Volumetric compression regulates the phase separation of AXIN and acts as an operational amplifier to bidirectionally modulate Wnt signaling in organoids

Domain: biology
Published: 2026-01-08
Editorial outcome: major_revision

Abstract
Protein phase separation has emerged as a crucial mechanism for spatio-temporal regulation of intracellular processes, yet its potential to integrate and compute diverse extracellular signals is not fully understood. Here, we show a mechano-biochemical circuit that harnesses phase separation to process mechanical and biochemical inputs, modulating cell fate decisions. We demonstrate that volumetric compression bidirectionally regulates canonical Wnt/β-catenin signaling, where the presence of Wnt ligands determines the locations of AXIN phase separation to form either LRP6 signalosomes on the cell membrane or β-catenin destruction complexes in the cytosol, while the mechanical stimulus promotes degree of phase separation to amplify either the positive or negative signal. This circuit enhances healthy intestinal organoid proliferation while suppressing patient-derived colorectal cancer organoid growth, revealing its potential for precise mechanotherapy. Our findings establish phase separation as a critical component in mechanical signal transduction and provide a framework for integrating mechanical and biochemical cues in cellular decision-making. This approach opens avenues for targeted therapies and deepens our understanding of how cells process complex environmental information.

Introduction
In multicellular organisms, human cells are subjected to dynamic mechanical cues in both healthy and diseased tissues1–5. The incorporation of mechanical cues in biological processes is essential for maintaining homeostasis in healthy tissues, while their dysregulated introduction leads to diseases6. For instance, dermal progenitors aggregate through contractility-driven cellular pulling to trigger the mechanosensitive activation of β-catenin in adjacent epidermal cells until follicle pattern formation7; aging-induced niche stiffening hinders the function of oligodendrocyte progenitors (OPCs) by activating PIEZO1 signaling8; tumor-induced compressive stresses reprogram adjacent adipocytes via the activation of Wnt/β-catenin signaling9. Despite of the reported mechanisms in understanding mechanoregulation10, the interplay between mechanical perturbations and biochemical signaling is still complex and elusive, with both promotional and inhibitory effects reported across different biological systems11–13. For instance, pressure from tumor growth induces tumorigenic β-catenin to elevate the expression of Wnt target genes in the intestinal epithelium12, while stretching has been reported to inhibit Wnt/β-catenin signaling in mineralizing osteoblasts14. This may be attributed to different forms of mechanical loads and varying biological contexts, which urges a framework to understand the crosstalk between mechanoregulation and biochemical signaling pathways as an integrated system for understanding diverse biological outcomes.

The current paradigm for understanding mechanical signaling transduction involves exploring the impact of mechanical cues on classic biochemical signaling pathways, such as Wnt signaling, Hippo pathway, BMP signaling, and Notch signaling, via specific responsive proteins13,15–18. Various patterns or modules in mechanoregulation have been discovered, including cell surface mechanotransducers19, mechanoresponsive ion channels20, nuclear translocations of transcription factors21, nuclear deformation22, and changes of chromatin dynamics23. In addition to these findings, our previous research and a few other studies present a framework where biomolecular condensates via phase separation sense intracellular molecular crowding caused by water efflux under mechanical stress, altering their phase separation states to affect signaling transduction13,22. While protein phase separation has recently been highlighted as a critical player in cells to spatiotemporally govern intracellular processes, yet the understanding of its role has mostly been limited to process individual stimuli. Instead, we propose that a biomolecular circuit built upon phase separation mechanism is able to process a combinatory of hybrid stimuli from both biochemical and mechanical environments. Toward this end, we hypothesize that a framework circuit can integrate the bi-directional outcomes of a certain mechanical cue on cell fate decisions via regulating Wnt/β-catenin signaling, which is one of the essential pathways controlling cell fate in various biological systems, including embryonic stem cells, mesenchymal stem cells, intestinal stem cells, and neuron progenitors23. This is reminiscent of genetic circuit, which is an application of synthetic biology where biological parts inside a cell are designed to perform logical functions mimicking those observed in electronic circuits, which enables cells to respond and compute multiple informations for cellular decisions24–26. Examples of genetic circuits include genetic logic gates, cascades, bandpass filters, switches, and memory27 for regulating circadian clocks, cell divisions28, and cell fate decision26,29,30. Whether mechanotransduction and biochemical signaling work together in an architecture similar to circuits in synthetic biology remains elusive. If such a mechano-biochemical circuit exists, how it performs and its consequences for biological systems still need to be explored.

Here, we report the mechano-biochemical circuit that integrates mechanical and biochemical signals to modulate cell fate decisions. Specifically, we demonstrate that volumetric compression interacts with the Wnt ligand to create an operational amplifier (opamp)-like function on canonical Wnt/β-catenin signaling. This circuit leverages the phase separation of AXIN puncta to receive and process information from both mechanical cues and biomolecular ligands, leading to outputs of either promotion or inhibition. Our findings further reveal that this circuit can differentially regulate the growth of healthy intestinal organoids (promotion) and colorectal cancer (CRC) organoids (inhibition) with a single input of volumetric compression. This circuit provides a framework for understanding mechanoregulation and offers avenues for developing therapies that precisely target cell fate decisions. By integrating mechanical and biochemical cues, our study paves the way for potential applications in regenerative medicine and cancer therapy.

Results
Translocated phase separation of AXIN enables the mechano-biochemical circuit for formation of two distinct membraneless organelles

Our previous study revealed that volumetric compression, as one of the mechanical cues, can promote Wnt/β-catenin signaling by stabilizing the LRP6-AXIN signalosome13. The formation of the LRP6-AXIN complex requires AXIN’s ability to undergo phase separation or head-to-tail polymerization31. In the absence of the Wnt ligand, AXIN still undergoes phase separation and puncta formation in the cytoplasm32,33. In the cytoplasm, AXIN co-localizes with adenomatous polyposis coli (APC) to form the β-catenin destruction complex, which degrades cytosolic β-catenin to maintain a low basal level of Wnt/β-catenin signaling32,33. Given that the promoting effect of volumetric compression on Wnt/β-catenin signaling relies on the phase separation of AXIN with LRP6 at the cell membrane13, we speculate that volumetric compression can also negatively regulate Wnt/β-catenin signaling in the absence of the Wnt ligand. Therefore, we hypothesize that volumetric compression can bidirectionally regulate Wnt/β-catenin signaling with the assistance of AXIN phase separation (Fig. 1a). This regulation circuit can be viewed as an opamp, an analog circuit block that takes a differential voltage input and produces a single-ended voltage output. Basically, the opamp can amplify weak electric signals from two different inputs. The difference is that one input inverts the signal in the opposite direction (i.e.: the signal is out of phase by 180 degrees in output), while the other does not. The operational amplifier can switch to each of its inputs. In our model, whether the Wnt ligand is presented determines the switch between two inputs, while the volumetric compression amplifies the strength of the signal (Fig. 1a). Given the involvement of Wnt/β-catenin signaling in many biological processes across multiple scales, this opamp-like circuit can be incorporated into many biological regulations.

To test our hypothesis, we constructed both phase-separable WT AXIN-mCherry and AXINΔDAX-mCherry with compromised phase separation capability in mammalian AXIN1 knockout (KO) 293T cells and RKO cells (Supplementary Fig. 1a). RKO cells have no intrinsic β-catenin transcriptional activity, due to the lack of either endogenous Wnt ligands or membrane cadherin-catenin complex; meanwhile, despite the fact that HEK293T cells have membrane β-catenin, their autocrine WNT ligands are limited, which is confirmed by our ELISA assays (Supplementary Fig. 1b), making it hard to trigger downstream signalosome formation and β-catenin accumulation. Then, we tested the phase separation behavior of AXIN puncta in these cells. The FRAP assays (Fig. 1b), along with live imaging of AXIN puncta splitting (Fig. 1c) and fusion (Fig. 1d), confirmed the dynamic exchange of AXIN proteins within puncta structures and their liquid-like behavior in the cytoplasm. AXIN puncta were consistently observed in WT AXIN cells, while AXINΔDAX-mCherry compromised the formation of AXIN puncta31,34–36.

Next, we compared the effect of volumetric compression on the condensate formation of AXIN with or without the DAX domain (Fig. 1e). For WT AXIN-mCherry, volumetric compression enriched a larger portion of AXIN into condensates (Fig. 1f) and increased the number of condensates formed by WT AXIN (Fig. 1g). This effect was also confirmed with endogenous AXIN using immunostaining (Fig. 1h), showing a larger portion of AXIN in condensates (Fig. 1i). In contrast, the impact of volumetric compression on AXIN-ΔDAX-mCherry condensates was limited (Fig. 1e); no significant increase in the number of AXIN condensates was found (Supplementary Fig. 1c), nor was there a change in the proportion of AXIN in condensates relative to cytoplasmic AXIN (Supplementary Fig. 1d).

Next, we explored whether the effect of volumetric compression on AXIN condensates directed the formation of functional membraneless organelles regulating Wnt/β-catenin signaling. Without the Wnt ligand, AXIN mostly localized in the cytoplasm, where it merged with APC to form the β-catenin destruction complex37. This complex is a critical tumor-suppressing membraneless organelle that maintains a consistently low level of cytoplasmic β-catenin by triggering its ubiquitination. Mutations or deletion of essential components in the β-catenin destruction complex can initiate colorectal cancers (CRCs)37. Stabilizing the β-catenin destruction complex holds the potential for suppressing tumor growth33,37. Our results showed many β-catenin destruction complexes with co-localized AXIN and APC forming yellow dots in the images (Fig. 1j). Under volumetric compression, the number of β-catenin destruction complexes, indicated by yellow spots, increased further (Fig. 1j, k). Quantitative analysis showed a 40% increase in β-catenin destruction complexes under volumetric compression (Fig. 1k). Meanwhile, without Wnt ligands, AXIN does not translocate to the membrane, no obvious colocalization between AXIN and LRP6 can be observed (Supplementary Fig. 2a). We also verified that the DAX domain mediated the phase separation-like formation of β-catenin destruction complexes (Fig. 1l). Deletion of the DAX domain disrupted the colocalization of APC and AXIN proteins, and prevented the promotion effect of volumetric compression on assembly of β-catenin destruction complexes in response to volumetric compression (Fig. 1l and Supplementary Fig. 1e, f).

In the presence of Wnt, the Wnt ligand triggers the phosphorylation of LRP6, which recruits AXIN from the cytoplasm to the cell membrane to form the LRP6 signalosome and initiates Wnt signaling transduction from the cell membrane into the cell38,39. When Wnt3a ligands were introduced to cultured cells, we observed the formation of LRP6 signalosomes as yellow condensates beneath the cell membrane (Fig. 1m). With additional volumetric compression, the number of LRP6 signalosomes nearly doubled (Fig. 1n). Interestingly, the effect of volumetric compression on the LRP6 signalosome was also mediated by the phase separation-like behavior controlled by the DAX domain within AXIN molecules (Fig. 1o); with the DAX domain deleted, the co-localization between LRP6 and AXIN proteins was weakened and no promotional effect of volumetric compression on the LRP6 signalosome formation existed (Fig. 1o and Supplementary Fig. 1g, h). Meanwhile, in presence of WNT ligands, we observe minimal cytoplasmic condensates showing AXIN-APC colocalization (Supplementary Fig. 2b). Nevertheless, we found that some residual AXIN-APC interaction persist in the cytoplasm, consistent with other literatures40,41; this is because the Wnt activation will not recruit all the cytoplasmic AXIN, but instead to compromise the capability of the APC destruction complex to degrade β-catenin to accumulate cytoplasmic β-catenin.

Together, the results showed that the condensate formation capability of AXIN via its DAX domain enabled a mechano-biochemical circuit that bidirectionally controlled the formation of two distinct membraneless organelles within Wnt/β-catenin signaling. In the presence of Wnt ligands, volumetric compression promoted the formation of the LRP6 signalosome, while in their absence, volumetric compression promoted the formation of the β-catenin destruction complex instead.

The mechano-biochemical circuit regulates canonical Wnt/β-catenin signaling

Given the importance of two distinct membraneless organelles that regulate Wnt/β-catenin signaling, we speculated that the mechano-biochemical circuit also regulated canonical Wnt/β-catenin signaling.

To verify our hypothesis, we tested either the activation or inhibition of canonical Wnt/β-catenin signaling generated by volumetric compression under different conditions. AXIN can bind to either β-catenin or LRP6: when AXIN binds with β-catenin, β-catenin undergoes ubiquitination and degradation, decreasing Wnt/β-catenin signaling41; when AXIN binds to LRP6, the degradation of β-catenin mediated by the APC destruction complex is inhibited, leading to the accumulation of β-catenin and an increase in Wnt/β-catenin signaling40. Thus, the mechano-biochemical circuit switches to the inverting input to promote AXIN-β-catenin binding when the Wnt ligand is absent; while switching to the non-inverting input, when the Wnt ligand is present, to promote AXIN-LRP6 binding. To test this model, Co-immunoprecipitation (Co-IP) assays were performed. In the absence of Wnt ligands, IP assays showed that volumetric compression increased the amount of β-catenin bound to AXIN (Fig. 2a, b), suggesting more β-catenin might be degraded under volumetric compression. In the presence of Wnt ligands, IP assays showed that volumetric compression doubled the amount of LRP6 bound to AXIN (Fig. 2c, d), suggesting potential accumulation of β-catenin in the cytoplasm; accordingly, we also confirmed that the binding ratio between AXIN and APC decreased (Supplementary Fig. 2c, d). These two bidirectional effects were also dependent on the DAX domain. Deletion of the DAX domain in AXIN eliminated the observed bidirectional promotion effects on protein binding (Fig. 2a–d).

