ADIOS: Antibody Development via Opponent Shaping
Authors: Sebastian Rene Towers
Aleksandra Kalisz
Philippe A. Robert
Alicia Higueruelo
Francesca Vianello
Chloe Ming-Han Tsai
Harrison Steel
Jakob Nicolaus Foerster
Venue: ICML 2025 poster (2025)
Keywords: Opponent Shaping
Antibody Design
Meta Learning
Game Theory
Computational Biology
Primary area: applications->health_medicine
TL;DR: We present ADIOS: a method for designing antibody "shapers" which both act as effective antiviral therapies and influence the viral evolution towards less harmful variants.

Abstract: Anti-viral therapies are typically designed to target only the current strains of a virus, a *myopic* response. However, therapy-induced selective pressures drive the emergence of new viral strains, against which the original myopic therapies are no longer effective. This evolutionary response presents an opportunity: our therapies could both *defend against and actively influence viral evolution*. This motivates our method ADIOS: Antibody Development vIa Opponent Shaping. ADIOS is a meta-learning framework where the process of antibody therapy design, the *outer loop*, accounts for the virus's adaptive response, the *inner loop*. With ADIOS, antibodies are not only robust against potential future variants, they also influence, i.e. *shape*, which future variants emerge. In line with the opponent shaping literature, we refer to our optimised antibodies as *shapers*. To demonstrate the value of ADIOS, we build a viral evolution simulator using the Absolut! framework, in which shapers successfully target both current and future viral variants, outperforming myopic antibodies. Furthermore, we show that shapers modify the distribution over viral evolutionary trajectories to result in weaker variants.
We believe that our ADIOS paradigm will facilitate the discovery of long-lived vaccines and antibody therapies while also generalising to other domains. Specifically, domains such as antimicrobial resistance, cancer treatment, and others with evolutionarily adaptive opponents. Our code is available at https://github.com/olakalisz/adios.

ADIOS: Antibody Development via Opponent Shaping
Sebastian Towers 12 Aleksandra Kalisz * 12 Philippe A. Robert Alicia Higueruelo
Francesca Vianello
Ming-Han Chloe Tsai Harrison Steel Jakob Foerster" 12
Abstract
1. Introduction
Anti-viral therapies are typically designed to tar- get only the current strains of a virus, a my- opic response. However, therapy-induced selec- tive pressures drive the emergence of new viral strains, against which the original myopic ther- apies are no longer effective. This evolution- ary response presents an opportunity: our ther- apies could both defend against and actively influ- ence viral evolution. This motivates our method ADIOS: Antibody Development vla Opponent Shaping. ADIOS is meta-learning framework where the process of antibody therapy design, the outer loop, accounts for the virus's 's adaptive re- sponse, the inner loop. With ADIOS, antibodies are not only robust against potential future vari- ants, they also influence, ie., shape, which fu- ture variants emerge. In line with the opponent shaping literature, we refer to our optimised an- tibodies shapers. To demonstrate the value of ADIOS, we build viral evolution simulator us- ing the Absolut! framework, in which shapers successfully target both current and future viral variants, outperforming myopic antibodies. Fur- thermore, we show that shapers modify the dis- tribution over viral evolutionary trajectories to result in weaker variants. We believe that ADIOS paradigm will facilitate the discovery of long-lived vaccines and antibody therapies while also generalising to other domains. Specifically, domains such as antimicrobial resistance, cancer treatment, and others with evolutionarily adap- tive opponents. Our code available at https: / //github. com/ o akaliszi /adios.
Designing effective therapies fight off viral pathogens crucial for limiting their devastating social and economic costs (Nandi & Shet; Orenstein & Ahmed, 2017; Samsudin et al., 2024; Faramarzi et al., 2024). However, traditional design approaches only target the current variant of virus. Although this myopic design approach may yield therapies with high initial efficacy, fails to account for viral adapta- tion, leaving treatments vulnerable to becoming ineffective over time (Weisblum et al., 2020; Doud et al., 2018; Lee et al., 2019; Dingens al., 2019; Greaney et al., 2021).
Myople Therapy
Indiuced Pressura
Myopic Therapy
Virus Variant
Virus Variant
Myopic Therapy
Shaper Therapy
Inducced Pressure
Shaper Therapy
Virus Variant C
Shaper Therapy
Variant A
Figure f. Myopic Therapies Become Ineffective Over Time. Ini- tial virus (variant A) evolves in response to the evolutionary pres- sures induced by therapies, resulting in variants. In case of traditional myopic therapies (top), the new emerging variants (vari- ant B) are often therapy resistant. In contrast, ADIOS designs shapers or shaper therapics (bottom) which remain effective and steer the viral evolution towards less harmful variants (variant C).
The COVID-19 pandemic starkly illustrated the challenges of adaptive viruses. While the rapid development of vac- cines remarkable achievement, concerns quickly arose about their long-term efficacy against new emerging COVID variants (Carabelli et al., 2023; Hu et al., 2021). For exam- ple, the 1.1.351 variant demonstrated that the vaccine loses its effectiveness against new strains (Madhi et al., 2021). This underscores the need for approaches that consider both the current and future efficacy of a designed therapy.
Equual contribution FLAII, Foerster Lab for AI Research 'Department Engineering, University of Oxford, Oxford, UK "Department of Biomedicine. University of Basel, Basel, Switzer- land 'Isomorphic Labs. London. UK 'Exccientia, Oxford, UK "Epsilogen Ltd., London, UK. Correspondence Sebastian Tow- ers <sebastian. towers @eng.eenncccc.. ww..p.....ccck... uk., Aleksandra Kalisz <alek- sandra.kalise @ eng. owt..ox.ae ac.ukk>>.
The virus inevitably adapts in response selective pressures imposed by our therapies, i.e., we influence the viral evolu- tion (Chéron et al., 2016; Meijers et al., 2022). Our work turns this influence in our favour, designing therapies that steer the virus towards less dangerous variants, see Figure 1.
Proceedings of the ndnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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ADIOS: Antibody Development via Opponent Shaping
a
Starting Antibdd
Starting Virus
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Generate possibile antiboiees
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Binding based viral firess evaluation with Absolut!
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Simulated Viral Escape via Evolution
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binding pases
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Figure 2. Main Components of ADIOS. a The ADIOS framework. In the Antibody Optimisation Loop (i.e., outer loop), we optimise the antibody to perform well against current and future virus variants; thus influencing the viral evolution. We approximate the future variants through our Simulated Viral Escape via Evolution (i.c., inner loop) where the viruses evolve escape from the current antibody over given horizon length. b The payoffs of the antibody and virus. Red arrows indicate binding interactions that players aim to minimise, while green arrows represent those they aim to maximise. The antibody optimises for binding to the virus while avoiding its anti-target. In this zero-sum game, the antibody's 's optimisation indirectly counters the virus's binding to its target, see Equation 1. Binding simulator. Our JAX (Bradbury et al., 2018) implementation of the binding calculation uses binding poses generated by Absolut! (Robert et al., 2022) and the Miyazawa-Jemiiaa energy potential matrix (Miyazawa & Jernigan, 1999).
To achieve this we utilise principles from opponent shaping (Foerster et al., 2018), a multi-agent reinforcement learning framework that allows agents to both anticipate and influ- ence the future policies of other agents in their environment. This approach, exemplified by methods such as Learning with Ooponenn-Learninng Awareness (Foerster et al., 2018) and Model-Free Opponent Shaping (Lu et al., 2022), allows agents to consider not only their current performance but also the consequences of their actions on their opponents' future behaviour.
the antibody's payoff is primarily determined by its bind- ing strength to the virus, while the virus has the opposite payoff (Figure 2b). Although our framework can use any binding model in principle, in this work we build on the Absolut! framework (Robert et al., 2022) to estimate the binding strength of protein-protein interactions. To improve computational efficiency, we reimplement parts of Absolut! in JAX (Bradbury et al., 2018) allowing GPU acceleration and a 10,000-fold speedup over the original implementation (Figure 2c).
Building on these principles, we introduce ADIOS: Anti- body Development vla Opponent Shaping. Antibodies are immune system proteins that bind to pathogens such viruses. While naturally produced by the body, it is also possible to design and synthetically produce antibodies as therapies. ADIOS frames the interaction between antibodies and viruses as a two-player zero-sum game, In this game,
We use this game to model viral escape - the process through which mutations allow a virus evade host's immune system (Lucas al., 2001). Following meta-learning ap- proach, ADIOS implements two nested optimisation loops, an inner loop and an outer loop (Figure 2a). In the inner loop, we simulate viral escape via evolution, where the virus adapts to the current antibody by repeatedly finding approx-
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ADIOS: Antibody Development via Opponent Shaping
imate best responses that decrease binding strength. The outer loop uses a genetic algorithm optimise the anti- bodies to be effective across viral evolutionary trajectories, resulting in antibodies we call shapers. This is in contrast to only optimising for binding to the initial virus, which results in myopic antibodics.
baldi al., 2024; Bennett al., 2024). The common ap- proaches antibody design utilise emergy-based antibody optimisation methods (Li et al., 2014; Adolf-Bryfogle et al., 2018; Pereira et al., 2024), sequence-based language mod- els (Liu et al., 2020; Saka et al., 2021) or structure- approaches relying on GNNs (Jin et al., 2022) and diffusion models (Martinkus et al., 2024).
Importantly, our simulations show that shapers not only out- perform myopic antibodies in long-term efficacy but also demonstrate the ability to shape viral evolution. Moreover, shapers guide viruses toward variants that are more suscep- tible to binding to a broad spectrum of antibodies, not just the shaper that induced the given viral evolution, providing insights into the scalability and potential for practical de- ployment of ADIOS. Our study also explores the trade-offs between the effectiveness of shapers and the computational resources required for their optimisation. Finally, we present an explainability analysis of the key features that distinguish shapers from myopic antibodies.
In contrast to these works, we are not interested in gen- erating better antibody design methods immediately, but rather in how we should make new methods in the future to account for our effect on evolving viruses.
Predicting Viral Escape: Recent machine learning meth- ods have demonstrated success in predicting future viral strains (Shanker et al., 2024; Wang et al., 2023; Nie et al., 2025). EVEscape (Thadani al.. 2023) decomposes the likelihood of mutation into three parts: maintaining fit- ness, accessibility to antibodies, and disrupting binding, demonstrating success through retrospective identification of COVID variants. Han et al. (2023) take a different ap- proach by modelling viral evolution through simulated fit- ness landscapes. Unlike these methods, ADIOS models the antibody influence on viral evolution, enabling both the simulation of viral escape trajectories and the optimisation of antibodies to minimise viral escape.
