altogether, we\nhave revised the text of the manuscript at lines 460-471 in Discussion to further clarify\nthese considerations.\n“Future research should explore experimental validation of MD-derived features such as\nCPP. The MD bilayer models presented in this work provide a simplified yet informative\nframework that provides significant correlations with delivery performance. However, future\nresearch should leverage the topology and parameter files provided in LNPDB to expand\nsimulation efforts to include additional delivery-relevant phenomena, such as membrane\nfusion dynamics, interactions with nucleic acids, and dynamic pH sensitivity during\nendosomal escape. To support MD simulations with larger system sizes, longer time\nscales, and the inclusion of nucleic acids, we plan to incorporate Martini 3 coarse-grained\nlipid and nucleic acid parameters75 in future versions of LNPDB. This will facilitate efficient\nsimulations for many more LNPs to further explore structure-function relationships.\nMoreover, although this version of LNPDB includes some LNPs with five lipid components,\nfuture versions will further incorporate LNPs with more than four components (e.g.,\nadditional lipids8 or lipids conjugated to targeting ligand76).”\n- Including mRNA in atomistic simulations remains challenging due to computational cost.\nPrevious works have attempted to include only short fragments of mRNA (a few\nnucleotides) at the coarse-grained level in order to explore global effects and the overall\nLNP structure (Tesei et al., PNAS, 2024; Grzetic et al., Mol. Pharm., 2024; Kjolbye et al.,\nChemRxiv, 2025). In contrast, our present study focuses on atomistically modeling\nthe outermost leaflets of the LNP, which directly interfaces with external environments such\nas aqueous solution, plasma membranes, and endosomal membranes. This modeling\napproach increased our sampling efficiency while retaining atomistic detail, and it ultimately\ndemonstrated significant correlations with delivery performance, which was our central\nobjective. Nevertheless, we agree future research should explore RNA interactions.\nAccordingly, we have added this text in lines 465-467 in Discussion.\n“To support MD simulations with larger system sizes, longer time scales, and the inclusion\nof nucleic acids, we plan to incorporate Martini 3 coarse-grained lipid and nucleic acid\nparameters75 in future versions of LNPDB.”\n- In our initial manuscript, we described our simulations as modeling “the bilayer assembly\nprocess”. Because we used Membrane Builder to initialize the bilayer, we have instead\nreplaced “assembly” with “equilibration” to be more precise in the revised manuscript.\n- With respect to excluding PEG lipids from these models, as we state in Methods in lines\n625-629, “PEG lipids were excluded from our analyses, as they are typically shed prior to\nendosomal escape18,52,53, the key bottleneck for effective delivery54 and the physiological\ncontext that we aim to model.” In other words, we were seeking to model the LNPs in the\nendosome environment due to its reported importance to delivery performance. PEG lipids\nare shed before this step; thus, we decided to exclude it. Nevertheless, this reviewer’s\ncomment motivated us to explore whether including PEG lipid would impact our reported\nCPP results. Thus, we ran 10 additional MD simulations with PEG lipid (whose details are\nshown in the table below taken from the revised Table S2) to evaluate whether the trend in\nCPP values differ compared to the comparable simulations without PEG lipid that were\nalready run.\n# molecules per leaflet\nHL water # # # # Duration Temp\nID LNP ID IL name XYZ (Å3)\nname IL IL thickness Na Cl waters atoms (ns) (K)\nHL Chol PEG\n(P) (N)\nLM_1 LNP_0003881 LM_A12Iso52DC18 DOPE 0 35 16 47 2 20 82x82x126 46 46 16849 72269 1,500 310\nLM_5 LNP_0003901 LM_A12Iso92DC18 DOPE 0 35 16 47 2 20 83x83x123 46 46 16500 71922 1,500 310\nLM_39 LNP_0004885 LM_A12Iso5C11 DOPE 0 35 16 47 2 20 85x85x129 52 52 18825 75549 1,500 310\nLM_40 LNP_0004889 LM_A12Iso9C11 DOPE 0 35 16 47 2 20 84x84x112 40 40 14791 64123 1,500 310\nLM_41 LNP_0004895 LM_A12Iso5C10 DOPE 0 35 16 47 2 20 84x84x122 46 46 16782 68988 1,500 310\nLM_42 LNP_0004899 LM_A12Iso9C10 DOPE 0 35 16 47 2 20 85x85x114 42 42 15548 65978 1,500 310\nLM_44 LNP_0004909 LM_A12Iso9C9 DOPE 0 35 16 47 2 20 84x84x141 58 58 20953 81805 1,500 310\nLM_46 LNP_0004919 LM_A12Iso9C8 DOPE 0 35 16 47 2 20 83x83x125 48 48 17140 69926 1,500 310\nLM_48 LNP_0004929 LM_A12Iso9C7 DOPE 0 35 16 47 2 20 81x81x119 42 42 14941 62897 1,500 310\nLM_50 LNP_0004939 LM_A12Iso9CC7 DOPE 0 35 16 47 2 20 84x84x114 42 42 15257 64125 1,500 310\nAs we show in the new Fig. S10 shown below, including PEG lipids yielded nearly the\nsame trend in CPP values as the comparable simulations without PEG lipids, with R2 =\n0.981 for CPP and R2 = 0.945 for CPP . We thank the reviewer for motivating this\nV Rg\nadditional analysis. Note that the figure below also shows results for the 10 additional\nsimulations that we ran at 298 K, which we discuss in response to Reviewer #2 Point #7.\nFig. S10: Reducing temperature to 298 K or including PEG lipid in molecular dynamics simulations does not\nsignificantly impact CPP trend. To evaluate whether reducing temperature or including PEG lipid affects CPP, 1.5 µs\nsimulations were run for stable fully-neutral LM_2019 LNPs with amine 12 (n = 10), either with a reduced temperature at\nLNP_0003881 with PEG lipid. PEG denotes C14 lipid with 25 monomeric PEG units. Strong correlations for c CPP and d\nV\nCPP between systems without PEG at 310 K (as introduced in Fig. 4), systems without PEG at 298 K (shown in blue),\nRg\nand systems with PEG at 310 K (shown in orange). Source data are provided as a Source data file.\nReviewer #2 Point #7\nMD Simulation Temperature: The bilayer structure indeed plays a central role in the proposed LNP\nstructural models, and this study primarily simulates the bilayer assembly process for selected LNP\nformulations. The Methods section states that simulations were conducted at 310 K. However, this\ntemperature differs from the 298 K typically used for in vitro LNP self-assembly. The justification for\nusing 310 K requires further explanation and the related results require further revision.\nOur Response to Reviewer #2 Point #7\nWe thank the reviewer for this suggestion.\n- First, we were seeking to model the endosomal environment where the temperature is\n~310 K; thus, our MD simulations were carried out at 310 K. We have added these\ndefinitions in Methods to clarify in lines 564 and 574-575, respectively.\n“simulations were conducted at 310 K (i.e., temperature of cells treated with LNPs)”\n“setting temperature to 298 K (i.e., temperature of LNP synthesis)”\n- To address this point, we assessed the impact of simulating at 298 K (i.e., the temperature\nat which LNPs are synthesized/self-assembled). Similar to our response to Reviewer #2\nPoint #6 regarding PEG, we ran 10 additional MD simulations at 298 K (whose details are\nshown in the table below taken from the revised Table S2) to evaluate whether the trend in\nCPP values differ compared to the comparable simulations at 310 K that were already run.\n# molecules per leaflet\nHL water # # # # Duration Temp\nID LNP ID IL name XYZ (Å3)\nname IL IL thickness Na Cl waters atoms (ns) (K)\nHL Chol PEG\n(P) (N)\nLM_1 LNP_0003881 LM_A12Iso52DC18 DOPE 0 35 16 47 0 20 83x83x66 12 12 4508 34082 1,500 298\nLM_5 LNP_0003901 LM_A12Iso92DC18 DOPE 0 35 16 47 0 20 86x86x67 14 14 4794 35644 1,500 298\nLM_39 LNP_0004885 LM_A12Iso5C11 DOPE 0 35 16 47 0 20 83x83x66 12 12 4486 31356 1,500 298\nLM_40 LNP_0004889 LM_A12Iso9C11 DOPE 0 35 16 47 0 20 84x84x64 12 12 4310 31528 1,500 298\nLM_41 LNP_0004895 LM_A12Iso5C10 DOPE 0 35 16 47 0 20 82x82x64 12 12 4111 29811 1,500 298\nLM_42 LNP_0004899 LM_A12Iso9C10 DOPE 0 35 16 47 0 20 81x81x65 12 12 4276 31006 1,500 298\nLM_44 LNP_0004909 LM_A12Iso9C9 DOPE 0 35 16 47 0 20 83x83x65 12 12 4317 30709 1,500 298\nLM_46 LNP_0004919 LM_A12Iso9C8 DOPE 0 35 16 47 0 20 82x82x65 12 12 4386 30496 1,500 298\nLM_48 LNP_0004929 LM_A12Iso9C7 DOPE 0 35 16 47 0 20 83x83x64 12 12 4178 29452 1,500 298\nLM_50 LNP_0004939 LM_A12Iso9CC7 DOPE 0 35 16 47 0 20 84x84x63 12 12 4530 30788 1,500 298\nAs we shown below in the new Fig. S10, changing the temperature to 298 K yielded nearly\nthe same trend in CPP values as the comparable simulations at 310 K, with R2 = 0.981 for\nCPP and R2 = 0.986 for CPP . Note that the figure below also shows results for the 10\nV Rg\nadditional simulations that we ran with PEG lipid, which we discussed in response to\nReviewer #2 Point #6. We also find insignificant difference in CPP trends between the\nsimulations at 298 K and the simulations with PEG lipid at 310 K. We thank the reviewer for\nmotivating this additional analysis. Accordingly, we add this sentence in lines 363-365 in\nResults and in lines 573-575 in Methods.\n“Moreover, we assessed whether the inclusion of PEG lipid or reducing temperature to 298\nK in simulations affected CPP and found no significant effect (Fig. S10).”\n“For ten bilayer systems, we additionally assessed whether the inclusion of PEG lipid or\nsetting temperature to 298 K (i.e., temperature of LNP synthesis) in simulations affected\nCPP and found no significant effect (Fig. S10).”