Persistent pseudopod splitting is an effective chemotaxis strategy in shallow gradients

TL;DR

The paper models chemotaxis as a stimulus-dependent actin competition among multiple pseudopods, eliminating the need for explicit gradient sensing. Actin recruitment follows overdamped Langevin dynamics with mutual inhibition and a Boltzmann-like receptor signaling factor, linking local concentrations to polymerization rates via $P_{on}$ and $\Delta F_i \\approx -\\kappa_c(c_i - c_0)$. Through deep reinforcement learning, the authors show that persistence with a small forward-oriented subset of pseudopods can achieve near-optimal chemotaxis in shallow or static gradients, while dynamic gradients favor de novo protrusions and adaptive suppression. The study provides Weber-like scaling of decision success with $SNR$ and reveals a fundamental speed–accuracy trade-off controlled by the number of candidate pseudopods, along with an optimal suppression policy that adapts to environmental dynamics, offering insights for biology and robotics alike.

Abstract

Single-cell organisms and various cell types use a range of motility modes when following a chemical gradient, but it is unclear which mode is best suited for different gradients. Here, we model directional decision-making in chemotactic amoeboid cells as a stimulus-dependent actin recruitment contest. Pseudopods extending from the cell body compete for a finite actin pool to push the cell in their direction until one pseudopod wins and determines the direction of movement. Our minimal model provides a quantitative understanding of the strategies cells use to reach the physical limit of accurate chemotaxis, aligning with data without explicit gradient sensing or cellular memory for persistence. To generalize our model, we employ reinforcement learning optimization to study the effect of pseudopod suppression, a simple but effective cellular algorithm by which cells can suppress possible directions of movement. Different pseudopod-based chemotaxis strategies emerge naturally depending on the environment and its dynamics. For instance, in static gradients, cells can react faster at the cost of pseudopod accuracy, which is particularly useful in noisy, shallow gradients where it paradoxically increases chemotactic accuracy. In contrast, in dynamics gradients, cells form de novo pseudopods. Overall, our work demonstrates mechanical intelligence for high chemotaxis performance with minimal cellular regulation.

Figures (5)