Our key contributions include:
ADIOS: framework that brings opponent shaping to antibody design address viral escape,
A GPU-accelerated JAX implementation of the binding simulator Absolut!, achieving 10,000x speedup.
An open-source instantiation of ADIOS applied to an- tibody design for both the dengue virus and three other viruses using our JAX implementation.
3. Background
Antibody Binding Simulators: In our setting, the inter- action between antibodies and viruses is characterised by their binding strength B(.,)) - a measure of how strongly the two "attach" to each other through molecular forces. Molecular dynamics simulations offer high accuracy but are computationally intensive (Hollingsworth & Dror, 2018) 8). Sequence-based ML models (Mason et al., 2021; Lim et al., 2022; Ruffolo et al., 2023; Yan Huang et al., 2022) provide faster alternatives but struggle to generalise beyond their training distribution, making them unsuitable for exploring novel viral mutations. To evaluate B(.,.) we use the Ab- solut! framework (Robert et al., 2022). Absolut! offers balance between speed and generalisation by modelling binding through discretised protein structures. It focuses on the CDRH3 region of the antibody, the most variable por- tion that primarily determines binding specificity (VanDyk & Meek, 1992). For each antibody-antigee pair, Absolut! enumerates possible binding poses and computes their en- ergy using the Miyazawa-Jernigan potential (Miyazawa & Jernigan, 1999). The binding strength B(.-) is then defined as the negative of the lowest binding energy, see Figure 2c and Appendix D for details.
Empirical results showing ADIOS-optimised shapers both significantly outperform myopic antibodies by limiting long-horizon viral escape and guide viral evo- lution towards variants that can be more easily targeted. Analysis of computational trade-offss in shaping hori- zons, providing practical guidance for deploying ADIOS in compute-constraineed settings, e.g. due to more realistic binding simulators.
Interpretability analysis into how antibody shapers in- fluence viral escape, which could, in principle. provide inspiration to antibody designers.
While our results provide a promising proof of concept, they are based on simplified models of binding and viral escape. However, we believe that as more sophisticated simulators emerge, the ADIOS framework has the potential to significantly impact future antiviral therapy design.
2. Related Work
Antibody Design: Antibodies are essential components of the immune system that bind to unique identifiers (antigens) present on pathogens, including viruses, to identify and neu- tralise them. While natural antibodies emerge through an immune response, it is also possible to design antibodies for use as therapies. Recent work has made significant progress in computational antibody design (Cutting et al., 2024; Zam-
Opponent Shaping: A multi-agent reinforcement learn- ing framework which allows agents to anticipate and influ- ence the future policies of other agents in their environment. Learning with Peponent-Learming Awareness (LOLA) (Fo- erster et al., 2018) introduced this concept by having LOLA
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ADIOS: Antibody Development via Opponent Shaping
Algorithm 1 Ev(0, a): Simulated Viral Escape (Inner Loop)
Algorithm 2 Antibody Optimisation (Outer Loop)
Input: virus 0, antibody a, horizon H, population size P, inverse temperature B
Input: antibody a,virus 0, horizon H., population size Pa
steps N Output: Trajectory of antibodies á = =[aP; at, ,. a~)
Output: Sampled viral trajectory ê = |60, 66 ,...... ......,," 8"] d <
âg < â
for i 0 to H/ - do
for i 0 to N - do
for k to do
aj < a'
of f- 0' @ Mutation
for k = 2 to Pa do
end for
a + al + Point Mutation
p(u) + P(r = =(+) x exp(3R 11 See Eq.
end for a'+l + arg max, [F (a)
6²+1 ~ p(t)
Seee Eq. 2
end for
end for
+ [00 [8...... ................................ dh1 return 0
â lão, ØN] return â
agents optimise against anticipated opponent updates rather than static opponent policies. They achieved this through an augmented value function that accounts for the opponent's learning step.
We define the set of 20 amino acids as A. Let N, be the virus sequence length and N, be the antibody sequence length. So action of the virus is v A NN and an action of the antibody is E A, Let B A, x A + R be our binding function, which measures the strength of the binding between the antibody and the virus with increasing values corresponding to stronger binding'.
Meta-leaming is a set of methods for optimising learn- ing process itself, "learning to learn". In multi-agent sys- tems, this concept extends to learning about and influencing how other agents learn. Model-Free Opponent Shaping (M-FOS) (Lu et al., 2022) showcases this idea by using gradient-free optimisation to learn meta-policies that accom- plish long-horizon opponent shaping. Our approach follows similar principle, using evolutionary optimisation to shape viral escape trajectories.
The payoff structure is designed to capture the biological in- centives of both players: the antibody aims to bind strongly to the virus while avoiding binding to human proteins (an anti-target), whereas the virus seeks to evade antibody bind- ing while maintaining its ability to bind to host cell receptors (a binding larget). Mathematically, we define the antibody's payoff Rg as:
4. Method
Ra a) B(e,a) - B(t,, -B(,,,
(I)
ADIOS frames antibody design as two-player game be- tween an antibody shaper agent and a naive virus agent, building on principles from opponent shaping (Figure 2). We present our method in three parts:
where B(e, a) represents the binding strength between the virus and antibody to is the antibody's 's anti- target, and 1 is the virus's binding target. The virus's payoff R. is simply the negative of the antibody's 's pay- off: (v, a) - Ru (v, a), see Figure 2b. This formula- tion also ensures that neither player can adopt an overly simplistic strategy: the virus can't become entirely inert without losing its ability to infect host cells, and the an- tibody can't 't become universally "sticky" without binding to the human protein, a "false positive", potentially caus- ing the immune system to attack the human body. We give the full Markov Decision Process (MDP) definition M = (8. A", A", P. R, n)) in Appendix E.
In Section 4.1, we introduce the virus-antibody game, defining the action spaces and payoffs for both players. Sec- tion 4.2 describes our simulated viral evolution process, modelling how viruses evolve to escape a given antibody. Finally, Section 4.3 presents our antibody optimisation ap- proach, which optimises the antibody shapers in a way that accounts for future viral mutations and learns to influence viral evolution away from escape.
4.1. Virus-Antibody Game
We formalise the interaction between antibodies and viruses as a two-player zero-sum game. In this game, two players- the virus and the antibody play a game where one player's gain is the other's loss. The game is defined by the set of actions available to each player and their respective payoffs. The players' actions are represented by their amino acid sequences. The sequences are of an antigen protein for the virus and fragment of hypervariable region of the heavy chain for the antibody.
4.2. Simulated Viral Escape via Evolution
We model the viral escape as a virus i naively evolving for H steps in response some fixed antibody a. The simulated viral escape via evolution, see Figure 2a and Algorithm 1, is defined as follows. Given a starting virus é, the fixed antibody a induces distribution Ev((, a) over sequences
'This is opposite to binding energies, which are smaller for stronger binding.

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ADIOS: Antibody Development via Opponent Shaping
of viruses 0 [00, 61 ; p......i Gd), where 6 = 6 and H is the chosen horizon length. We write i Ev(ö; a) to denote this relationship.
could, in principle, start from any antibody, but for simplic- ity we opt start from purely random antibodies, meaning à is random. In most of our experiments N = =30.
We define the process of generating the escape trajectories inductively. In generation i, we have a virus 6'_ We gener- ate a population of viruses vi, v2 Up up by duplicating 6f P times, then randomly applying mutations such that on average there is one amino acid mutation per viral sequence:
At the start of antibody optimisation step i, we have an an- tibody â'_ We first generate a population of Pa antibodies [ai ag ........p... .p, by taking both the antibody a' and Pa - 1 copies of it, with each copy having exactly a single ran- dom mutation in the amino acid sequence of à', For our experiments, Pa = 40.
o = 6³ @ Mutation
We then sample their fitness values F (a)) with a fixed number of Monte Carlo roll-outs, i.c., we sample inde- pendent viral escape trajectories, each with horizon H viral escape steps. We found ry = 5 to be sufficient. Finally, we select äf+1 to be the best-performing antibody:
In our experiments P 15. For every virus in the popu- lation, we evaluate its fitness given by Rg (vi,, a). We then sample new virus gi+1 based the fitness values, in particular:
P( = v x exp(BR,
a'+1 = arg max
[F (af)
k
With duplicates in the population being considered dis- tinct, so that the likelihood of a particular variant increases with the number of duplicates. Furthermore, f is a con- stant which reflects how random the selection process is, with 3 + Do reflecting deterministic max-fitness selec- tion. After H generations, a full escape trajectory â = [69, 62, 02, ,."","""""""" " has been generated and the simulated viral escape process ends.
Once the final optimised antibody a is generated, full op- timisation trajectory is complete, â [a a a², ..... a Jm and the antibody optimisation process finishes.
5. Experimental Setup
5.1. Absolut! Speedup
To meet the computational demands of our opponent shap- ing approach, which requires rapid evaluation of numer- ous antibody-virus interactions, reimplement the core binding calculation of Absolut! (Robert al., 2022) using JAX (Bradbury et al., 2018), framework that facilitates GPU-accelerated computation (Figure 2c). Our efficient JAX implementation and the GPU acceleration results in a 10,000-fold speedup compared to the original implementa- tion, see Table
4.3. Antibody Optimisation
We define the antibody fitness P (a) such that it represents the true objective of the antibody, which accounts for the viral escape. Given a horizon H and starting virus é the antibody fitness is:
F# (a) = (v
Σ
R
(6
a)
(2)
H H+1
Absolut!
Absolut! + JAX
Note that if H = 0 this fitness defaults to a naive antibody payoff that ignores viral escape, i.e., (a(() (a) = R. (o, a). We
Hardware Time/Antigen (s)
Apple M2 Max 1.8
Nvidia A40
2.1 10
refer to this as the myopic objective.
To optimise both shapers and myopic antibodies, we employ Monte Carlo simulations to estimate the antibody fitness, combined with an evolutionary optimisation algorithm. We refer to this process as the antibody optimisation loop, see Figure 2a and Algorithm/ 2. In meta-learning terms, this the outer loop or the meta-loop, contrasting to the inner loop, which the simulated viral escape via evolution.
Table 1. Comparison the time taken to compute a single binding query between the original implementation of Absolut! (Robert et al., 2022) and our reimplementation Absolut! JAX (Brad- bury et al., 2018). The original Absolut! implementation runs on CPU only, hence the difference in evaluation hardware.