Next, we directly assessed the accumulation of β-catenin with different combinations of volumetric compression and Wnt3a ligand stimulation using immunostaining assays42. In most cases, the basal level of β-catenin is relatively low, and a further decrease might have a minor impact on cell functions and downstream gene expression. However, β-catenin can also be increased independently of Wnt ligands and phosphorylated LRP6, such as in pathological accumulations of β-catenin resulting from mutations in APC, glycogen synthase kinase-3 (GSK-3), and β-catenin itself43,44. Suppression of such pathological accumulations of β-catenin can be a therapeutic target for treating diseases like colorectal cancers (CRCs)45. We used CHIR to accumulate β-catenin independently of Wnt ligands and LRP6 by inhibiting GSK3, a kinase that leads to the degradation of β-catenin46. CHIR99021 is a highly specific GSK-3β inhibitor that prevents β-catenin phosphorylation and subsequent degradation, thereby stabilizing cytoplasmic β-catenin through a mechanism that completely bypasses the need for Wnt ligand-LRP5/6 receptor engagement46,47. In this case, even though cytosolic β-catenin increased, volumetric compression still decreased the amount of cytosolic β-catenin in the absence of Wnt ligands (Fig. 2e, f). This suggests potential applications of volumetric compression to inhibit the pathological accumulation of β-catenin in diseases.

Additionally, we also tested the impact of volumetric compression on β-catenin in the presence of Wnt ligands. Indeed, the results showed that Wnt3A induced the accumulation of cytosolic β-catenin, which was further augmented by volumetric compression (Fig. 2h, i). Thus, the mechano-biochemical circuit can augment β-catenin in the canonical pathway and suppress pathological accumulation of β-catenin with designed combinations of Wnt ligands and volumetric compression. Again, this mechano-biochemical circuit’s effect on both canonical and pathological accumulations of β-catenin could be eliminated by removing the DAX-driven phase separation of AXIN condensates (Fig. 2e, g, h, j). Western blot assays also supported the DAX domain as the hub for constructing this mechano-biochemical circuit and produced consistent results that various combinations of Wnt ligands and volumetric compression diverted the accumulation or degradation of β-catenin (Fig. 2k, l).

Since the accumulation of β-catenin leads to the gene expression of Wnt target genes, which is key to drive long-term cell fate decisions, we further used RT-qPCR assays to verify the regulation of the mechano-biochemical circuit at the gene expression level. In the absence of Wnt ligands, volumetric compression suppressed the basal expression of key Wnt target genes, including AXIN2, LEF1, and SP5 (Fig. 2m). Conversely, in the presence of Wnt ligands, compression further enhanced the expression levels of all three genes (Fig. 2n). Moreover, the effect of volumetric compression in both conditions (with or without Wnt ligands) was eliminated by the deletion of the DAX domain in AXIN (Fig. 2o, p).

Overall, given its capability for regulation of canonical Wnt/β-catenin signaling at both the protein and gene expression levels, the mechano-biochemical circuit functions as an opamp to either inhibit or elevate Wnt/β-catenin signaling, holding potential for engineering and diverting cell fate in distinct biological systems.

The mechano-biochemical circuit diverts cell fate of organoids from intestinal epithelium

Here, we further explored the incorporation of the mechano-biochemical circuit in engineering multicellular living systems, including healthy mouse intestinal organoids and human patient-derived CRC organoids. In intestinal organoids, Lgr5+ intestinal stem cells (ISCs) self-renew when maintaining high-level Wnt/β-catenin signaling and further organize cells into crypts and villi in vivo and into intestinal organoids in vitro48. The activation of Wnt/β-catenin signaling is maintained by Wnt ligands from either mesenchyme or Paneth cells in the intestinal epithelium in vivo and by extraneous Wnt ligands or R-spondin (a Wnt signaling amplifier) in the medium for organoids in vitro49–51. When canonical Wnt/β-catenin signaling is suppressed, the intestinal epithelium/organoids undergo differentiation, eventually leading to apoptosis52. Given the bidirectional effect of the mechano-biochemical circuit, we anticipated a potential impact of volumetric compression on the growth and fate decision of intestinal organoids.

Since the presence of Wnt ligands is essential for the growth of intestinal organoids, we suggested that the mechano-biochemical circuit worked with a non-inverting input switch-on to promote the growth of organoids (Fig. 3a). We hypothesized that volumetric compression would augment canonical Wnt/β-catenin signaling and eventually affected the growth of intestinal organoids. Thus, we respectively cultured murine ISC organoids and crypt intestinal organoids with or without volumetric compression (supplemented with 1% PEG 300). Indeed, we observed a promotive effect of volumetric compression on the growth of ISC organoids (Fig. 3b), as shown by both their areas and diameters (Fig. 3c, d). Additionally, this promotion effect was more obvious on crypt intestinal organoids (Fig. 3e) with Organoid (Og) medium. The reason could be that the Wnt/β-catenin signaling in ISC organoids is already near saturation due to the over-supplied Wnt ligands, but the Wnt/β-catenin signaling in intestinal organoids is largely dependent on the endogenous Wnt ligand, leaving space for further augmenting. A result was that the volumetric compression resulted in a large portion of crypt intestinal organoids transiting into spherical organoids (Fig. 3f), which is believed to be more naïve with more ISCs presented in ISC organoids. To confirm this observation, we have therefore performed single-cell RNA sequencing (scRNA-seq) on both control and compressed organoids to provide a precise assessment at three levels: cell composition, gene expression, and signaling pathway activity. Compressed organoids showed increased proportions of stem cells and transit-amplifying (TA) cells (cells with the capability to differentiate into different types of intestinal epithelial cells), while the proportions of terminally differentiated secretory and absorptive cells were decreased compared to controls (Supplementary Fig. 3a). This demonstrates a clear shift toward a less differentiated cellular state. In compressed organoids, stemness-related genes such as Lgr5 and Smoc2, as well as proliferation markers like Mki67, showed upregulated expression. Conversely, differentiation-associated genes were downregulated (Supplementary Fig. 3b, c). This gene expression profile is characteristic of a more primitive, stem-like state. Additionally, signaling pathways associated with cell proliferation were activated in compressed organoids, while pathways driving cell differentiation were inhibited (Supplementary Fig. 3d). This further confirms that volumetric compression maintains organoids in a more proliferative, less differentiated state.

Moreover, with additional CHIR in Og medium, the promotion effect of volumetric compression on the growth of intestinal organoids was consistently observed (Fig. 3g), due to the presence of endogenous Wnt ligands from Paneth cells in organoids. Practically, volumetric compression also enlarged both the area (Fig. 3h) and the diameter (Fig. 3i) of the intestinal organoid, as well as led rounder morphology (Fig. 3j). These results suggested that the volumetric compression could synergize with other promotive small molecules such as CHIR to further augment the growth of intestinal organoids. Lgr5+ intestinal stem cells (ISCs) in organoids depend on active Wnt/β-catenin signaling for self-renewal and proliferation. Without exogenous Wnt3a (ISC medium) or the synergy between R-spondin supplementation (Og medium) and endogenous Wnt ligands from Paneth cells, healthy intestinal organoids undergo differentiation and apoptosis within days. This Wnt dependency is a fundamental characteristic of normal intestinal epithelium. Thus, for healthy intestinal organoids, only the ON state of Wnt signaling can guarantee the growth of healthy intestinal organoids.

As compared to intestinal organoids/epithelium, 70% of CRC patients display APC mutations within the Wnt/β-catenin pathway, resulting in constitutive β-catenin accumulation and pathway activation independent of upstream Wnt ligands and LRP6 receptors53. These CRC organoids can survive and proliferate without any exogenous Wnt supplementation—a hallmark of their transformed state. Moreover, there are no Paneth cells in CRC organoids, which means that there is no endogenous production of Wnt ligands. Thus, the CRC organoids naturally exist with an OFF state of Wnt signaling upstream activation. To absolutely confirm our CRC organoids were functioning independently of Wnt ligands, we have treated CRC organoids with IWP2 (Porcupine inhibitor that blocks all Wnt ligand secretion). We also conducted human WNT3A ELISA experiments to quantify endogenous Wnt3a in CRC organoid culture supernatant. Results showed Wnt3a protein concentration was near zero both with and without IWP2 treatment (Supplementary Fig. 4a). Targeting Wnt signaling and suppressing pathological β-catenin has long been viewed as a potential therapeutic approach for many related diseases, including CRC45. However, due to the widespread effect and essential role of canonical Wnt/β-catenin signaling in the development and homeostasis of many cell lineages and tissues, safely targeting Wnt signaling has rarely been achieved through biochemical or genetic means. Given the precise and multifaceted effect of volumetric compression on Wnt/β-catenin signaling via mechano-biochemical circuits, we hypothesized that this mechanical approach could suppress CRC growth without perturbing or even promoting other healthy tissues. Given the loss of function of Wnt ligands in CRC organoids due to mutated Wnt pathway, we suggested that the mechano-biochemical circuit switched to inverting input for inhibiting growth of CRC organoids (Fig. 3k). To test this hypothesis, we obtained patient-derived CRC organoids with APC mutations and subjected these organoids to volumetric compression. To confirm that the growth of patient-derived CRC organoids was independent of Wnt ligands, we also cultured CRC organoids with IWP2 treatment, which blocks endogenous Wnt ligand secretion and therefore prevents signaling upstream of complex formation54. The IWP2 treatment had no effect on CRC organoids (Fig. 3l–p). To ensure no Wnt ligands were present in the culturing condition, IWP2 was added when we applied volumetric compression. Indeed, volumetric compression inhibited the growth of CRC organoids (Fig. 3l), as indicated by both the areas (Fig. 3m) and diameters of the organoids (Fig. 3n), and affected their morphology by roundness (Fig. 3o). Notably, volumetric compression with 3% PEG 300 solely inhibited the growth of CRC organoids without affecting the viability of cells in the organoids (Fig. 3p); a larger volumetric compression with 4% PEG 300 further inhibited the growth of CRC organoids but slightly reduced viability of cells (Fig. 3p).

Together, under the framework of mechano-biochemical circuit, volumetric compression promoted the growth of healthy intestinal organoids while suppressing the growth of patient-derived CRC organoids, thereby enabling the safe and precise targeting of Wnt signaling for cancer inhibition and the potential regeneration of healthy intestinal cells.

Volumetric compression interplays with Wnt/β-catenin signaling for regulation of intestinal epithelium

To further confirm that this regulation induced by volumetric compression is enabled by a phase-separation-driven mechano-biochemical circuit, we explored the activation of Wnt/β-catenin signaling and the importance of AXIN phase separation in the regulation of intestinal systems. First of all, WT AXIN-mCherry was delivered into CRC organoids via lentivirus to image the phase separation and condensate formation of AXIN under volumetric compression. In patient-derived CRC organoids, the FRAP assay had been conducted to confirm the dynamic feature of AXIN condensates (Fig. 4a). Additionally, we showed that volumetric compression promoted the formation of AXIN condensates in CRC organoids, with a larger fraction of AXIN observed in condensates under volumetric compression (Fig. 4b, c). In the next step, we further evaluated whether β-catenin was differentially regulated under volumetric compression between CRC organoids and healthy intestinal organoids. Within the context of CRC, where volumetric compression inhibited the growth of CRC organoids (Fig. 3k), our experiments showed that volumetric compression decreased the accumulated β-catenin in CRC organoids (Fig. 4d, e). By quantifying the intensity of total β-catenin per organoid, we found that volumetric compression from an additional 3% PEG 300 decreased total β-catenin by 5-fold, demonstrating its capability to efficiently inhibit the pathological accumulation of β-catenin in CRC. We also conducted both bulk and single-cell (sc) transcriptome profiling on CRC organoids with and without volumetric compression. Our results clearly showed that Wnt/β-catenin signaling was regulated under volumetric compression, as indicated by both the signature genes (Fig. 4f) and enriched GO/KEGG terms (Supplementary Fig. 4b). Additionally, the sc-seq assays also revealed a decrease in Wnt signaling-associated or target genes such as AXIN2, MYC, CCND1, JUN, LGR5, PPARD, CTNNB1, SOX9, and WNT2B in individual cells within the population (Fig. 4k, l). A Gene Set Enrichment Analysis (GSEA) also confirmed the downregulated canonical WNT pathway (Supplementary Fig. 4c).

In healthy intestinal epithelium, where volumetric compression promoted the growth of healthy intestinal organoids (Fig. 3a), our experiments showed that volumetric compression increased the accumulated β-catenin in both mouse healthy ISC spheroids (with ISC medium) (Fig. 4g, h) and intestinal organoids (with Og medium) (Fig. 4i, j). Given these evidences, we confirmed that the mechano-biochemical circuits regulated cell fate in healthy intestinal organoids and CRC organoid via differentially interfering with activation of Wnt/β-catenin signaling.

To further confirm that the phase separation based mechano-biochemical circuit happens in organoids under the operation of volumetric compression, we performed immunofluorescence imaging in two organoid systems representing distinct Wnt states. For the Wnt-ON model, the ISC organoids require active Wnt signaling for survival and represent a canonical Wnt-ON state. Under basal conditions, we observed AXIN condensates with some localization to the cell membrane. Following PEG compression, AXIN condensates showed enhanced enrichment at the plasma membrane (Supplementary Fig. 5a, b), consistent with increased LRP6 signalosome formation as observed in our HEK293T experiments. For the Wnt-OFF model, the CRC organoids harbor APC mutations that disrupt the destruction complex, representing a state where β-catenin is constitutively accumulated downstream, but the upstream ligand-dependent machinery is non-functional. We observed AXIN condensates co-localizing with APC in the cytoplasm. Following PEG compression, the degree of AXIN-APC colocalization was further enhanced (Supplementary Fig. 5c, d), indicating increased destruction complex assembly, which is consistent with our observation that compression decreases β-catenin levels in CRC organoids (Fig. 4d, e).

