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Structure, composition and stability of ecological populations are shaped by the inter- and intra-species interactions within these communities. It remains to be fully understood how the interplay of these interactions with other factors, such as immigration, control the structure, diversity and the long term stability of ecological systems in the presence of noise and fluctuations. We address this problem using a minimal model of interacting multi-species ecological communities that incorporates competition, immigration and demographic noise. We find that the complete phase diagram exhibits rich behavior with multiple regimes that go beyond the classical 'niche' and 'neutral' regimes, extending and modifying the 'neutral-like' or 'niche-like' dichotomy. In particular, we observe novel regimes that cannot be characterized as either 'niche' or 'neutral' where a multimodal species abundance distribution is observed. We characterize the transitions between the different regimes and show how they arise from the underlying kinetics of the species turnover, extinction and invasion. Our model serves as a minimal null model of noisy competitive ecological systems, against which more complex models that include factors such as mutations and environmental noise can be compared., Comment: Main: 13 pages, 5 figures. Supplementary: 12 pages, 6 figures

Multicellular organisms comprise a diverse collection of stable tissues built from different cell types. It remains unclear how large numbers of interacting cells can precisely coordinate their gene expression during tissue self-organization. We develop a generalized model of multicellular gene expression that includes intracellular and intercellular gene interactions in tissue-like collectives. We show that tuning the intercellular signaling strength results in a cascade of transitions from single-cell autonomy towards different self-organized collective states. Despite an enormous number of possible tissue states, signaling tends to stabilize a small number of compositionally and spatially simple tissue types even for disordered interaction networks. Statistical properties of the stable phenotypes are preserved for different interaction networks and initial conditions. These results provide a theoretical framework to study how collections of cells in distinct organisms robustly self-organize into relatively simple tissues even for complex interaction networks mediated by large numbers of different molecules, and how different stable tissues are maintained in homeostasis and disease. The close alignment between this theoretical model of tissue self-organization and modern sequencing techniques, particularly spatial transcriptomics, will enable future applications in broad biological contexts., Comment: 15 pages, 6 figures

Hopfield networks (HNs) and Restricted Boltzmann Machines (RBMs) are two important models at the interface of statistical physics, machine learning, and neuroscience. Recently, there has been interest in the relationship between HNs and RBMs, due to their similarity under the statistical mechanics formalism. An exact mapping between HNs and RBMs has been previously noted for the special case of orthogonal (uncorrelated) encoded patterns. We present here an exact mapping in the case of correlated pattern HNs, which are more broadly applicable to existing datasets. Specifically, we show that any HN with $N$ binary variables and $p

Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each specific outcome, effectively corresponding to a single-exit process and assuming the independence of each exit process. But the presence of other exits influences the statistical properties and dynamics measured at any specific exit. Here, we present theoretical arguments to explicitly show the existence of different time scales, such as mean exit times and inverse exit fluxes, for dynamic processes with multiple exits. This implies that the statistics of any specific exit dynamics cannot be considered without taking into account the presence of other exits. Several illustrative examples are described in detail using analytical calculations, mean-field estimates, and kinetic Monte Carlo computer simulations. The underlying microscopic mechanisms for the existence of different time scales are discussed. The results are relevant for understanding the mechanisms of various biological, chemical, and industrial processes, including transport through channels and pores.

Living cells sense their environment through the binding of extra-cellular molecular ligands to cell surface receptors. Puzzlingly, vast numbers of signaling pathways exhibit a high degree of cross talk between different signals whereby different ligands act through the same receptor or shared components downstream. It remains unclear how a cell can accurately process information from the environment in such cross-wired pathways. We show that a feature which commonly accompanies cross talk - signaling pleiotropy (the ability of a receptor to produce multiple outputs) - offers a solution to the cross talk problem. In a minimal model we show that a single pleiotropic receptor can simultaneously identify and accurately sense the concentrations of arbitrary unknown ligands present individually or in a mixture. We calculate the fundamental limits of the signaling specificity and accuracy of such signaling schemes. The model serves as an elementary "building block" towards understanding more complex cross-wired receptor-ligand signaling networks.