5.2. Dengue Virus
We use the antigen protein from the Dengue Virus for our main experiments, specifically, the structure with Protein Data Bank (PDB) code 2R29 (Berman et al., 2000; Lok et al., 2008). First, Absolut! processes this structure to generate binding-relevant information, which is then used by our JAX implementation (details given in Appendix D). In the viral escape step, we mutate only the amino acid sequence of
Given starting antibody à, starting virus i and viral escape horizon H. the antibody optimisation process gen- erates a trajectory of antibodies à = [a", â à² ",,...,a"" J. where N is the number of antibody optimisation steps (i.e., meta-steps). In the trajectory, â = à is the starting antibody and āy is the final optimised antibody. This optimisation
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ADIOS: Antibody Development via Opponent Shaping
b
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Optimisation
Binding Samples
Figure 3. Shapers Outperform Myopic Antibodies. Distribution of antibody shapers optimised with horizon 100 (orange) vs. myopic antibodics distribution (bluc). We highlight the top 10% shapers with respect to Fy in red, and the top 10% myopic antibodies with respect R., R.(e, a) in green. The x-axis is myopic antibody fitness R. (v, a) and the y-axis the escape averaged antibody fitness for H 100, i... F2 (a)) Higher values on both axes indicate better performance. b Viral escape curves (inner loop performance) for different steps of antihody optimisation process (outer loop) for antibody shapers optimised with horizon 100 (solid lines) and myopic antibodies (dashed lines). The lighter lines indicate early antibody optimisation steps, and the darker lines show the later steps. The x-axis shows the evolutionary steps of viral escape. The y-axis represents the virus fitness/payoff Ry (v, a). where higher values indicate better virus fitness (and lower values denote better antibody performance, lower is better for us). c, d Antibody optimisation learning curves (outer loop performance) for a varying horizon length. The x-axis shows the antibody optimisation steps, i.e., meta-steps (c) the number of samples from the binding simulator (d). The y-axis shows antibody fitness F:100 (a). Error bars correspond to the standard error. Higher values indicate better performance.
the dengue envelope antigen, which is composed of N, 97 amino acids, and do not consider other components of Dengue Virus. Importantly, the antigen does not significantly change over the course of viral escape. All experiments but the ones we discuss in Section 6.3 and Appendix A use the dengue virus.
MERS- CoV Virus with PDB code SDO2 (Li al., 2015). Furthermore, we show that ADIOS can be easily applied to other pathogens, such bacteria, too. We perform extra experiment with the Clostridium Difficile Bacterium, PDB code 4NP4 (Orth et al., 2014).
assume that the structure of
6. Results
5.3. Additional Viruses and Bacterium
To demonstrate robustness of the experimental results we achieve with ADIOS on dengue virus we conduct addi- tional experiments with three other viruses and one bac- terium. The three viral antigens we use are: West Nile Virus, PDB code IZTX (Nybakken et al., 2005); Influenza Neu- raminidase Virus, PDB code 4QNP (Wan al., 2015) and
6.1. Shapers vs. Myopic Antibodies
We validate the effectiveness of the antibody shapers in optimising the escape-averaged antibody fitness function F (a) compared to myopic antibodies that only respond to the current virus v. For our shaper antibodies, we se- lect long horizon of H = 100 to capture extended viral
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ADIOS: Antibody Development via Opponent Shaping
West Nite Minu
Influenoes Vinus
MERS-OW Wius
Cineriiuum Biftcile Batterium
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Figure 4. Shapers Outperform Myopic Antibodies on Other Viruses and Bacterium. Antibody optimisation learning curves (outer loop performance) for varying horizon lengths across three viruses- West Nile Virus, Influenza Virus, and MERS-CoV as well as the bacterium Clostridium Difficile. The x-axis shows the antibody optimisation steps, i.e, meta-steps and the y-axis shows the antibody fitness F (a). Raw fitness values are dependent on Absolut! scores and are relative to the specific antigen, i.c., absolute values should not be compared between different viruses bacterium hut rather the overall trends. Error bars correspond to the standard error. Higher values indicate better performance. Full set of ADIOS results for these four pathogens is provided in Appendix A.
escape trajectories. Both shapers and myopic antibodies are optimised for N = 30 steps. Figure 3a presents the performance distributions of shapers and myopic antibodies under both objective functions.
These results show that as the antibody optimisation process progresses, shapers learn to influence viral trajectories in a way that minimises long-term viral escape, albeit at the cost of initial performance. While myopic antibodies may offer better immediate control, shapers provide more sustained effectiveness against evolving viral populations.
Our results demonstrate clear advantage of shapers in the escape-averaged objective (a). The mean of the shapers distribution significantly exceeds that of the my- opic distribution, as evident from the marginal density plot in Figure 3a. Notably, none of the myopic antibodies out- perform any of the top 10% of shapers in this long-term objective. However, there is trade-off between short-term and long-term optimisation. While shapers do better the escape-averaged objective, they underperform on the myopic objective R. (v, a).
6.2. Antibody Shapers with Varying Horizons
Finally, we investigate the impact of varying horizons H the optimisation process of antibody shapers. We optimise myopic antibodies and shapers using horizons H = (5, 10, 20, 100} for N = 30 steps. To evaluate these antibodies against a consistent "true" objective, we simu- late viral escape over H = 100 steps for each antibody, regardless of the horizon used during its optimisation. Fig- ure 3c presents these results, demonstrating that shapers optimised with longer horizons H consistently yield bet- ter performance throughout all steps of the optimisation process.
We next examine the influence of antibody shapers on viral escape trajectories, comparing H = 100 shapers with my- opic antibodies, both optimised for N 30 steps. Figure 3b illustrates the viral escape curves induced by both anti- body types at different stages of their optimisation process. We first complete the antibody optimisation process, saving antibodies generated at steps 0, 10, 20, and 30. For each of these optimisation steps, we then simulate viral escape over !! = 100 evolutionary steps using the corresponding saved antibodies. The presented viral escape curves are averages derived from multiple simulations.
However, the number of antibody optimisation steps does not accurately reflect the computational or experimental cost of optimisation. Each simulation of viral escape requires a number of binding samples that increases linearly with the horizon length H. Yet, shorter horizon antibodies optimise objective that diverges further from our "true" antibody objective F! (a). Due to this trade-off, we observe that the optimal training horizon varies depending on the available computational budget.
At the outset of the antibody optimisation process (step 0), both the shapers and the myopic antibodies induce similar escape curves, an expected outcome given their initialisation from random antibody sequences. However, as we exam- ine antibodies from later optimisation steps, we observe diverging trends. Myopic antibodies cause the viral fitness to be lower in the initial escape steps, outperforming the shapers. After about 10 escape steps, corresponding to & 10 viral mutations, the two antibody types perform similarly. Beyond that, shapers demonstrate superior results in later escape stages, more effectively preventing viral escape.
To illustrate this trade-off, we conduct an additional ex- periment shown in Figure 3d. Here, instead of fixing the number of optimisation steps N, we constrain the total num- ber of binding samples queries to our binding strength simulator used to evaluate all antibody and virus payoffs throughout the optimisation process to be constant across different horizons. This approach provides a performance comparison that accounts for the computational resources
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ADIOS: Antibody Development via Opponent Shaping
necessary across varying horizon lengths. Interestingly, H 20 shapers perform strongly, nearly matching the per- formance of those optimised with horizon H 100 for given number of antibody optimisation steps, and far exceed- ing it when accounting for the differing computational cost. This suggests that using a cheaper, shorter-horize proxy for the true antibody objective 12000 (a) can yield substantial benefits.
evolutionary trajectory of the virus itself, creating evolution- ary pressures that guide viral mutations in direction more favourable to antibody binding an "attack" approach.
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85
-93
More generally, we find that the optimisation horizon sig- nificantly influences the performance of antibody shapers. While longer horizons lead to better long-term performance, the optimal horizon length is dependent on the available computational resources. Thus, it is important to consider the balance between computational cost and the fidelity of the optimisation objective when designing antibodies for
313
B108
-95
long-term effectiveness against evolving viral populations.
vepani
Vise
6.3. Antibody Shapers for Other Viruses and Bacterium
Viruses Induced by Antibodies
To test whether the shaping effects observed on dengue gen- eralise, we evaluate ADIOS on three additional viruses: West Nile, Influenza, and MERS-CoW, Clostridium Difficile bacterium (Figure 4, Appendix A). In all cases, we observe consistent trends: shapers outperform myopic antibodies in escape-averaged fitness, confirming that ADIOS can successfully achieve shaping across diverse pathogens.
Figure S. Robustness vs. Shaping. We optimise 80 different
well as the
antibodies ag across multiple horizons (Myopic, H 5, H 10, = 20, = 100), these are represented by the y-axis. We simulate the viral escape to each of these antibodies for 100 steps, and we group the escape viruses ty by the horizon body that induced them; these escape viruses represented by the x-axis. In colour, we show the mean antibody payoff' R., (UH, azr² for each group of optimised antibodies agr against the final es- cape viral variant vy induced by other antibodies optimised with horizon H. Darker colours correspond better antibody payoff.
the anti-
For West Nile virus and MERS-CoV, и 100 shapers appear to perform worse than shorter-horizon // = 20 an- tibodies, see Figure 4. However, given that all antibodies are only optimised for 30 meta-steps, and the compute- normalised (bottom row) plots in Figure A.I show clearly that = 100 shapers have not yet converged, we hypothe- sise that H- 100 shapers would ultimately yield the best performance if given more optimisation time.
To disentangle these strategies, we separately evaluate the antibodics and the viruses that evolve in response to them. To do this, we compare the viruses against other antibodies which did not influence the viral evolution. The intuition is that an antibody which is good at shaping (good attack), but less robust (poor defence), will induce viruses which other antibodies will perform well against. Specifically, we generate antibodies a for each horizon H and simulate viral escape against these antibodies for 100 steps, resulting in viruses vy- For all pairs of horizons (H, H'), we then cross-evaluate the antibody payoff R2 (VH, agr). Figure 5 presents the result of this analysis.
Interestingly, the shaping effect is especially strong on the Clostridium difficile bacterium, where H = 100 shapers significantly outperform all other antibody types across all reported metrics; see right-most row in Figure A. These results suggests that different antigens can exhibit very dif- ferent behaviour in a shaping setting. However, ADIOS is able to produce antibodies with effective shaping behaviour across them.