Methods
Cell culture
HEK293T cells (GNHu17) and RKO cells (TCHu116) were purchased from National Collection of Authenticated Cell Cultures (NCACC). Mouse L cells (CRL-2648), L Wnt-3A cells (CRL-2647) and L-WRN cells (CRL-3276) were obtained from American Type Culture Collection (ATCC). All cell lines were authenticated by the suppliers using STR profiling and tested negative for mycoplasma contamination.
HEK293T cells and RKO cells were maintained in DMEM (Gibco) supplemented with 10% FBS (Gibco) at 37°C in a humidified, 5% CO2 incubator. Mouse L cells and LWnt3A cells were used for preparation of control and Wnt3A conditioned medium according to ATCC protocol. L-WRN cells were used to collect WRN conditioned medium for murine organoid culture.

CRISPR/Cas9 genome editing and plasmid construction
HEK293T and RKO cells were transfected with plasmids encoding Cas9 and a single-guide RNA (sgRNA: 5’-TTCGCTGTACCGTCTACTGG-3’; targeting exon 1 of the AXIN1 gene) using Lipo8000 (Beyotime C0533). Following transfection, cells expressing Cas9 and sgRNA were selected using puromycin. Western blot analysis was performed to assess AXIN1 protein expression levels, and genomic PCR followed by Sanger sequencing was conducted to verify mutations at the target site. Two AXIN1 knockout clones (KO1 and KO2) with high knockout efficiency were obtained and used in this study. The mCherry-AXIN1ΔDAX mutant plasmid was generated by deleting the DAX domain (amino acids 746-862) from the full-length AXIN1 plasmid using standard cloning techniques. All unique plasmids and stable cell lines generated in this study are available from the corresponding author upon reasonable request.

Lentivirus production and transduction
Lentiviral particles expressing mCherry-AXIN1 or mCherry-AXIN1ΔDAX were generated in HEK293T cells by co-transfection of the plasmids with the third-generation lentivirus packaging vectors (psPAX2 and pMD2.G). Forty-eight hours after transfection, the supernatant was collected and filtered. When AXIN1-KO RKO cells were approximately 70% confluence, the supernatant was added to the medium for 24h of infection. Stably transduced cell lines were obtained by 2–3 rounds of puromycin selection. For CRC organoids stably expressing mCherry-AXIN1, the filtered supernatant was ultracentrifuged at 80,000×g for 2h at 4°C, and the pellet was resuspended in CRC medium. CRC organoids were cultured as two-dimensional monolayers on Matrigel and incubated with the viral medium for 24h. Stably transduced CRC organoids were achieved through 2–3 rounds of puromycin selection.

Fluorescence recovery after photo-bleaching (FRAP)
To investigate the diffusion dynamics of mCherry-AXIN1, FRAP experiments were performed on a Fluoview FV3000 confocal laser scanning microscope equipped with a 100× UPLSAPO oil immersion objective (NA 1.4; Olympus). A region of interest (ROI) within an mCherry-AXIN1 condensate in HEK293T cells was selected and bleached using a 594nm laser at 100% intensity. Time-lapse images were acquired at an interval of 10.8ms between frames. In CRC organoids, images were captured every 16.1ms. To analyze fluorescence recovery kinetics, FRAP analysis was completed using the ImageJ FRAP Profiler plugin (Hardin lab: https://worms.zoology.wisc.edu/research/4d/4d.html#frap). The FRAP curves were generated using GraphPad Prism (v9.0), and the half-time of recovery (t₁/₂) was calculated by fitting the curve with a one-phase association function.

Osmotic stress
To induce cellular volume compression, PEG300 was added to the isotonic culture medium. Generally, we typically used a 2% PEG300 (v/v) concentration and stimulated cells for short periods (1–2min) or prolonged periods (e.g., 12h for gene expression assays, or up to several days for growth assays). To minimize potential osmotic shock and cellular damage, the PEG300-containing hypertonic medium was added gently and gradually to the culture vessel. For organoid experiments, human CRC organoids were treated with 3% (v/v) PEG300, while murine ISC organoid were treated with 1% (v/v) PEG300. To investigate the dynamic response of AXIN1 condensates to osmotic stress, a 2D organoid monolayer culture system was established. Briefly, confocal dishes were pre-coated with 25μL of Matrigel and incubated at 37°C for 30min for polymerization. CRC organoids were dissociated and seeded onto the Matrigel to form a confluent monolayer. Osmotic stress was induced by adding 3% (v/v) PEG300 to the culture medium, followed immediately by time-lapse imaging.

Immunoblotting and co-immunoprecipitation (Co-IP)
For immunoblotting, cell lysates were prepared on ice with the RIPA lysis buffer. For the preparation of cytosolic proteins, cells were lysed with 0.015% digitonin in PBS containing a cocktail of protease inhibitors. Lysates were centrifuged at 12,000×g for 10min, and the supernatants were collected, separated by 10% SDS-PAGE, and transferred to polyvinylidene fluoride (PVDF) membranes. After blocking with QuickBlock buffer for 15min at room temperature, the membranes were incubated with primary antibodies overnight at 4°C and followed by secondary antibodies IRDye 800CW goat anti-mouse IgG and/or IRDye 680LT goat anti-rabbit IgG (LI-COR Biosciences; 1:10,000 dilution) for 1h at room temperature. Signals were detected using the Odyssey CLx Imaging System (LI-COR Biosciences) and analyzed with Fiji (ImageJ v1.54f). For Co-IP, HEK293T cells were lysed on ice with NP40 lysis buffer (50mM Tris-HCl, pH 7.4, 150mM NaCl, 0.5% NP-40, 1.5mM MgCl2, 10% glycerol and protease inhibitors). Lysates were centrifuged at 12,000×g, and after taking an aliquot for total protein expression analysis, immunoprecipitation was performed by adding BeyoMag™ Anti-Flag Magnetic Beads to the remaining cell lysate followed by incubation at 4°C overnight with gentle rotation. The immune complex was isolated by 16-Tube SureBeads™ Magnetic Rack (Bio-Rad), washed three times with lysis solution, eluted by boiling in SDS sample buffer, and analyzed by SDS-PAGE and immunoblotting. Uncropped scans of blots are provided in the Source Data file. Detailed information regarding antibody sources, catalog numbers, and dilutions is provided in Supplementary Table 1, while commercial reagents and their corresponding supplier details are listed in Supplementary Table 2.

Immunofluorescence (IF)
For cell immunofluorescence, cells were fixed in 4% paraformaldehyde (PFA) for 15min at room temperature, washed three times with cold PBS (5min each time), blocked in 5% BSA in PBS containing 0.3% Triton X-100 at room temperature for 1h, and incubated with primary antibodies at 4°C overnight. After removing primary antibodies and washing with PBS, cells were treated with secondary antibodies for 1h at room temperature. After thorough washing, the stained cells were visualized using a spinning disk confocal microscope. For organoid immunofluorescence, murine ISC colonies or human CRC organoids embedded in Matrigel were fixed in 4% PFA for 30min at room temperature. Suspended tissues were collected and centrifuged 500×g for 5min to remove the PFA, washed with ultra-pure water and pelleted. Following resuspension in water, the organoids were spread on 20-mm glass-bottom culture dishes and allowed to attach by air-drying. Attached organoids were rehydrated and blocked in 5% BSA in PBS containing 0.3% Triton X-100 at 4°C for 48h, and incubated with primary antibodies at 4°C for 48h. After removal of primary antibodies and washing with PBS, samples were incubated with secondary antibody at 4°C for 24h. Following extensive washing, the samples were imaged with confocal microscopy. Detailed information regarding antibody sources, catalog numbers, and dilutions is provided in Supplementary Table 1.

Reverse transcription quantitative PCR (RT-qPCR)
Total RNA was extracted from RKO cells using Qiagen RNeasy mini kit and converted to cDNA with HiScript III All-in-one RT SuperMix Perfect for qPCR. RT-qPCR was performed on an Agilent AriaMx 96 Real-Time PCR System using Taq Pro Universal SYBR qPCR Master Mix. The relative expression levels of target genes (AXIN2, LEF1, and SP5) were normalized to that of the housekeeping gene GAPDH using the 2−ΔΔCt method. The sequences of all primers used in this study are listed in Supplementary Table 3.

Intestinal crypt isolation
Murine intestinal crypts were isolated from 6-week-old male C57BL/6J mice obtained from Shulaibao (Wuhan) Biotechnology Company. Mice were housed in a specific pathogen-free (SPF) facility under a standard 12-h light/12-h dark cycle, with a controlled ambient temperature of 22±2°C and relative humidity of 40–60%. Male mice were selected to minimize potential experimental variability, although the isolation protocol is applicable to both sexes. Briefly, the proximal part of the intestines was isolated, opened longitudinally, and gently scraped to remove luminal contents and villi using a glass slide. The intestinal tissue was chopped into 1 to 2 mm pieces and washed 12–15 times with ice-cold PBS until the supernatant was clear. Crypts were released by incubating intestinal pieces in ice-cold 2 mM EDTA in PBS for 30min at room temperature. The digested tissue was then resuspended and shaken vigorously to liberate the crypts. The supernatant was collected and passed through a 70-μm strainer for enrichment. The crypt fraction was centrifuged at 290×g for 5min at 4°C to remove single cells and debris. The enriched crypts were embedded in Matrigel.

Organoid culture
Murine intestinal crypts and human CRC organoids were embedded in Matrigel and dispensed as 50μL droplets in 24-well plates. After polymerization for 30min at 37°C, the gels were overlaid with 500μL of culture medium. For murine organoids, the culture medium consisted of Advanced DMEM/F12 supplemented with Glutamax, HEPES, penicillin-streptomycin, B27, N2, and N-acetylcysteine, as well as growth factors including EGF, Noggin, Wnt3a, and R-spondin (conditioned medium from mouse L-WRN cells). To generate differentiated intestinal organoids, Wnt3a was omitted from the culture medium to induce maturation. For human CRC organoid culture, the complete medium consisted of Advanced DMEM/F12 supplemented with Glutamax, HEPES, penicillin-streptomycin, B27, N2, N-acetylcysteine, EGF, A83-01, SB202190, and [Leu15]-Gastrin I. Detailed information including supplements and inhibitors are listed in Supplementary Table 2.

Transcriptome and single-cell sequencing
Bulk RNA-seq was performed on human CRC organoids, and scRNA-seq was performed on both human CRC organoids and murine small intestinal organoids. In all experiments, organoids were treated with or without PEG 300. Sequencing services were provided by Tsingke Biotechnology for bulk RNA-seq, Mozhuo Biotech for human scRNA-seq, and Seek Gene for murine scRNA-seq. Differential expression analysis for bulk RNA-seq was performed using DESeq2 in R. Single-cell data matrices were processed and analyzed using Scanpy in Python, including quality control, dimensionality reduction, and clustering.

