Cells in natural environments like tissue or soil sense and respond to extracellular ligands with intricately structured and non-monotonic spatial distributions that are sculpted by processes such as fluid flow and substrate adhesion. Nevertheless, traditional approaches to studying cell sensing assume signals are either uniform or monotonic, neglecting spatial structures of natural environments. In this work, we show that spatial sensing and navigation can be optimized by adapting the spatial organization of signaling pathways to the spatial structure of the environment. By viewing cell surface receptors as a sensor network, we develop an information theoretic framework for computing the optimal spatial organization of a sensing system for a given spatial signaling environment. Applying the framework to simulated environments, we find that spatial receptor localization maximizes information acquisition in many natural contexts, including tissue and soil. Receptor localization extends naturally to produce a dynamic protocol for redistributing signaling receptors during cell navigation and can be implemented in a cell using a feedback scheme. In a simulated tissue environment, dynamic receptor localization boosts navigation efficiency by 30-fold. Broadly, our framework readily adapts to studying how the spatial organization of signaling components other than receptors can be modulated to improve cellular information processing.
Cells sense and respond in spatially-structured environments, where signal distributions are determined by a range of chemical and physical processes from substrate adhesion to fluid flow. In tissue and soil, distributions of extracellular ligands can be discontinuous, consisting of local ligand patches that differ strongly from monotonic gradients. In tissue, diffusive signaling molecules are transported by interstitial fluid through a porous medium. These molecules are then captured by cells and a non-uniform network of extracellular matrix (ECM) fibers, taking on a stable, yet uneven distribution. For example, ECM-bound chemokine (CCL21) gradients extending from lymphatic vessels take on stable spatial structures, characterized by regions of high ligand concentration separated by spatial discontinuities. Similar observations have been made for the distribution of other chemokines, axon guidance cues and morphogens in tissues. In soil, a heterogeneous pore network influences the spatial distribution of nutrients by dictating both the locations of nutrient sources as well as where nutrients likely accumulate. Free-living cells detect chemical cues released by patchy distributions of microorganisms, where molecules are moved via fluid flow and diffusion. Cells in these and other natural environments experience surface ligand profiles with varying concentration peaks, non-continuity and large dynamic range, far different from that of a smoothly varying, purely-diffusive environment.
Modern signal processing theory shows that sensing strategies must adapt to the statistics of the input signals, suggesting that spatial sensing in cells should be adapted to the spatial structure of signaling molecules in the cells’ native environments. For example, when designing electronic sensor networks sensing spatial phenomena, adapting sensor placement to the spatial statistic of the signal can significant improve information acquisition. Similar considerations may apply to the spatial organization of cell signaling pathways. Furthermore, spatial navigation where sensing plays a key role may also benefit from such adaptation, as suggested by work from robot navigation. For example, cells navigating up interstitial gradients can potentially get trapped by local concentration peaks. Adapting sensing to patchy structure of the gradient may allow cells to overcome local traps.
Traditional approaches to studying cell sensing often use highly simplified environmental models, where signals are either uniform or monotonic, neglecting the complex spatial structure in natural cell environments. Classic work beginning with the seminal paper by Berg and Purcell (1977) studied cell sensing in homogeneous environments. This and subsequent works were extended to study the detection of spatially-varying concentrations, where monotonic gradients remain the canonical environmental model. Recent work studied more complex sensing environment by adding spatially-uncorrelated fluctuations to a monotonic gradient, which does not capture the spatial structure of natural environments. As a practical consequence, little effort in cell engineering has gone into addressing challenges posed by non-monotonic spatial distribution of ligands found in natural environments. Fundamentally, it’s not clear what sense and response strategies are well-adapted to operate in environments where signals are distributed in complex spatial patterns.
