Immune cells use active tugging forces to distinguish affinity and accelerate evolution

Abstract

Cells are known to exert forces to sense their physical surroundings for guidance of motion and fate decisions. Here, we propose that cells might do mechanical work to drive their own evolution, taking inspiration from the adaptive immune system. Growing evidence indicates that immune B cells-capable of rapid Darwinian evolution-use cytoskeletal forces to actively extract antigens from other cells' surfaces. To elucidate the evolutionary significance of force usage, we develop a theory of tug-of-war antigen extraction that maps receptor binding characteristics to clonal reproductive fitness, revealing physical determinants of selection strength. This framework unifies mechanosensing and affinity-discrimination capabilities of evolving cells: Pulling against stiff antigen tethers enhances discrimination stringency at the expense of absolute extraction. As a consequence, active force usage can accelerate adaptation but may also cause extinction of cell populations, resulting in an optimal range of pulling strength that matches molecular rupture forces observed in cells. Our work suggests that nonequilibrium, physical extraction of environmental signals can make biological systems more evolvable at a moderate energy cost.

Keywords: adaptive evolution; antigen recognition; immune response; physical dynamics of cells.

Fig. 1.

B cells acquire antigen and discriminate receptor affinity through a molecular tug of war. (A) Schematic illustration of an extraction attempt in a tug-of-war configuration: pulling force exerted by a B cell stretches a BCR–Ag–APC complex on the surface of an antigen-presenting cell (APC), leading to one of two outcomes—a sooner rupture of the Ag–APC bond makes a success, whereas a faster dissociation of the BCR–Ag bond yields a failure. The Ag–APC bond coarse-grains potentially complex interactions including Ag-tether association and strength of the APC membrane; a short-lived Ag–APC bond under force can be due to a weak Ag-tether bond or a soft APC membrane, which we do not distinguish. (B) System state can be specified in terms of the extension of the Ag–APC bond and that of the BCR–Ag bond. Stochastic Ag extraction occurs via thermal escape from the bound state (attractor at A) over one of the activation barriers (saddles at S_a and S_b) in the binding free energy landscape (color coded). A complex ruptures as soon as the trajectory (black trace) hits one of the absorbing boundaries located at rupture lengths x_a = x_a^‡ and x_b = x_b^‡ (dashed lines). In the absence of force, a relatively high BCR affinity (ΔG_b^‡ = 12k_BT) leads to a high chance of Ag extraction (η = 82%); the gray histograms show the distribution of exit position at each boundary, i.e., the extension of the remaining bond when the other breaks. (C) An increase in BCR affinity (12k_BT → 14k_BT) leads to a moderate fractional increase in the already high extraction likelihood (82%→96%). (D and E) A tugging force (F = 20 pN) deforms the binding free energy landscape, displacing the attractor and two saddles, as well as lowering two barriers by different amounts. Such deformation reduces the absolute level of extraction (82%→43%, 96%→78%) but greatly enhances the contrast between similar affinities (82% vs. 96%→43% vs. 78%). Parameters: ΔG_a^‡ = 12k_BT, x_a^‡ = 1.5 nm, x_b^‡ = 2 nm.

Fig. 2.

Tug-of-war antigen extraction enables mechanosensing and affinity discrimination. The slip-bond characteristic of BCR–Ag interaction underlies reduced extraction and enhanced discrimination stringency when B cells pull against stiff antigen tethers. (A) Antigen extraction can decrease or increase due to pulling, depending on whether the APC–Ag bond is stiffer (red, x_a^‡ < x_b^‡) or softer (blue, x_a^‡ > x_b^‡) than the BCR–Ag bond. Mean rupture force is predictive of antigen extraction, whether the pulling force is constant (circle) or ramping up over time (square; loading rate: 1 − 10⁶ pN/s). Brownian dynamics simulations (symbols, 1,000 runs each) show excellent match with the constant-force predictions based on Eqs. 3 and 5 (solid lines). Bell’s model (dashed lines) works for low force but fails already under modest force below 10 pN. ΔG_a^‡ = ΔG_b^‡ = 10k_BT; red: x_a^‡ = 1.5 nm, blue: x_a^‡ = 3 nm. (B) Discrimination stringency, measured by the ratio of extraction probability between B cells with different affinities (15k_BT vs 19k_BT), increases with the difference in bond lengths x_b^‡ − x_a^‡; a larger difference indicates a stiffer Ag-APC bond. The solid line is theory and black dots are averages over repeated simulations. Insets show statistics of extraction levels at two stiffness values indicated with a red diamond and a blue star, respectively. ΔG_a^‡ = 14k_BT, F = 20 pN.

