Interpreting T-cell search "strategies" in the light of evolution under constraints

Abstract

Two decades of in vivo imaging have revealed how diverse T-cell motion patterns can be. Such recordings have sparked the notion of search "strategies": T cells may have evolved ways to search for antigen efficiently depending on the task at hand. Mathematical models have indeed confirmed that several observed T-cell migration patterns resemble a theoretical optimum; for example, frequent turning, stop-and-go motion, or alternating short and long motile runs have all been interpreted as deliberately tuned behaviours, optimising the cell's chance of finding antigen. But the same behaviours could also arise simply because T cells cannot follow a straight, regular path through the tight spaces they navigate. Even if T cells do follow a theoretically optimal pattern, the question remains: which parts of that pattern have truly been evolved for search, and which merely reflect constraints from the cell's migration machinery and surroundings? We here employ an approach from the field of evolutionary biology to examine how cells might evolve search strategies under realistic constraints. Using a cellular Potts model (CPM), where motion arises from intracellular dynamics interacting with cell shape and a constraining environment, we simulate evolutionary optimization of a simple task: explore as much area as possible. We find that our simulated cells indeed evolve their motility patterns. But the evolved behaviors are not shaped solely by what is functionally optimal; importantly, they also reflect mechanistic constraints. Cells in our model evolve several motility characteristics previously attributed to search optimisation-even though these features are not beneficial for the task given here. Our results stress that search patterns may evolve for other reasons than being "optimal". In part, they may be the inevitable side effects of interactions between cell shape, intracellular dynamics, and the diverse environments T cells face in vivo.

Fig 1. A computational model of cell migration with indirect genotype-phenotype mapping.

A: CPM tissues are collections of pixels that each belong to one cell. Pixels try to copy their cell “identity” into neighbouring pixels of another cell. B: Their success rate P_copy depends on how this would change the energy associated with different physical properties, such as surface tension (“adhesion”, left), or deviating from the normal cell size (“volume”, middle; an analogous constraint can be posed on the cell’s perimeter). The Act-CPM [33] adds another such property (right): each pixel’s “activity” represents the time since its most recent protrusive activity. Copy attempts from more into less active pixels are stimulated (negative ΔH_act), placing positive feedback on protrusions. C: Cells in the Act-CPM can have an amoeboid (stop-and-go) or a keratocyte-like (persistent) migration mode, which are associated with different cell shapes. D: Non-trivial genotype-phenotype mapping in the Act-CPM.

Fig 2. Evolution of optimal search behaviour in Act cells is subject to constraints and trade-offs.

A: Simulated evolution in an evolutionary algorithm. A population of 10 Act cells with their own (max_act,λ_act) parameters each produce three daughter cells with randomly “mutated” parameters (see Methods for details). After simulating migration for all 40 cells, only the 10 “fittest” cells (i.e. those that explored the largest area) survive as the next generation. Here, fitness is defined as the total area explored by the simulated cell during the simulation (normalized by the area of the cell itself). The fitness is zero if the cell breaks during the simulation. B: Evolution of λ_act and max_act over 50 generations. Black line + shaded area shows the mean ± SD within each generation. Thin gray lines show the same curve for 9 other, independent runs. C: Evolution of λ_act and max_act in the context of the median “fitness” experienced by cells with those parameters. The red trajectory represents one single run; the (blue) fitness landscape is constructed by averaging measured fitnesses from all cells of all (10) independent runs at given parameters.

Fig 3. Evolution of optimal search in Act cells is subject to constraints and trade-offs.

A: Speed and persistence measured at different points in the fitness landscape of Fig 2C. B: Speed, persistence, and cell breaking measured around the evolved optimum (max_act = 50, λ_act = 1165).

Fig 4. Act cells in different environments evolve similar parameters but different shapes and behaviour.

A: Evolution trajectories of the (max_act,λ_act) parameters compared between different runs of evolution in empty space (“free”, see also Fig 2) and evolution in a rigid simulated tissue (“skin”). Black lines represent the “free” cells evolved from the higher λ_act = 100, while gray lines show the trajectories from Fig 2. Zoomed square shows where parameters converge in the two different environments after 50 generations, at similar (max_act,λ_act) values. B: Cells evolved in different environments have similar parameters but different shapes and behaviours. See also S1 Movie. C: Speed and persistence of cells with parameters evolved in simulated skin (“skin-skin”), parameters evolved in an empty environment(“free-free”), or parameters evolved in simulated skin but analysed in an empty environment (“free-skin”). Speeds are represented as instantaneous speeds of each individual step in the simulation, and persistence times reflect 6 independent measurements at the same parameters (see Methods for details).