\nFig. S5: Reducing temperature to 298 K or including PEG lipid in molecular dynamics simulations does not\nsignificantly impact CPP trend. To evaluate whether reducing temperature or including PEG lipid affects CPP, 1.5 µs-\nlong simulations were run for stable fully-neutral LM_2019 LNPs with amine 12 (n = 10), either with a reduced\ntemperature at 298 K or PEG lipid included. a Snapshot at 1.5 µs timepoint for LNP_0003881 simulated at 298 K. b\nSnapshot at 1.5 µs timepoint for LNP_0003881 with PEG lipid. PEG denotes C14 lipid with 25 monomeric PEG units.\nStrong correlations for c CPP and d CPP between systems without PEG at 310 K (as introduced in Fig. 4), systems\nV Rg\nwithout PEG at 298 K (shown in blue), and systems with PEG at 310 K (shown in orange). Source data are provided as a\nSource data file.\nReviewer #2 Point #8\nCritical Packing Parameter (CPP) Correlation: The CPP, previously used to correlate lipid shape with\nphase behavior, was calculated for ionizable lipids in 34 LNP formulations using both volume and\nradius of gyration methods in this study. Its correlation with delivery performance yielded intriguing\nresults. For instance, lines 321-339 state: \"Interestingly, compared to protonated ionizable lipids,\nneutral ionizable lipids in fully-neutral systems demonstrate slightly stronger correlations between\nCPP and delivery performance.\" The reasons behind this observation deserve further exploration.\nFurthermore, could the type of nucleic acid cargo (mRNA, siRNA, pDNA) interacting with these lipids\ninfluence the CPP values and their correlation with performance?\nOur Response to Reviewer #2 Point #8\nWe thank the reviewer for this suggestion and agree further exploration into our CPP results\nwould strengthen the manuscript.\n- Rather than assuming the relationship between delivery efficacy and ionizable lipid CPP to\nbe linear across the entire range of CPP values, we also focused in on only the\nsubset of LNPs with mean CPP > 1. This threshold corresponds theoretically to the onset of\nnegative curvature and thus may represent a minimum CPP required to achieve the\nfavorable geometry (with head groups localized to leaflet at aqueous interface) for delivery.\nAs we now demonstrate in Fig. S9 shown below, when we focused our correlative analyses on the\nsubset of LNPs with mean CPP > 1, the correlative performance improved substantially for\nboth the CPP and CPP methods. We thank the reviewer for motivating this additional\nV Rg\nanalysis.\nFig. S9: Correlation between CPP of neutral ionizable lipids and experimental delivery performance for the LNPs\nfrom LM_2019 which formed stable, equilibrated bilayers with CPP > 1. Similar analysis to Figs. 4e-f, S5 but with\ncorrelation only computed for LNPs whose ionizable lipids have mean CPP > 1, indicating an inverse conical shape\nconducive to hexagonal phase formation. This CPP > 1 thresholding improves correlative performance. CPP values\ncomputed using a CPP = V/(a l ) and b CPP = Rg /Rg . Pearson r and p values are noted for the overall trend as\nV 0c Rg tail head\nwell as for each ionizable lipid amine group (A12, A2, A3), which are also represented by point color. Points denote mean\nvalues, and error bars denote +/- SEM for CPP and standard deviation for CPP . Source data are provided as a Source\nV Rg\ndata file.\n- Whereas neutral ionizable lipids have slightly lower correlative performance in the original\ncorrelation analysis, in this new analysis the protonated ionizable lipids have slightly higher\ncorrelative performance. However, the observed differences are small and may fall within\nthe variability expected for this type of analysis. Thus, we have revised the manuscript in\n349-350 to highlight that protonated and neutral ionizable lipids perform comparably, rather\nthan emphasizing differences.\n“Compared to protonated ionizable lipids, neutral ionizable lipids in fully-neutral systems\ndemonstrate comparably strong correlations between CPP and delivery performance.”\n- As noted in our response to Reviewer #2 Point #6, it is challenging to include nucleic acid\ncargo in our current all-atom simulations, and further studies are warranted to examine the\ninfluence of nucleic acids on CPP.\nReviewer #2 Point #9\nProtonation Site Assignment: In the Methods section (lines 476-490 / 492-496), the authors describe\na set of rules used to determine the protonation site(s) for each ionizable lipid, followed by charge\nassignment for protonation. However, this study seems to have considered only a single protonation\nsite (+1e charge). This approach is clearly suitable for classic ionizable lipids containing only a single\ntertiary amine (e.g., MC3, SM102). Yet, when an ionizable lipid possesses multiple nitrogen atoms\n(the study notes the number of N atoms per lipid ranges from 1 to 17), meaning multiple potential\nprotonation sites exist, the applicability and validity of the current method and its results need careful\nassessment.\nOur Response to Reviewer #2 Point #9\nWe thank the reviewer for this feedback. We have revised the manuscript as described below.\n- In lines 525-536, we include additional details regarding the decision tree that was applied\nto select the single protonation site for each ionizable lipid.\n“To select the nitrogen for protonation for each ionizable lipid, the following rule-based\ndecision tree was applied. If the lipid contained only a single nitrogen, that nitrogen was\nprotonated. If multiple nitrogens were present, the nitrogen with the highest priority was\nprotonated based on the following hierarchy: tertiary amine, secondary amine, primary\namine, imidazole, pyridine, tertiary aromatic amine, secondary aromatic amine, and primary\naromatic amine. Groups comprising amide or sulfonamide structures and quaternary\nnitrogens were excluded. If multiple candidates of the same class were found, the nitrogen\nclosest to the molecular periphery of the ionizable lipid head – defined as having the\ngreatest graph eccentricity (i.e. the longest existing graph distance to a terminal atom) –\nwas selected. For specific cases within the KZ_2016 dataset involving ionizable lipids with\ntail amines, the most centrally-located candidate (i.e., the lowest average squared distance\nto all other atoms) was chosen.”\n- We have opted to build LNPDB so each ionizable lipid has the neutral form and one\nplausible protonated form. Due to practical considerations regarding storage (as the\nnumber of possible protonation forms goes up to 217 for the ionizable lipids with 17\nnitrogens) and our view that the more robust solution lies in improved pKa\nmeasurement/prediction and dynamic protonation conditions, we have opted to maintain\nour inclusion of one plausible protonated form. We have included these sentences in lines\n537-538 to address this perspective.\n“Future research is warranted to explore more accurate, dynamic protonation conditions61.”\nTo further emphasize this future research direction of dynamic pH simulations, we now\ninclude a citation in the above sentence for Jansen et al., J. Chem. Inf. Model. (2024),\nwhich describes a software tool to allow dynamic protonation states in molecular dynamics\nsimulations. We also convey this direction in Discussion in line 465 where we mention\nfuture research should incorporate “dynamic pH sensitivity”.\nReviewer #3:\nOur Overall Response:\nWe appreciate the reviewer’s constructive feedback. We believe the insightful comments have\nsignificantly improved the quality of our manuscript. Shown below are our point-by-point responses.\nAny new text added to the revised manuscript is shown in red.\nReviewer #3 Point #1\nThe authors should explicitly discuss their specific methods for data harmonization and\nstandardization across the diverse experimental conditions included in LNPDB. Given the dataset\nencompasses varying experimental parameters such as distinct cell lines, diverse target organs, lipid\ncompositions and molar ratios, differing lipid-to-nucleic acid ratios, dosage variations, and varying\nreporting formats for luminescence measurements (including units and normalization methods), a\ndetailed explanation of how these factors are systematically standardized or normalized is necessary.\nClearly articulating this process will enhance understanding of the dataset’s consistency, reliability,\nand suitability for predictive modeling and comparative analyses across different studies.\nOur Response to Reviewer #3 Point #1\nWe thank the reviewer for this suggestion to further elaborate on our featurization methods.\nWe agree further discussion on featurization is advantageous. We have revised our Methods\nsubsections “Data collection” and “Featurization” to make these points clearer.\n- To better clarify our literature screening strategy for the publications in LNPDB, we have\nadded the following sentences in lines 483-486 of Methods.\n“In summary, publications were selected from the literature based on the presence of large\nscreening datasets, primarily focused on ionizable lipids, to allow for meaningful within-\ndataset comparisons. Additional publications were selected to broaden representation of\nhelper lipids, cholesterols, and PEG lipids.”\n- Rather than simply citing a prior study (Witten et al., Nat. Biotechnol. (2024)) for details\nabout how delivery results were extracted from papers, we now explicitly reiterate more\ndetails in the following sentences in lines 487-496.