Synergistic and antagonistic interactions in multi-species populations - such as resource sharing and competition - result in remarkably diverse behaviors in populations of interacting cells, such as in soil or human microbiomes, or clonal competition in cancer. The degree of inter- and intra-specific interaction can often be quantified through the notion of an ecological "niche". Typically, weakly interacting species that occupy largely distinct niches result in stable mixed populations, while strong interactions and competition for the same niche results in rapid extinctions of some species and fixations of others. We investigate the transition of a deterministically stable mixed population to a stochasticity-induced fixation as a function of the niche overlap between the two species. We also investigate the effect of the niche overlap on the population stability with respect to external invasions. Our results have important implications for a number of experimental systems., Comment: 32 pages, 12 figures

Often sharp changes in cellular behavior are triggered by thresholded events, i.e., by the attainment of a threshold value of a relevant cellular or molecular dynamical variable. Since the governing variable itself typically undergoes noisy or stochastic dynamics, there is a corresponding variability in the times when the same change occurs in each cell of a population. This time is called the "first passage" time and the corresponding process is a "first passage" (FP) process, referring to the event when a random variable first passes the threshold value. In this review we first present and elucidate fundamentals of the FP formalism within a unified conceptual framework, which naturally integrates the existing techniques. We then discuss applications thereof, with emphasis on the practical use of FP techniques in biophysical systems. Our focus here is on covering a diverse set of analytical techniques; the number of reviewed biological applications is thus limited, out of necessity. We focus on three specific areas: channel transport; receptor binding and adhesion; and single-cell growth and division.

Some female moths attract male moths by emitting series of pulses of pheromone filaments propagating downwind. The turbulent nature of the wind creates a complex flow environment, and causes the filaments to propagate in the form of patches with varying concentration distributions. Inspired by moth navigation capabilities, we propose a navigation strategy that enables a flier to locate a pulsating odor source in a windy environment using a single threshold-based detection sensor. The strategy is constructed based on the physical properties of the turbulent flow carrying discrete puffs of odor and does not involve learning, memory, complex decision making or statistical methods. We suggest that in turbulent plumes from a pulsating point source, an instantaneously measurable quantity referred as a "puff crossing time", improves the success rate as compared to the navigation strategy based on "internal counter" that does not use this information. Using computer simulations of fliers navigating in turbulent plumes of the pulsating point source for varying flow parameters: turbulent intensities, plume meandering and wind gusts, we obtained trajectories qualitatively resembling male moths flights towards the pheromone sources. We quantified the probability of a successful navigation as well as the flight parameters such as the time spent searching and the total flight time, with respect to different turbulent intensities, meandering or gusts. The concepts learned using this model may help to design odor-based navigation of miniature airborne autonomous vehicles.

Mixtures of nanoparticles and polymer-like objects are encountered in many nanotechnological applications and biological systems. We study the behavior of grafted polymer layers decorated by nanoparticles that are attracted to the polymers using lattice gas based mean field theory and accompanying coarse-grained Brownian dynamics simulations. We find that the presence of nanoparticles can induce large morphological transitions in the layer morphology. In particular, at moderate nanoparticle concentrations, the nanoparticles cause a reduction in the height of the polymer layer above the grafting surface, which occurs via a novel first-order phase transition for sufficiently strong attraction between the polymers and the nanoparticles and smoothly for weak attractions. The predictions of the theory qualitatively agree with the observed behavior of grafted natively unfolded protein strands upon binding of proteins. The results also inform ways of designing nanopolymer layer morphologies.

