Inference of germinal center evolutionary dynamics via simulation-based deep learning

Reviewer #1 (Public review):

Summary:

This paper aims to characterize the relationship between affinity and fitness in the process of affinity maturation. To this end, the authors develop a model of germinal center reaction and a tailored statistical approach, building on recent advances in simulation-based inference. The potential impact of this work is hindered by the poor organization of the manuscript. In crucial sections, the writing style and notations are unclear and difficult to follow.

Strengths:

The model provides a framework for linking affinity measurements and sequence evolution and does so while accounting for the stochasticity inherent to the germinal center reaction. The model's sophistication comes at the cost of numerous parameters and leads to intractable likelihood, which are the primary challenges addressed by the authors. The approach to inference is innovative and relies on training a neural network on extensive simulations of trajectories from the model.

Weaknesses:

The text is challenging to follow. The descriptions of the model and the inference procedure are fragmented and repetitive. In the introduction and the methods section, the same information is often provided multiple times, at different levels of detail. This organization sometimes requires the reader to move back and forth between subsections (there are multiple non-specific references to "above" and "below" in the text).

The choice of some parameter values in simulations appears arbitrary and would benefit from more extensive justification. It remains unclear how the "significant uncertainty" associated with these parameters affects the results of inference. In addition, the performance of the inference scheme on simulated data is difficult to evaluate, as the reported distributions of loss function values are not very informative.

Finally, the discussion of the similarities and differences with an alternative approach to this inference problem, presented in Dewitt et al. (2025), is incomplete.

Reviewer #2 (Public review):

Summary:

This paper presents a new approach for explicitly transforming B-cell receptor affinity into evolutionary fitness in the germinal center. It demonstrates the feasibility of using likelihood-free inference to study this problem and demonstrates how effective birth rates appear to vary with affinity in real-world data.

Strengths:

(1) The authors leverage the unique data they have generated for a separate project to provide novel insights into a fundamental question.

(2) The paper is clearly written, with accessible methods and a straightforward discussion of the limits of this model.

(3) Code and data are publicly available and well-documented.

Weaknesses (minor):

(1) Lines 444-446: I think that "affinity ceiling" and "fitness ceiling" should be considered independent concepts. The former, as the authors ably explain, is a physical limitation. This wouldn't necessarily correspond to a fitness ceiling, though, as Figure 7 shows. Conversely, the model developed here would allow for a fitness ceiling even if the physical limit doesn't exist.

(2) Lines 566-569: I would like to see this caveat fleshed out more and perhaps mentioned earlier in the paper. While relative affinity is far more important, it is not at all clear to me that absolute affinity can be totally ignored in modeling GC behavior.

(3) One other limitation that is worth mentioning, though beyond the scope of the current work to fully address: the evolution of the repertoire is also strongly shaped by competition from circulating antibodies. (Eg: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3600904/, http://www.sciencedirect.com/science/article/pii/S1931312820303978). This is irrelevant for the replay experiment modeled here, but still an important factor in general repertoires.