High fidelity information processing in folic acid chemotaxis of Dictyostelium amoebae

Trade-offs in concentration sensing in dynamic environments

When cells measure concentrations of chemical signals, they may average multiple measurements over time in order to reduce noise in their measurements. However, when cells are in an environment that changes over time, past measurements may not reflect current conditions-creating a new source of error that trades off against noise in chemical sensing. What statistics in the cell's environment control this trade-off? What properties of the environment make it variable enough that this trade-off is relevant? We model a single eukaryotic cell sensing a chemical secreted from bacteria (e.g., folic acid). In this case, the environment changes because the bacteria swim-leading to changes in the true concentration at the cell. We develop analytical calculations and stochastic simulations of sensing in this environment. We find that cells can have a huge variety of optimal sensing strategies ranging from not time averaging at all to averaging over an arbitrarily long time or having a finite optimal averaging time. The factors that primarily control the ideal averaging are the ratio of sensing noise to environmental variation and the ratio of timescales of sensing to the timescale of environmental variation. Sensing noise depends on the receptor-ligand kinetics, while environmental variation depends on the density of bacteria and the degradation and diffusion properties of the secreted chemoattractant. Our results suggest that fluctuating environmental concentrations may be a relevant source of noise even in a relatively static environment.

Physical limits on galvanotaxis

Eukaryotic cells can polarize and migrate in response to electric fields via "galvanotaxis," which aids wound healing. Experimental evidence suggests cells sense electric fields via molecules on the cell's surface redistributing via electrophoresis and electroosmosis, though the sensing species has not yet been conclusively identified. We develop a model that links sensor redistribution and galvanotaxis using maximum likelihood estimation. Our model predicts a single universal curve for how galvanotactic directionality depends on field strength. We can collapse measurements of galvanotaxis in keratocytes, neural crest cells, and granulocytes to this curve, suggesting that stochasticity due to the finite number of sensors may limit galvanotactic accuracy. We find cells can achieve experimentally observed directionalities with either a few (∼100) highly polarized sensors or many (∼10^{4}) sensors with an ∼6-10% change in concentration across the cell. We also identify additional signatures of galvanotaxis via sensor redistribution, including the presence of a tradeoff between accuracy and variance in cells being controlled by rapidly switching fields. Our approach shows how the physics of noise at the molecular scale can limit cell-scale galvanotaxis, providing important constraints on sensor properties and allowing for new tests to determine the specific molecules underlying galvanotaxis.

Confirmation and variability of the Allee effect in Dictyostelium discoideum cell populations,possible role of chemical signaling within cell clusters

In studies of the unicellular eukaryote Dictyostelium discoideum, many have anecdotally observed that cell dilution below a certain "threshold density" causes cells to undergo a period of slow growth (lag). However, little is documented about the slow growth phase and the reason for different growth dynamics below and above this threshold density. In this paper, we extend and correct our earlier work to report an extensive set of experiments, including the use of new cell counting technology, that set this slow-to-fast growth transition on a much firmer biological basis. We show that dilution below a certain density (around 10E4 cells/ml) causes cells to grow slower on average and exhibit a large degree of variability: sometimes a sample does not lag at all, while sometimes it takes many moderate density cell cycle times to recover back to fast growth. We perform conditioned media experiments to demonstrate that a chemical signal mediates this endogenous phenomenon. Finally, we argue that while simple models involving fluid transport of signal molecules or cluster-based signaling explain typical behavior, they do not capture the high degree of variability between samples but nevertheless favor an intra-cluster mechanism.