Statistics and reproducibility
Statistical analyses were performed using GraphPad Prism (v9.0). Data are presented as mean ± standard deviation (s.d.) with individual data points shown where applicable. Comparisons between two groups were performed using unpaired or paired two-tailed Student’s t test, ratio paired t-test, or one-sample t-test for normalized data, as indicated in the figure legends. For comparisons among more than two groups, one-way analysis of variance (ANOVA) or the Kruskal–Wallis test (for non-normally distributed data) was employed, followed by Tukey’s or Dunn’s multiple comparisons test, respectively. Exact p values are indicated on the figures, and values less than 0.05 were considered statistically significant. For Western blot analysis, band intensities were quantified using Fiji (ImageJ v1.54f). For Co-IP experiments, densitometry data were analyzed using raw ratios or normalized values as specified. Source data are provided as a Source Data file. No statistical method was used to predetermine sample size. No data were excluded from the analyses. The experiments were not randomized. The Investigators were not blinded to allocation during experiments and outcome assessment. All experiments were repeated at least three times independently with similar results, unless otherwise stated.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this article by Shi et al, the authors tried to understand how volumetric compression differentially regulated Wnt signaling output under different conditions. They found that AXIN, a central regulator of the Wnt pathway forms condensates at different locations of the cell: it colocalizes with APC in the cytoplasm as part of the destruction complex when Wnt ligand is absent, and with LRP6 on the membrane when Wnt ligand is present. Phase separation induced by volumetric compression seems to amplify the responses in both ways. The authors further tested their theories in different organoid systems. I find the article interesting. However, there are a number of places where the conclusions are not supported by the experimental evidence which undermines the overall rigor of the study.\nMajor concerns:\n1. The authors showed the colocalization of AXIN with APC (Fig. 1l) without showing the absence of colocalization with LRP6, and the colocalization of AXIN with LRP6 (Fig.1p) without showing the absence of colocalization with APC. To show that there is indeed difference in colocalization in Wnt-free and -present conditions, the authors need to not only show the colocalizations but also absence of colocalization with the other protein.\n2. Similar to concern #1, in the IP experiments (Fig.2e,f), the authors also need to show that when AXIN is interacting more with LRP6 under compression, it is interacting less with APC.\n3. In Fig.1h and 1l, the AXIN condensates are in the nucleus, not the cytoplasm (where the destruction complex is supposed to be), raising the concern that these condensates are not biological. The authors need to explain why the AXIN condensates are in the nucleus.\n4. Can the system they use (HEK cells) already have active Wnt signaling without adding Wnt3A? The authors either need to explain better (citing previous literature) or show the experimental evidence that the Wnt signaling is not active before adding Wnt3A (like lack of downstream genes activation using qPCR).\n5. I find the CHIR data puzzling. The authors show that when treated with CHIR, in Fig.2h-i PEG decreases beta-actin intensity, but in Fig.3g, PEG increases Wnt signaling. How would the authors explain the discrepancy?\n6. The authors claimed to use CHIR to accumulate beta-catenin independently of Wnt ligands and LRP6 by inhibiting GSK3 (lines 218-219) without showing any data. They need to really show the data to back up their claims.\n7. When showing the activity of Wnt signaling, the authors only used one target gene AXIN2 (Fig.2q). They need to use more than one target genes to be convincing.\n8. Again, the authors lack data to show that in the specific cases they are testing, the Wnt signaling is on or off (like concern #4) in the organoid system. They speculated the ON/OFF states based on their experimental results (lines 272-274), which is not scientific at all. They need to show the data of the ON/OFF states in the organoid system to be convincing.\n9. The authors need to show that IWP2 addition really depletes all Wnt ligands. (line 302)\n10. The authors need to show the spherical organoids are more naïve (Fig. 3f) using markers of naiveness (instead of saying they are “believed to be more naïve”). Otherwise the data in this entire figure is uninterpretable.\n11. In figures 3 and 4, the authors merely used volumetric compression without showing AXIN condensate formation on different locations of the cell (membrane vs. cytoplasm) is involved in differential regulations of Wnt signaling outputs. Even though they showed some FRAP data at Fig 4a, the images are too small to be interpretable. For example, does the volumetric compression at different Wnt ON/OFF states also regulate the differential locations of AXIN condensates in organoid models? Does the colocalization of AXIN with LRP6 and APC change? Without these data the Fig 3 and 4 seem to be unrelated to the central arguments of the paper.\n12. In many places of the paper the authors write a hypothesis like an experimental result making it confusing for the readers. Examples are sentences in lines 210-212, 224-226, 237-238, 294-296. I also find the biological operational amplifer images throughout the figures excessive. The readers will be more convinced by the real experimental data than the drawings showing what the authors think is happening.", "reviewer_2": "The manuscript entitled “A mechano-biochemical operational amplifier via phase separation for orthogonally diverting cell fate in organoid”, authored by Jinyun Shi et al., explores how mechanical and biochemical cues collectively influence cell fate decisions in intestinal epithelia. The authors hypothesize that mechanical compression from surrounding cells reduces cell volume and increases macromolecular crowding in the cytoplasm, thereby promoting liquid–liquid phase separation (LLPS). A novel concept presented is that two distinct AXIN-dependent LLPS events occur at separate intracellular locations depending on the presence or absence of Wnt/β-catenin signaling. This mechanism is proposed to resemble the function of an operational amplifier, with AXIN-APC complexes in the cytoplasm promoting β-catenin degradation, and AXIN-LRP6 complexes at the plasma membrane enhancing Wnt/β-catenin signaling.\nThe biological question addressed in this study is of broad relevance, intersecting fields such as cell biology, developmental biology, mechanobiology, and cancer biology. The conceptual framework is original and could provide insights into how mechanical stimuli are converted into biochemical signals. However, aspects of the experimental design and interpretation warrant further scrutiny. Below, I outline several major concerns regarding the conceptual design and interpretation of the experimental results.\n1. Concerns Regarding Conceptual Design of the Experiments\nThe authors describe the Wnt/β-catenin pathway as a “mechano-biochemical” operational amplifier. In most experiments, volumetric compression is used as the mechanical input, and AXIN-mediated LLPS serves as the readout. They propose that compression increases macromolecular crowding, thereby facilitating LLPS. However, it is unclear whether volumetric compression qualifies as a mechanical stimulus per se. Mechanical stimuli are typically sensed by known mechanosensors, including mechanosensitive ion channels, the cytoskeleton, and cell adhesion molecules. In contrast, the increase in crowding observed here appears to be a consequence of cytoplasmic volume reduction, not mechanotransduction.\nThis raises the question: is the input truly mechanical, or merely a change in chemical concentration? The phenomenon that higher polymer concentrations promote phase separation is well-established in physical chemistry. Therefore, I suggest the authors more carefully reconsider whether the input stimulus in their system should be categorized as mechanical. While mechanical compression from neighboring cells in the intestinal crypt is indeed physiological, the PEG-induced volumetric compression of HEK293T cells used here may not faithfully recapitulate the native mechanical environment.\n2. Interpretation of the \"Operational Amplifier\" Analogy\nThe authors compare Wnt/β-catenin signaling to an operational amplifier, illustrated in multiple figures (e.g., Fig. 1a, k, o), suggesting that the system amplifies input signals. However, it is unclear how signal amplitudes before and after amplification were quantitatively compared. In this case, the input (volumetric compression) and output (Wnt/β-catenin signaling activity) are fundamentally different in nature—physical vs. biochemical—which makes direct comparison of signal “amplitude” difficult.\nIn conventional operational amplifiers, both input and output are in the same medium (e.g., electrical signals), allowing for direct amplitude comparison. Here, the authors must clarify the basis on which they conclude that the output signal is amplified relative to the input. This is a crucial point that requires further experimental justification.\n3. Physiological relevance of Organoid Experiments\nIn Figures 3 and 4, the authors use intestinal organoids and show that volumetric compression induces LLPS in stem cells. However, the physiological relevance of globally compressing the entire organoid is unclear. The study aims to understand how mechanical forces in the intestinal crypt influence cell fate. Organoids are indeed a powerful system for this investigation. However, compressing the entire organoid via PEG treatment affects all cells non-specifically and may not mimic localized mechanical cues, such as compression from neighboring cells at the crypt base.\nA more physiologically relevant approach might involve applying localized pressure to specific cell populations (e.g., stem cells). The current method—immersing organoids in PEG—induces uniform volumetric compression, which may not accurately reflect the in vivo mechanical microenvironment.\n4. Additional Concerns Regarding Experimental Results\n4-1.Localization of AXIN LLPS in Organoids (Fig. 4):\nWhile the authors show that volumetric compression induces LLPS of AXIN in organoids, they do not identify the subcellular localization of these condensates. Based on HEK293T experiments, LLPS occurs in the cytoplasm when Wnt signaling is off, and at the plasma membrane when Wnt signaling is on (Figs. 1 and 2). The authors should investigate and report whether similar compartmentalization occurs in different organoid cell types (e.g., stem cells vs. Paneth cells).\n4-2. Physiological Relevance of Volume Reduction (Figs. 1 and 2):\nThe authors apply volumetric compression to HEK293T cells using PEG. However, the extent of volume reduction used to mimic physiological pressure in the intestinal crypt is not justified. If the reduction is outside physiological range, the results may not be biologically meaningful, as elevated macromolecular concentration alone can drive LLPS. The authors should estimate the physiological volume reduction experienced in vivo and relate it to their experimental setup, ideally referencing phase diagrams for AXIN condensates."}, "author_response": "The authors tried to understand how volumetric compression differentially\nregulated Wnt signaling output under different conditions. They found that AXIN, a\ncentral regulator of the Wnt pathway forms condensates at different locations of\nthe cell: it colocalizes with APC in the cytoplasm as part of the destruction complex\nwhen Wnt ligand is absent, and with LRP6 on the membrane when Wnt ligand is\npresent. Phase separation induced by volumetric compression seems to amplify\nthe responses in both ways. The authors further tested their theories in different\norganoid systems. I find the article interesting. However, there are a number of\nplaces where the conclusions are not supported by the experimental evidence\nwhich undermines the overall rigor of the study.\nReply: We sincerely thank you for your thorough evaluation of our manuscript and\nfor recognizing the interesting aspects of our work. We greatly appreciate your\ncareful assessment that our study demonstrates how volumetric compression\ndifferentially regulates Wnt signaling through AXIN condensate formation at\ndistinct subcellular locations - with APC in the cytoplasm (Wnt-OFF) and with LRP6\nat the membrane (Wnt-ON) - and that phase separation amplifies responses in\nboth directions.\nWe acknowledge your concerns regarding experimental rigor and the need for\nstronger evidence to support our conclusions. We have taken these critiques very\nseriously and have conducted substantial additional experiments to address each\nconcern comprehensively.\nMajor concerns:\n1. The authors showed the colocalization of AXIN with APC (Fig. 1l) without\nshowing the absence of colocalization with LRP6, and the colocalization of AXIN\nwith LRP6 (Fig.1p) without showing the absence of colocalization with APC. To\nshow that there is indeed difference in colocalization in Wnt-free and -present\nconditions, the authors need to not only show the colocalizations but also absence\nof colocalization with the other protein.\nReply: We sincerely appreciate your insightful comment regarding the need for\ncomplete colocalization analysis. You are absolutely correct that a comprehensive\n1\ncolocalization study must demonstrate not only the presence of specific protein\ninteractions but also the absence of alternative interactions under different\nconditions. Following your suggestion, we have performed the missing control\nexperiments to provide a complete picture of AXIN's differential binding partners.\nAs shown by our new experiments, with Wnt-free conditions, APC recruits\ncytoplasmic AXIN into condensates to form the β-catenin destruction complex.\nImportantly, under these conditions, AXIN does not translocate to the membrane,\nand we observe no obvious colocalization between AXIN and LRP6 (Fig. S2a).\nThis confirms that in the absence of Wnt ligands, AXIN specifically assembles with\nAPC in the cytoplasm rather than forming membrane-associated signalosomes.\nUnder Wnt-present conditions, AXIN dissociates from the APC destruction\ncomplex and translocates to the plasma membrane to form LRP6 signalosomes.\nUnder these conditions, we observe minimal cytoplasmic condensates showing\nAXIN-APC colocalization (Fig. S2b). Nevertheless, we believed that some residual\nAXIN-APC interaction may persist in the cytoplasm, which is also supported by our\nCo-IP experiments (also discussed in reply to comment #2) as well as other\nliteratures (Vivian S W Li, et al., Cell, 2012, 149(6): 1245-1256; Sung-Eun Kim,et\nal., Science, 2013, 340(6134):867-870); this is because the Wnt activation will not\nrecruit all the cytoplasmic AXIN, but instead to compromise the capability of APC\ndestruction complex to degrade beta-catenin to accumulate cytoplasmic beta-\ncatenin.\nChanges have been made to the manuscript (Page 7, Lines 165-166).\n“Meanwhile, without Wnt ligands, AXIN does not translocate to the membrane, no obvious\ncolocalization between AXIN and LRP6 can be observed.” (Page 8, Lines 182-187).