\n“Functional data – most commonly delivery performance – were extracted from published\nheatmaps and bar plots by digitizing the figures and interpolating values based on either\nthe color scale (heatmaps) or bar height (bar plots) as defined in the accompanying\nlegends. Because delivery values are often reported on different scales across studies and\nmodalities, for each publication and for each delivery context (e.g., in vivo or in vitro within\nthe same publication), functional delivery data were standardized to have mean 0 and\nstandard deviation 1. When raw luminescence values spanned several orders of\nmagnitude, they were first log-transformed prior to standardization. Thus, datapoints were\ntreated as directly comparable within individual screens, but not necessarily across different\nscreens or assay modalities, and transformations were applied to prevent overemphasis of\nany single dataset.”\nWith respect to improving cross-study comparisons, we have our comment in Discussion in\nlines 454-455 regarding encouraging “researchers to incorporate standardized LNP\ncontrols in future in vitro and in vivo screens to enable more effective cross-study\ncomparisons.”\nReviewer #3 Point #2\nThe authors should refer to the article (https://doi.org/10.1021/acsabm.4c01716) as this study\nexplicitly investigates the impact of various lipid compositions, including helper lipids, cholesterol, and\nPEG-lipids, on LNP performance. The manuscript should clearly delineate how LNPDB advances or\nexpands upon such existing work.\nOur Response to Reviewer #3 Point #2\nWe thank the reviewer for bringing this to our attention.\n- First, we note that this paper was published after we prepared our draft, and we have since\nreviewed and cited this paper in the following sentence in Introduction in lines 92-94.\n“All of these methods, including a recent effort to synchronize data across studies18, reflect\nimportant first steps in bringing machine learning to lipid nanomedicine; however, there are\nareas for improvement.”\n- As for how LNPDB expands upon this work, LNPDB features greater than 3x more LNPs\n(see our response to Reviewer #3 Point #3 for information regarding the data added to\nLNPDB for this revised manuscript). Moreover, LNPDB introduces a new modality –\nmolecular dynamics – for featurization. Next, LNPDB offers a platform for researchers to\nupload new LNP structure-function data, enabling LNPDB to expand over time as new data\nare added. Lastly, our manuscript introduces our new state-of-the-art deep learning model\nLiON. We have revised the manuscript to make this point clearer in lines 254-256 and lines\n111-116.\n“Importantly, LNPDB establishes a framework of training data for the continued\ndevelopment of next-generation deep learning models for LNP design.”\n“Future user contributions are supported, enabling LNPDB to expand over time as new\ndata are deposited. Additionally, LNPDB provides CHARMM24 force field topology and\nparameter files for all constituent lipids, allowing molecular dynamics (MD) simulations to\ngenerate three-dimensional, time-resolved lipid data that can enhance predictive modeling.\nFor rational LNP design, MD simulations offer a new modality to generate dynamic\nstructural data for lipids not readily accessible with current experimental methods.”\nReviewer #3 Point #3\nThe dataset described in the manuscript (as shown in Fig. 2b-c) exhibits significant imbalance.\nSpecifically, despite featuring over 10,000 distinct ionizable lipids, the distribution is heavily skewed:\nmost ionizable lipids contain only up to four nitrogen atoms (despite a range of 1–17 nitrogen atoms),\napproximately 50% of ionizable lipids have tail lengths concentrated at 18 or 19 carbons (despite a\nbroader range of 3–37 carbons), and most formulations use an ionizable lipid-to-nucleic acid ratio of\nabout 10. Additionally, only seven helper lipid types are represented, with nearly half (45.7%) being\nDOPE, followed by DSPC (26.9%) and DOTAP (14.4%), leaving minimal representation (<5%) for\nother types such as MDOA, DDAB, 14:0 PA, and 18:0 PG. The dataset is similarly limited for PEG-\nlipids, predominantly including only DMG-PEG2000 and DMPE-PEG2000. Given these substantial\nimbalances, the authors need to thoroughly discuss potential impacts on predictive accuracy,\nmodel generalizability, and potential biases introduced by such imbalances. They should explicitly\naddress how these limitations might influence the reliability of data-driven models trained on this dataset and\nprovide a justification or rationale for how the current dataset can still effectively support accurate and\ngeneralizable modeling efforts.\nOur Response to Reviewer #3 Point #3\nWe thank the reviewer for this perspective.\n- First, we have significantly expanded LNPDB to better capture the LNP design space,\nnotably expanding diversity in the components besides the ionizable lipid. This has led to\nmarked increases in the overall quantity and diversity of LNPs in LNPDB and thus reduces\nsome issues of imbalance. For example, the dataset now features more cholesterol types\nand PEG types (so no longer just DMG-PEG2000 and DMPE-PEG2000).\nAltogether, the revised database has increased…\no from 17,116 to 19,528 LNPs\no from 10,524 to 12,845 unique ionizable lipids, and\no from 28 to 42 publications\nBecause new datasets have been added, LNPDB now has more rows (i.e., LNP\nformulations). Additionally, we have added more columns (i.e., features) to LNPDB to better\nrepresent each LNP. These new columns include Aqueous_buffer, Dialysis_buffer,\nfifthcomponent_name, fifthcomponent_SMILES, fifthcomponent_molratio,\nDose_ug_nucleicacid.\nAll figures are thus updated to reflect this new larger version of LNPDB.\n- Here is a more detailed breakdown of the 14 specific publications added to LNPDB. Note\nthat this information is also reflected in the updated Fig. 2, Table S1, and Fig. S1.\no Study evaluating from Moderna evaluating SM-102 and 9 other ionizable lipids. This\nstudy was added due to the clinical significance of SM-102 for the field.\n SS_2018 (https://doi.org/10.1016/j.ymthe.2018.03.010)\no Study evaluating different cholesterols. This study was added to increase chemical\ndiversity of cholesterols.\n SP_2020 (https://www.nature.com/articles/s41467-020-14527-2)\no Studies evaluating different PEG lipids. These studies were added to increase chemical\ndiversity of PEG lipids.\n LL_2025 (https://doi.org/10.1039/D5NR00433K)\n LX_2025 (https://doi.org/10.1016/j.jconrel.2025.01.071)\no Studies evaluating different fifth component LNP formulations. These studies were\nadded to introduce fifth-component design LNPs into LNPDB.\n SB_2024 (https://doi.org/10.1016/j.bioactmat.2024.05.012)\n SY_2025 (https://doi.org/10.1002/adhm.202403366):\no Studies evaluating new ionizable lipid libraries. These recent studies were added to\nfurther increase ionizable lipid diversity.\n JL_2024\n(https://jnanobiotechnology.biomedcentral.com/articles/10.1186/s12951-024-\n02919-1)\n LX_2024_2 (https://pubs.acs.org/doi/10.1021/jacs.4c10265)\n LX_2024_3 (https://www.nature.com/articles/s41565-024-01747-6)\n SW_2024\n(https://www.sciencedirect.com/science/article/abs/pii/S0168365924007016)\n XH_2024_2 (https://www.nature.com/articles/s41551-024-01267-7)\n AP_2025 (https://www.nature.com/articles/s42004-025-01516-z)\n SX_2025 (https://www.nature.com/articles/s41551-025-01480-y)\n XH_2025 (https://www.biorxiv.org/content/10.1101/2025.02.25.640222v1)\n- Nevertheless, some issues of imbalance (e.g., overrepresentation of DOPE/DSPC/DOTAP,\ndisproportionate representation of a specific ionizable lipid-to-nucleic acid ratio of 10) still\nremain, as this reflects the historical bias of the field toward certain lipid compositions and\nratios. We agree that further discussion is warranted to explain how these imbalances may\ninfluence data-driven models. We have added/expanded on the following sentences in lines\n436-449 in Discussion.\n“Furthermore, MD is data-efficient: it does not require large training datasets, making it\nbeneficial for evaluating novel chemistries as well as underrepresented formulation spaces\nthat existing datasets do not effectively capture. This is especially relevant for LNPs, where\nthe large combinatorial space of lipid types and ratios results in sparse data that can pose a\nmajor challenge for machine learning model generalization. For example, when screening\nnovel or underrepresented helper lipids, ML models trained on LNPDB may struggle to\ngeneralize because the dataset is disproportionately enriched for DOPE, DSPC, and\nDOTAP (Fig. 2c), reflecting the field’s longstanding reliance on these lipids. In such cases,\nMD can provide complementary value by directly modeling the physical interactions of\nthese underrepresented helper lipids, offering mechanistic insights that are not dependent\non prior training data. Moreover, MD is also generally well-suited for small molecules like\nlipids, where dynamic shape, orientation, and local interactions can have outsized effects\non function. In future applications, MD and machine learning may complement one another,\nwith MD simulations contributing dynamic structural data as input features for deep learning\nmodels.”\n- Lastly, the data imbalance concern is a good observation which warrants further discussion\nof how this concern manifests depending on the specific LNP library in question. To\naddress this question, we have added the following sentences in lines 254-259 in Results.\n“Importantly, LNPDB establishes a framework of training data for the continued\ndevelopment of next-generation deep learning models for LNP design. Moreover, given our\nresults demonstrate significant variation in model accuracy across libraries, future research\ncan leverage the training data of LNPDB to design alternative models that may be better\nsuited for the specific LNP design strategy (e.g., helper lipid optimization) or delivery target\n(e.g., in vivo muscle) under investigation.”