Interestingly, viruses U100 induced by H = 100 shapers are consistently more exploitable by antibodies across all optimisation horizons. This suggests that H = 100 shapers actively shape the escape trajectories of the virus in a way that makes the resulting variants more susceptible tibody binding in general. However, this shaping effect comes at cost. The H 100 shapers (a100) show slightly lower payoffs compared to the peak performance of shorter- horizon antibodies (as and aıo) against the viruses V000 induced by the H = 100 shapers (see rightmost column of Figure 5). This trade-off indicates that to exert a stronger shaping influence on viral evolution, H 100 shapers sac-
6.4. Attack is the Best Defence
Our previous results demonstrate that antibody shapers, par- ticularly those optimised with longer horizons, manage to effectively minimise viral escape. However, we hypothesise they can achieve this through two distinct strategies: robust- ness or shaping. A robustness strategy involves developing antibodies that are inherently resistant to a wide range of potential viral variants - a "good defence" approach. In contrast, a shaping strategy aims to actively influence the
an-
8

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ADIOS: Antibody Development via Opponent Shaping
rifice some degree of immediate performance or robustness, that is, their ability to perform well against a wide range of viruses. Therefore, potential strategy could involve using mixture of antibodies as therapy, where some are optimised for shaping the virus's evolutionary trajectory, and others are designed for strong immediate binding.
preserve robustness against viral mutation since the virus cannot easily escape by avoiding specific, high-binding. parts of the antibody.
Through analysis of binding using pose matrices, represent- ing which parts of the antibody and virus bind with each other, we observe these interaction patterns significantly change as the virus adapts. However, the type of antibody influences the nature of these changes: H 100 shapers actively constrain viral evolution by both preventing un- favourable binding configurations and preserving favourable ones, While these findings are specific to our Absolut! bind- ing simulator, they hint at explainable strategies that shapers use to influence viral evolution, which could inform future antibody design approaches.
-92
asyomil
Antibody Payoff R. an)
Evaluation Antibodies
85
-93
018
-94
ar8
7. Conclusion & Future Work
-95
In this work, we introduce ADIOS, a meta-learning frame- work for designing therapeutic antibodies that not only de- fend against current viral strains but instead actively shape viral evolution. We provide a GPU-accelerated JAX imple- mentation of Absolut!, enabling rapid simulation of viral escape trajectories and outer-loop optimisation. Our results demonstrate that shapers are not only more robust against viral escape, but they also shape viral evolution toward more targetable variants. Lastly, we provide an explainability analysis of how shapers achieve this level of robustness and influence, which we hope will inspire practitioners.
Vayoa vvt
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Viruses Induced by Antibodies
Figure 6. Shaping with External Pressure. A similar experiment to Figure 5, but with the additional external pressure of a separate myopic antibody (see Equation 3).
To investigate whether shaping persists in more realistic scenarios with multiple therapeutic pressures, we conduct an additional experiment. Using the same groups of anti- bodies an, we simulate viral escape with external pressure from a myopic antibody agz (not included in the original amgopic set). The viruses Ext now evolve according to a modified payoff:
Although dengue virus served as our primary benchmark, we evaluated ADIOS on three other viruses (West Nile, In- fluenza and MERS-CoV) and on the bacterium Clostridium Difficile. In all four cases ADIOS consistently achieves shaping. These results confirm that ADIOS can gener- alise across a diverse set of pathogens. More broadly, the same opponent-shaping principle can be transferred to mooncelnal--nttiodd, (mAb) therapy for cancer (Zahavi & Weiner, 2020). In that setting, the outer loop would optimise therapeutic mAbs, while the inner loop would simulate the evolution of cancer-cell growth-factor receptors; the goal would be to shape cancer cells into cells that do not pro- liferate well. Exploring this direction, together with other bacterial or ceatiirroobal--sistaaataa scenarios, remains an exciting avenue for future work.
1 R Fant (v, 0, a = (v, a) + (u aot)
2
which represents the scenario where multiple therapies are present in the environment (for example, during COVID-19 19 when multiple vaccines were available). Figure 6 shows that while the shaping effect is somewhat reduced compared to our original results, remains clearly visible. This demon- strates that our shaping approach transfers to test regimes where external pressures from other therapies are present.
6.5. Explainability Analysis
While our current implementation uses simplified binding and evolutionary escape models that prevent direct thera- peutic application, ADIOS could be integrated with more sophisticated models, like AlphaFold3 (Abramson et al., 2024), to better capture evolving viral and antibody struc- tures. As computational models of protein interactions and evolutionary processes continue to improve, ADIOS has the potential to transform how we develop therapies against viruses, cancers, and other evolving adversaries.
To understand what distinguishes shapers from myopic anti- bodies, we conduct two complementary analyses of amino acid distributions and binding poses (Appendices B and C). Examining amino acid distributions, we find that long- horizon shapers exhibit more uniform distributions, while myopic antibodies tend to cluster around amino acids with extreme binding energies. We hypothesise that by maintain- ing diversity in their amino acid composition, shapers can

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ADIOS: Antibody Development via Opponent Shaping
Acknowledgements
for computational tional Biology, 14(4):e April 2018. ISSN
antibody design. PLOS Compula-
We would like to thank Marius Urbonas, Duygu Açıkalın, Michael Matthews, Benjamin Ellis, Benedetta L. Mussati, Mattie Fellows, Lisa Zillig, Ting Lee, Matthew Raybould and Charlotte Deane for their invaluable contributions to this work. Their thoughtful insights helped guide the project direction, their detailed feedback on carlier drafts signifi- cantly enhanced the manuscript's clarity and accessibility, and their support during the review process was instrumen- tal in addressing reviewers' concerns. We also thank the anonymous reviewers for their constructive feedback, which led improvements in the paper. This work was supported by UK Research and Innovation and the European Research Council Jakob Foerster is partially funded by the UKRI grant EP/Y028481/1 I/1, originally selected for funding by the ERC. This work was also supported by Exscientia, which provided Aleksandra Kalisz with PhD studentship.
1553-7358.
doi: 10.1371/jormal..cbii pcbi..000112.. https: httpss://oouraas.ppp www.ppoooooggooooo org/
URL p Library of Science.
Publisher: Public
Bennett, N. R., Watson, L., Ragotte, R. J., Borst, A. J.,
See, D. L., Weidle, C., Biswas, R., Shrock, E. L.,, Leung, P. J. Y., Huang, B., Goreshnik, I,, Ault, R., Carr, K. D., Singer, B., Criswell, C.. Vafeados, D., Sanchez, M. G., Kim, H. M., Torres, S. V., Chan, S., and Baker, D. Atomi- cally accurate de novo design of songle-domain antibodies, March 2024. URL https: /www biorxiv www.ooivvorroooooooooooooooooooe org/ content /10 1ww.121212222111 03. 14. 5851035113
Pages: 2024.05.14.585103
Section: New Results.
Berman, H. M., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T. N. Weissig, H., Shindyalov, I. N., and Bourne, P. E. The Protein Data Bank. Nucleic Acids Research, 28(1): 235 235-242, January 2000. ISSN 0305-1048, doi: 10.1093/ nar/28.1 1.235. URL https: 2..2....
Impact Statement
This work introduces a machine learning framework for antibody design that could contribute to developing more effective therapies against evolving pathogens like viruses. While this has potential positive societal impact through improved disease treatment and pandemic preparedness, we acknowledge that therapeutic development tools earry risks if misused. Our current implementation uses simplified models and significant additional research and safety vali- dation would be required before any real-world therapeutic applications.
/oii http:////ooo.o////.../o///o
Bradbury, J., Frostig, R., Hawkins, P., Johnson, M. J., Leary, C., Maclaurin, D., Necula, G., Paszke, A., VanderPlas, J., and Wanderman-Milng S. JAX: composable transforma- tions of Python+ NumPy programs. 2018. URL https: / 8 htt.o//aw....ooo.....c////aaaaaa
Carabelli, A. M., Peacock, T. P., Thorne, L. G., Harvey, W. T., Hughes, J., de Silva, T. I., Peacock, S. Barclay, W. S., de Silva, T. I., Towers, G. J., and Robertson, D. L. SARS-CoVe variant biology: immune escape, transmis- sion and fitness. Nature Reviews Microbiology, 21(3):
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ADIOS: Antibody Development via Opponent Shaping
A. Experimental Results on Other Viruses and Bacterium
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Figure A. Shapers Outperform Myopic Antibodics on Other Viruses and Bacterium. The figure shows results across four different pathogens: West Nile Virus, Influenza Virus, MERS-CoV Virus, and Clostridium Difficile Bacterium (left to right columns). First row Distribution of antibody shapers optimised with borizon H 100 (orange) myopic antibodies distribution (blue). We highlight the top 10% shapers with respect to F3 (a) in red, and the top 10% myopic antibodics with respect to R. (v. a) in green. The x-axis the myopic antibody fitness R. (v. a) and the y-axis is the escape averaged antibody fitness for H 100, i.e., F200 (a). Higher values on both axes indicate better performance. Second row Viral escape curves (inner loop performance) for diffeerent steps of the antibody optimisation process (outer loop) for antibody shapers optimised with horizon H 100 (solid lines) and myopic antibodies (dashed lines). The lighter lines indicate carly antibody optimisation steps, and the darker lines show the later steps. The x-axis shows the evalutionary steps of viral escape. The y-axis represents the virus fitness/payoff R2 (v. a), where higher values indicate better virus fitness (and lower values denote better antibody performance, so lower is better for us). Third row Antibody optimisation learning curves (outer loop performance)
varying horizon lengths. The x x-axis shows the antibody optimisation steps, i.e., meta- step-s the y-axis shows antibody fitness F! Forth row Antibody optimisation learning curves accounting for computational cost. The x-axis shows the number of samples from the binding simulator, and the y-axis shows antibody fitness 1000 (a). Higher values indicate better performance. Error bars correspond to the standard error. In all these results, payoff/fitness values are dependent Absolut! scores and are relative to the specific antigen, i.c., absolute values should not be compared between different viruses or bacterium but rather the overall trends.
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ADIOS: Antibody Development via Opponent Shaping
B. Amino Acid Distribution in Shapers and Myopic Antibodies
To further understand the performance differences between myopic antibodies and shapers, we analyse how the amino acid distributions of the antibodies change with the optimisation horizon H. Within our model, each amino acid is solely characterised by its binding strength other amino acids as defined by the Miyazawa-Jernigan energy potential matrix (Miyazawa & Jernigan, 1999). However, despite this simplicity, we still see interesting patterns in the amino acid distribution. Figure B. showcases the results of our experiment.