Fig. 3.

Test of constant-force theory via dynamic-force measurements. The theoretical curve of extraction probability under constant force (solid line), based on Eqs. 3 and 5, is able to collapse data (open symbols) obtained by transforming the simulated rupture force histograms (insets) according to Eq. 9. For rupture forces greater than 20 pN, we extend the theoretical curve with Brownian dynamics simulations; each filled symbol on the dashed line represents the success rate out of 200 extraction attempts at a given force magnitude. Rupture force histograms cover three decades of loading rate (colors); note that rupture forces of BCR–Ag–APC complexes (UpperInset, p(F)) tend to have lower values than those of Ag–APC bonds (LowerInset, p_a(F)), reflecting the fact that τ = τ_aτ_b/(τ_a + τ_b)≤min(τ_a, τ_b), i.e., the shortest-lived bond sets the lifetime and hence rupture force of the entire complex. Parameters: $\mathrm{\Delta }{G}_a^{‡}=\mathrm{\Delta }{G}_b^{‡}=20k_{\mathrm{B}}T,x_a^{‡}=1.5\mathrm{nm},x_b^{‡}=2\mathrm{nm}$.

Fig. 4.

Tugging forces stretch the extraction curve and expand the discrimination range. (A) Extraction probability as a function of BCR affinity under different force magnitudes. Bell’s model predicts a mere shift of the curve as force increases (dashed lines) since it neglects force-induced landscape deformation. Kramers theory properly accounts for such deformation and predicts stretching of the response curve, supported by simulations (colored symbols, 200 runs each). (B) The range of distinguishable affinities (orange region), defined by η(ΔG_b^‡; F)∈[η_min, η_max], expands as force increases, according to the landscape model (solid lines) and simulations (diamonds). Bell’s model expects no expansion; dashed lines marking the range remain in parallel. η_min = 0.1, η_max = 0.9; ΔG_a^‡ = 20k_BT, x_a^‡ = 1.5 nm, x_b^‡ = 2 nm.

Fig. 5.

A schematic of GC reaction with fixed versus renewable antigen tethers illustrates the impact of antibody feedback. Cycles of antigen extraction, death, differentiation/recycle, replication and mutation alter the composition and size of a B cell population over time. (A) If tethers are fixed, higher-affinity clones (green) will likely extract a larger amount of antigen (red dot) and produce more offspring, expanding in size at the expense of lower-affinity clones (blue). Hence, population affinity increases but eventually hits a ceiling, once all clones carry BCRs stickier than the fixed tether and efficiently acquire antigen. (B) Tethers are constantly updated with antibodies secreted by most potent plasma cells available, as they compete better for antigen binding and presentation on the APC. This causes a steadily elevated selection pressure: Clones with inferior or similar affinity to the tether are likely to lose the tug of war and die (blue). More potent clones (magenta), instead, will likely win over the tether (secreted by green cells), acquire antigen, and differentiate into plasma cells that supply feedback antibodies as renewable tethers in subsequent GC cycles. As a result, affinity ceiling is lifted; sustained adaptation results from antibody feedback.

Fig. 6.

Optimal tugging forces balance the quality and magnitude of emergent responses. Time trajectories of population-mean affinity and population size, along with force dependence of the ceiling affinity and adaptation rate are presented for fixed (Upper row) and renewable (Lower row) antigen tethers. (A and B) For fixed tethers, mean affinity approaches saturation (A) as population size recovers to a force-independent steady level following an early bottleneck (B). (C) Stronger forces raise the affinity ceiling (black symbols: mean affinity at the end of 300 GC cycles from 100 simulations; solid line: analytical prediction based on η(ΔG_b^‡, F)=0.96). Too strong pulling leads to a rapid fall in population survival (red symbols: fraction of surviving populations; dashed line is to guide the eye). (D and E) With feedback antibodies renewing the tethers, mean affinity exhibits a steady increase (D) and population size stabilizes to force-dependent values (E). (F) The rate of affinity increase, v_G, shows a nonmonotonic dependence on force (black symbols: mean adaptation rate over the last 200 GC cycles from 100 runs; solid line: prediction from Eq. 11). Population survival shows a similar rapid decline as in panel (C), but starting at a lower pulling strength. In panels A, B, D, and E, each solid line represents an average over 100 runs with the shade indicating variation among runs. Simulation steps and parameters are provided in SI Appendix.