\nReviewer #3 Point #4\nAlthough the authors have visually demonstrated diversity using UMAP embeddings (Fig. 2a), the\noverlaps visible between data points from different sources suggest that additional quantitative\nmeasures, such as Tanimoto similarity scores or cluster purity metrics, would be beneficial. Providing\nsuch quantitative analyses would strengthen the authors' claims about the distinctiveness of LNP\nformulations sourced from different studies.\nOur Response to Reviewer #3 Point #4\nWe thank the reviewer for this suggestion.\n- We have added Fig. S2 (shown below). In Fig. S2a, as the reviewer suggested, we\ndemonstrate how LNP nearest neighbors within a single library have higher similarity than\nthose across different libraries. Note we use cosine instead of Tanimoto to compute\nsimilarity, as the latter is ideal for binary values but our feature space is not entirely binary.\nAdditionally, in Fig S2b, we thought it would be interesting to consider an alternative UMAP\nembedding approach. Here, we extract the encodings from the penultimate linear layer of\nthe LiON model’s feedforward neural network trained on LNPDB; we then perform UMAP\ndimensionality reduction on these encodings (“fingerprints”).\nFig. S2: Additional LNP embedding analysis. a Probability distributions of cosine similarities for the top 50 nearest\nneighbors for each LNP, computed separately within library and across libraries. This analysis is based on the original\nLNP embedding space shown in Fig. 2a prior to UMAP dimensionality reduction. Probability density functions are plotted,\nwith vertical lines indicating median values and significant Kolmogorov-Smirnov p value shown (Kolmogorov-Smirnov\nstatistic = 0.76). Intra-library LNP neighbors show higher similarity, reflecting greater homogeneity within studies, whereas\ninter-experiment LNP neighbors are more broadly distributed. b UMAP visualization of high-dimensional LNP embedding\nlandscape (i.e., “fingerprints”) from LiON model of LNP formulations. Fingerprints were extracted from the penultimate\nlinear layer of the LiON model’s feedforward neural network trained on LNPDB as shown in Fig. 3a. This is an alternative\nembedding approach to that visualized in Fig. 2a. Source data are provided as a Source data file.\n- Moreover, in support of this new Fig. S2, we have added the following sentences in lines\n173-176 in Results.\n“This is reinforced by our finding that within-library LNP pairs exhibit significantly higher\ncosine similarity than across-library pairs (Fig. S2a), and a UMAP of LiON-learned LNP\nfingerprints similarly yields library-specific clusters, albeit with less pronounced separation\n(Fig. S2b).”\nReviewer #3 Point #5\nThe authors have employed Spearman correlation coefficient as their primary evaluation metric (Fig.\n3a-b). Given that Spearman correlation assesses rank correlation rather than absolute predictive\naccuracy, it might not fully capture predictive performance, particularly in practical applications where\nprecise quantitative predictions are essential. The authors should consider or discuss the applicability\nand advantages of additional metrics such as Pearson correlation, mean absolute error (MAE), root\nmean squared error (RMSE), or even classification-based metrics if delivery outcomes could be\ndiscretized. Justifying the choice of Spearman correlation and/or demonstrating the robustness of\ntheir model across these alternative metrics would significantly enhance the manuscript.\nOur Response to Reviewer #3 Point #5\nWe thank the reviewer for this suggestion.\n- For our machine learning results in Fig. 3, we opted for rank-based Spearman correlations\nfor a couple reasons. First, Spearman does not assume normality, and some publications\nhave somewhat skewed experiment values (see Fig. S1b bottom). Second, rank-based\ncorrelations can perform better at the margins for non-normal distributions, and, during the\ndesign and testing of an LNP library, a practical consideration for an in silico method is\nwhether it can identify the best (rank #1) formulation out of some potential library of many\ncandidate LNPs. For these reasons, we have opted to maintain Spearman correlations for\nour main Fig. 3. However, we agree that additional analysis using linear Pearson\ncorrelation is useful with which to compare. Accordingly, we have added Fig. S3 (shown\nbelow), which presents the same analysis as the main Fig. 3 except uses Pearson\ncorrelations instead of Spearman correlations. The same key results are largely replicated,\ni.e., LiON achieves improved predictive performance for 5 out of the 7 test datasets when\ntrained on the larger LNPDB dataset, and LiON trained on LNPDB achieves better\npredictive performance compared to AGILE for the 4 held-out test sets evaluated. Note that\nSL_2020 has the smallest sample size and thus shows more divergence between\nSpearman and Pearson results.\nFig. S3: Pearson correlation results for deep learning models. a Analogous to Fig. 3a but measured using Pearson\ncorrelation. b Analogous to Fig. 3b but measured using Pearson correlation. Source data are provided as a Source data\nfile.\n- This suggestion to emphasize linear correlation strategies where possible has motivated us\nto change our correlation method for reporting molecular dynamics results in Figs. 4\n(shown below), S8, S9, S11. The underlying distributions for these molecular dynamics\nLNPs fit the normality criterion well and thus are good candidates for the linear Pearson\ncorrelation method. Hence, we changed the reported r and p values for our molecular\ndynamics results from Spearman to Pearson.\nFig. 4: LNPDB facilitates MD simulations of LNP membrane dynamics, uncovering new structure-function\nrelationships towards predicting delivery performance. a Schematic illustration of the LNP MD simulation workflow\nenabled by LNPDB: select an LNP formulation of interest, initialize a representative bilayer with the provided CHARMM\nforce field topology and parameter files for the constituent lipids in the selected LNP formulation, run an MD simulation,\nand extract features from the resulting trajectory to assess correlation with experimental delivery performance. b\nSimulated bilayers for three example LNP formulations available in LNPDB: LNP_0009476 (left; Onpattro formulation from\nZH_202343), LNP_0003881 (center; from LM_20197), and LNP_0004075 (right; from LM_20197). Snapshots are taken at\n1.5 µs for LNP_0009476 and LNP_0003881, and 100 ns for LNP_0004075. For LNP_0009476 and LNP_0003881, which\nformed stable bilayers, separate simulation snapshots are shown for the fully-neutral and half-protonated ionizable lipid\n(IL) conditions; density profiles are provided. For LNP_0004065, which failed to form a stable bilayer as indicated by the\nescaped ionizable lipids, the simulation snapshot from the half-protonated ionizable lipid condition is shown. c Violin plot\ndemonstrating that simulated bilayer stability of N = 54 LNP formulations from LM_20197 is predictive of experimental\ndelivery performance, as measured in the LM_2019 study by normalized luciferase activity in HeLa cells. p value resulting\nfrom two-sided Wilcoxon signed-rank test is shown. d Method for calculating critical packing parameter (CPP). Analyses\nare performed on every 1 ns from the final 500 ns of 1.5 µs trajectories of LNP formulations that formed stable,\nequilibrated bilayers. For each of these timesteps, the coordinates for ionizable lipids are extracted, and the CPP value is\ncomputed for each ionizable lipid. e For N = 34 LNP formulations from LM_20197 that formed stable bilayers (subset from\noriginal N = 54 as N = 20 were unstable), the mean CPP value – computed as CPP = V/(a l ) of ionizable lipids –\nV V 0c\nsignificantly correlates with experimental delivery performance; this is the case for both protonated ionizable lipids in the\nhalf-protonated systems (top), as well as neutral ionizable lipids in the fully-neutral systems (bottom). Pearson r and p\nvalues are noted for the overall trend as\nwell as for each ionizable lipid amine group (A12, A2, A3), which are also represented by point color. Points denote mean\nvalues, and error bars denote +/- SEM for CPP and standard deviation for CPP . Additional details of all bilayer simulations analyzed in this study are provided in Table S2. Source data are provided as a Source data file.\nReviewer #1:\nThe authors have made substantial revision to the ms, and conducted additional analyses (e.g. CPP).\nI am satisfied with the revisions and support the publication of this timely contribution.\nOur Response:\nWe thank the reviewer for recognizing the value of our work and supporting its publication.\nReviewer #2:\nOur Overall Response:\nWe appreciate this feedback. Shown below are our point-by-point responses.\nReviewer #2 Point #1\nThis study presents methodological concerns regarding data integration. The authors employed\nsimple log-transformation and standardization before directly merging data from different studies.\nHowever, such basic standardization cannot effectively eliminate systematic biases arising from\ndifferent laboratories, experimental conditions, and measurement protocols. This approach may\ncreate a misleading impression of data comparability and potentially introduce issues in subsequent\nmodel training. More rigorous data integration methods should be employed to address data\nintegration challenges.