Molecular Tug of War Reveals Adaptive Potential of an Immune Cell Repertoire

The adaptive immune system constantly remodels its lymphocyte repertoire for better protection against future pathogens. Its ability to improve antigen recognition on the fly relies on somatic mutation and selective expansion of B lymphocytes expressing high-affinity antigen receptors. However, this rapid evolution inside an individual appears ineffective, hitting a modest ceiling of antigen-binding affinity. Only recently, experiments began to reveal that evolving B cells physically extract antigens from presenting cells using active forces, and that the extraction level dictates clonal fitness. These observations challenge the prevailing view that the equilibrium constant of receptor-antigen binding determines selective advantage of a B cell clone. Here, we present a theoretical framework to explore ways in which tug-of-war antigen extraction impacts the quality and diversity of an evolved B cell repertoire. We propose that the apparent “ineffectiveness” of in vivo selection can be a direct consequence of nonequilibrium antigen recognition. Our theory predicts, on the one hand, that the physical limits of antigen tether strength, under tugging forces, set the affinity ceiling. On the other hand, intriguingly, cells can use force heterogeneity to diversify binding phenotype without compromising fitness, thus remaining plastic under resource constraint. These results suggest that active probing of receptor quality—via a molecular tug of war during antigen recognition—limits the potency of response to current antigens, but confer adaptive benefit against future variants. By bridging physical mechanisms and evolved functions, this work reveals a multifaceted role of active forces in immune adaptation, which rationalizes key observations on repertoire dynamics.

Popular Summary

Biological systems learn by accumulating incremental changes to better suit future environments. The immune system does so through a rapid evolutionary process inside the host that improves antigen recognition on the fly. However, this Darwinian-like process appears surprisingly ineffective—why and how so remains a key puzzle. Recently, immune cells were found to acquire antigens from other cells using active forces, rather than relying on equilibrium binding. Here, we explore whether and when active probing of receptor quality during antigen recognition confers an adaptive benefit. By assessing the macroscopic impact of microscopic dynamics, we show how the nonequilibrium nature of antigen recognition limits the potency of response to current targets and yet enables plasticity against future threats.

Specifically, we present a theoretical framework that bridges the gap between molecular interaction and clonal selection through tug-of-war antigen extraction by cells. This active extraction process is shown to unify multiple in vivo observations and predict new ones: It rationalizes the apparent ineffectiveness of natural selection through a balance between depth and breadth of protection with limited resources, explains low specificity and high diversity of memory cells, and predicts a persistent variety of receptor-antigen binding affinities.

This work proposes a new paradigm of biological recognition via nonequilibrium, physical acquisition of stimuli, which may complement the current view centered on biochemical signaling. Meanwhile, it offers a fresh and informative angle for understanding biological learning in light of physical influences on evolution. Our findings have broad implications for physically modulating immune responses and steering adaptive evolution.

Figure 1

Model overview. Evolutionary learning of a B cell repertoire crucially depends on physical extraction of antigen (Ag) via a molecular tug of war. (a) Affinity maturation takes place in germinal centers (GCs)—structured microenvironments where cellular players meet and interact. Iterative evolutionary learning proceeds through cycles of GC reaction: somatic hypermutations during proliferation cause changes in BCR properties (affinity and flexibility) that alter B cells’ efficiency of acquiring antigen from the surface of antigen presenting cells (APCs) and subsequently presenting to helper T cells. This efficiency, in turn, determines the selective advantage of competing clones. Positively selected cells (avoiding apoptosis) either differentiate into memory or plasma cells and exit the GC or join the next cycle of reaction. (b) Central to this evolutionary program is the mapping from BCR-Ag binding characteristics to clonal reproductive fitness, arising from nonequilibrium antigen extraction under tugging forces. A BCR-Ag-APC complex coarse grains the protein chain linking a B cell to the APC. (c),(d) The essence of tug-of-war antigen extraction is competitive bond rupture under pulling force. System dynamics proceed on a combined free-energy surface $U(x_a,x_b)$ over a 2D space spanned by $x_a$ and $x_b$, the extension of the Ag-APC and BCR-Ag bonds, respectively. With probability $\eta$, extraction occurs via thermally aided escape from the bound state over the activation barrier corresponding to Ag-APC bond rupture ($x_a=x_a^{‡}$). BCR is B cell receptor.