Antibodies optimised with longer horizons, especially the H/ = 100 shapers, exhibit a more uniform distribution of amino acids, while those with shorter horizons show a tendency to cluster around amino acids associated with either high or low binding energies. The flatter distribution of long-horizon shapers suggests a more diverse and balanced approach to viral antigen binding. We hypothesise that this strategy helps to preserve robustness against viral mutations. By maintaining a more even distribution across energy levels, these antibodies may be less susceptible to viral escape.
In contrast, the clustering behaviour we observe in shorter-horizon antibodies indicates a more specialised strategy. By concentrating on amino acids at the extremes of the binding energy spectrum, these antibodies may achieve strong immediate binding but potentially at the cost of long-term robustness. However, while this analysis hints at the robustness of long-term shapers, it does not fully explain the shaping behaviour we observed in our previous results. In the next section, we investigate the distribution of amino acids within specific binding poses.
11 100
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Figure B. Distribution of amino acids in myopic antibodies and shapers. The antibodics are optimised for N 30 steps using different viral escape horizons H. Longer horizon shapers push the amino acid distribution closer to a uniform distribution.
C. Influence of Antibody Shapers on Binding Poses
In the Absolut! framework (Robert et al., 2022), binding poses are defined as sets of interacting residue pairs between the antibody and the antigen. The binding energy of a pose is calculated by populating these residuc locations with the amino acid sequences of both the antibody and the virus and then summing the pairwise interaction energies defined by (Miyazawa & Jernigan, 1999). Absolut! considers a vast number of possible poses (on the order of 10") and determines the overall interaction energy as the energy of the minimum pose, refer to Appendix D for more details. Importantly, only small part of the viral sequence contributes to this minimum energy pose.
As both the virus and the antibody mutate during our optimisation process, the lowest energy pose can change. To capture these dynamics, we introduced the concept of a pose matrix: a 20 x 20 matrix with one entry for each possible pair of amino acids. One dimension corresponds to the antibody amino acids, and the other to the viral amino acids. The entries in this matrix represent the number of interactions between the specific amino acid pairs the lowest energy pose for the binding configuration between an antibody and an antigen.
Figure C. presents average pose matrices from multiple optimisation runs of both myopic antibodies and long-horizon shapers. We observe two key trends. First, as viral escape steps increase (top row vs bottom row), the pose matrices become more "diffused". This is expected, as the virus explores more "pose possibilities" through mutations during escape. Second, as the horizon of antibody optimisation increases, the poses also become more "diffused"" This is particularly interesting, as all antibodies have the same number of mutations regardless of the horizon, suggesting that this diffusion might relate to the increased robustness of shapers.
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ADIOS: Antibody Development via Opponent Shaping
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Figure C.I. Influence of antibody shapers on binding poses. Average pose matrices between antibodics optimised using different horizons and the virus at various stages of its escape. The escape steps increase from left right, and the horizon inereases from top bottom. The full grid of matrices with more antibody horizons and virus escape steps is available in the Supplementary Information. Figure C.2. b, e Aggregated sum pose matrices w.r.t antibody (b) and w.r.t the virus axis (c). The plots show change in the interaction counts in the poses from the viral escape step to 100. Red indicates decrease in the interaction count and green increase.
To further understand these pose dynamics, we aggregate the pose matrices along the antibody axis (Figure C.1b) and the virus axis (Figure C.Ic). These figures show the change interaction counts between viral escape steps 0 and 100. Figure C.lb shows that as the virus escapes it includes more of the antibody's lowest binding amino acids (particularly K, Lysine) in the pose. Notably, long-horizon shapers, especially H 100 shapers, most effective at preventing this increase in K (Lysine) interactions. Furthermore, Figure C. shows another viral escape strategy, where the virus removes its high-binding amino acids (Isoleucine) and M (Methionine) from the pose. Again, H = 100 shapers are most successful in counteracting this trend, although they cannot completely prevent it.
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ADIOS: Antibody Development via Opponent Shaping
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Figure C.2. Full grid of pose matrices. They represent the average pose interactions between myopic antibodies or antibody shapers optimised with different horizons and viruses at different stages of their escape.
Based on these observations, we hypothesise that the shaping ability of = 100 shapers relies on two main mechanisms. Preventing the virus from including the antibody's lowest binding amino acids in the pose, and inhibiting the virus from removing its own high-binding amino acids from the pose. These strategies constrain the viral escape trajectories, making the resulting viral variants more susceptible antibody binding in general. While these results are specifie to Absolut! binding simulator, they demonstrate that the behaviour of antibody shapers is both explainable and intuitive. This work serves as proof of concept, showing that opponent shaping techniques can optimise antibodies to more effectively prevent viral escape.
D. Binding Function
In general, ADIOS is independent of the choice of the binding function B A. A. -> R. In our work, we rely on the Absolut! framework (Robert et al., 2022) to implement the binding function. In this section, we mathematically formalise the binding energy calculation that Absolut! uses. For further explanation, readers are recommended to refer to the original Absolut! paper (Robert et al., 2022).
For two given protein structures, there are many possible joint configurations. Each of these joint configurations yields an energy. The configurations which are associated with lower energy will require more external energy to cause the system to leave that state, meaning in turn that they are more stable. If the configuration is sufficiently stable, this may be referred as binding pose.
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ADIOS: Antibody Development via Opponent Shaping
In Absolut, poses are represented as pairs of residues² which are adjacent each other in that pose. In particular, the pairs may be from the antigen to the antibody, or from the antibody to itself. We define the space of possible poses t:
T NNNN 2
Where N,, and N₂ are taken to be the set of integers up N, and No. respectively.
The energy of a complex of a virus E A. and an antibody E A, in given pose (6*xo, .(xx) E & is defined by sum of the energies of each adjacent residues. The energy between a residue pair is determined by which two amino acids it contains, given by a symmetric interaction matrix M : A x A + R, which is determined experimentally (Miyazawa & Jernigan, 1999).
We then define the energy of a single pose to be:
(a, by (xx (axa), M)= M)
Σ M(va,az)+ +
M az)
(K))
Finally, given a set of poses S C $ the binding strength is:
B(u, a) = a,,
a; M) = min (v,,a; PES
(4)
Absolut! generates S through two-step process. First, Absolut! discretises given structure of the virus v (or any antigen) which is taken from the PDB (consortium, 2018). Second, Absolut! does a brute-force search over possible (discretised) poses for an antibody a to join to the viral structure. The exact details are not necessary for this paper, we refer interested readers to the original paper.
However, we find that Absolut! generates more poses than we require. Since the energy function, E' is a minimum over poses, certain poses contribute far more than others. In particular, if a pose & tends yield higher energies, so E(a, b; o, M) is relatively large, it will have little impact on the result of B.
To give more concrete example, for this paper, we use the dengue virus antigen (Lok et al., 2008). Absolut! gives R 1.5 million poses for this structure. Absolut! also comes with x 20 million real-world antibody sequences. When using the base dengue sequence as the antigen, across the 20 million binding calculations only 1027 binding poses are ever the minimum. Furthermore, the relevance of each pose drops exponentially. The most relevant pose accounts for 20% of binding configurations, and by using the top 100 poses one would get the exact same result for binding in 95% of antibodies. This gives us a way to make the computation 1000 times faster? for negligible accuracy drop for this particular antigen sequence.
However, this leads to more errors as soon as we change the viral antigen sequence. Looking at the particular poses which lead to binding reveals another way to cut down on the total number of poses: all of the poses contain at least 18 pairs of residues. As the interaction matrix M is strictly negative, having more pairs of residues always makes the binding energy of a pose lower, meaning it is more likely to be where binding occurs. Out of the original 1.5 million poses, only approximately 37 thousand (1 in 40) contain 18 or more pairs of residues. When using only these residues, see no differences across any of the evolutionary simulations. It is possible that pose with 17 or less pairs is the dominant one for some antigen with antibody a, but if so, then such pairs appear to be extremely rare.
Using these methods of pruning poses gives us two subsets of the original set of poses, a larger one which almost exactly matches performance, and another which sometimes differs, but is much faster to compute. We refer to these as the high-resolution and low-resolution binding simulators, respectively. Note that for the low-resolution binding simulator, the more mutations the virus undergoes, the less accurate it becomes. Furthermore, we also do binding to the antibody anti-target, to- To account for this, we compute the relevant poses for this anti-target too.
When running dengue virus experiments, we always train with the low-resolution binding simulator, then perform "verifi- cation" with the high-resolution one, and these are the results we report throughout the paper. For the other viruses and the bacterium we run "verification" in differently initialised instantiation of the low-resolution simulator. The reason is
A single amino acid position on protein
In practice, the difference is closer to 10, 000, likely due to the GPU having to move less data.
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ADIOS: Antibody Development via Opponent Shaping
twofold. Firstly this enables us run many more evolution experiments. Secondly, this mimics the real-life process of transferring out of simulation the real world. By showing transfer from the low-resolution binding simulation the slower, high-resolution binding simulation, we use and that any result will not disappear as soon more accurate simulation is used. We emphasise that Absolut! does not represent an accurate model of antibody binding. It is instead a toy simulation to demonstrate our methodology. For example, we do not expect our framework when used with this simulation model to yield highly effective, superior antibodies for real-world applications.
demonstrate that our results are not extremely specific to the exact simulation
E. MDP for the Virus-Antibody Game
We formalise single interaction round between antibody and virus the finite-horizon Markov Decision Process M:
M (S, A", A P. R. H).
State space: S No x ANa, where a state & = (v, a) is the pair of viral (v) and antibody (a) amino-acid sequences.
Action spaces (chosen simultaneously):
(3 = A (* A
Transition kernel (episode terminates after one step):
P(s' 8 "a,a",a" a²) = lyma.
8x is terminal.
Reward vector (Ry, Ra). Given joint action (a", aa)) in state s,
Ra(s,a", d²)) 1B(a", a²) B(t,, - D(a,,tt),
Ry = -
Initial-state distribution μ puts mass on the wild-type virus and the initial antibody candidate: (0, ao)
Because this is single-step MDP, the return equals the immediate reward R and the discount factor is irrelevant.