• Figure 1: Schematics of the decision-making model and actin dynamics.(a) Pseudopod splitting in a Dictyostelium cell performing chemotaxis under agar (provided by Robert Insall) andrew_chemotaxis_2007. Arrows indicate likely actin flows, and the scale bar is 20µ m. (b) Diagram of the cell morphology during a splitting event. Pseudopod formation occurs due to competition during actin recruitment. In this instance, only two pseudopods emerge even though $n=12$ candidates start the competition. Finally, only one remains after decision-making time $T_D$, altering the cell orientation and advancing its position. The movement step is completed at time $T$. (c) Segmentation of actin filaments inside pseudopodia of small platelets with permission from sorrentino_structural_2021 based on high-resolution structural analysis. Actin filaments are in blue, red, and yellow, while receptors are shown in green. (d) Schematics of the simplified polymerization of actin into filaments (F-actin) at the internal membrane surface from actin monomers (G-actin), forming pseudopods. The diagram also shows how pseudopods suppress neighbors by redistributing their actin filaments and mutually inhibiting each other's growth.
• Figure 2: Actin and pseudopods dynamics during decision-making.(a-b) Sample trajectories of F-actin levels of each of the $n=12$ candidate directions of the cell, shown in the circular diagram in (a), in a linear concentration profile Eq. (\ref{['eq:concentration-profile']}) in a shallow (a: $g_x{=}0.01$, $c_0{=}50$) and a steeper (b: $g_x{=}1$, $c_0{=}150$) gradient environment, respectively. The inset in (b) shows a closeup of the initial dynamics of the competing pseudopods on log time. The proportion of G-actin is shown as a black line. The decision time $T_D$ is also marked with a vertical line set by Eq. (\ref{['eq:decision_time']}). (c) Duration distribution of the events $T$ and the decision times $T_D$. (d) Decision time as a function of the chemoattractant gradient for different noise levels set by the concentration value.
• Figure 3: Weber-like law and speed-accuracy tradeoff.(a) A heatmap of the success rate at different values of gradient and background concentration. Each rate value (square) is calculated by averaging $10^5$ independent splitting events with randomly oriented cells and considering it a success if the final movement of the cell has led it to a higher concentration, i.e., $c(x_T) > c(x_0)$. The blue line indicates the minimum gradient at which the accuracy of choosing the direction up the gradient reaches 0.95, the threshold rate at which we consider the cell to be making the correct decision unambiguously, as the perfect rate is subject to numerical fluctuations. The vertical dashed line indicates the threshold at which we consider the linear regime to begin ($c(x) > 30$). A linear fit is shown in a dashed line on top of the minimum gradient for the linear region. (b) The minimum gradient line changes for different actin exchange parameters $\varepsilon$. The inset showcases what is commonly understood as Weber's law, a scalar ratio between the perceived change in stimulus ($dS$) and stimulus value $S$. (c) Accuracy of aligning the cell body with the gradient, given by the chemotactic index (CI). The solid line showcases the optimal CI of a perfect absorbing cell set by Eq. (\ref{['eq:optimal-similarity']}), while the dashed line adjusts it by a factor $0.9$. The inset exemplifies the resulting distributions of the alignment of the cell at low and high gradients, respectively. (d) CI (black) and mean decision time $T_D$ (red) as a function of the number of candidate pseudopods at the highest gradient ($g_x=2$). The inset shows the rate of alignment, fitted to the power law $n^{-\nu}$.
• Figure 4: Chemotaxis performance depends on SNR.(a) Sample of $3\,10^2$ chemotaxis trajectories of our model, composed of 30 splitting events, at different levels of SNRs. The vertical black line indicates the initial positions of the cell. Since SNR changes along a trajectory, low here contains SNR $\in~[10^{-5.874}, 10^{-5.875}]$, mid contains $[10^{-3.26},10^{-3.29}]$ and high $[10^{-1.87}, 10^{-2.06}]$. (b) Final displacement distribution ($N=7\, 10^3$) of the trajectories in (a). A distribution for the splitting configuration with $n=2$ at low SNR is also included in blue. (c) Chemotactic index (CI) as a function of SNR, plotted on a $\log_{10}$ scale. The fundamental physical limit for a static spherical ligand absorber is given by Eq. (\ref{['eq:optimal-similarity']}) endres_accuracy_2008, fitted to the experimental data from tweedy_distinct_2013van_haastert_biased_2007. Additionally, the performance of an all-knowing cell that estimates the gradient based on ($n=12$) sensors uniformly distributed across its body is shown in a dashed line (see SI for details). In yellow is the resulting CI of $10^4$ independent trajectories, from which at each timestep the CI is calculated using Eq.(\ref{['eq:ci']}) and binned according to the SNR at the start of the event. Similarly, the purple line shows the results for a cell with only activated $\mathcal{P}_2$ and $\mathcal{P}_{10}$. For clarity, the lines are fitted to a logistic function using the numerical simulations binned by SNR.
• Figure 5: Optimal pseudopod suppression strategy.(a) Schematics of the DRL training process, where (1) the policy outputs activation probabilities of each candidate, (2) a sampling occurs to suppress certain directions, and (3) a splitting event is simulated, resulting on a new outcome which we use to optimize the weights of the policy, and a new SNR that will be used as input for the next step. (b) The cell diagrams show the resulting activation probability $p_\theta$ of the 12 candidates at different SNR for both $\alpha=0$ and $\alpha=0.3$. On the schematics, the cell direction movement is up. (c) Evaluation of the optimal policy $p_\theta$ using PPO with $\gamma=0.2$, based on how well pseudopods align with the gradient compared to the results from Fig. \ref{['fig:chemotaxis-results']}c. The resulting points are fitted with a logistic function and are the result of $10^4$ independent simulated trajectories, from which, at each time step, the CI is calculated and binned by SNR. Both the policy strained on static profile concentrations ($\alpha=0$), and the one trained with a high rate of changing gradient direction ($\alpha=0.3$) are shown despite being evaluated on a static gradient. (d) Trajectories of the suppression policy trained in a static gradient (black) and in a dynamic gradient with a high rate of switching (red). The initial position of the cell is marked with a cross, while the point of the trajectory at which the gradient sign is changed is indicated by a dot.