\n“Meanwhile, with presence of WNT ligands, we observe minimal cytoplasmic condensates\nshowing AXIN-APC colocalization. Nevertheless, we believed that some residual AXIN-APC\ninteraction persist in the cytoplasm, consistent with other literatures40,41; this is because the\nWnt activation will not recruit all the cytoplasmic AXIN, but instead to comprosise the capability\nof APC destruction complex to degrade β-catenin to accumulate cytoplasmic β-catenin.” (SI,\nPage 13, Figure S2a and b).\nligands.\nFigure S2b caption. Images show minimal cytoplasmic condensates of AXIN-APC in the presence\nof Wnt ligands.\n2. Similar to concern #1, in the IP experiments (Fig.2e,f), the authors also need to\nshow that when AXIN is interacting more with LRP6 under compression, it is\ninteracting less with APC.\nReply: We completely agree with your point and have performed the experiment\nyou suggested. Under identical experimental conditions (same cell line,\n3\ncompression treatment, and time points), we examined AXIN-APC interaction in\nthe presence of Wnt ligands and found that volumetric compression further\ndecreases the interaction between AXIN and APC when Wnt signaling is active\n(Fig. S2c and d).\nChanges have been made to the manuscript (Page 9, Lines 212-213).\n“accordingly, we also confirmed that the binding ratio between AXIN and APC decreased.” (SI,\nPage13, Figure S2c and d).\nFigure S2c-d caption. Western blot assay shows that volumetric compression significantly\ndecreases the binding between AXIN and APC in the presence of wnt ligands, also as indicated by\nquantification.\n3. In Fig.1h and 1l, the AXIN condensates are in the nucleus, not the cytoplasm\n(where the destruction complex is supposed to be), raising the concern that these\ncondensates are not biological. The authors need to explain why the AXIN\ncondensates are in the nucleus.\nReply: Thank you for this comment. We agree that extensive nuclear accumulation\nof endogenous AXIN is inconsistent with its expected cytoplasmic localization as\npart of the destruction complex. Upon re-evaluation, we believe the original\nimmunostaining may have suffered from non-specific nuclear staining due to\nsuboptimal antibody performance.\nTo ensure data reliability, we have repeated this experiment with a new AXIN\nantibody from a different supplier (Invitrogen MA5-48643). The new\nimmunostaining results (now updated in revised Fig. 1h) clearly show that\n4\nendogenous AXIN is predominantly localized in the cytoplasm, consistent with the\ncanonical destruction complex localization, with distinct cytoplasmic condensates\nvisible under volumetric compression. We apologize for any confusion caused by\nthe previous antibody artifact and thank you for helping us improve the data quality.\nWe also reconduct the experiments in Fig. 1l. We have replaced the original\nFig. 1l with representative images (now updated in revised Fig. 1j) that show\npredominantly cytoplasmic AXIN-APC colocalization, which more unambiguously\nsupports our model of destruction complex assembly in the cytoplasm under Wnt-\nfree conditions. The reason cause AXIN appearance in nucleus could be the\nknown technical phenomenon in transfection systems: proteins can exhibit altered\nsubcellular distribution, including increased nuclear entry.\nWe appreciate your careful scrutiny, which has helped us present clearer and\nmore accurate data.\nChanges have been made to the manuscript (Page 23, Figure 1h-j).\nFigure 1h-i caption. Volumetric compression significantly promotes the formation of endogenous\nAXIN condensates inside cells by fluorescent immunostaining, as indicated by the fraction of total\nAXIN in condensates.\ncomplex (co-localized puncta structure of AXIN and APC) inside cells.\n4. Can the system they use (HEK cells) already have active Wnt signaling without\nadding Wnt3A? The authors either need to explain better (citing previous literature)\nor show the experimental evidence that the Wnt signaling is not active before\nadding Wnt3A (like lack of downstream genes activation using qPCR).\nReply: Thank you for raising this important question. You are correct that before\ninterpreting the effects of exogenous Wnt3A, we must thoroughly characterize the\nbaseline endogenous Wnt signaling activity in our HEK293 cell system. We\ncompletely agree with your point and have experimentally validated this critical\naspect.\nAt first place, we designed this experiments based on couples of important\nliteratures [Vivian S W Li, et al., Cell, 2012, 149(6): 1245-1256; Sung-Eun Kim,et\nal., Science, 2013, 340(6134):867-870; Lei Ji, et al., Nature Communications, 2019,\n10(1):4184]. HEK293 cells are a widely used model system for studying Wnt/β-\ncatenin signaling, with numerous publications reporting low basal endogenous Wnt\npathway activity, making them an ideal tool for investigating pathway activation in\nresponse to exogenous stimuli.\nAdditionally, to directly assess endogenous Wnt ligand production in our\nexperimental system, we performed the following experiments:\n1. ELISA quantification of secreted Wnt3A: We used a human WNT3A ELISA\n6\nkit to quantify Wnt3A protein levels in the culture supernatant of untreated\ncontrol HEK293 cells. The results showed that endogenous Wnt3A protein\nconcentration in the medium was extremely low, approaching zero (Fig. S1b).\nFigure S1b caption. Standard curve for the quantification of Wnt3a in HEK293T cell culture\nsupernatant. The concentration of Wnt3a in conditioned medium from HEK293T cells under normal\nculture conditions was determined by ELISA. The curve was generated using serial dilutions of\nrecombinant Wnt3a protein.\n2. qRT-PCR assay: We performed qRT-PCR assay for HEK293 cells under basal\nconditions versus after IWP2 treatment (a porcupine inhibitor that blocks all\nWnt ligand secretion to remove all endogenous Wnt ligands). The results\nshowed that the expression of Wnt target genes LEF1/SP5 exhibited no\nsignificant differences, suggesting HEK293 cells exhibit minimal autocrine Wnt\nsignaling activity under standard culture conditions (see figure below).\nFigure caption. LEF1 and SP5 expression is not altered by IWP2 treatment in HEK293T cells.\nqPCR analysis of LEF1and SP5mRNA levels show no significant difference in HEK293T cells under\nnormal culture conditions versus after treatment with IWP2.\n7\n3. β-catenin nuclear translocation assay: We performed immunofluorescence\nstaining for β-catenin in HEK293 cells under basal conditions versus after\nWnt3A stimulation. Under physiological conditions, β-catenin showed minimal\nnuclear localization in HEK293 cells, suggesting undetectable activation with\nendogenous conditions; whereas clear nuclear accumulation was observed\nupon Wnt3A activation (see figure below).\nFigure caption. Wnt3a treatment induces β-catenin expression and nuclear translocation in\nHEK293T cells. Images show that β-catenin is low and primarily retained in the membrane under\nbasal conditions but accumulates in the nucleus following treatment with Wnt3a, confirming Wnt-\ninduced nuclear translocation.\nThese data conclusively demonstrate that endogenous Wnt/β-catenin\nsignaling is not active at baseline in our HEK293 experimental system. This\nvalidates our use of exogenous Wnt3A as a specific activator and ensures that the\ndifferential effects we observe truly reflect Wnt-ON versus Wnt-OFF states rather\nthan variations in pre-existing pathway activity.\nChanges have been made to the manuscript (Page 6, Lines 133-137). “RKO\ncells have no intrinsic β-catenin transcriptional activity, due to lacking of either endogenous\nWnt ligands or membrane cadherin-catenin complex; meanwhile, despite that HEK293T cells\nhave membrane β-catenin, their autocrine WNT ligands are limited, which is confirmed by our\nELISA assays, hard to trigger downstream signalosome formation and β-catenin accumulation.”\n(SI, Page 11-12, Figure S1b).\n8\n5. I find the CHIR data puzzling. The authors show that when treated with CHIR,\nin Fig.2h-i PEG decreases beta-actin intensity, but in Fig.3g, PEG increases Wnt\nsignaling. How would the authors explain the discrepancy?\nReply: Thank you for this important question. The apparent discrepancy between\nFig. 2h-i and Fig. 3g stems from a critical difference in Wnt ligand availability, which\ndetermines how our mechano-biochemical circuit operates.\nIn Figure 2h-i, cells are cultured without Wnt ligands. CHIR stabilizes β-catenin\nby inhibiting GSK-3β, mimicking pathological accumulation that occurs in\ncolorectal cancer due to APC mutations—independent of upstream Wnt receptor\nactivation. Under these \"Wnt-OFF\" conditions, AXIN remains in cytoplasm;\nvolumetric compression enhances AXIN-APC destruction complex assembly (Fig.\n1j-k), which degrades β-catenin despite GSK-3β inhibition. This demonstrates that\ncompression can partially reverse pathological β-catenin accumulation.\nIn Figure 3g, organoids are cultured in Og medium containing R-spondin\ninstead of no exogenous Wnt3a. However, endogenous Wnt ligands are present\nthrough constitutive secretion by Paneth cells within the organoids—a requirement\nfor intestinal organoid survival (Sato et al., Nature, 2011, 469:415-418). R-spondin\npotentiates this endogenous Wnt signaling. Under these \"Wnt-ON\" conditions,\nAXIN translocates to the membrane to form LRP6 signalosomes, and compression\nenhances this signalosome formation (Fig. 1m-n), amplifying canonical Wnt\nsignaling. CHIR then synergizes with this enhanced pathway activation to\nmaximize β-catenin accumulation and promote growth.\nTherefore, the key distinction lies in the presence of Wnt ligands, which\ndictates AXIN localization. In the absence of Wnt, compression promotes the\ncytoplasmic degradation of β-catenin. In the presence of Wnt, compression\namplifies membrane-based signalosome formation. In essence, our data\ndemonstrate that Wnt ligand availability instructs the mechanical compression to\nfunction in two distinct functional modes: a degradative mode that degrades β-\ncatenin and an amplifying mode that potentiates canonical Wnt signaling.\nChanges have been made to the manuscript (Page 12, Lines 307-308). “due\nto the presence to endogenous WNT ligands from Paneth cells in orgnaoids.”\n9\n6. The authors claimed to use CHIR to accumulate beta-catenin independently of\nWnt ligands and LRP6 by inhibiting GSK3 (lines 218-219) without showing any\ndata. They need to really show the data to back up their claims.\nReply: Thank you for this comment. We understand your concern about the need\nfor data to support this claim in the manuscript.\nWe would like to clarify that the mechanism by which CHIR99021 accumulates\nβ-catenin independently of Wnt ligands and LRP6 by inhibiting GSK-3β is a well-\nestablished and extensively validated pharmacological property of this compound.\nFor example, Ring, D. B. et al., Diabetes, 2012, 52(3): 588-595 demonstrating\nCHIR99021's selective GSK-3β inhibition (IC50 = 6.7 nM); Law & Zheng, iScience,\n2022, 25(4):104159 comprehensively reviewing the premise and mechanisms of\nWnt signaling activation through GSK-3β inhibition.\nCHIR99021 is a highly specific GSK-3β inhibitor that prevents β-catenin\nphosphorylation and subsequent degradation, thereby stabilizing cytoplasmic β-\ncatenin through a mechanism that completely bypasses the need for Wnt ligand-\nLRP5/6 receptor engagement. This is the recognized and foundational mechanism\nfor which CHIR99021 is widely used as a standard tool compound in the Wnt\nsignaling field.\nOur use of CHIR99021 in this study was precisely to leverage this well-\ncharacterized property—to specifically accumulate β-catenin without involving\nexogenous Wnt ligands or LRP6 receptor activation. This allowed us to test\nwhether our mechano-biochemical circuit could suppress pathological β-catenin\naccumulation (as occurs in many cancers) even when that accumulation is\nindependent of canonical Wnt pathway activation.\nWe believe that relying on established pharmacological mechanisms with\nproper citation is scientifically appropriate and avoids unnecessary duplication of\nwell-documented findings.\nWe appreciate your attention to proper documentation and have ensured all\nmechanistic claims are now properly referenced.\nChanges have been made to the manuscript (Page 9, Lines 225-228).\n“CHIR99021 is a highly specific GSK-3β inhibitor that prevents β-catenin phosphorylation and\n10\nsubsequent degradation, thereby stabilizing cytoplasmic β-catenin through a mechanism that\ncompletely bypasses the need for Wnt ligand-LRP5/6 receptor engagement46,47.”\n7. When showing the activity of Wnt signaling, the authors only used one target\ngene AXIN2 (Fig.2q). They need to use more than one target genes to be\nconvincing.\nReply: Thank you for this comment. Demonstrating Wnt/β-catenin signaling\nactivity using multiple validated downstream target genes is more rigorous and\ncomprehensive than relying on a single gene (AXIN2). We have therefore\nsupplemented our analysis with two additional classical Wnt pathway target genes:\n1. LEF1 (lymphoid enhancer-binding factor 1) - an intermediate response gene and\nkey transcription factor in Wnt signaling; 2. SP5 (Sp5 transcription factor) - a late\nresponse gene that is highly specific to Wnt/β-catenin pathway activation. The new\nqRT-PCR data show that the expression patterns of LEF1 and SP5 are consistent\nwith AXIN2 across all experimental conditions (Fig. 2m, n, o, p).\nFigure 2m, n, o, p caption. qRT-PCR assay shows that volumetric compression inhibits the\nexpression of Wnt target genes LEF1/SP5 in the absence of Wnt ligands, but this inhibitory effect\nis prevented when DAX domain was deleted. Also, volumetric compression elevates the expression\nof LEF1/SP5 in the presence of Wnt ligands, the elevation effect is prevented when DAX domain\nwas deleted in AXIN protein.\nChanges have been made to the manuscript (Page 10, Lines 251-256). “This\nobservation are consistently found on other two classic Wnt pathway target genes: 1. LEF1\n(lymphoid enhancer-binding factor 1) - an intermediate response gene and key transcription\n11\nfactor in Wnt signaling; 2. SP5 (Sp5 transcription factor) - a late response gene that is highly\nspecific to Wnt/β-catenin pathway activation. The new qRT-PCR data show that the expression\npatterns of LEF1 and SP5 are consistent with AXIN2 across all experimental conditions.”\n(Page 25-26, Figure 2m, n, o, p).\n8. Again, the authors lack data to show that in the specific cases they are testing,\nthe Wnt signaling is on or off (like concern #4) in the organoid system. They\nspeculated the ON/OFF states based on their experimental results (lines 272-274),\nwhich is not scientific at all. They need to show the data of the ON/OFF states in\nthe organoid system to be convincing.\nReply: You raise an important point about the need for direct evidence of Wnt\npathway status in our organoid systems. We appreciate the opportunity to clarify\nthis critical aspect with proper mechanistic context.\n(1) Mechanistic rationale based on Wnt dependency of healthy intestinal\norganoids:\nIt is well-established that healthy intestinal organoids absolutely require\nWnt ligands for survival and growth. Lgr5+ intestinal stem cells (ISCs) depend\non active Wnt/β-catenin signaling for self-renewal and proliferation. Without\nexogenous Wnt3a (ISC medium) or the synergy between R-spondin\nsupplementation (Og medium) and endogenous Wnt ligands from Paneth cells,\nhealthy intestinal organoids undergo differentiation and apoptosis within days. This\nWnt dependency is a fundamental characteristic of normal intestinal epithelium.