20


Reviews:
[{"review_id": "TUyctsTImj", "reviewer": "Reviewer_Y7Ln", "summary": "The manuscript presents ADIOS as a method for optimizing antibodies while considering viral escape. In essence, the proposed approach is a simplified version of adversarial training. Experiments were conducted using a binding prediction method (Absolut!), and the results indicate that the proposed method outperforms the one that does not account for viral escape.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your review. Below we address your concerns and questions:\n# Extra Experiments\nFollowing your feedback, we have now conducted extra experiments with 3 additional viruses: flu, MERS and the West Nile virus. In all of these cases, our experiments show that the antibody shapers generated by ADIOS successfully shape the viruses, limiting viral escape. We have now added these results to the paper, alongside correcting the enumeration of appendix figures.\n# Sampling Outside of Absolut!’s Distribution\nThank you for bringing up the important problem of a binding model's distribution, or in other words its domain of applicability. We have carefully considered this problem and, in fact, one of the main reasons we decided to use Absolut! as our binding simulator is to avoid sampling outside of the distribution.\n\nAs we explain in Section 3 of our paper, sequence-based ML models like Mason et al., 2021 (https://doi.org/10.1038/s41551-021-00699-9); Lim et al., 2022 (https://doi.org/10.1080/19420862.2022.2069075); Yan Huang et al., 2022 (https://doi.org/10.3389/fimmu.2022.1053617), as data-driven predictive models struggle to generalise beyond their training distribution and are therefore not suitable for our application which explores novel viral mutations.\n\nHowever, Absolut! is a mechanistic model (not data-driven) that we use as an oracle for querying the binding strength of new sequences. As we write in Section 3, “For any antibody-antigen pair, Absolut! enumerates possible binding poses and computes their energy using the Miyazawa-Jernigan potential” This process doesn’t have a training distribution or a domain of applicability and is well suited to our application which requires mutating both the virus (antigen) and the antibody.\n# Real-World Applicability\nWe appreciate the challenges of binding prediction, and acknowledge that using Absolut! (or any other simulator) comes at a cost of real-world applicability. However, it has been shown that ML models that perform better on Absolut! perform well on real-world datasets too (https://doi.org/10.1038/s43588-022-00372-4). Besides, using more realistic models is extremely expensive and cheaper data-driven models are not suitable due to their limited domain, making Absolut! an ideal choice for the current work.\n\nMore broadly, breakthroughs in biology have come from building on previous computational works with initially limited real-world applicability. For example, the development of effective mRNA vaccines has been credited at least in part to RNA Folding algorithm. Original papers such as Nussinov and Jacobson, 1980 (https://doi.org/10.1073/pnas.77.11.6309) and Zucker and Stiegler, 1981 (https://doi.org/10.1093/nar/9.1.133) laid the foundations to more modern heuristics for RNA structure prediction and therefore therapeutics applications.\n\nWe are currently working on extensions to this work,  where instead of using Absolut! as our binding simulator we use more complex models. These include AlphaFold3 (and similar), to predict the changing structure of antibodies and viruses, as well as protein-protein docking models to estimate the binding strength based on the structure. We also account for additional factors that influence viral escape. However, Absolut! is a necessary first step to prove that ADIOS is feasible and effective. Due to its speed, it is also a great testbed for developing methods which can then be scaled to more computationally expensive models. \n# Answers to Questions\n1. In Figure 2d, we show the number of binding samples required to achieve a given antibody fitness for different shaping horizons. In Table 1, we report how long a single binding sample takes in our GPU-accelerated implementation: $2.1 ×10^{−4}s$. As the binding calculation is the main computational cost, a single run takes up to 4000s ~ 1h. For Figure 2d we chose to show binding samples on the x-axis (instead of runtime) because it provides a reference point for future work where one will want to use a more expensive (i.e. slower) binding simulator. Would it be helpful to discuss in the paper how binding calculation is the main computational cost? Or show a plot with the computational speed of our method (on our hardware) on the x-axis?\n2. Our binding simulator, Absolut!, is not a pre-trained predictive model but a mechanistic one instead. Absolut! applies the same scoring computation to any possible binding pose to calculate the binding energy, a priori, there is no one pose where the binding calculation is systematically more “correct”. Thus, we hypothesise that mean correctness of the binding score should not systematically change as we mutate the sequences and/or change binding poses.\n# Conclusion\nWe value and respect your critique, but we believe it is in large part due to a misunderstanding of Absolut!. If you disagree, please let us know why! We are always looking to improve the quality of our work. Otherwise, we would appreciate a re-evaluation of your review score.", "claims_and_evidence": "One major concern with the method is that the optimization results are evaluated using Absolut!, while the proposed method may generate data that lies outside of Absolut!’s distribution. Therefore, an improvement in the results measured by Absolut! does not necessarily reflect an actual enhancement in the final antibody. It is highly likely that the resulting sequences fall outside the distribution of Absolut!, which is, in fact, a key challenge in this field. As an application-oriented paper, such considerations should be addressed. Thus, the results presented in the manuscript cannot conclusively demonstrate that the proposed method leads to antibodies with improved properties in real-world scenarios.", "methods_and_evaluation_criteria": "The performance of the proposed method is evaluated using Absolut!, which does not demonstrate the method's applicability in real-world scenarios. Additionally, the proposed method is tested with only one type of antigen, making it impossible to conclude that the method would be effective for other antigens.", "theoretical_claims": "There's no theoretical claims in this manuscript.", "experimental_designs_or_analyses": "I have reviewed all the experimental designs, and I found issues with both the evaluation metrics (the computed binding scores) and the data (only one type of antigen was used). These limitations prevent the proposed method from demonstrating its performance and generalizability in real-world scenarios.", "relation_to_broader_scientific_literature": "Antibody optimization is a critical area of research, with significant implications for drug and vaccine design, while viral escape remains a major challenge in vaccine development. Numerous efforts have been made to build antibody binding prediction models, but none have achieved perfect accuracy. Although the motivation behind this paper is sound, the method and experimental design fail to address the key challenges encountered in real-world applications.", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "Strengths: The acceleration of Absolut! contributes to the broader user community of Absolut!.\n\nWeaknesses:\n\n1. The novelty of the algorithm is limited.\n\n2. In terms of paper presentation, the figures in the supplementary material should be renumbered rather than continuing the numbering from the main text.", "other_comments_or_suggestions": "No other comments", "questions_for_authors": "1. What is the computational speed of the proposed method?\n2. How is the correctness of the \"binding\" prediction determined when binding poses change?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "xRFrAU0pB1", "reviewer": "Reviewer_NEd6", "summary": "This paper introduces a long-term strategy using opponent shaping, a concept from game theory and reinforcement learning, to design antibodies that not only bind effectively to the virus but also influence the virus's evolutionary trajectory to make it less dangerous over time.\n\nThe algorithm involves three main components:\n- Virus-Antibody Game: Models the interaction between the virus and the antibody as a two-player zero-sum game.\n- Simulated Viral Escape: Simulates how the virus evolves to escape the antibody over time.\n- Antibody Optimization: Optimizes the antibody to perform well against both the current virus and its future evolved variants.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your review!\n\nAs we understand, you have three primary concerns:\n1. Lack of discussion of antibody design methods\n2. Unclear how Myopic Antibodies are generated\n3. No comparison to other reinforcement learning algorithms\n## 1. Discussion of Antibody Design Methods\nYou are completely correct, and we have updated the paper to include references to more antibody design methods. The reason we didn’t include such references originally is because ADIOS is somewhat agnostic to the choice of the antibody optimization algorithm used, the primary difference is that ADIOS emphasises the importance of accounting for the adaptation of the virus using simulated evolution. However, it is important to discuss the breadth of different antibody design methods in our related work section, which we have now rectified with additional references. In particular, we now reference energy-based antibody optimization methods (https://doi.org/10.1371/journal.pone.0105954, https://doi.org/10.1371/journal.pcbi.1006112), including optimization methods based on GFlowNets (https://doi.org/10.48550/arXiv.2411.13390), sequence-based language models (https://doi.org/10.1093/bioinformatics/btz895, https://doi.org/10.1038/s41598-021-85274-7) and structure-based approaches relying on GNNs (https://doi.org/10.48550/arXiv.2207.06616) and diffusion models (https://doi.org/10.48550/arXiv.2308.05027).\n## 2. Generation of Myopic Antibodies\nThe Myopic Antibodies are generated in the exact same way as the other shaper antibodies, but with a horizon of 0 in the objective. We now recognise that our explanation of this was unclear, as we didn’t explicitly state that we also optimize myopic antibodies in the same way we optimize shapers. We have now changed line 233 from “To optimise antibody shapers, we …” to “To optimise both shapers and myopic antibodies, we …” to rectify this. Thank you for bringing this to our attention!\n## 3. Comparison to RL Baselines\nWe don’t compare against several baselines because the core question of our current work is whether it is possible to apply opponent shaping to viruses and design effective antibody shapers, which we have now successfully demonstrated.\n\nHowever, your suggestion is a natural follow-up question - given that we can shape viral evolution, what algorithms (PPO, Rainbow DQN, etc.) allow us to create the optimal antibody shapers in the outer loop? This becomes significantly more viable to test due to our enormous speed up of Absolut! (x10,000), making fast, full training rollouts on the GPU possible. Still, there are some challenges in adapting a few of the works you mentioned to our problem setting. In particular, a lot of opponent shaping literature, such as LOLA and AAA, rely on assumptions suitable for RL-trained/humanlike agents, but less suitable to biological adaptive agents, such as viruses, which do not perform value iteration but evolve instead.\n## Back-Testing on Historical Data\nThank you for this suggestion. We fully agree with you! We are already planning on doing the back-testing, but it requires a much higher fidelity simulation of both binding and viral escape. As a result, we are working on extensions to this work, where instead of using Absolut! as our binding simulator we use more complex models. These include AlphaFold3 (and similar) to predict the changing structure of antibodies and viruses, as well as protein-protein docking models to estimate the binding strength based on the structure. Using other predictive models like EVEscape (https://doi.org/10.1038/s41586-023-06617-0), we also account for additional factors that influence viral escape. We can retrospectively evaluate the ‘Myopic’ case by using historical antibodies. I.e. we can show that by setting up our simulator to a state equivalent to the beginning of the pandemic and simulating viral escape as a response to some of these real-world antibodies, the real viral strains observed later in the pandemic are ‘in distribution’ of our simulator’s outputs. That would show the simulator is ‘trustworthy’, and successfully running ADIOS in it would indicate real-world applicability.