Figure 2

Effective tether strength sets evolvable antibody affinity. Ceiling affinity—evolved activation energy or barrier height $\mathrm{\Delta }{G}_b^{‡}$—largely follows a logarithmic dependence on relative tether strength $s\equiv {\tau }_a/{\tau }_{b0}$, as estimated by Eq. (5) (dashed line). Symbols are obtained from simulations over a wide range of tether strengths realized by varying the tether rupture length ($x_a^{‡}$, 0.5–4 nm) and force magnitude ($F$, 0–30 pN); each symbol results from 100 runs for a given pair of $x_a^{‡}$ and $F$ values. Modest deviation of symbols from the straight line arises due to relatively strong forces (darker blue circles) scaled by the critical force $f^{*}=\min \{3\mathrm{\Delta }{G}_a^{‡}/(2x_a^{‡}),3\mathrm{\Delta }{G}_b^{‡}/(2x_b^{‡})\}$ at which the barrier to rupture vanishes. While the ceiling affinity rises with tether strength (circles), the fraction of surviving populations (red squares) vanishes quickly above tether strengths a few-fold stronger than the founder BCR-Ag bond. Here, binding affinity $\mathrm{\Delta }{G}_b^{‡}$ evolves, while the bond length $x_b^{‡}$ remains fixed. $\mathrm{\Delta }{G}_a^{‡}=\mathrm{\Delta }{G}_{b0}^{‡}=14k_{B}T$, $x_b^{‡}=2\mathrm{nm}$. ${\eta }_{\mathrm{th}}=0.97$. We used a linear-cubic free-energy profile to calculate extraction probability (see SM [56]) in all the results presented in this work.

Figure 3

Active force usage steers B cell evolution and causes discrepancy between B cell fitness and antibody quality. (a) Example evolutionary trajectories of population-mean binding affinity $\mathrm{\Delta }{G}_b^{‡}$ and bond length $x_b^{‡}$, guided by fitness landscape (contour map of extraction probability $\eta$) and subject to stochasticity in mutation and reproduction. The green region indicates high intrinsic binding quality ($Q\ge {\log }_{10}50$). Stronger pulling (left to right, $F=0$, 5, 20 pN) selects for stiffer BCR-Ag bonds (smaller $x_b^{‡}$), whereas varying tether stiffness (top to bottom, $x_a^{‡}=4$, 1.5, 0.5 nm) tunes the range and steepness of fitness gradient. Evolved BCRs appear to match the stiffness of antigen tethers; see main text for explanation. (b) Effective tether strength as a function of force magnitude $F$ and tether bond length $x_a^{‡}$, obtained from mean first-passage time calculation. Stronger forces strengthen stiff tethers ($x_a^{‡}<x_b^{‡}$) but weaken soft tethers ($x_a^{‡}>x_b^{‡}$), yielding maximum tether strengths at low force and soft tether or high force and stiff tether (red regions). (c) Dependence of evolved B cell fitness (fold increase in reproduction rate) on pulling force and tether stiffness largely follows the trend of tether strength (b). (d) Evolved antibody quality increases toward weak force and soft tether (upper left-hand corner) just as evolved fitness does (c). However, strong force and stiff tether (lower right-hand corner) lead to high B cell fitness yet low antibody quality. In (c) and (d), each pixel represents an average over 20 simulations, with equal mutation rates for $\mathrm{\Delta }{G}_b^{‡}$ and $x_b^{‡}$; initial conditions are $\mathrm{\Delta }{G}_{b0}^{‡}=\mathrm{\Delta }{G}_a^{‡}=14k_{B}T$ and $x_{b0}^{‡}=2\mathrm{nm}$.