\nThus, only ON state of Wnt signaling can guarantee the growth of healthy intestinal\norganoids.\nIn contrast, ~70% of colorectal cancer (CRC) organoids (including ours used\nin the experiments) harbor APC mutations that disable the β-catenin destruction\ncomplex, resulting in constitutive β-catenin accumulation and pathway activation\nindependent of upstream Wnt ligands and LRP6 receptors. These CRC organoids\ncan survive and proliferate without any exogenous Wnt supplementation—a\nhallmark of their transformed state. Moreover, there is no Paneth cells in CRC,\nwhich means that there is no endogenous production of Wnt ligands. Thus, the\nCRC organoids naturally exist with a OFF state of Wnt signaling upstream\nactivation.\n(2) Further experimental validation:\nTo absolutely ensure our CRC organoids were functioning independently of\nWnt ligands, we have treated CRC organoids with IWP2 (Porcupine inhibitor that\nblocks all Wnt ligand secretion). The results showed no effect on CRC organoid\ngrowth (Fig. 3l-p), directly confirming that these organoids do not require Wnt\nligands for proliferation.\nWe also conducted human WNT3A ELISA experiments to quantify\nendogenous Wnt3a in CRC organoid culture supernatant. Results showed Wnt3a\nprotein concentration was near zero both with and without IWP2 treatment (Fig.\nS4a).\nFigure S4a caption. Standard curve for quantitative analysis of Wnt3a protein by ELISA assay. The\ngreen and red dots respectively represent the calculated concentration of Wnt3a detected in CRC\nconditioned medium with or without IWP2 treatment.\nTherefore, our experimental design is built on solid biological principles:\nhealthy organoids represent a ligand-dependent, canonical Wnt-ON state, while\nAPC-mutant CRC organoids represent a ligand-independent, downstream-\nactivated state that we can manipulate with our mechano-biochemical circuit at the\nlevel of the destruction complex.\nAlso, we have made changes in our manuscript (Page 12, Lines 312 to Page\n13, Lines 318 and Page 13, Lines 320-330). “Lgr5+ intestinal stem cells (ISCs) in\norganoids depend on active Wnt/β-catenin signaling for self-renewal and proliferation. Without\nexogenous Wnt3a (ISC medium) or the synergy between R-spondin supplementation (Og\nmedium) and endogenous Wnt ligands from Paneth cells, healthy intestinal organoids undergo\n13\ndifferentiation and apoptosis within days. This Wnt dependency is a fundamental characteristic\nof normal intestinal epithelium. Thus, for healthy intestinal organoids, only ON state of Wnt\nsignaling can guarantee the growth of healthy intestinal organoids.” “resulting in constitutive\nβ-catenin accumulation and pathway activation independent of upstream Wnt ligands and\nLRP6 receptors53. These CRC organoids can survive and proliferate without any exogenous\nWnt supplementation—a hallmark of their transformed state. Moreover, there is no Paneth\ncells in CRC, which means that there is no endogenous production of Wnt ligands. Thus, the\nCRC organoids naturally exist with a OFF state of Wnt signaling upstream activation. To\nabsolutely ensure our CRC organoids were functioning independently of Wnt ligands, we have\ntreated CRC organoids with IWP2 (Porcupine inhibitor that blocks all Wnt ligand secretion).\nWe also conducted human WNT3A ELISA experiments to quantify endogenous Wnt3a in CRC\norganoid culture supernatant. Results showed Wnt3a protein concentration was near zero\nboth with and without IWP2 treatment.” (SI, Page 16, Figure S4a).\n9. The authors need to show that IWP2 addition really depletes all Wnt ligands.\nReply: Thank you for this important question. IWP2 is a highly specific Porcupine\n(PORCN) inhibitor that blocks the palmitoylation of Wnt proteins, a post-\ntranslational modification essential for their secretion from cells [Chen, B. et al.,\nNature Chemical Biology 2009, 5(2):100-107]. By inhibiting PORCN, IWP2\nprevents Wnt protein secretion into the extracellular space, thereby blocking Wnt\nsignaling at the most upstream level—before ligand-receptor engagement.\nFor experimental validation, as we described in our reply to comment #8, we\nperformed direct quantification of Wnt ligand levels using a human WNT3A ELISA\nkit on the culture supernatant from our experimental system. The results\ndemonstrated that there is no detectable Wnt3a protein in the IWP2-treated group\n(below detection limit).\nFor the experiments with CRC organoids. The data reveal that even without\nIWP2 addition, our experimental system has no endogenous Wnt3a interference.\nThis is consistent with that the Paneth cells are the only Wnt ligands producer in\nintestinal epithelium, which are not presented in CRC organoids. The purpose of\nusing IWP2 was to provide double assurance from a scientific rigor perspective,\naiming to thoroughly eliminate any theoretically possible, trace amounts of Wnt\n14\nligands to maximally ensure the reliability of the \"Wnt-OFF\" baseline.\nWe appreciate your attention to this methodological detail, which reinforces\nconfidence in our experimental design.\nChanges have been made to the manuscript (Page 13, Lines 320-330).\n“resulting in constitutive β-catenin accumulation and pathway activation independent of\nupstream Wnt ligands and LRP6 receptors53. These CRC organoids can survive and\nproliferate without any exogenous Wnt supplementation—a hallmark of their transformed state.\nMoreover, there is no Paneth cells in CRC, which means that there is no endogenous\nproduction of Wnt ligands. Thus, the CRC organoids naturally exist with a OFF state of Wnt\nsignaling upstream activation. To absolutely ensure our CRC organoids were functioning\nindependently of Wnt ligands, we have treated CRC organoids with IWP2 (Porcupine inhibitor\nthat blocks all Wnt ligand secretion). We also conducted human WNT3A ELISA experiments\nto quantify endogenous Wnt3a in CRC organoid culture supernatant. Results showed Wnt3a\nprotein concentration was near zero both with and without IWP2 treatment.”\n10. The authors need to show the spherical organoids are more naïve (Fig. 3f)\nusing markers of naiveness (instead of saying they are “believed to be more\nnaïve”). Otherwise the data in this entire figure is uninterpretable.\nReply: Thank you for this important comment. Inferring the \"naïve\" state of\norganoids based solely on morphological features is insufficient and lacks rigor.\nObjective molecular evidence is essential. We have therefore performed single-\ncell RNA sequencing (scRNA-seq) on both control and volumetrically compressed\norganoids to provide precise assessment at three levels: cell composition, gene\nexpression, and signaling pathway activity.\nFor cell composition analysis: Compressed organoids showed significantly\nincreased proportions of stem cells and transit-amplifying (TA) cells (cells with\ncapability to differentiate into different type of intestinal epithelial cells), while the\nproportions of terminally differentiated secretory and absorptive cells were\nsignificantly decreased compared to controls (Fig. S3a). This demonstrates a clear\nshift toward a less differentiated cellular state.\nFor gene expression analysis: In compressed organoids, stemness-related\ngenes such as Lgr5 and Smoc2, as well as proliferation markers like Mki67,\n15\nshowed significantly upregulated expression. Conversely, differentiation-\nassociated genes were significantly downregulated (Fig. S3b and c). This gene\nexpression profile is characteristic of a more primitive, stem-like state.\nFor pathway enrichment analysis: Signaling pathways associated with cell\nproliferation were significantly activated in compressed organoids, while pathways\ndriving cell differentiation were significantly inhibited (Fig. S3d). This further\nconfirms that volumetric compression maintains organoids in a more proliferative,\nless differentiated state.\nAdditionally, in other literatures, the spherical organoids contained high purity\nof Lgr5+ stem cells and more Ki67+ proliferative cells as compared to the crypt-\nshaped organoids (Nikolce Gjorevski, et al., Nature, 2016, 539(7630):560-564).\nThese results are highly consistent with our current scRNA-seq findings.\nWe have made changes to the manuscript (Page 12, Lines 290-305). “To\nconfirm this observation, we have therefore performed single-cell RNA sequencing (scRNA-\nseq) on both control and compressed organoids to provide precise assessment at three levels:\ncell composition, gene expression, and signaling pathway activity. Compressed organoids\nshowed significantly increased proportions of stem cells and transit-amplifying (TA) cells (cells\nwith capability to differentiate into different type of intestinal epithelial cells), while the\nproportions of terminally differentiated secretory and absorptive cells were significantly\ndecreased compared to controls (Fig. S3a). This demonstrates a clear shift toward a less\ndifferentiated cellular state. In compressed organoids, stemness-related genes such as Lgr5\nand Smoc2, as well as proliferation markers like Mki67, showed significantly upregulated\nexpression. Conversely, differentiation-associated genes were significantly downregulated\n(Fig. S3b and c). This gene expression profile is characteristic of a more primitive, stem-like\nstate. Addtionally, signaling pathways associated with cell proliferation were significantly\nactivated in compressed organoids, while pathways driving cell differentiation were\nsignificantly inhibited (Fig. S3d). This further confirms that volumetric compression maintains\norganoids in a more proliferative, less differentiated state.” (SI, Page 14-15, Figure S3a,\nb, c, d).\ndifferentiated state. a, Umap images show the cell composition and ratio of crypt intestinal\n17\norganoids with and without volumetric compression. b-c, In intestinal organoids, stemness-related\ngenes such as Lgr5 and Smoc2, as well as proliferation markers like Mki67, showed significantly\nupregulated and differentiation-associated genes were significantly downregulated under\nvolumetric compression as indicated by umap images (b), as well as quantification of mean\nexpression of genes (c). d, GSEA showed that signaling pathways associated with cell proliferation\nwere significantly activated in compressed organoids, while pathways driving cell differentiation\nwere significantly inhibited.\n11. In figures 3 and 4, the authors merely used volumetric compression without\nshowing AXIN condensate formation on different locations of the cell (membrane\nvs. cytoplasm) is involved in differential regulations of Wnt signaling outputs. Even\nthough they showed some FRAP data at Fig 4a, the images are too small to be\ninterpretable. For example, does the volumetric compression at different Wnt\nON/OFF states also regulate the differential locations of AXIN condensates in\norganoid models? Does the colocalization of AXIN with LRP6 and APC change?\nWithout these data the Fig 3 and 4 seem to be unrelated to the central arguments\nof the paper.\nReply: Thank you for raising this important concern. We now have conducted\nadditional experiments to addressing AXIN subcellular localization in organoids\nunder different Wnt states:\nTo directly answer the question \"does volumetric compression at different Wnt\nON/OFF states regulate the differential locations of AXIN condensates in organoid\nmodels?\", we performed immunofluorescence imaging in two organoid systems\nrepresenting distinct Wnt states:\n1. For intestinal stem cell (ISC) organoids (Wnt-ON model):\nThese organoids require active Wnt signaling for survival and represent a\ncanonical Wnt-ON state. Under basal conditions, we observed AXIN condensates\nwith some localization to the cell membrane. Following PEG compression\ntreatment, AXIN condensates showed enhanced enrichment at the plasma\nmembrane (Fig. S5a and b), consistent with increased LRP6 signalosome\nformation as observed in our HEK293T experiments.\n2. Colorectal cancer (CRC) organoids (Wnt-OFF/bypassed model):\nThese organoids harbor APC mutations that disrupt the destruction complex,\n18\nrepresenting a unique state where the beta-catenin is constitutively accumulated\ndownstream but the upstream ligand-dependent machinery is non-functional. We\nobserved AXIN condensates co-localizing with APC in the cytoplasm. Following\nPEG compression, the degree of AXIN-APC colocalization was further enhanced\n(Fig. S5c and d), indicating increased destruction complex assembly, which is\nconsistent with our observation that compression decreases β-catenin levels in\nCRC organoids (Fig. 4d-e).\nWe have made changes to the manuscript (Page 15, Lines 392 to Page 16,\nLines 406). “To further confirm that the phase separation based mechanochemical circuit\nhappens in organoids under the operation of volumetric compression, we performed\nimmunofluorescence imaging in two organoid systems representing distinct Wnt states. For\nWnt-ON model, the ISC organoids require active Wnt signaling for survival and represent a\ncanonical Wnt-ON state. Under basal conditions, we observed AXIN condensates with some\nlocalization to the cell membrane. Following PEG compression treatment, AXIN condensates\nshowed enhanced enrichment at the plasma membrane (Fig. S5a and b), consistent with\nincreased LRP6 signalosome formation as observed in our HEK293T experiments. For Wnt-\nOFF/bypassed model, the CRC organoids harbor APC mutations that disrupt the destruction\ncomplex, representing a unique state where the beta-catenin is constitutively accumulated\ndownstream but the upstream ligand-dependent machinery is non-functional. We observed\nAXIN condensates co-localizing with APC in the cytoplasm. Following PEG compression, the\ndegree of AXIN-APC colocalization was further enhanced (Fig. S5c and d), indicating\nincreased destruction complex assembly, which is consistent with our observation that\ncompression decreases β-catenin levels in CRC organoids (Fig. 4d-e).” (SI, Page 17,\nFigure S5a, b, c, d).\ndistinct membraneless organelles based on translocated phase separation in two organoid systems.\na-b, Volumetric compression significantly promotes the enrichment at the plasma membrane in ISC\norganoids (a), as indicated by quantifying colocalization of AXIN at the plasma membrane (b). c-d,\nVolumetric compression significantly promotes the formation of APC destruction complex in CRC\norganoids (c), as indicated by quantifying colocalization of AXIN and APC (d).\n20\n12. In many places of the paper the authors write a hypothesis like an experimental\nresult making it confusing for the readers. Examples are sentences in lines 210-\n212, 224-226, 237-238, 294-296. I also find the biological operational amplifer\nimages throughout the figures excessive. The readers will be more convinced by\nthe real experimental data than the drawings showing what the authors think is\nhappening.\nReply: Thank you for these important observations about clarity and presentation.\nIt is important to clearly distinguishing between hypotheses and experimental\nresults is essential for scientific rigor, and that figures should prioritize experimental\ndata over conceptual illustrations.\nWe have carefully reviewed the manuscript and revised the sentences at lines\n210-212, 224-226, 237-238, 294-296, as well as other similar instances throughout\nthe text.\nWe accept your recommendation and have removed repetitive operational\namplifier diagrams from the main figures. We have retained only a few minimal\nversions (Fig. 1a, Fig. 3a and k) solely to introduce and clarify the core concept.