\n## Additional Experiments\nTo better evaluate ADIOS we have now also conducted extra experiments with 3 additional viruses: flu, MERS and the West Nile virus. In all of these cases, described in the updated manuscript, our experiments show that the antibody shapers generated by ADIOS can successfully shape the viruses. The results of these experiments are now added to the paper as well.\n## Conclusion\nHopefully, we have addressed all your concerns! If we did, would you consider raising your score for our paper? If not, please let us know any further questions or suggestions. We are very focused on making this paper as high quality as possible, so we really appreciate your feedback.", "claims_and_evidence": "Clams are clear.", "methods_and_evaluation_criteria": "Yes, they make sense.", "theoretical_claims": "No theoretical claims in this paper.", "experimental_designs_or_analyses": "I am not sure how Myopic Antibodies are generated. I believe we could have more baselines to be compared with. For example, PPO, rainbow DQN and even LOLA (https://arxiv.org/abs/1709.04326), AAA (https://arxiv.org/abs/2406.14662).\nI also think since we already have some trajectories of the virus mutation. We can do back test on these trajectories and see if \"simulates how the virus evolves to escape the antibody over time\" really have a good prediction and the designed antibody would really perform good on the virus in the \"future\" in back test.", "relation_to_broader_scientific_literature": "Medical science, drug discovery.", "essential_references_not_discussed": "The paper should also discuss more related work about antibody design such as Biological Sequence Design with GFlowNets, Reinforcement Learning for Sequence Design Leveraging Protein Language Models and more...", "other_strengths_and_weaknesses": "The paper is overall clear to me.", "other_comments_or_suggestions": "I think more discussion about antibody design methods and more baseline would make the paper better. I am not sure how Myopic Antibodies are generated. I believe we could have more baselines to be compared with. For example, PPO, rainbow DQN and even LOLA (https://arxiv.org/abs/1709.04326), AAA (https://arxiv.org/abs/2406.14662).\nI also think since we already have some trajectories of the virus mutation. We can do back test on these trajectories and see if \"simulates how the virus evolves to escape the antibody over time\" really have a good prediction and the designed antibody would really perform good on the virus in the \"future\" in back test.", "questions_for_authors": "See Other Comments Or Suggestions", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "H2KYhh12UY", "reviewer": "Reviewer_EjC1", "summary": "The authors consider a very interesting and important problem of antibody development against viral strains which would control and defend against newer strains evolved from this one. So, the antibody development problem is viewed as a sequential decision making problem which is modeled as a two player zero-sum game between the antibody developer and the viral strain. The authors call their approach ADIOS (Antibody Development vIa Opponent Shaping) and the non-myopic antibodies they design as 'shapers'. They label their approach as a meta-learning problem where the outer loop is the antibody (shaper) design process and the inner one is the virus' adaptive (evolutionary) response. To demonstrate their approach, the authors build a simulator using the Absolut! framework.\n\n**Update after rebuttal**\nBased on the authors' responses to my review and the other reviews, I would like to retain my overall recommendation. I have highlighted my concerns and response to rebuttal in my comments.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your detailed review! We address everything possible within the character limit:\n## Accuracy + Real-World Utility of Absolut!\nTo address the real-world utility of our simulator we quote the original Absolut! paper: “Of note, Absolut! is neither suited nor designed to directly predict if and where an antibody sequence binds to an antigen in the real world. Rather, Absolut! has been developed with the premise that a successful ML antibody-binding strategy for experimental (real world) datasets should also perform well on synthetic datasets (and vice versa)”. Hence Absolut! is not designed for direct real-world predictions, but it has been shown that ML models which perform better according to Absolut! also perform well on real-world datasets. This makes Absolut! ideal as a testing ground for ADIOS. We reference this in Appendix Section C, where we explain Absolut! in more detail. To make this more clear, we can incorporate an additional explanation in the background section?\n\n## Notation and MDP Definition\nWe note that the functions $R_v$ and $F_v^H$ were not defined in the algorithms; we have therefore added their definitions. As for the formal definition of the MDP, we agree and have added a section detailing the MDP to the methods section.\n## Answering Questions\n1. Simulating viral evolution is generally challenging and computationally involved. However, recent works, such as EVEscape (https://doi.org/10.1038/s41586-023-06617-0) have had success forecasting viral mutations, so it is possible to have some predictive power, which is likely to increase as models and data improve. In our viral escape simulation, the virus responds to two main factors, the antibody and the viral target. In more accurate simulators you might want to account for other factors too, for example in real life the evolution will depend on: how chronic the virus is, what is the percentage of people that will be infected, and the mortality. To keep our approach computationally feasible we omit some of these factors.\n2. See above.\n3. The key consideration in antibody design is the specificity of the antibody, i.e. does it bind to the correct antigen and nothing else (https://doi.org/10.1186/s12929-019-0592-z). In ADIOS we just consider a region of the antibody sequence which is responsible for the specificity, the CDRH3 region. Designing the rest of the antibody sequence will affect many developability parameters in the human body such as PK, half-life, and effector functions, which are also important for antibody design but engineering these is independent of the specificity. Typically, the CDRH3s can be grafted to antibody scaffolds with good profiles of other properties, so our approach is suitable for the specificity question and selective pressure it creates.\n4. The development of antibody therapeutics in the US on average takes about 8 years until the drug receives an FDA approval (https://doi.org/10.4161/mabs.2.6.13603). Viral evolution is very different between viruses, for example, RNA viruses (e.g. HIV, SARS-Cov2)  evolve faster than DNA viruses (e.g. Herpesvirus). In general, a higher mortality rate limits viral evolution and needs a faster immune response, while a higher R0 means more evolution opportunities for the virus given the higher number of infections. \n5. See the section on Absolut! above.\n6. In this work we mainly focus on viral escape potential and how easily targetable the virus is. However, in future work, with higher fidelity simulators we can model other factors such as mortality or co-morbidities.\n7. In this work we assume a fixed sequence length for the antibody and the virus, we explain this in more detail in Section 4.1. An extension of this work where we allow insertions and deletions to the sequence is certainly possible, one way to adapt the action space to allow this would be to have a max sequence length for the insertions and an additional ‘None’ token for the deletions.\nProtein structure prediction models, such as AlphaFold3 (AF3), would be useful to validate the feasibility of structures resulting from the mutated sequences of antibodies and antigens. However, the action space would remain in the sequence space, and we could just include an extra ‘structure check’ of the sequence by passing it through AF3.\n8. Yes, there can be multiple anti-targets in our model, but in our experiments, we stick to 1.\n9. We don’t define the antibody’s policy function explicitly but we can easily add that if you think it’s helpful.\n10. Figure 2b and Figure 2c show viral and antibody evolution plateauing. Eventually, an equilibrium must be reached, however, this may take an extremely long time. Do you think it would be interesting to run an ultra-long horizon experiment, to better understand the behaviour?\n## Conclusion\nWe appreciate the interest you have shown in our work! Is there anything we could change for you to raise your review to a “strong accept”? Also, any future work ideas would be great too!", "claims_and_evidence": "The authors present a new approach for antibody design and demonstrate it using a simulated environment (based on work from literature). They do not make any theoretical claims.", "methods_and_evaluation_criteria": "The authors do not use any benchmark datasets, but they use a simulator to show the efficacy of their approach. This simulator is based on other published work, but it would be good if the authors can add a note on the accuracy and real-word utility of this simulator. They do mention that their simulator is based on simplified models, but not its practical implication. Can they be used to generate a good proof of concept?", "theoretical_claims": "There are no theoretical claims in this paper. The authors propose a new approach, which is actually a novel combination of existing approaches to a new problem.", "experimental_designs_or_analyses": "The authors perform several experiment using a simulator and also provide detailed analyses of their results.", "relation_to_broader_scientific_literature": "This paper provides a novel way of considering antibody design (to the best of my knowledge), thereby providing interesting downstream research opportunities for the community.", "essential_references_not_discussed": "I am not aware of any essential references that have been missed.", "other_strengths_and_weaknesses": "Strengths:\n1. The paper is very well written and the authors' approach is clearly explained.\n2. The approach presented by the author provides a way to try several other ideas from multi-objective RL and game theory in antibody design and thus is a useful research contribution.\n\n\nWeaknesses:\n1. Novelty: While the application is definitely novel to the best of my knowledge, the various components in the approach are taken from literature.", "other_comments_or_suggestions": "1. It would be good to describe the variables used in the algorithms where they are mentioned. For example $R_V$ in Algorithm 1, $F^H_{\\hat v}$ in Algorithm 2.\n2. It would be useful to the readers if the authors formally define the two player game including the various state, action and observation spaces, transition probabilities, observation functions, payoff functions, horizon and discounting used (if any).", "questions_for_authors": "1. How difficult is it to simulate virus evolution/mutation. Doesn't it depend on factors beyond antibodies, such as possibly another (non-human) host etc.?\n2. Is it computationally involved to simulate viral evolution? Are the potential trajectories tractable?\n3. What are the practical considerations involved in antibody design? Does the current approach account for effect of antibodies on human beings?\n4. What are the time scales for evolution of viruses and development of new antibodies? How do these vary with respect to the disease progression timescale, severity/mortality rate of the disease, R0 etc.?\n5. How accurate is the Absolut! framework based environment in estimating the binding strength of protein-protein interactions? Do these work for novel antibodies?\n6.  When considering the potential harmful effects of future variants of viruses, are co-morbidities taken into account or just escape potential?\n7. Is the action of the virus evolution and or antibody generation composes of generating a fixed-length amino-acid sequence at each time step or can this be a variable length sequence with some maximum length? Does protein folding play a role in designing feasible structures? The authors mention this as a future step in Section 7, but it would be interesting to note how will this affect the action space itself.\n8. In equation (1), can there be multiple anti-targets for an antibody?\n9. Have the authors explicitly defined a policy/strategy function, which is a mapping from the current state for the antibody design to a new antibody design?\n10. Is some kind of an equilibrium reached by the authors' algorithm? Is an equilibrium expected? If so, what would be its characteristics?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {"ethical_review_concerns": "The authors already highlight potential concerns in their Impact Statement on Page 9."