Settlement of marine larvae on a substrate is a fundamental problem of marine life. The probability of settlement is one of the quantitative characteristic of the settlement process. The probability of larval contact with a substrate is the upper bound of the probability of settlement. This work addresses the problem of contact probability and contact rate of marine invertebrate larvae with an isolated protruding collector located in an unbounded sea current. There are two common approaches to the problem of contact probability. In one, a collector induces certain cues, which help a larvae find the collector. In such a case, the larva moves towards the collector deliberately, using its navigation and propulsion devices. In the second approach, a larva moves towards a collector as a passive small particle. In this case, the cause of contact of a larva with a collector is a mechanical collision of a small moving body with a large obstacle. We considered a larva which does not know the location of the collector, which does not use its navigation device yet uses its self-propulsion. We mimicked a larva by a tiny self-propelled underwater vehicle, moving in shear flow of a large obstacle. We illustrated our approach by studying contact of a larva of the Bryozoan Bugula neritina with a cylindrical collector. We observed the behavior of this larva in a laboratory flume, and according to the observations formulated a mathematical model of larval motion in shear flow. The trajectories of a large number of larvae, starting their motion far from a collector with random initial conditions are calculated numerically, and the probability of their contact with a collector is estimated. The results of Monte-Carlo simulations illustrate that larval self-propulsion may increase the probability of their contact with a collector by orders of magnitude compared to passive particles., Comment: 17 pages, 14 figures, 2 tables

Transport through nano-channels plays an important role in many biological processes and industrial applications. Gaining insights into the functioning of biological transport processes and the design of man-made nano-devices requires an understanding of the basic physics of such transport. A simple exclusion process has proven to be very useful in ex- plaining the properties of several artificial and biological nano-channels. It is particularly useful for modeling the influence of inter-particle interactions on transport characteristics. In this paper, we explore several models of the exclusion process using a mean field approach and computer simulations. We examine the effects of crowding inside the channel and its immediate vicinity on the mean flux and the transport times of single molecules. Finally, we discuss the robustness of the theory's predictions with respect to the crucial characteristics of the hindered diffusion in nano-channels that need to be included in the model.

Many biological channels perform highly selective transport without direct input of metabolic energy and without transitions from a 'closed' to an 'open' state during transport. Mechanisms of selectivity of such channels serve as an inspiration for creation of artificial nano-molecular sorting devices and bio-sensors. To elucidate the transport mechanisms, it is important to understand the transport on the single molecule level in the experimentally relevant regime when multiple particles are crowded in the channel. In this paper we analyze the effects of inter-particle crowding on the non-equilibrium transport times through a finite-length channel by means of analytical theory and computer simulations.

Many biological and artificial transport channels function without direct input of metabolic energy during a transport event and without structural rearrangements involving transitions from a 'closed' to an 'open' state. Nevertheless, such channels are able to maintain efficient and selective transport. It has been proposed that attractive interactions between the transported molecules and the channel can increase the transport efficiency and that the selectivity of such channels can be based on the strength of the interaction of the specifically transported molecules with the channel. Herein, we study the transport through narrow channels in a framework of a general kinetic theory, which naturally incorporates multi-particle occupancy of the channel and non-single-file transport. We study how the transport efficiency and the probability of translocation through the channel are affected by inter-particle interactions in the confined space inside the channel, and establish conditions for selective transport. We compare the predictions of the model with the available experimental data - and find good semi-quantitative agreement. Finally, we discuss applications of the theory to the design of artificial nano-molecular sieves., Comment: 27 pages, 6 figures, 1 Appendix, in press in Biophysical Journal