\nThe revised figures now focus predominantly on presenting actual experimental\ndata.\nThrough optimizing hypothesis/result distinctions and streamlining conceptual\nfigures, we believe the overall quality and clarity of the manuscript have been\nsignificantly improved. We sincerely thank you for these constructive suggestions,\nwhich have enhanced both the readability and scientific rigor of our work.\nThe manuscript entitled “A mechano-biochemical operational amplifier via phase\nseparation for orthogonally diverting cell fate in organoid”, authored by Jinyun Shi\net al., explores how mechanical and biochemical cues collectively influence cell\nfate decisions in intestinal epithelia. The authors hypothesize that mechanical\ncompression from surrounding cells reduces cell volume and increases\nmacromolecular crowding in the cytoplasm, thereby promoting liquid–liquid phase\nseparation (LLPS). A novel concept presented is that two distinct AXIN-dependent\nLLPS events occur at separate intracellular locations depending on the presence\nor absence of Wnt/β-catenin signaling. This mechanism is proposed to resemble\nthe function of an operational amplifier, with AXIN-APC complexes in the\ncytoplasm promoting β-catenin degradation, and AXIN-LRP6 complexes at the\nplasma membrane enhancing Wnt/β-catenin signaling.\nThe biological question addressed in this study is of broad relevance, intersecting\nfields such as cell biology, developmental biology, mechanobiology, and cancer\nbiology. The conceptual framework is original and could provide insights into how\nmechanical stimuli are converted into biochemical signals. However, aspects of\nthe experimental design and interpretation warrant further scrutiny. Below, I outline\nseveral major concerns regarding the conceptual design and interpretation of the\nexperimental results.\nReply: We sincerely thank you for your thoughtful evaluation of our manuscript.\nWe appreciate your recognition that our study addresses a question of broad\nrelevance across multiple fields and that our conceptual framework is original.\nWe have carefully considered each of your major concerns and have\nsubstantially revised our manuscript accordingly. After addressing the concerns\naccording to your suggestion, we believe that the quality of the manuscript has\nbeen dramatically improved.\nMajor comments:\n1. Concerns Regarding Conceptual Design of the Experiments\noperational amplifier. In most experiments, volumetric compression is used as the\nmechanical input, and AXIN-mediated LLPS serves as the readout. They propose\nthat compression increases macromolecular crowding, thereby facilitating LLPS.\nHowever, it is unclear whether volumetric compression qualifies as a mechanical\nstimulus per se. Mechanical stimuli are typically sensed by known\nmechanosensors, including mechanosensitive ion channels, the cytoskeleton, and\ncell adhesion molecules. In contrast, the increase in crowding observed here\nappears to be a consequence of cytoplasmic volume reduction, not\nmechanotransduction.\nThis raises the question: is the input truly mechanical, or merely a change in\nchemical concentration? The phenomenon that higher polymer concentrations\npromote phase separation is well-established in physical chemistry. Therefore, I\nsuggest the authors more carefully reconsider whether the input stimulus in their\nsystem should be categorized as mechanical. While mechanical compression from\nneighboring cells in the intestinal crypt is indeed physiological, the PEG-induced\nvolumetric compression of HEK293T cells used here may not faithfully recapitulate\nthe native mechanical environment.\nReply: We appreciate this fundamental question about whether volumetric\ncompression should be classified as a mechanical stimulus. This touches on an\nimportant conceptual issue in mechanobiology that deserves careful consideration.\nWe agree that volumetric compression differs from classical\nmechanotransduction through dedicated mechanosensor proteins (e.g., Piezo\nchannels, integrins). However, we respectfully maintain that osmotic and\nvolumetric compression represent legitimate forms of mechanical regulation,\nsupported by extensive literature. Osmotic stress has long been recognized as a\nmechanical stimulus because it generates pressure differentials that drive water\nflux across membranes, alter cell volume, and mechanically deform cellular\nstructures. Hoffmann and colleagues' comprehensive review in Physiological\nReviews (2009, 89:193-277) establishes cell volume regulation as a fundamental\nmechanical response involving mechanosensitive channels, cytoskeletal\nreorganization, and altered membrane tension. Similarly, Burg et al. (Physiological\nmechanical deformation of membrane-associated structures and the cytoskeleton,\nnot merely through chemical concentration changes.\nThe key distinction is that while classical mechanotransduction involves\nforce-induced conformational changes in specific sensor proteins, volumetric\nmechanobiology operates through bulk physical changes in cellular organization.\nExternal forces, whether compressive stress from tissue crowding, osmotic\npressure gradients during digestion, or matrix confinement, drive water efflux and\nreduce cellular volume. This constrains macromolecules within smaller physical\nspace, increasing excluded volume fraction and altering the thermodynamic\nlandscape for protein-protein interactions. Our previous work (Li et al., Cell Stem\nCell, 2021) demonstrated through FRAP and optical tweezers measurements that\ncompression decreases molecular diffusion rates and increases cytoplasmic\nstiffness—both are mechanical properties reflecting changes in the physical state\nof the cytoplasm, not simply chemical concentrations.\nImportantly, diverse mechanical perturbations converge on volumetric\ncompression as a common downstream consequence. Our Cell Stem Cell paper\nshowed that mechanical compression in 3D hydrogels (Fig. 2J), substrate stiffness\nvariations (Fig. 2I), and biaxial stretch (Fig. 2K) all produce quantitatively similar\neffects on cell volume and Wnt signaling activation. This demonstrates that\nvolumetric compression serves as a physical integrator of multiple upstream\nmechanical inputs rather than an isolated artificial perturbation. Cai et al. (Nature\nCell Biology, 2019, 21(12): 1578-1589.) similarly demonstrated that osmotic stress\npromote YAP signaling and downstream activation of target genes, when\nmimicking a osmotic pressure that indeed happens in vivo in kidney.\nThe physiological relevance of volumetric compression in intestinal\nepithelium is well-documented. Intestinal epithelial cells naturally experience\nsignificant osmotic variations, with luminal osmolarity ranging from approximately\n300 to 450 mOsm during daily digestion and water absorption (Nature 568, 98–\n102 (2019); Nature 602, 468–474 (2022)). Our in vivo measurements (Li et al., Cell\nStem Cell, 2021) revealed that Lgr5+ stem cells at crowded crypt bases exhibit\nvolumes of 200-300 μm³, approximately 50% smaller than differentiated cells in\nless crowded regions (400-600 μm³), with deformed nuclear morphology indicating\nspatial constraint.\nWe employed PEG 300-induced osmotic compression as an experimental\ntool because it provides precise, reversible, and quantitative control over cell\nvolume while maintaining viability—essential for mechanistic dissection. The PEG\nconcentrations we used (1-3%) produce volume reductions (23-38%) well within\nthe physiological range observed in vivo (up to 50%), and these compression\nlevels maintain organoid viability and functionality.\nTo address your valid concern about conceptual clarity, we propose a\ncomplimentary mode of mechanical regulation where physical forces alter bulk\nproperties of the cellular interior (volume, macromolecular crowding, excluded\nvolume fraction) that subsequently modulate signaling through thermodynamic\neffects on protein interactions. This mechanism complements rather than replaces\nclassical sensor-based mechanotransduction. Recent work has increasingly\nrecognized that cells integrate mechanical information through multiple parallel\nmechanisms: dedicated mechanosensors that undergo conformational changes,\nand bulk physical properties that alter the energetic landscape for biochemical\nreactions (Elosegui-Artola et al., Cell, 2017, 171:1397-1410).\nWe have revised the manuscript to address this conceptual issue more\nexplicitly. A new discussion section has been added into the revised manuscript\n(Page17, Lines 435-448). “Our findings reveal that cells sense mechanical forces not only\nthrough dedicated mechanosensor proteins but also through bulk physical changes in cellular\norganization. While classical mechanotransduction involves force-induced conformational\nchanges in specific sensors (Piezo channels, integrins, YAP/TAZ), volumetric compression\noperates through altered thermodynamic landscapes for molecular interactions. Multiple\nphysiological mechanical inputs—tissue crowding, osmotic gradients, matrix confinement, and\ntumor pressure—converge on reduced cellular volume and increased macromolecular\ncrowding. Our demonstration that diverse mechanical perturbations (3D compression,\nsubstrate stiffness, stretch) produce similar effects on cell volume and Wnt signaling supports\nthis convergence model. The mechanism operates through excluded volume effects: external\nforces drive water efflux, constraining macromolecules within smaller physical space and\nshifting equilibria for protein-protein interactions to favor phase separation. This volumetric\n25\nmechanobiology complements sensor-based transduction, with phase separation serving as\na critical molecular mediator linking physical constraint to biochemical outputs.”\n2. Interpretation of the \"Operational Amplifier\" Analogy\nThe authors compare Wnt/β-catenin signaling to an operational amplifier,\nillustrated in multiple figures (e.g., Fig. 1a, k, o), suggesting that the system\namplifies input signals. However, it is unclear how signal amplitudes before and\nafter amplification were quantitatively compared. In this case, the input (volumetric\ncompression) and output (Wnt/β-catenin signaling activity) are fundamentally\ndifferent in nature—physical vs. biochemical—which makes direct comparison of\nsignal “amplitude” difficult.\nIn conventional operational amplifiers, both input and output are in the same\nmedium (e.g., electrical signals), allowing for direct amplitude comparison. Here,\nthe authors must clarify the basis on which they conclude that the output signal is\namplified relative to the input. This is a crucial point that requires further\nexperimental justification.\nReply: Thank you for this important question about the quantitative basis of our\noperational amplifier analogy. We agree that comparing signal \"amplitudes\"\nbetween physically distinct inputs (volumetric compression) and outputs (Wnt\nsignaling activity) requires careful justification.\nWe acknowledge upfront that our operational amplifier analogy is functional\nrather than quantitative. We cannot calculate a dimensionally equivalent gain\nfactor because the input and output exist in different physical domains. However,\nwe use this analogy to describe a specific computational property: the system\nintegrates two distinct inputs (mechanical compression and Wnt ligand\npresence/absence) to produce outputs whose magnitude and direction depend on\nboth inputs—analogous to how operational amplifiers process differential signals.\nOur experimental data demonstrate clear amplification behavior in the\nfunctional sense. Consider the canonical Wnt-ON pathway: without compression,\n100 ng/mL Wnt3a treatment increases total β-catenin intensity by 1.7-fold over\nbaseline (Fig. 2e, quantified in 2f). With volumetric compression (2% PEG),\\ the\nidentical Wnt3a dose increases nuclear β-catenin by -2.1-fold (Fig. 2e-f). Similarly,\nfor target gene expression, Wnt3a alone increases AXIN2 mRNA by 2.4-fold, while\nWnt3a plus compression increases AXIN2 by 3.1-fold (Fig. 2n). This demonstrates\nthat compression acts as a gain control element that substantially enhances\npathway output for a given biochemical input, meeting the functional definition of\namplification even without dimensional equivalence.\nThe \"operational amplifier\" framework captures three key features of our\ncircuit: (1) Dual input integration: The system processes both mechanical\n(compression) and biochemical (Wnt ligand) inputs simultaneously, rather than\nresponding to either alone. (2) Input-dependent switching: Like an op-amp with\ninverting and non-inverting inputs, Wnt ligand presence determines whether\ncompression enhances (Wnt-ON) or suppresses (Wnt-OFF) signaling. (3) Signal\namplification: Compression increases the magnitude of the output response to the\nbiochemical input, whether that response is positive or negative. We submit that\nthese functional parallels justify the analogy as a conceptual framework for\nunderstanding circuit behavior, even though the physical nature of signals differs\nfrom electronic systems.\nWe recognize this analogy has limitations and may not be the optimal\ndescriptor. Alternative terms such as \"signal processor,\" \"signal integrator,\" or\n\"mechanical modulator\" might more accurately reflect the mechanism without\nimplying strict quantitative equivalence between input and output domains. We are\nopen to revising our terminology if the reviewer believes this would improve clarity.\nWe have revised the Discussion section to explicitly state that this analogy is\nbased on functional and behavioral similarities rather than direct comparison of\nphysical quantities, thereby avoiding potential misunderstanding. We emphasize\nthat our claim is about qualitative amplification behavior, that compression\nenhances signaling responses, rather than quantitative dimensional equivalence\nbetween physical and biochemical signals.\nWe thank you for this comment, which has prompted us to more carefully\ndescribe both the utility and the limitations of our conceptual framework.\nA new discussion section has been added into the revised manuscript\n(Page16, Lines 413-419). “The mechano-biochemical circuit integrates mechanical and\nbiochemical inputs to bidirectionally regulate Wnt signaling. We describe this as functionally\n27\nanalogous to an operational amplifier based on three properties: dual input integration, input-\ndependent mode switching (Wnt ligands determine inverting vs. non-inverting behavior), and\nsignal amplification (compression enhances Wnt responses 2-4-fold; Fig. 2h-i, 2n). This circuit-\nlike information processing through phase separation.”\n3. Physiological relevance of Organoid Experiments\nIn Figures 3 and 4, the authors use intestinal organoids and show that volumetric\ncompression induces LLPS in stem cells. However, the physiological relevance of\nglobally compressing the entire organoid is unclear. The study aims to understand\nhow mechanical forces in the intestinal crypt influence cell fate. Organoids are\nindeed a powerful system for this investigation. However, compressing the entire\norganoid via PEG treatment affects all cells non-specifically and may not mimic\nlocalized mechanical cues, such as compression from neighboring cells at the\ncrypt base.\nA more physiologically relevant approach might involve applying localized pressure to specific cell populations (e.g., stem cells). The current method—immersing organoids in PEG—induces uniform volumetric compression, which may not accurately reflect the in vivo mechanical microenvironment.