Computational methods and diffusion theory in triangulation sensing to model neuronal navigation.

Computational methods are now recognized as powerful and complementary approaches in various applied sciences such as biology. These computing methods are used to explore the gap between scales such as the one between molecular and cellular. Here we present recent progress in the development of computational approaches involving diffusion modeling, asymptotic analysis of the model partial differential equations, hybrid methods and simulations in the generic context of cell sensing and guidance via external gradients. Specifically, we highlight the reconstruction of the location of a point source in two and three dimensions from the steady-state diffusion fluxes arriving to narrow windows located on the cell. We discuss cases in which these windows are located on the boundary of a two-dimensional plane or three-dimensional half-space, on a disk in free space or inside a two-dimensional corridor, or a ball in three dimensions. The basis of this computational approach is explicit solutions of the Neumann-Green's function for the mentioned geometry. This analysis can be used to design hybrid simulations where Brownian paths are generated only in small regions in which the local spatial organization is relevant. Particle trajectories outside of this region are only implicitly treated by generating exit points at the boundary of this domain of interest. This greatly accelerates the simulation time by avoiding the explicit computation of Brownian paths in an infinite domain and serves to generate statistics, without following all trajectories at the same time, a process that can become numerically expensive quickly. Moreover, these computational approaches are used to reconstruct a point source and estimating the uncertainty in the source reconstruction due to an additive noise perturbation present in the fluxes. We also discuss the influence of various window configurations (cluster vs uniform distributions) on recovering the source position. Finally, the applications in developmental biology are formulated into computational principles that could underly neuronal navigation in the brain.

Integrin signaling downregulates filopodia during muscle-tendon attachment.

Cells need to sense their environment to ensure accurate targeting to specific destinations. This occurs in developing muscles, which need to attach to tendon cells before muscle contractions can begin. Elongating myotube tips form filopodia, which are presumed to have sensory roles, and are later suppressed upon building the attachment site. Here, we use live imaging and quantitative image analysis of lateral transverse (LT) myotubes in Drosophila to show that filopodia suppression occurs as a result of integrin signaling. Loss of the integrin subunits αPS2 and ßPS (also known as If and Mys, respectively, in flies) increased filopodia number and length at stages when they are normally suppressed. Conversely, inducing integrin signaling, achieved by the expression of constitutively dimerised ßPS cytoplasmic domain (diß), prematurely suppressed filopodia. We discovered that the integrin signal is transmitted through the protein G protein-coupled receptor kinase interacting ArfGAP (Git) and its downstream kinase p21-activated kinase (Pak). Absence of these proteins causes profuse filopodia and prevents the filopodial inhibition mediated by diß. Thus, integrin signaling terminates the exploratory behavior of myotubes seeking tendons, enabling the actin machinery to focus on forming a strong attachment and assembling the contractile apparatus.

Triangulation Sensing to Determine the Gradient Source from Diffusing Particles to Small Cell Receptors.

How does a cell locate the source of molecular guidance cues from within a concentration gradient? We present a computational approach to recover the source from the absorbed fluxes at narrow receptor windows located on the surface of the cell. In the limit of fast binding, we solve the steady-state diffusion equation using an asymptotic approach and hybrid stochastic-analytical simulations. We show that the sensitivity to the gradient direction decays too rapidly to enable long-distance sensing. We illustrate how this constraint can be alleviated when triangulating the source with an increasing number of receptor windows and quantify the susceptibility of this process to flux perturbations.

Steric Effects Induce Geometric Remodeling of Actin Bundles in Filopodia.

Filopodia are ubiquitous fingerlike protrusions, spawned by many eukaryotic cells, to probe and interact with their environments. Polymerization dynamics of actin filaments, comprising the structural core of filopodia, largely determine their instantaneous lengths and overall lifetimes. The polymerization reactions at the filopodial tip require transport of G-actin, which enter the filopodial tube from the filopodial base and diffuse toward the filament barbed ends near the tip. Actin filaments are mechanically coupled into a tight bundle by cross-linker proteins. Interestingly, many of these proteins are relatively short, restricting the free diffusion of cytosolic G-actin throughout the bundle and, in particular, its penetration into the bundle core. To investigate the effect of steric restrictions on G-actin diffusion by the porous structure of filopodial actin filament bundle, we used a particle-based stochastic simulation approach. We discovered that excluded volume interactions result in partial and then full collapse of central filaments in the bundle, leading to a hollowed-out structure. The latter may further collapse radially due to the activity of cross-linking proteins, hence producing conical-shaped filament bundles. Interestingly, electron microscopy experiments on mature filopodia indeed frequently reveal actin bundles that are narrow at the tip and wider at the base. Overall, our work demonstrates that excluded volume effects in the context of reaction-diffusion processes in porous networks may lead to unexpected geometric growth patterns and complicated, history-dependent dynamics of intermediate metastable configurations.

Environmental versus demographic variability in two-species predator-prey models.

We investigate the competing effects and relative importance of intrinsic demographic and environmental variability on the evolutionary dynamics of a stochastic two-species Lotka-Volterra model by means of Monte Carlo simulations on a two-dimensional lattice. Individuals are assigned inheritable predation efficiencies; quenched randomness in the spatially varying reaction rates serves as environmental noise. We find that environmental variability enhances the population densities of both predators and prey while demographic variability leads to essentially neutral optimization.