\nOur Response to Reviewer #2 Point #1\nWe thank the reviewer for inviting additional discussion here.\n- The matter of systematic biases from different labs/experiments is a fundamental limitation\nof the field itself, one whose effect we sought to minimize by transformation and\nstandardization that we mentioned in Methods. Although it would be ideal for all compiled\ndata to emerge from a single lab, limiting our current dataset in such a way would\nsignificantly reduce the quantity and diversity of LNPs. Our chosen standardization\napproach represented a practical strategy to enable cross-study comparison given the\navailable data, and we acknowledge in lines 498-507 of Methods that this approach is\nimperfect.\n“Predictive performance results were separated by publication, as datapoints were treated\nas directly comparable within individual screens, but not necessarily across different\nscreens or assay modalities. Moreover, standardization was applied to prevent\noveremphasis of any single dataset. The deep learning models used in this study do train\nacross datasets to maximize the diversity of trainable data, though we recognize that the\nability of data from one study to inform structure-function relationships in another is limited\nby inherent differences in experimental protocols, measurement modalities, and assay\nsensitivities across studies that may introduce systematic biases. LNPDB introduces\nexperimental condition variables (e.g., solvents, dose) towards bridging studies, but these\nadditions can only partially mitigate the systematic differences across laboratories and\nexperimental setups.”\n- Moreover, this discussion reinforces why we argue in Discussion in lines 455-462 for the\ninclusion of standardized controls for the field going forward, so as to enable more effective\ncross-study comparisons.\n“A key limitation of current LNP data – including those compiled in LNPDB – is the difficulty\nof comparing across studies due to variability in experimental methods (e.g., dose, cell\ntype, animal model, nucleic acid purity, imaging equipment, injection technique, etc.). By\nestablishing LNPDB as a centralized repository, we aim to encourage researchers to\nincorporate standardized LNP controls in future in vitro and in vivo screens to enable more\neffective cross-study comparisons. These standardized LNP controls could be Spikevax2\n(50% SM-102, 10% DSPC, 38.5% cholesterol, 1.5% DMG-PEG2000) or Onpattro74 (50%\nDLin-MC3-DMA, 10% DSPC, 38.5% cholesterol, 1.5% DMG-PEG2000), FDA-approved\nLNPs for COVID-19 and transthyretin-induced amyloidosis, respectively.”\nReviewer #2 Point #2\nThe marked performance variations of the LiON model across different databases are likely\nattributable to inadequate data integration strategies, which may systematically obscure the true\npredictive value and distinctive contributions of the LNPDB database. Alternative modeling\napproaches should be considered, such as dataset-specific modeling or multi-task learning\nframeworks to more appropriately integrate heterogeneous data sources, thereby yielding more\nreasonable and reliable model results to reflect the LNPDB quality.\nOur Response to Reviewer #2 Point #2\nWe thank the reviewer for inviting additional discussion and analysis here, similar to Point #1.\n- Towards dataset-specific modeling, we introduce Fig. S5. We trained our LiON model on\nindividual datasets (70%-15%-15% train-validation-test split) and compared performance to\nthe same model trained on the integrated LNPDB dataset. As shown in Fig. S5, models\ntrained exclusively on a single dataset (three randomly selected) yielded poorer predictive\nperformance than those trained across studies, supporting the benefit of data integration\nacross studies in capturing broader structure-function relationships, even in spite of the\nlimitations of data integration that we noted in Point #1.\nFig. S5: Learning from outside datasets improves predictive performance of LiON. Training LiON exclusively on a\nsingle dataset yields poorer predictive performance (measured by Spearman correlation) than when trained on LNPDB.\nThis suggests that integrating data from multiple studies enables the model to capture broader structure-function\nrelationships. Source data are provided as a Source data file.\n- Accordingly, we have added the following sentence in lines 244-248 in Results.\n“Moreover, despite limitations of integrating data from multiple studies as discussed in\nMethods, LiON models trained across datasets achieved higher predictive performance\nthan those trained on single datasets (Fig. S5), suggesting that training across multiple\nstudies in LNPDB enabled LiON to learn more generalizable structure-function\nrelationships (Fig. S5).”\n- Lastly, we hope that introducing LNPDB as a public, centralized data repository will\nmotivate future research to design other deep learning models. Our intention is not to\npresent our LiON model shown here as a finalized approach, but rather as a foundation\nupon which future, more specialized models can be developed. This echoes our discussion\nin lines 258-263.\n“Importantly, LNPDB establishes a framework of training data for the continued\ndevelopment of next-generation deep learning models for LNP design. Moreover, given our\nresults demonstrate significant variation in model accuracy across libraries, future research\ncan leverage the training data of LNPDB to design alternative models that may be better\nsuited for the specific LNP design strategy (e.g., helper lipid optimization) or delivery target\n(e.g., in vivo muscle) under investigation.”\nReviewer #2 Point #3\nThe authors used two algorithms to calculate the CPP values of 34 different LNP formulations from\nthe LM_2019 library (lines 340–365) and subsequently correlated them with experimental delivery\nperformance (Fig. 4). The current sample size (34) is too small to represent the 19,528 LNPs and\n12,845 unique ionizable lipids in the LNPDB. It is recommended to increase the number of tested\nformulations to further validate the correlation and conclusion obtained in this study.\nOur Response to Reviewer #2 Point #3\n- This manuscript involved simulating a total of 134 bilayers (77 fully-neutral, 57 half-\nprotonated) from the LM_2019 dataset. As we state in lines 646-648 of Methods, “This\nsubset, drawn from a single combinatorial ionizable lipid library, was chosen as a\nrepresentative example of systematic lipid library design commonly employed in the field,\nwhile keeping the scope feasible within computational limits.” The reviewer is correct that\nafter selecting for only the stable bilayers, the CPP analysis shown in Fig. 4e-f includes 34\nsimulated bilayers each for protonated and neutral conditions. Note that the preceding\nstability analysis in Fig. 4c includes 54 simulated bilayers.\n- The central focus of this manuscript is developing LNPDB and demonstrating two proof-of-\nconcept applications for deep learning and molecular dynamics simulations. We do not\nclaim that the subset of LNPs that we simulated in this study represent all ~20,000 LNPs in\nthe entire database. This is stated in lines 301-308 of Results.\n“To demonstrate how LNPDB can be used to facilitate MD simulations, we simulated the\nbilayer equilibration process for a subset of LNP formulations and extracted structural\nfeatures to assess correlation with experimental transfection (Fig. 4a). This use case\nrepresents just one of many potential simulation strategies enabled by the database (see\n“Discussion”).”\n- Moreover, as we state in lines 464-475 of Discussion, we encourage future research to use\nthe topology and parameter files provided in LNPDB to expand simulation efforts beyond\nthe dataset evaluated in this study.\n“Future research should explore experimental validation of MD-derived features such as\nCPP. The MD bilayer models presented in this work provide a simplified yet informative\nframework that yields significant correlations with delivery performance for the evaluated\ndataset. However, future research should leverage the topology and parameter files\nprovided in LNPDB to expand simulation efforts to include additional delivery-relevant\nphenomena, such as membrane fusion dynamics, interactions with nucleic acids, and\ndynamic pH sensitivity during endosomal escape. To support MD simulations with larger\nsystem sizes, longer time scales, and the inclusion of nucleic acids, we plan to incorporate\nMartini 3 coarse-grained lipid and nucleic acid parameters75 in future versions of LNPDB.\nThis will facilitate efficient simulations for many more LNPs to further explore structure-\nfunction relationships. Moreover, although this version of LNPDB includes some LNPs with\nfive lipid components, future versions will further incorporate LNPs with more than four\ncomponents (e.g., additional lipids8 or lipids conjugated to targeting ligand76).”\n- We are actively working on simulating many more LNP systems in different contexts, as\nalluded to in the above sentences in Discussion. These will be included in future\npublications. For the sake of this manuscript whose principal aim is to introduce LNPDB,\nwe consider our current simulation data to be sufficiently robust.\nReviewer #2 Point #4\nWe have noticed that this study currently considers different quantities of auxiliary lipids (CHOL,\nDSPC, DOPE) when calculating CPP, with DOPE being the main one. Therefore, whether the\ndifferences and changes in the quantity of these helper lipids have an impact on the ionizable lipid\nCPP should be further compared and explained. The revised manuscript only mentions that the\nimpact of PEG is not significant.