Figure 4

Dynamic selection pressure sustains adaptation and improves evolved binding quality. (a) Evolutionary dynamics with (solid lines) and without (dashed lines) antibody feedback. With fixed antigen tethers (red dashed line), the rate of increase in BCR affinity slows down over time (black dashed line). With renewing tethers sampled from high-affinity plasma cells (top-$K$ rank in $\mathrm{\Delta }{G}_b^{‡}$), the overall tether strength (red solid line) and BCR affinity (black solid line) improve at similar steady rates, indicating sustained adaptation. The shade shows variation among 10 simulations. $\mathrm{\Delta }{G}_a^{‡}=14k_{B}T$, $x_a^{‡}=1.5\mathrm{nm}$, $x_b^{‡}=2\mathrm{nm}$, $F=20\mathrm{pN}$, $K=100$. (b) Population-average evolution trajectories (left) and outcomes (right) under constant and oscillatory forces. Under constant forces, the fitness landscape (contour map of extraction probability) has a shallow affinity gradient and drives evolution toward stiff BCR-Ag bonds (upper left-hand panel), leading to a rapid fall in evolved binding quality with increasing force magnitude (right-hand panel, black symbols). Under not too slow oscillatory forces, populations evolve in an effective time-averaged fitness landscape (lower left-hand panel) that has an attractor at high affinity and matching stiffness ($x_b^{‡}\sim x_a^{‡}$), resulting in high quality over a wide range of force magnitude (right-hand panel, blue symbols). Constant force, $F=20\mathrm{pN}$; oscillatory force, $F=F_{\max }[1+\cos (2\pi t/T_F)]/2$, with $F_{\max }=20\mathrm{pN}$, $T_F=50$, $t_f=300$. Error bars indicate variation among 20 simulations. $\mathrm{\Delta }{G}_a^{‡}=14k_{B}T$, $x_a^{‡}=1.5\mathrm{nm}$; $\mathrm{\Delta }{G}_{b0}^{‡}=14k_{B}T$, $x_{b0}^{‡}=2\mathrm{nm}$.

Figure 5

An intermediate level of heritable force heterogeneity yields a broad range of binding quality and rate of diversity loss. (a) A saddle point in the fitness landscape (contour map showing extraction probability) is present at $F\simeq 9\mathrm{pN}$ and $x_b^{†}=1.5\mathrm{nm}$. The ridge line (dashed black line) traces along the direction of the positive principal curvature near the saddle point. The line of steady states (solid red line), where the gradient in $x_b^{‡}$ vanishes for a given $F$, deviates from the ridge line as force gets weaker, reflecting an asymmetry about the saddle point. (b) Snapshots of evolving population density (color coded) in the $F\text{−}{x}_b^{‡}$ space, starting from different levels of force heterogeneity. Extraction contours are evaluated with population-mean affinity at each time point. At an intermediate force heterogeneity (middle row, ${\sigma }_{F_0}=0.6F_{\mathrm{av}}$), a population splits into two and remains bimodal for extended periods of time. Very small or very large heterogeneity (top and bottom rows) leads to a single crowd with similar force magnitudes. (c),(d) Distributions of the evolved antibody quality $Q$ and B cell fitness $\lambda$ for zero (blue), intermediate (red), and maximum (brown) initial force heterogeneity; dashed lines indicate initial distributions. B cell lineages with diverse binding qualities (c) can have similar fitness (d) and coexist. (e) A violin plot shows that an intermediate force heterogeneity results in a broad range of diversity ${\sigma }_Q$ of evolved binding quality. Each violin is obtained from 20 simulations, with the horizontal bar indicating the ensemble average. (f)–(h) Evolution of the diversity of binding quality ${\sigma }_Q$ at zero (f), intermediate (g), and high (h) initial force heterogeneity. The histogram on the side shows the final distribution of ${\sigma }_Q$. Parameters are $\mathrm{\Delta }{G}_a^{‡}=14k_{B}T$, $x_a^{‡}=1.5\mathrm{nm}$, $F_{\mathrm{av}}=10\mathrm{pN}$, $t_f=100$. Mean and width of initial distributions are $\mathrm{\Delta }{G}_{b0}^{‡}=14k_{B}T$, ${\sigma }_{0,G_b}=0.2k_{B}T$, $x_{b0}^{‡}=2\mathrm{nm}$, ${\sigma }_{0,x_b}=0.5\mathrm{nm}$. Constant force, no antibody feedback.