Genome sequence of Leishmania mexicana MNYC/BZ/62/M379 expressing Cas9 and T7 RNA polymerase.

We present the genome sequence of Leishmania mexicana MNYC/BZ/62/M379 modified to express Cas9 and T7 RNA-polymerase, revealing high similarity to the reference genome (MHOM/GT2001/U1103). Through RNAseq-based annotation of coding sequences and untranslated regions, we provide primer sequences for construct and sgRNA template generation for CRISPR-assisted gene deletion and endogenous tagging.

Stochastic combinations of actin regulatory proteins are sufficient to drive filopodia formation.

Assemblies of actin and its regulators underlie the dynamic morphology of all eukaryotic cells. To understand how actin regulatory proteins work together to generate actin-rich structures such as filopodia, we analyzed the localization of diverse actin regulators within filopodia in Drosophila embryos and in a complementary in vitro system of filopodia-like structures (FLSs). We found that the composition of the regulatory protein complex where actin is incorporated (the filopodial tip complex) is remarkably heterogeneous both in vivo and in vitro. Our data reveal that different pairs of proteins correlate with each other and with actin bundle length, suggesting the presence of functional subcomplexes. This is consistent with a theoretical framework where three or more redundant subcomplexes join the tip complex stochastically, with any two being sufficient to drive filopodia formation. We provide an explanation for the observed heterogeneity and suggest that a mechanism based on multiple components allows stereotypical filopodial dynamics to arise from diverse upstream signaling pathways.

A direct role for SNX9 in the biogenesis of filopodia.

Filopodia are finger-like actin-rich protrusions that extend from the cell surface and are important for cell-cell communication and pathogen internalization. The small size and transient nature of filopodia combined with shared usage of actin regulators within cells confounds attempts to identify filopodial proteins. Here, we used phage display phenotypic screening to isolate antibodies that alter the actin morphology of filopodia-like structures (FLS) in vitro. We found that all of the antibodies that cause shorter FLS interact with SNX9, an actin regulator that binds phosphoinositides during endocytosis and at invadopodia. In cells, we discover SNX9 at specialized filopodia in Xenopus development and that SNX9 is an endogenous component of filopodia that are hijacked by Chlamydia entry. We show the use of antibody technology to identify proteins used in filopodia-like structures, and a role for SNX9 in filopodia.

Reconstructing the gradient source position from steady-state fluxes to small receptors.

Recovering the position of a source from the fluxes of diffusing particles through small receptors allows a biological cell to determine its relative position, spatial localization and guide it to a final target. However, how a source can be recovered from point fluxes remains unclear. Using the Narrow Escape approach for an open domain, we compute the diffusion fluxes of Brownian particles generated by a steady-state gradient from a single source through small holes distributed on a surface in two dimensions. We find that the location of a source can be recovered when there are at least 3 receptors and the source is positioned no further than 10 cell radii away, but this condition is not necessary in a narrow strip. The present approach provides a computational basis for the first step of direction sensing of a gradient at a single cell level.

Relaxation dynamics of vortex lines in disordered type-II superconductors following magnetic field and temperature quenches.

We study the effects of rapid temperature and magnetic field changes on the nonequilibrium relaxation dynamics of magnetic vortex lines in disordered type-II superconductors by employing an elastic line model and performing Langevin molecular dynamics simulations. In a previously equilibrated system, either the temperature is suddenly changed or the magnetic field is instantaneously altered which is reflected in adding or removing flux lines to or from the system. The subsequent aging properties are investigated in samples with either randomly distributed pointlike or extended columnar defects, which allows us to distinguish the complex relaxation features that result from either type of pinning centers. One-time observables such as the radius of gyration and the fraction of pinned line elements are employed to characterize steady-state properties, and two-time correlation functions such as the vortex line height autocorrelations and their mean-square displacement are analyzed to study the nonlinear stochastic relaxation dynamics in the aging regime.

Pinning time statistics for vortex lines in disordered environments.

We study the pinning dynamics of magnetic flux (vortex) lines in a disordered type-II superconductor. Using numerical simulations of a directed elastic line model, we extract the pinning time distributions of vortex line segments. We compare different model implementations for the disorder in the surrounding medium: discrete, localized pinning potential wells that are either attractive and repulsive or purely attractive, and whose strengths are drawn from a Gaussian distribution; as well as continuous Gaussian random potential landscapes. We find that both schemes yield power-law distributions in the pinned phase as predicted by extreme-event statistics, yet they differ significantly in their effective scaling exponents and their short-time behavior.

Spatial variability enhances species fitness in stochastic predator-prey interactions.

We study the influence of spatially varying reaction rates on a spatial stochastic two-species Lotka-Volterra lattice model for predator-prey interactions using two-dimensional Monte Carlo simulations. The effects of this quenched randomness on population densities, transient oscillations, spatial correlations, and invasion fronts are investigated. We find that spatial variability in the predation rate results in more localized activity patches, which in turn causes a remarkable increase in the asymptotic population densities of both predators and prey and accelerated front propagation.