\nOur Response to Reviewer #2 Point #4\n- The molecular dynamics analysis in this manuscript focused on the LM_2019 dataset,\nwhich varied the ionizable lipid type. The reviewer makes a great point about exploring how\nother helper lipid types may affect the CPP of the ionizable lipid. We are actively working\non simulating different LNPs with different helper lipids and ratios and thus far have\npromising preliminary results. These results will be reported in a future publication where\nnovel LNP formulations will be disclosed. Echoing our response to Point #3, the main focus\nof this manuscript is to introduce LNPDB.\n- As requested, we introduced the PEG lipid analysis in response to this Reviewer #2’s Point\n#6 during the first revision round to demonstrate its inclusion has no significant effect on\nCPP.\nReviewer #2 Point #5\nThe authors noted that when only considering the subset with CPP > 1 (Fig. 4 & Fig. S9), the\ncorrelative performance improved substantially for both the CPPV and CPPRg methods. Since the\nsubset size was significantly reduced to fewer than 10, the improvement in correlation is expected.\nHowever, it remains uncertain whether this conclusion would hold when more ionizable lipids are\nincluded.\nOur Response to Reviewer #2 Point #5\n- Subsetting by CPP > 1 did not lead to the overall sample size being less than 10. As shown\nin the pre-existing Fig. S10 (formerly titled Fig. S9), the overall subset sample size ranges\nfrom 16 to 27 (see red text in figure) depending on the protonation condition being\nconsidered. These sample sizes are sufficiently robust for correlative analysis. The overall\ncorrelation coefficient values (see red text in figure) are indeed higher than their non-\nsubsetted counterparts as shown in the main Fig 4e-f. Thus, we hold that our main claim\nregarding improved predictive performance is substantiated.\n- The reviewer is correct that the subsets once stratified by amine are usually less than 10\ndepending on protonation condition, which could limit conclusions. To no longer highlight\nany correlation results for sample sizes less than 10, we now have omitted stating the\ncorrelation coefficient values of the amine-specific analysis in lines 356-362.\n“Moreover, when we focused our analyses on the subset of LNPs with mean CPP values\ngreater than 1 – corresponding theoretically to a transition to negative curvature – the\ncorrelative performance improved substantially for both the CPP method (protonated:\nV\noverall r = 0.723; neutral: overall r = 0.680) and CPP method (protonated: overall r =\nRg\n0.621; neutral: overall r = 0.646) (Fig. S10). Some correlations for amine 3 did not reach\nstatistical significance, likely due to its limited representation of LNPs with CPP > 1.”\nReviewer #2 Point #6\nThe authors mentioned that using the CPPV method (lines 670-674), \"...CPPV values exhibit greater\nvariability across lipids and time steps compared to CPPRg…\". Such variability may be normal.\nIt is suggested to perform a cluster analysis to relate the complexity of LNP formulations and the\npolymorphism of ionizable lipids to delivery efficiency.\nOur Response to Reviewer #2 Point #6\nWe thank the reviewer for inviting additional analysis here to assess whether the variance of\nCPP may itself be a predictor of delivery efficiency.\n- Towards this, we introduce Fig. S13, shown below. We assess whether the standard error\nof the mean for CPP (Fig. S13a) or standard deviation for CPP (Fig. S13b) normalized\nV Rg\nby the mean CPP value correlates with delivery performance. Interestingly, to the\nreviewer’s point, this variance measure for CPP significantly correlates with delivery\nV\nperformance. This significant relationship suggests greater ionizable lipid polymorphism (as\nmeasured by greater CPP variance) allows for more effective delivery, potentially due to\nV\nincreased capacity to accommodate more inverse-conical lipid geometries. This\nrelationship, however, is not found to be significant for the CPP metric.\nRg\nFig. S13. Relationship between CPP variance and delivery performance. a Analogous to Fig. 4e but assessing SEM\nnormalized by mean CPP values. This significant relationship suggests greater ionizable lipid polymorphism (as\nV\nmeasured by greater CPP variance) allows for more effective delivery, potentially due to increased capacity to\nV\naccommodate more inverse-conical lipid geometries. b This relationship is insignificant for CPP . SEM denotes standard\nRg\nof the mean. SD denotes standard deviation. Pearson r and p values are noted. Source data are provided as a Source\ndata file.\n- Accordingly, we have added the following sentence in lines 372-375 in Results.\n“Interestingly, CPP variance also significantly predicts delivery performance, suggesting\nV\nthat greater ionizable lipid polymorphism allows for more effective delivery, potentially due\nto increased capacity to accommodate more inverse-conical lipid geometries (Fig. S13).”\nReviewer #2 Point #7\nA comparison of computational equipment and time consumption between the CPPV and CPPRg\nmethods should be provided to help other researchers choose the appropriate method.\nOur Response to Reviewer #2 Point #7\nWe thank the reviewer for this point.\n- In lines 589-595 of Methods, we now state the following.\n“We ran all MD simulations on 48 NVIDIA RTX A5000 GPUs in parallel. Across the neutral\nsystems, the average throughput was 363.86 ± 14.93 ns/day; across the protonated\nsystems, it was 319.11 ± 11.65 ns/day. For the LM_2019 bilayers with run duration of 1.5\nμs, this corresponds to 4.1 days per neutral system and 4.7 days per protonated system.\nThe full LM_2019 simulation batch, run on 48 GPUs (one per simulation), completed in\nabout 10 days. Subsequent CPP calculations for all systems, executed on 384 CPU cores\nin parallel, finished in 5 hours, with comparable compute times for CPP and CPP .”\nV Rg\nReviewer #3:\nI appreciate the authors’ careful and thorough revision. In my view, all of my prior concerns have\nbeen adequately addressed in both the main manuscript and the Supporting Information. The\nadditions and clarifications substantially improve the clarity, rigor, and reproducibility of the work. I\ntherefore recommend the manuscript for publication. By way of summary: the revised version clearly\ndocuments data processing and standardization, positions the contribution relative to prior efforts,\nexpands and analyzes the dataset to contextualize limitations, and provides quantitative checks that\nsupport the principal conclusions. These updates resolve my earlier requests and strengthen the\nmanuscript’s impact and transparency.\nOur Response:\nWe thank the reviewer for their constructive comments during the first round and endorsement of the\nrevised manuscript.\n10"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have made substantial revision to the ms, and conducted additional analyses (e.g. CPP). I am satisfied with the revisions and support the publication of this timely contribution.", "reviewer_2": "The revised manuscript answered some questions. However, there are still several issues to be addressed before publication.\n1. This study presents methodological concerns regarding data integration. The authors employed simple log-transformation and standardization before directly merging data from different studies. However, such basic standardization cannot effectively eliminate systematic biases arising from different laboratories, experimental conditions, and measurement protocols. This approach may create a misleading impression of data comparability and potentially introduce issues in subsequent model training. More rigorous data integration methods should be employed to address data integration challenges.\n2. The marked performance variations of the LiON model across different databases are likely attributable to inadequate data integration strategies, which may systematically obscure the true predictive value and distinctive contributions of the LNPDB database. Alternative modeling approaches should be considered, such as dataset-specific modeling or multi-task learning frameworks to more appropriately integrate heterogeneous data sources, thereby yielding more reasonable and reliable model results to reflect the LNPDB quality.\n3. The authors used two algorithms to calculate the CPP values of 34 different LNP formulations from the LM_2019 library (lines 340–365) and subsequently correlated them with experimental delivery performance (Fig. 4). The current sample size (34) is too small to represent the 19,528 LNPs and 12,845 unique ionizable lipids in the LNPDB. It is recommended to increase the number of tested formulations to further validate the correlation and conclusion obtained in this study.\n4. We have noticed that this study currently considers different quantities of auxiliary lipids (CHOL, DSPC, DOPE) when calculating CPP, with DOPE being the main one. Therefore, whether the differences and changes in the quantity of these helper lipids have an impact on the ionizable lipid CPP should be further compared and explained. The revised manuscript only mentions that the impact of PEG is not significant.\n5. The authors noted that when only considering the subset with CPP > 1 (Fig. 4 & Fig. S9), the correlative performance improved substantially for both the CPPV and CPPRg methods. Since the subset size was significantly reduced to fewer than 10, the improvement in correlation is expected. However, it remains uncertain whether this conclusion would hold when more ionizable lipids are included.