Cellular signaling processes depend on specific spatiotemporal distributions of their molecular components. Multi-color high-resolution microscopy now permits detailed assessment of such distributions, providing the input for fine-grained computational models that explore the mechanisms governing dynamic assembly of multi-molecular complexes and their role in shaping cellular behavior. However, incorporating into such models both complex molecular reaction cascades and the spatial localization of signaling components within dynamic cellular morphologies presents substantial challenges. Here we introduce an approach that addresses these challenges by automatically generating computational representations of complex reaction networks based on simple bi-molecular interaction rules embedded into detailed, adaptive models of cellular morphology. Using examples of receptor-mediated cellular adhesion and signal-induced localized MAPK activation in yeast, we illustrate the capacity of this simulation technique to provide insights into cell biological processes. The modeling algorithms, implemented in a version of the Simmune tool set, are accessible through intuitive graphical interfaces as well as programming libraries.

Summary Chemoattractant-mediated recruitment of hematopoietic cells to sites of pathogen growth or tissue damage is critical to host defense and organ homeostasis. Chemotaxis is typically considered to rely on spatial sensing, with cells following concentration gradients as long as these are present. Utilizing a microfluidic approach, we found that stable gradients of intermediate chemokines (CCL19 and CXCL12) failed to promote persistent directional migration of dendritic cells or neutrophils. Instead, rising chemokine concentrations were needed, implying that temporal sensing mechanisms controlled prolonged responses to these ligands. This behavior was found to depend on G-coupled receptor kinase-mediated negative regulation of receptor signaling and contrasted with responses to an end agonist chemoattractant (C5a), for which a stable gradient led to persistent migration. These findings identify temporal sensing as a key requirement for long-range myeloid cell migration to intermediate chemokines and provide insights into the mechanisms controlling immune cell motility in complex tissue environments.

We derive an exact Green's function of the diffusion equation for a pair of disk-shaped interacting particles in two dimensions subject to a backreaction boundary condition. Furthermore, we use the obtained function to calculate exact expressions for the survival probability and the time-dependent rate coefficient for the initially unbound pair and the survival probability of the bound state. The derived expressions will be of particular utility for the description of reversible membrane-bound reactions in cell biology. [http://dx.doi.org/10.1063/1.4737662] Diffusion, or Brownian motion, and its microscopic basis, random walks, are key concepts of non-equilibrium statistical mechanics and the theory of stochastic processes. Their ubiquity renders them applicable in numerous areas of physics and beyond, for instance, engineering, chemistry, biology, and mathematical finance, see, for example, Refs. 1 and 2 and references therein.In the theory of diffusion-influenced reactions, 3 solutions of the diffusion equation which satisfy certain boundary conditions can be used to investigate different types of chemical reactions. Among those solutions, Green's functions (GF) enjoy a privileged role because they permit calculating the solution for any given initial distribution and can be used to derive important other quantities, for instance survival probabilities and time-dependent reaction rate coefficients. [4][5][6] In this sense, knowledge of the GF is tantamount to a "completely solved" problem. However, in most cases, an analytical representation of the GF remains elusive, a notable exception being the case of an isolated pair. Here, GFs and derived quantities have not only been important from a conceptual point of view but have also been used to fit experimental data for a diffusion model with reversible reactions 7 and to investigate how the reduced parameter set could be determined from experimental data describing geminate recombination. Motivated by the desire to understand the influence of stochastic fluctuations and spatial heterogeneities on the behavior of biochemical networks, the last decade has witnessed an increased interest in theoretical approaches describing diffusion-influenced reactions at the molecular level. Analytical representations of GFs describing an isolated pair figure prominently in a number of proposed particle-based stochastic simulation algorithms, because a reaction network may be thought of as composed of unimolecular and bimolecular reactions A + B → products. In this context, GFs can be used to enhance the efficiency of Brownian dynamics simulations.9-11 Moreover, the knowledge of exact analytical expressions permits to validate newly devised stochastic simulation algorithms. Exact analytic expressions for the GF of an isolated pair that can undergo a reversible reaction have been derived for the one and three dimensional cases, 4, 6 whereas a corresponding expression in the time domain for the two dimensional case has been lacking and analytical approaches were limited to approxi...