Observations of dynamic receptor rearrangement in leukocytes, neurons, and keratinocytes suggest that cells might modulate the placement of surface receptors to exploit the spatial structure of ligand distribution. For example, multiple classes of axon guidance receptors can dynamically rearrange on the surface of growth cones. In all such cases, receptors rearrange constantly, adjusting local surface densities in response to changes in ligand distribution across the cell surface. Chemokine receptors in lymphocytes and growth factor receptor in keratinocytes exhibit similar spatial dynamics. However, there are also T cell and neutrophil receptors that are constantly uniform, even when ligands are distributed non-uniformly. In addition, during antigen recognition, T-cell receptors (TCRs) take on different placements, ranging from uniform to highly polarized, depending on the density of antigen molecules on the surface of the opposing cell. Thus, across a diverse range of cell surface receptors, we see different, even contradictory rearrangement behavior in response to changes in environmental structure. It remains unclear whether dynamic receptor rearrangement has an overarching biological function across disparate biological contexts.
We formulate a mathematical framework to solve for receptor placements that maximizes information acquisition in natural environments, generating such environments using existing computational models of tissue and soil microenvironments. Using this framework, we show that dynamic localization of receptors is an effective spatial sensing strategy in natural cell environments, but inconsequential in purely diffusive environments. Thus, anisotropic receptor dynamics previously observed in cells are nearly optimal. Specifically, information acquisition is maximized when receptors are localized and oriented, forming a cap at the region of highest ligand concentration. This placement strategy offers significant improvement over uniformly distributed receptors, but only in natural environments, leading to 2 fold increase in information acquisition. Receptor localization maximizes information acquisition by taking advantage of patchy ligand distribution, reallocating sensing resource from low signal region to a small but high signal region on the cell surface where most of the information is concentrated.
Our framework extends naturally to produce a dynamic protocol for continuously relocalizing receptors in response to a dynamic environment. We show that a simple feedback scheme implements this protocol within a cell, and improves cell navigation significantly. Compared to cells with uniform receptor placement, cells using this scheme achieve more than 30-fold improvement in their ability to localize to the peak of simulated interstitial gradients. Since this strategy is purely spatial, it can be applied across a wide range of chemical environments. Taken together, our model serves as a useful conceptual framework for understanding the role of spatial organization of signal transduction pathway in spatial sensing, and provides a sensing strategy that is both effective in natural cell environments and amenable to cell engineering.
We are interested in optimal strategies for a task we refer to as spatial sensing. Spatial sensing is an inference task where a cell infers external profiles of varying ligand level across its surface from an internal profile of varying receptor activity across its membrane. This is a useful model task since optimizing performance on this task should improve the cell’s ability to infer diverse environmental features.
We developed a theoretical framework to study whether manipulating the placement of cell surface receptors can improve the spatial sensing performance. Optimizing spatial sensing by tuning receptor placement is analogous to optimizing distributed electronic sensor network by adjusting the location of sensors, which has been extensively studied in signal processing. In the optimization of distributed sensor networks monitoring spatial phenomena (Figure 1A), it is well-known that adjusting the placement of a limited number of sensors can significantly boost sensing performance, where the optimal placement strategy is dictated by the statistics of the input signals. The collection of a limited number of receptors on the cell surface also functions as a (distributed) sensor network, sensing a spatial profile of varying ligand concentration (Figure 1A). Therefore, we hypothesized that receptor placement can be tuned to improve spatial sensing, and that the optimal strategy depends on the statistics of ligand profiles that cells typically encounter. Traditionally, sensor network optimization focuses on finding a single placement strategy. However, cells can rearrange their receptors within a matter of minutes, thus leading to a potentially much richer class of strategies. Thus, instead of considering a single placement strategy, we examined a function ϕ that assigns a receptor placement to each ligand profile. We define the optimal placement strategy as the one that maximizes mutual information between ligand profiles and active receptor profiles, while keeping total receptor number fixed. Mutual information quantifies the extent to which observing one random variable (i.e. the membrane profile of active receptors), reduces uncertainties about another (i.e. the surface profile of ligand counts). This metric sets a theoretical bound on the accuracy of spatial sensing. Notably, this metric is agnostic to the decoding process in that it does not assume any details about downstream signaling, nor the exact environmental features a cell may try to decode, expanding the scope of our results.