\n6. The authors mentioned that using the CPPV method (lines 670-674), \"...CPPV values exhibit greater variability across lipids and time steps compared to CPPRg…\". Such variability may be normal. It is suggested to perform a cluster analysis to relate the complexity of LNP formulations and the polymorphism of ionizable lipids to delivery efficiency.\n7. A comparison of computational equipment and time consumption between the CPPV and CPPRg methods should be provided to help other researchers choose the appropriate method.", "reviewer_3": "I appreciate the authors’ careful and thorough revision. In my view, all of my prior concerns have been adequately addressed in both the main manuscript and the Supporting Information. The additions and clarifications substantially improve the clarity, rigor, and reproducibility of the work. I therefore recommend the manuscript for publication.\nBy way of summary: the revised version clearly documents data processing and standardization, positions the contribution relative to prior efforts, expands and analyzes the dataset to contextualize limitations, and provides quantitative checks that support the principal conclusions. These updates resolve my earlier requests and strengthen the manuscript’s impact and transparency."}, "author_response": "Point-by-point response for consideration at Nature Communications\nReviewer #1:\nThe authors have made substantial revision to the ms, and conducted additional analyses (e.g. CPP).\nI am satisfied with the revisions and support the publication of this timely contribution.\nOur Response:\nWe thank the reviewer for recognizing the value of our work and supporting its publication.\nReviewer #2:\nOur Overall Response:\nWe appreciate this feedback. Shown below are our point-by-point responses.\nReviewer #2 Point #1\nThis study presents methodological concerns regarding data integration. The authors employed\nsimple log-transformation and standardization before directly merging data from different studies.\nHowever, such basic standardization cannot effectively eliminate systematic biases arising from\ndifferent laboratories, experimental conditions, and measurement protocols. This approach may\ncreate a misleading impression of data comparability and potentially introduce issues in subsequent\nmodel training. More rigorous data integration methods should be employed to address data\nintegration challenges.\nOur Response to Reviewer #2 Point #1\nWe thank the reviewer for inviting additional discussion here.\n- The matter of systematic biases from different labs/experiments is a fundamental limitation\nof the field itself, one whose effect we sought to minimize by transformation and\nstandardization that we mentioned in Methods. Although it would be ideal for all compiled\ndata to emerge from a single lab, limiting our current dataset in such a way would\nsignificantly reduce the quantity and diversity of LNPs. Our chosen standardization\napproach represented a practical strategy to enable cross-study comparison given the\navailable data, and we acknowledge in lines 498-507 of Methods that this approach is\nimperfect.\n“Predictive performance results were separated by publication, as datapoints were treated\nas directly comparable within individual screens, but not necessarily across different\nscreens or assay modalities. Moreover, standardization was applied to prevent\noveremphasis of any single dataset. The deep learning models used in this study do train\nacross datasets to maximize the diversity of trainable data, though we recognize that the\nability of data from one study to inform structure-function relationships in another is limited\nby inherent differences in experimental protocols, measurement modalities, and assay\nsensitivities across studies that may introduce systematic biases. LNPDB introduces\nexperimental condition variables (e.g., solvents, dose) towards bridging studies, but these\nadditions can only partially mitigate the systematic differences across laboratories and\nexperimental setups.”\n- Moreover, this discussion reinforces why we argue in Discussion in lines 455-462 for the\ninclusion of standardized controls for the field going forward, so as to enable more effective\ncross-study comparisons.\n“A key limitation of current LNP data – including those compiled in LNPDB – is the difficulty\nof comparing across studies due to variability in experimental methods (e.g., dose, cell\ntype, animal model, nucleic acid purity, imaging equipment, injection technique, etc.). By\nestablishing LNPDB as a centralized repository, we aim to encourage researchers to\nincorporate standardized LNP controls in future in vitro and in vivo screens to enable more\neffective cross-study comparisons. These standardized LNP controls could be Spikevax2\n(50% SM-102, 10% DSPC, 38.5% cholesterol, 1.5% DMG-PEG2000) or Onpattro74 (50%\nDLin-MC3-DMA, 10% DSPC, 38.5% cholesterol, 1.5% DMG-PEG2000), FDA-approved\nLNPs for COVID-19 and transthyretin-induced amyloidosis, respectively.”\nReviewer #2 Point #2\nThe marked performance variations of the LiON model across different databases are likely\nattributable to inadequate data integration strategies, which may systematically obscure the true\npredictive value and distinctive contributions of the LNPDB database. Alternative modeling\napproaches should be considered, such as dataset-specific modeling or multi-task learning\nframeworks to more appropriately integrate heterogeneous data sources, thereby yielding more\nreasonable and reliable model results to reflect the LNPDB quality.\nOur Response to Reviewer #2 Point #2\nWe thank the reviewer for inviting additional discussion and analysis here, similar to Point #1.\n- Towards dataset-specific modeling, we introduce Fig. S5. We trained our LiON model on\nindividual datasets (70%-15%-15% train-validation-test split) and compared performance to\nthe same model trained on the integrated LNPDB dataset. As shown in Fig. S5, models\ntrained exclusively on a single dataset (three randomly selected) yielded poorer predictive\nperformance than those trained across studies, supporting the benefit of data integration\nacross studies in capturing broader structure-function relationships, even in spite of the\nlimitations of data integration that we noted in Point #1.\nFig. S5: Learning from outside datasets improves predictive performance of LiON. Training LiON exclusively on a\nsingle dataset yields poorer predictive performance (measured by Spearman correlation) than when trained on LNPDB.\nThis suggests that integrating data from multiple studies enables the model to capture broader structure-function\nrelationships. Source data are provided as a Source data file.\n- Accordingly, we have added the following sentence in lines 244-248 in Results.\n“Moreover, despite limitations of integrating data from multiple studies as discussed in\nMethods, LiON models trained across datasets achieved higher predictive performance\nthan those trained on single datasets (Fig. S5), suggesting that training across multiple\nstudies in LNPDB enabled LiON to learn more generalizable structure-function\nrelationships (Fig. S5).”\n- Lastly, we hope that introducing LNPDB as a public, centralized data repository will\nmotivate future research to design other deep learning models. Our intention is not to\npresent our LiON model shown here as a finalized approach, but rather as a foundation\nupon which future, more specialized models can be developed. This echoes our discussion\nin lines 258-263.\n“Importantly, LNPDB establishes a framework of training data for the continued\ndevelopment of next-generation deep learning models for LNP design. Moreover, given our\nresults demonstrate significant variation in model accuracy across libraries, future research\ncan leverage the training data of LNPDB to design alternative models that may be better\nsuited for the specific LNP design strategy (e.g., helper lipid optimization) or delivery target\n(e.g., in vivo muscle) under investigation.”\nReviewer #2 Point #3\nThe authors used two algorithms to calculate the CPP values of 34 different LNP formulations from\nthe LM_2019 library (lines 340–365) and subsequently correlated them with experimental delivery\nperformance (Fig. 4). The current sample size (34) is too small to represent the 19,528 LNPs and\n12,845 unique ionizable lipids in the LNPDB. It is recommended to increase the number of tested\nformulations to further validate the correlation and conclusion obtained in this study.\nOur Response to Reviewer #2 Point #3\n- This manuscript involved simulating a total of 134 bilayers (77 fully-neutral, 57 half-\nprotonated) from the LM_2019 dataset. As we state in lines 646-648 of Methods, “This\nsubset, drawn from a single combinatorial ionizable lipid library, was chosen as a\nrepresentative example of systematic lipid library design commonly employed in the field,\nwhile keeping the scope feasible within computational limits.” The reviewer is correct that\nafter selecting for only the stable bilayers, the CPP analysis shown in Fig. 4e-f includes 34\nsimulated bilayers each for protonated and neutral conditions. Note that the preceding\nstability analysis in Fig. 4c includes 54 simulated bilayers.\n- The central focus of this manuscript is developing LNPDB and demonstrating two proof-of-\nconcept applications for deep learning and molecular dynamics simulations. We do not\nclaim that the subset of LNPs that we simulated in this study represent all ~20,000 LNPs in\nthe entire database. This is stated in lines 301-308 of Results.