}}, {"review_id": "YBY6DvU5w7", "reviewer": "Reviewer_kBGh", "summary": "The paper introduces ADIOS (Antibody Development via Opponent Shaping), a meta-learning framework that designs antibodies capable of both neutralizing current viral strains and influencing viral evolution to favor less dangerous variants. By framing antibody-virus interactions as a two-player zero-sum game, the method uses nested optimization loops: an inner loop simulating viral escape and an outer loop optimizing antibodies against long-term viral adaptation. ADIOS is implemented within the Absolut! framework, leveraging GPU acceleration for a 10,000x speedup. The authors demonstrate that ADIOS-optimized antibodies, or \"shapers,\" outperform conventional myopic antibodies in long-term efficacy, shaping viral evolution to produce more targetable variants.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for your thorough review and feedback! We appreciate it a lot. We are glad that you thought that applying opponent shaping to antibody design is \"a good contribution that extends beyond traditional ML-based antibody optimisation\"!\n\n# Answering Questions\n## 1. Evaluating ADIOS on Other Viruses\nWe agree that testing ADIOS against a wider range of viruses would help further validate our claims. To address this, we have conducted additional shaping experiments with three more viral antigens: the flu, MERS, and the West Nile virus. For all three, our experiments show that the antibody shapers generated by ADIOS successfully shape the new viruses, limiting viral escape. Interestingly, the computational trade-offs of shaping horizons are dependent on the virus but follow the same main trends. We have added these new results to the paper.\n## 2. Sensitivity of ADIOS to Hyperparameters\nBased on our experiments ADIOS is not very sensitive to choices of different evolutionary parameters. As an example, we experimented with different mutation rates of the virus and found qualitatively similar results. To test the transferability of our results we also designed the external pressure experiment, the results of the experiment are in Figure 4. This result demonstrates the robustness of ADIOS to a domain shift. Even with an added pressure of an external antibody we can still see a shaping effect induced on the virus by the long horizon shapers. Additionally, the new results of the extra experiments on 3 other viruses show that ADIOS achieves shaping and limits viral escape for all the selected viruses, not only Dengue. Overall, this demonstrates that ADIOS is not sensitive to the choice of evolutionary parameters.\n## 3. Incorporating Dynamics\nAbsolut! already allows us to incorporate an aspect of ‘dynamics’, as it tests binding over a larger number of potential poses, and the antibody structure is permitted to change between poses. The minimum energy poses change dramatically throughout the evolution of antibody/antigen, and we study the influence of shapers on binding poses in Appendix B.\n\nThat said, you are completely correct about the static structure of the antigen which is used to generate these binding poses in Absolut!. In future work, we plan to directly account for the changes in the antigen structure by using structure prediction models like AlphaFold3 (AF3), which can now accurately predict the structure of an antibody-antigen complex. We are building a binding simulator that combines the AF3 structure with a protein-protein docking score to achieve a more accurate binding affinity score. We plan to use this new binding simulator which accounts for antigen structure changes, instead of Absolut!, to further evaluate the ADIOS framework and demonstrate its real-world applicability.\n## 4. Real-World Validation\nWe want to conduct a real-world evaluation of ADIOS in the new simulator mentioned above by using data from past COVID variants. All SARS-CoV-2 pandemic strain sequences are available through GISAID (https://gisaid.org/). Additionally, a dataset of COVID antibodies is also available through CoV-AbDab (https://doi.org/10.1093/bioinformatics/btaa739). We could retrospectively evaluate the ‘Myopic’ case by using these antibodies. I.e. we can show that by setting up our simulator to a state equivalent to the beginning of the pandemic and simulating viral escape as a response to some of these real-world antibodies, the real viral strains observed later in the pandemic are ‘in distribution’ of our simulator’s outputs. That would show the simulator is ‘trustworthy’, and successfully running ADIOS in it would indicate real-world applicability.\n\nGoing beyond simulation, we can validate ADIOS using bacteria phages, i.e. viruses that infect bacteria, and run shaping experiments in a wet lab with mutating bacteria and bacteria phages. Co-evolving bacteria phages (https://doi.org/10.1073/pnas.2104592118) would be a good real-world test ground for ADIOS, that is experimentally tractable and low-risk. ADIOS’s inner loop would correspond to bacteria phage evolving while the outer loop would be evolving the actual bacteria.\n## 5. ADIOS for Cancer Therapy\nMonoclonal antibodies (mAb) are a common therapy used for cancer treatment. The way to adapt ADIOS to cancer therapy would be to still optimise antibodies in the outer loop, this time these would correspond to mAb antibodies. Instead of viral escape simulation in the inner loop, we would simulate the evolution of cancer cell’s growth factor receptors. The goal would be to design antibodies that shape cancer cells into cells that don’t proliferate well. We have added a short phrase to our manuscript suggesting this as a potential domain of application.\n\nAgain, thank you for your detailed feedback! Hopefully, we have addressed all your concerns. If we did, could you consider updating your score for our paper?", "claims_and_evidence": "- The paper claims that ADIOS-optimized antibodies shape viral evolution toward weaker, more targetable variants. This claim is supported through simulation results demonstrating that shapers lead to viruses more susceptible to a broader range of antibodies.  \n- The claim that ADIOS outperforms myopic antibodies in long-term protection is substantiated by comparative evaluations, showing superior performance over extended evolutionary trajectories.  \n- The authors suggest that ADIOS has applications beyond antiviral therapy, including antimicrobial resistance and cancer treatment. While plausible, this claim remains speculative and would require further validation in these domains.  \n- The paper asserts that its GPU-accelerated JAX implementation of Absolut! achieves a 10,000x speedup. The performance comparison is well-documented, demonstrating substantial computational gains.", "methods_and_evaluation_criteria": "- The method is evaluated within the Absolut! simulation framework, which is appropriate for modelling antibody-virus interactions.  \n- The evaluation compares ADIOS to myopic antibodies, demonstrating superior long-term efficacy. However, additional comparisons against existing evolutionary models would further validate ADIOS’s impact.  \n- The paper explores the trade-offs between short-term efficacy and long-term viral shaping, providing valuable insights into practical applications.", "theoretical_claims": "- The theoretical framing of ADIOS as a two-player zero-sum game is well-grounded in reinforcement learning and opponent shaping literature.  \n- The meta-learning approach to optimising antibodies across viral evolutionary trajectories is effectively justified.", "experimental_designs_or_analyses": "- The experimental setup effectively evaluates the model’s ability to shape viral evolution and sustain long-term efficacy.  \n- The choice of the dengue virus as a test case is reasonable, though additional validation on other viruses would strengthen the study.  \n- The paper provides clear analyses of the computational trade-offs in shaping horizons, offering practical guidance for deploying ADIOS in resource-constrained settings.", "relation_to_broader_scientific_literature": "- The work builds on prior research in computational antibody design, reinforcement learning, and viral escape modeling.  \n- The integration of opponent shaping into antibody therapy design represents a good contribution that extends beyond traditional machine learning-based antibody optimisation.  \n- The study effectively situates ADIOS within the broader context of viral adaptation and therapy resistance, demonstrating its relevance to long-term immunotherapy strategies.", "essential_references_not_discussed": "- The paper sufficiently engages with prior work on opponent shaping, reinforcement learning, and antibody-virus interactions.", "other_strengths_and_weaknesses": "- Strengths:  \n  - ADIOS introduces a novel approach to antibody design by explicitly modeling viral adaptation, moving beyond conventional myopic strategies.  \n  - The study provides empirical validation, demonstrating that shapers outperform myopic antibodies in long-term efficacy.  \n  - The GPU-accelerated JAX implementation significantly improves computational efficiency, making large-scale evolutionary simulations feasible.  \n  - The exploration of shaping trade-offs provides valuable insights for real-world deployment.  \n  - The method has potential applications beyond virology, including antimicrobial resistance and cancer treatment.  \n\n- Weaknesses:  \n  - While the study presents compelling results, additional validation on a broader range of viruses would strengthen its generalizability.  \n  - The claim that ADIOS is applicable to antimicrobial resistance and cancer therapy remains speculative without experimental evidence.  \n  - The evaluation focuses primarily on simulation results, and real-world validation would be necessary to confirm ADIOS’s practical impact. \n  - The authors assume that the structure of the antigen does not significantly change over the course of viral escape.", "other_comments_or_suggestions": "NA", "questions_for_authors": "- Have you considered evaluating ADIOS on other viruses beyond dengue to test its generalizability?  \n- How sensitive is ADIOS to different choices of evolutionary parameters in the viral escape simulation?  \n- How would you incorporate dynamics (going beyond the assumption of static antigen structure), to improve accuracy?  \n- Although it might be difficult, how would go about real-world validation?  \n- How do you envision ADIOS being applied to cancer therapy, and what adaptations would be required for such use cases?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: The paper "ADIOS: Antibody Development via Opponent Shaping" presents a novel approach to designing antibody therapies that not only defend against current viral strains but also shape viral evolution toward less harmful variants. This is achieved through a meta-learning framework involving viral evolution simulation and antibody optimisation. The method's novelty lies in its game-theoretic approach combined with mechanistic modelling using Absolut!. The Absolut! software from Victor Greiff's lab takes PDB antigens, converts them into lattice representation with integer positions together with CDR3 Amino Acid sequences, and computes their best binding around a lattice antigen, and then generates features of antibody-antigen bindings directly usable for downstream ML such as in this paper. Notably Absolut! is a mechanistic model and not an ML model, which seemed to cause some confusion with one reviewer in particular. The work is significant in enhancing the understanding of long-term immune strategies, with potential implications for antimicrobial resistance and cancer treatment.

The paper received mixed reviews initially, with scores of 2, 3, and 4. Reviewers highlighted the rigorous methodology and potential significance of the work, though they expressed concerns regarding the real-world applicability and comparisons with existing methods. In the discussion, the authors provided additional experimental data, addressed misunderstandings related to the Absolut! framework, and conducted extra experiments on three more viruses. This effort improved the perception of the paper, with reviewers appreciating the clarifications and additional data, though they maintained their initial scores (the reviewer who gave the lowest score didn't respond to the rebuttal).

The primary strengths of this submission are its novel integration of computational techniques to address viral evolution and its empirical validation through simulations. However, the limitations include reliance on simulation models for validation and the lack of real-world experimental data. The paper's clarity and logical structure make it accessible to both computational and biological audiences, although some points, like the role of Absolut!, initially required deeper explanation to avoid reviewer misconceptions.

Although the work's real-world impact is yet to be fully determined, the novel computational approach and comprehensive feedback integration indicate significant academic merit. Therefore, I recommend accepting this paper as a valuable contribution to ICML.
Decision: Accept (poster)