\nReply: We appreciate this important concern about the physiological relevance of\nglobal organoid compression versus localized mechanical forces in native crypts.\nThis raises valid questions about experimental design that deserve careful\nconsideration.\nWe acknowledge that PEG-mediated compression affects all cells uniformly,\nwhereas in vivo mechanical forces may be spatially heterogeneous. However, we\nrespectfully argue two aspect: first, the osmolarity in intestinal microenvironment\nindeed varied globally during digestion cycles and water adsorption; second, our\napproach captures the essential downstream physical consequence from diverse\nmechanical inputs in native tissue, the decreased cell volume and increased\nintracellular macromolecular crowding.\nSeveral lines of evidence support the physiological relevance of our approach.\nFirst, our in vivo measurements (Li et al., Cell Stem Cell, 2021) demonstrate that\nvolumes (200-300 μm³) compared to differentiated cells in less crowded regions\n(400-600 μm³), with deformed nuclear morphology indicating spatial constraint.\nISCs exhibited a large cell volume expansion (7-8 folds) immediately after isolated\nfrom native tissue to matrigel 3D culturing. The PEG concentrations we employed\n(1-3%) produce volume reductions of 23-38% in cultured cells and organoids, well\nwithin this physiologically observed range.\nSecond, intestinal epithelial cells naturally experience significant osmotic\nvariations that cause volume changes throughout the day. Luminal osmolarity\nvaries cyclically during digestion cycles (300-500 mOsm), creating physiological\nvolume fluctuations that all epithelial cells must accommodate (Li Y, et al., Nature\nReviews Bioengineering, 2024, 2(12): 1023-1038.). Recent studies measured\nosmolarity in mice intestine in a range between 300 mOsm and 1100 mOsm\n(Tropini C, et al. Cell, 2018, 173(7): 1742-1754. e17; Ng K M, et al. MBio,\n2023, 14(4): e00753-23.); another study measure gastrointestinal osmolarity in a\nrange of 300 to 900 mOsm in Rock Hyrax. The in vivo stimuli of physiological\nrelevant osmotic change in animal studies are widely using 500 mOsm and even\n1500 mOsm (Ichiki T, et al. Nature, 2022, 602(7897): 468-474; Zimmerman C A,\net al. Nature, 2019, 568(7750): 98-102.). Our use of osmotic compression, with an\nosmolarity of of 362.5 mOsm (+1% PEG 300) to 400 mOsm (+2% PEG 300), and\n437.5 mOsm (+3% PEG 300), thus models a naturally occurring challenge rather\nthan an artificial perturbation in physiological relevant range. Furthermore, our\nprevious work demonstrated that multiple distinct mechanical inputs—3D hydrogel\ncompression, substrate stiffness variations, and biaxial stretch—all converge on\nsimilar volumetric compression and produce comparable Wnt signaling responses\n(Li et al., Cell Stem Cell, 2021, Figs. 2I-K). This suggests that volumetric\ncompression represents a common downstream integrator of diverse upstream\nmechanical forces.\nThird, we emphasize that our primary scientific question is: when cell volume\ndecreases and intracellular crowding increases, how do phase separation\nmechanisms transduce this physical state into biochemical signaling outputs?\nGlobal PEG compression provides a tractable experimental system to\nsystematically test this mechanism while maintaining cell viability and enabling\n29\nquantitative imaging of intracellular condensate dynamics.\nWe agree that future studies incorporating spatial heterogeneity would\nstrengthen the physiological relevance. Microfluidic devices enabling localized\ncompression of organoid subregions, or optogenetic approaches to spatially\ncontrol crowding, would be valuable extensions. However, we believe our current\napproach successfully identifies the core mechanism (crowding-driven AXIN\nphase separation bidirectionally regulates Wnt signaling) and demonstrates its\nfunctional consequences in organoid systems. The consistency between our in\nvitro observations and in vivo stem cell volume measurements supports the\nphysiological relevance of this mechanism.\nWe have added Discussion text (Page18, Lines 476 to Page 19, 482) “Our\ncurrent experimental approach employs global PEG-mediated compression, which differs from\nthe spatially heterogeneous forces in native crypts. Nevertheless, intestinal epithelium\nexperiences daily osmotic variations with a range within couples of hudreds of mOsm55-59,\nvalidating osmotic manipulation as physiologically relevant. Future studies incorporating\nspatial heterogeneity through microfluidic devices or in vivo imaging of condensate dynamics\nwould provide valuable complementary insights into whether mechanical force patterns create\ncellular heterogeneity beyond biochemical niche factors.” explicitly addressing this\nlimitation and clarifying that: (1) our approach models the downstream physical\nconsequence (crowding) shared by multiple mechanical inputs; (2) physiological\nvolume reductions in native stem cells fall within our experimental range; (3)\nosmotic compression represents a naturally occurring challenge in intestinal\nepithelium; and (4) future studies incorporating spatial heterogeneity would provide\nvaluable complementary insights. We believe this addresses your valid concern\nwhile maintaining that our experimental design is appropriate for the mechanistic\nquestions we aimed to answer.\n4. Additional Concerns Regarding Experimental Results\n4-1.Localization of AXIN LLPS in Organoids (Fig. 4):\nWhile the authors show that volumetric compression induces LLPS of AXIN in\norganoids, they do not identify the subcellular localization of these condensates.\nBased on HEK293T experiments, LLPS occurs in the cytoplasm when Wnt\n30\nsignaling is off, and at the plasma membrane when Wnt signaling is on (Figs. 1\nand 2). The authors should investigate and report whether similar\ncompartmentalization occurs in different organoid cell types (e.g., stem cells vs.\nPaneth cells).\nReply: We thank you for this comment. You query about the subcellular\nlocalization of AXIN condensates in different organoid cell types. However, the\ncurrent technical challenge exists in performing simultaneous, multi-color live-cell\nimaging to definitively distinguish AXIN condensate and their co-components\ndynamics in specific cell types (e.g., stem cells, Paneth cells, and more) within the\nsame 3D organoid, due to limitations in robust, multiplexed cell-type-specific\nfluorescent labeling systems.\nGiven this technical context, we strategically focused our investigation on the\ncell populations where the AXIN-based mechanochemical circuit is theoretically\nmost critical and biologically relevant. For Wnt-OFF/bypassed model, it can only\nhappens in CRC organoids, since healthy intestinal organoids required Wnt\nligands to survival. And for CRC organoids, there is only colorectal cancer cells\nexisting, there is neither intestinal stem cells or Paneth cells. For Wnt-ON model,\neven though there are stem cells or Paneth cells: the Paneth cells are terminally\ndifferentiated cells; their following cell fate are not regulated by Wnt signaling\nactivation. Instead, the fate of intestinal stem cells (ISCs) are mastered by the Wnt\nsignaling activity. A high Wnt signaling leads to self-renewing of ISCs; a modulate\nactivation of Wnt signaling leads to differentiation of ISCs; and a depleted Wnt\nsignaling results in the death of ISCs. Thus, the function of this AXIN based\nmechanochemical circuit is important in ISCs. For this reason, we imaged the\nformation of AXIN condensates for Wnt-ON state in ISC organoids, which is a\nformation of intestinal organoids with high purity of ISCs.\nAs a result, we have conducted fluorescence-based imaging assays in two\norganoid models representing distinct Wnt signaling states:\n1. Intestinal stem cell (ISC) organoids (Wnt-ON model):\nThese organoids are cultured in ISC medium with Wnt ligands and represent\na canonical Wnt-ON state. We observed that AXIN condensates showed\nenrichment at the cell membrane under basal conditions. Following PEG\ncompression, AXIN condensates showed further enhanced membrane localization\n31\n(Fig. S5a and b), consistent with increased LRP6 signalosome formation.\n2. Colorectal cancer (CRC) organoids (Wnt-OFF/bypassed model):\nThese organoids harbor APC mutations that disrupt the destruction complex.\nWe observed AXIN condensates colocalizing with APC in the cytoplasm. Following\nPEG compression, the degree of AXIN-APC colocalization was further enhanced\n(Fig. S5c and d), consistent with increased destruction complex assembly.\nOverall, the results confirmed the subcellular localization of AXIN-based\ncondensates in different formats of organoid systems.\nWe have made changes to the manuscript (Page 15, Lines 392 to Page 16,\nLines 406). “To further confirm that the phase separation based mechanochemical circuit\nhappens in organoids under the operation of volumetric compression, we performed\nimmunofluorescence imaging in two organoid systems representing distinct Wnt states. For\nWnt-ON model, the ISC organoids require active Wnt signaling for survival and represent a\ncanonical Wnt-ON state. Under basal conditions, we observed AXIN condensates with some\nlocalization to the cell membrane. Following PEG compression treatment, AXIN condensates\nshowed enhanced enrichment at the plasma membrane (Fig. S5a and b), consistent with\nincreased LRP6 signalosome formation as observed in our HEK293T experiments. For Wnt-\nOFF/bypassed model, the CRC organoids harbor APC mutations that disrupt the destruction\ncomplex, representing a unique state where the beta-catenin is constitutively accumulated\ndownstream but the upstream ligand-dependent machinery is non-functional. We observed\nAXIN condensates co-localizing with APC in the cytoplasm. Following PEG compression, the\ndegree of AXIN-APC colocalization was further enhanced (Fig. S5c and d), indicating\nincreased destruction complex assembly, which is consistent with our observation that\ncompression decreases β-catenin levels in CRC organoids (Fig. 4d-e).” (SI, Page 17,\nFigure S5a, b, c, d).\ndistinct membraneless organelles based on translocated phase separation in two organoid systems.\na-b, Volumetric compression significantly promotes the enrichment at the plasma membrane in ISC\norganoids (a), as indicated by quantifying colocalization of AXIN at the plasma membrane (b). c-d,\nVolumetric compression significantly promotes the formation of APC destruction complex in CRC\norganoids (c), as indicated by quantifying colocalization of AXIN and APC (d)\n4-2. Physiological Relevance of Volume Reduction (Figs. 1 and 2):\nThe authors apply volumetric compression to HEK293T cells using PEG. However,\nthe extent of volume reduction used to mimic physiological pressure in the\nintestinal crypt is not justified. If the reduction is outside physiological range, the\nresults may not be biologically meaningful, as elevated macromolecular\n33\nconcentration alone can drive LLPS. The authors should estimate the physiological\nvolume reduction experienced in vivo and relate it to their experimental setup,\nideally referencing phase diagrams for AXIN condensates.\nReply: We thank you for this comment. The physiological relevance of volume\nreduction is important to be included in this paper.\nIntestinal epithelial cells naturally experience significant osmotic variations in\nvivo. Studies have documented that luminal osmolarity in the intestine ranges from\napproximately 300 to 450 mOsm during daily digestion and drinking (Li Y, et al.,\nNature Reviews Bioengineering, 2024, 2(12): 1023-1038.), creating a dynamic\nosmotic environment that cells must continuously adapt to. Recent studies\nmeasured osmolarity in mice intestine in a range between 300 mOsm and 1100\nmOsm (Tropini C, et al. Cell, 2018, 173(7): 1742-1754. e17; Ng K M, et al. MBio,\n2023, 14(4): e00753-23.); another study measure gastrointestinal osmolarity in a\nrange of 300 to 900 mOsm in Rock Hyrax. The in vivo stimuli of physiological\nrelevant osmotic change in animal studies are widely using 500 mOsm and even\n1500 mOsm (Ichiki T, et al. Nature, 2022, 602(7897): 468-474; Zimmerman C A,\net al. Nature, 2019, 568(7750): 98-102.). This physiological osmotic variability\nprovides important context for understanding how cells in the intestinal epithelium\nrespond to volume changes and crowding. The osmolarity we employed in this\npaper is roughly 362.5 mOsm (+1% PEG 300) to 400 mOsm (+2% PEG 300), and\n437.5 mOsm (+3% PEG 300); all are within a physiologically-relevant range. Our\nuse of PEG 300 to induce osmotic compression thus models a naturally occurring\nphysical challenge that intestinal cells regularly encounter.\nThe PEG concentrations used in our experiments (1-2%) were carefully\ncalibrated to replicate physiologically relevant compression levels. In our previous\nwork (Li et al., Cell Stem Cell 2021), we quantified cell volumes in mouse intestinal\ncrypts and found that Lgr5+ stem cells at the crowded crypt base exhibit volumes\nof ~200-300 μm³, while Lgr5− differentiated cells in less crowded regions show\nvolumes of ~400-600 μm³, representing approximately 50% volume reduction\nunder physiological crowding. To validate our in vitro system, we directly measured\ncell volumes under different PEG concentrations and found that untreated cells\n(~2600 μm³) undergo 23% volume reduction with 1% PEG (~2000 μm³) and 38%\nreduction with 2% PEG (~1600 μm³). These experimental compression levels fall\n34\nwell within the physiological range observed in vivo.\nFurthermore, published in vitro reconstitution studies demonstrate that AXIN\nphase separation occurs at approximately 2.5% PEG8000 (with 150 mM NaCl and\n1 μM protein), confirming that our concentrations (1-2%) are at or below the\nthreshold required to trigger condensate formation. Importantly, our compressed\norganoids maintain viability and functionality, with healthy intestinal organoids\nshowing enhanced growth and CRC organoids exhibiting growth inhibition without\nsignificant cytotoxicity at 3% PEG. These data demonstrate that our PEG-\nmediated compression accurately models the physiological crowding and osmotic\nchallenges experienced by intestinal epithelial cells in vivo.\nA new discussion section has been added into the revised manuscript\n(Page18, Lines 476 to Page 19, Lines 482). “Our current experimental approach\nemploys global PEG-mediated compression, which differs from the spatially heterogeneous\nforces in native crypts. Nevertheless, intestinal epithelium experiences daily osmotic variations\nwith a range within couples of hudreds of mOsm55-59, validating osmotic manipulation as\nphysiologically relevant. Future studies incorporating spatial heterogeneity through microfluidic\ndevices or in vivo imaging of condensate dynamics would provide valuable complementary\ninsights into whether mechanical force patterns create cellular heterogeneity beyond\nbiochemical niche factors.”\n35"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The article is much improved. I don't have further comments.", "reviewer_2": "I have carefully reviewed the revised version of the manuscript. I appreciate the authors’ thorough and thoughtful responses to all of my previous comments. The revisions have significantly improved the clarity, rigor, and overall quality of the manuscript. I have no further concerns, and I support the manuscript in its current form."}, "author_response": ""}]

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