\n“To demonstrate how LNPDB can be used to facilitate MD simulations, we simulated the\nbilayer equilibration process for a subset of LNP formulations and extracted structural\nfeatures to assess correlation with experimental transfection (Fig. 4a). This use case\nrepresents just one of many potential simulation strategies enabled by the database (see\n“Discussion”).”\n- Moreover, as we state in lines 464-475 of Discussion, we encourage future research to use\nthe topology and parameter files provided in LNPDB to expand simulation efforts beyond\nthe dataset evaluated in this study.\n“Future research should explore experimental validation of MD-derived features such as\nCPP. The MD bilayer models presented in this work provide a simplified yet informative\nframework that yields significant correlations with delivery performance for the evaluated\ndataset. However, future research should leverage the topology and parameter files\nprovided in LNPDB to expand simulation efforts to include additional delivery-relevant\nphenomena, such as membrane fusion dynamics, interactions with nucleic acids, and\ndynamic pH sensitivity during endosomal escape. To support MD simulations with larger\nsystem sizes, longer time scales, and the inclusion of nucleic acids, we plan to incorporate\nMartini 3 coarse-grained lipid and nucleic acid parameters75 in future versions of LNPDB.\nThis will facilitate efficient simulations for many more LNPs to further explore structure-\nfunction relationships. Moreover, although this version of LNPDB includes some LNPs with\nfive lipid components, future versions will further incorporate LNPs with more than four\ncomponents (e.g., additional lipids8 or lipids conjugated to targeting ligand76).”\n- We are actively working on simulating many more LNP systems in different contexts, as\nalluded to in the above sentences in Discussion. These will be included in future\npublications. For the sake of this manuscript whose principal aim is to introduce LNPDB,\nwe consider our current simulation data to be sufficiently robust.\nReviewer #2 Point #4\nWe have noticed that this study currently considers different quantities of auxiliary lipids (CHOL,\nDSPC, DOPE) when calculating CPP, with DOPE being the main one. Therefore, whether the\ndifferences and changes in the quantity of these helper lipids have an impact on the ionizable lipid\nCPP should be further compared and explained. The revised manuscript only mentions that the\nimpact of PEG is not significant.\nOur Response to Reviewer #2 Point #4\n- The molecular dynamics analysis in this manuscript focused on the LM_2019 dataset,\nwhich varied the ionizable lipid type. The reviewer makes a great point about exploring how\nother helper lipid types may affect the CPP of the ionizable lipid. We are actively working\non simulating different LNPs with different helper lipids and ratios and thus far have\npromising preliminary results. These results will be reported in a future publication where\nnovel LNP formulations will be disclosed. Echoing our response to Point #3, the main focus\nof this manuscript is to introduce LNPDB.\n- As requested, we introduced the PEG lipid analysis in response to this Reviewer #2’s Point\n#6 during the first revision round to demonstrate its inclusion has no significant effect on\nCPP.\nReviewer #2 Point #5\nThe authors noted that when only considering the subset with CPP > 1 (Fig. 4 & Fig. S9), the\ncorrelative performance improved substantially for both the CPPV and CPPRg methods. Since the\nsubset size was significantly reduced to fewer than 10, the improvement in correlation is expected.\nHowever, it remains uncertain whether this conclusion would hold when more ionizable lipids are\nincluded.\nOur Response to Reviewer #2 Point #5\n- Subsetting by CPP > 1 did not lead to the overall sample size being less than 10. As shown\nin the pre-existing Fig. S10 (formerly titled Fig. S9), the overall subset sample size ranges\nfrom 16 to 27 (see red text in figure) depending on the protonation condition being\nconsidered. These sample sizes are sufficiently robust for correlative analysis. The overall\ncorrelation coefficient values (see red text in figure) are indeed higher than their non-\nsubsetted counterparts as shown in the main Fig 4e-f. Thus, we hold that our main claim\nregarding improved predictive performance is substantiated.\n- The reviewer is correct that the subsets once stratified by amine are usually less than 10\ndepending on protonation condition, which could limit conclusions. To no longer highlight\nany correlation results for sample sizes less than 10, we now have omitted stating the\ncorrelation coefficient values of the amine-specific analysis in lines 356-362.\n“Moreover, when we focused our analyses on the subset of LNPs with mean CPP values\ngreater than 1 – corresponding theoretically to a transition to negative curvature – the\ncorrelative performance improved substantially for both the CPP method (protonated:\nV\noverall r = 0.723; neutral: overall r = 0.680) and CPP method (protonated: overall r =\nRg\n0.621; neutral: overall r = 0.646) (Fig. S10). Some correlations for amine 3 did not reach\nstatistical significance, likely due to its limited representation of LNPs with CPP > 1.”\nReviewer #2 Point #6\nThe authors mentioned that using the CPPV method (lines 670-674), \"...CPPV values exhibit greater\nvariability across lipids and time steps compared to CPPRg…\". Such variability may be normal.\nIt is suggested to perform a cluster analysis to relate the complexity of LNP formulations and the\npolymorphism of ionizable lipids to delivery efficiency.\nOur Response to Reviewer #2 Point #6\nWe thank the reviewer for inviting additional analysis here to assess whether the variance of\nCPP may itself be a predictor of delivery efficiency.\n- Towards this, we introduce Fig. S13, shown below. We assess whether the standard error\nof the mean for CPP (Fig. S13a) or standard deviation for CPP (Fig. S13b) normalized\nV Rg\nby the mean CPP value correlates with delivery performance. Interestingly, to the\nreviewer’s point, this variance measure for CPP significantly correlates with delivery\nV\nperformance. This significant relationship suggests greater ionizable lipid polymorphism (as\nmeasured by greater CPP variance) allows for more effective delivery, potentially due to\nV\nincreased capacity to accommodate more inverse-conical lipid geometries. This\nrelationship, however, is not found to be significant for the CPP metric.\nRg\nFig. S13. Relationship between CPP variance and delivery performance. a Analogous to Fig. 4e but assessing SEM\nnormalized by mean CPP values. This significant relationship suggests greater ionizable lipid polymorphism (as\nV\nmeasured by greater CPP variance) allows for more effective delivery, potentially due to increased capacity to\nV\naccommodate more inverse-conical lipid geometries. b This relationship is insignificant for CPP . SEM denotes standard\nRg\nof the mean. SD denotes standard deviation. Pearson r and p values are noted. Source data are provided as a Source\ndata file.\n- Accordingly, we have added the following sentence in lines 372-375 in Results.\n“Interestingly, CPP variance also significantly predicts delivery performance, suggesting\nV\nthat greater ionizable lipid polymorphism allows for more effective delivery, potentially due\nto increased capacity to accommodate more inverse-conical lipid geometries (Fig. S13).”\nReviewer #2 Point #7\nA comparison of computational equipment and time consumption between the CPPV and CPPRg\nmethods should be provided to help other researchers choose the appropriate method.\nOur Response to Reviewer #2 Point #7\nWe thank the reviewer for this point.\n- In lines 589-595 of Methods, we now state the following.\n“We ran all MD simulations on 48 NVIDIA RTX A5000 GPUs in parallel. Across the neutral\nsystems, the average throughput was 363.86 ± 14.93 ns/day; across the protonated\nsystems, it was 319.11 ± 11.65 ns/day. For the LM_2019 bilayers with run duration of 1.5\nμs, this corresponds to 4.1 days per neutral system and 4.7 days per protonated system.\nThe full LM_2019 simulation batch, run on 48 GPUs (one per simulation), completed in\nabout 10 days. Subsequent CPP calculations for all systems, executed on 384 CPU cores\nin parallel, finished in 5 hours, with comparable compute times for CPP and CPP .”\nV Rg\nReviewer #3:\nI appreciate the authors’ careful and thorough revision. In my view, all of my prior concerns have\nbeen adequately addressed in both the main manuscript and the Supporting Information. The\nadditions and clarifications substantially improve the clarity, rigor, and reproducibility of the work. I\ntherefore recommend the manuscript for publication. By way of summary: the revised version clearly\ndocuments data processing and standardization, positions the contribution relative to prior efforts,\nexpands and analyzes the dataset to contextualize limitations, and provides quantitative checks that\nsupport the principal conclusions. These updates resolve my earlier requests and strengthen the\nmanuscript’s impact and transparency.\nOur Response:\nWe thank the reviewer for their constructive comments during the first round and endorsement of the\nrevised manuscript.\n10"}, {"round": 3, "reviewer_comments": {"reviewer_2": "The authors answered the reviewers' questions."}, "author_response": ""}]

Decision letter