Leader cells in collective chemotaxis: Optimality and trade-offs

Clusters of cells can work together in order to follow a signal gradient, chemotaxing even when single cells do not. Cells in different regions of collectively migrating neural crest streams show different gene expression profiles, suggesting that cells may specialize to leader and follower roles. We use a minimal mathematical model to understand when this specialization is advantageous. In our model, leader cells sense the gradient with an accuracy that depends on the kinetics of ligand-receptor binding, while follower cells follow the cluster's direction with a finite error. Intuitively, specialization into leaders and followers should be optimal when a few cells have more information than the rest of the cluster, such as in the presence of a sharp transition in chemoattractant concentration. We do find this-but also find that high levels of specialization can be optimal in the opposite limit of very shallow gradients. We also predict that the best location for leaders may not be at the front of the cluster. In following leaders, clusters may have to choose between speed and flexibility. Clusters with only a few leaders can take orders of magnitude more time to reorient than all-leader clusters.

Collective gradient sensing and chemotaxis: modeling and recent developments

Cells measure a vast variety of signals, from their environment's stiffness to chemical concentrations and gradients; physical principles strongly limit how accurately they can do this. However, when many cells work together, they can cooperate to exceed the accuracy of any single cell. In this topical review, I will discuss the experimental evidence showing that cells collectively sense gradients of many signal types, and the models and physical principles involved. I also propose new routes by which experiments and theory can expand our understanding of these problems.

Extracellular Processing of Molecular Gradients by Eukaryotic Cells Can Improve Gradient Detection Accuracy

Eukaryotic cells sense molecular gradients by measuring spatial concentration variation through the difference in the number of occupied receptors to which molecules can bind. They also secrete enzymes that degrade these molecules, and it is presently not well understood how this affects the local gradient perceived by cells. Numerical and analytical results show that these enzymes can substantially increase the signal-to-noise ratio of the receptor difference and allow cells to respond to a much broader range of molecular concentrations and gradients than they would without these enzymes.

Cell-to-cell variation sets a tissue-rheology-dependent bound on collective gradient sensing

When a single cell senses a chemical gradient and chemotaxes, stochastic receptor-ligand binding can be a fundamental limit to the cell's accuracy. For clusters of cells responding to gradients, however, there is a critical difference: Even genetically identical cells have differing responses to chemical signals. With theory and simulation, we show collective chemotaxis is limited by cell-to-cell variation in signaling. We find that when different cells cooperate, the resulting bias can be much larger than the effects of ligand-receptor binding. Specifically, when a strongly responding cell is at one end of a cell cluster, cluster motion is biased toward that cell. These errors are mitigated if clusters average measurements over times long enough for cells to rearrange. In consequence, fluid clusters are better able to sense gradients: We derive a link between cluster accuracy, cell-to-cell variation, and the cluster rheology. Because of this connection, increasing the noisiness of individual cell motion can actually increase the collective accuracy of a cluster by improving fluidity.

Stochastic modelling suggests that an elevated superoxide anion - hydrogen peroxide ratio can drive extravascular phagocyte transmigration by lamellipodium formation

Chemotaxis, integrates diverse intra- and inter-cellular molecular processes into a purposeful patho-physiological response; the operatic rules of which, remain speculative. Here, I surmise, that superoxide anion induced directional motility, in a responding cell, results from a quasi pathway between the stimulus, surrounding interstitium, and its biochemical repertoire. The epochal event in the mounting of an inflammatory response, is the extravascular transmigration of a phagocyte competent cell towards the site of injury, secondary to the development of a lamellipodium. This stochastic-to-markovian process conversion, is initiated by the cytosolic-ROS of the damaged cell, but is maintained by the inverse association of a de novo generated pool of self-sustaining superoxide anions and sub-critical hydrogen peroxide levels. Whilst, the exponential rise of O2(.-) is secondary to the focal accumulation of higher order lipid raft-Rac1/2-actin oligomers; O2(.-) mediated inactivation and redistribution of ECSOD, accounts for the minimal concentration of H2O2 that the phagocyte experiences. The net result of this reciprocal association between ROS/ RNS members, is the prolonged perturbation and remodeling of the cytoskeleton and plasma membrane, a prelude to chemotactic migration. The manuscript also describes the significance of stochastic modeling, in the testing of plausible molecular hypotheses of observable phenomena in complex biological systems.