All materials enter or exit the cell nucleus through nuclear pore complexes (NPCs), efficient transport devices that combine high selectivity and throughput. A central feature of this transport is the binding of cargo-carrying soluble transport factors to flexible, unstructured proteinaceous filaments called FG-nups that line the NPC. We have modeled the dynamics of transport factors and their interaction with the flexible FG-nups as diffusion in an effective potential, using both analytical theory and computer simulations. We show that specific binding of transport factors to the FG-nups facilitates transport and provides the mechanism of selectivity. We show that the high selectivity of transport can be accounted for by competition for both binding sites and space inside the NPC, which selects for transport factors over other macromolecules that interact only non-specifically with the NPC. We also show that transport is relatively insensitive to changes in the number and distribution of FG-nups in the NPC, due mainly to their flexibility; this accounts for recent experiments where up to half of the total mass of the NPC has been deleted, without abolishing the transport. Notably, we demonstrate that previously established physical and structural properties of the NPC can account for observed features of nucleocytoplasmic transport. Finally, our results suggest strategies for creation of artificial nano-molecular sorting devices., Comment: 38 pages, six figures

We predict the thermodynamic and structural behavior of solutions of long cross-linked filaments. We find that at the mean field level, the entropy of self-assembled junctions induces an effective attraction between the filaments that can result in a phase separation into a connected network, in equilibrium with a dilute phase. A connected network can also be formed in a non-thermodynamic transition upon increase of the chain, or cross link density, or with decreasing temperature. For rigid rods, at low temperatures, we predict a transition from an isotropic network, to anisotropic bundles of rods tightly bound by cross links, that is triggered by the interplay between the configurational entropy of the cross-link distribution among the rods, and the rotational and translational entropy of the rods., Comment: typos and graphics corrected; 6 pages 1 figure

We study theoretically a model system of a transient network of microemulsion droplets connected by telechelic polymers and explain recent experimental findings. Despite the absence of any specific interactions between either the droplets or polymer chains, we predict that as the number of polymers per drop is increased, the system undergoes a first order phase separation into a dense, highly connected phase, in equilibrium with dilute droplets, decorated by polymer loops. The phase transition is purely entropic and is driven by the interplay between the translational entropy of the drops and the configurational entropy of the polymer connections between them. Because it is dominated by entropic effects, the phase separation mechanism of the system is extremely robust and does not depend on the particlular physical realization of the network. The discussed model applies as well to other polymer linked particle aggregates, such as nano-particles connected with short DNA linkers.

We analyze both the static and dynamic fluctuation spectrum of the red-blood cell in a unified manner, using a simple model of the composite membrane. In this model, the two-dimensional spectrin network that forms the cytoskeleton is treated as a rigid shell which is located at some constant average separation from the lipid bilayer. The cytoskeleton thereby confines both the static and dynamic fluctuations of the lipid bilayer. The predictions of the model account for the wavevector and frequency dependence of the experimental data. The observed amplitude of the thermal fluctuations is related to effects of ATP-driven fluctuations., Comment: 6 pages, 3 figures

We study a generic model of self-assembling chains which can branch and form networks with branching points (junctions) of arbitrary functionality. The physical realizations include physical gels, wormlike micells, dipolar fluids and microemulsions. The model maps the partition function of a solution of branched, self-assembling, mutually avoiding clusters onto that of a Heisenberg magnet in the mathematical limit of zero spin components. The model is solved in the mean field approximation. It is found that despite the absence of any specific interaction between the chains, the entropy of the junctions induces an effective attraction between the monomers, which in the case of three-fold junctions leads to a first order reentrant phase separation between a dilute phase consisting mainly of single chains, and a dense network, or two network phases. Independent of the phase separation, we predict the percolation (connectivity) transition at which an infinite network is formed that partially overlaps with the first-order transition. The percolation transition is a continuous, non thermodynamic transition that describes a change in the topology of the system. Our treatment which predicts both the thermodynamic phase equilibria as well as the spatial correlations in the system allows us to treat both the phase separation and the percolation threshold within the same framework. The density-density correlation correlation has a usual Ornstein-Zernicke form at low monomer densities. At higher densities, a peak emerges in the structure factor, signifying an onset of medium-range order in the system. Implications of the results for different physical systems are discussed., Comment: Submitted to Phys. Rev. E