Search

Large interacting systems in biology often exhibit emergent dynamics, such as coexistence of multiple time scales, manifested by fat tails in the distribution of waiting times. While existing tools in statistical inference, such as maximum entropy models, reproduce the empirical steady state distributions, it remains challenging to learn dynamical models. We present a novel inference method, called generalized Glauber dynamics. Constructed through a non-Markovian fluctuation dissipation theorem, generalized Glauber dynamics tunes the dynamics of an interacting system, while keeping the steady state distribution fixed. We motivate the need for the method on real data from Eco-HAB, an automated habitat for testing behavior in groups of mice under semi-naturalistic conditions, and present it on simple Ising spin systems. We show its applicability for experimental data, by inferring dynamical models of social interactions in a group of mice that reproduce both its collective behavior and the long tails observed in individual dynamics.

Biological circuits such as neural or gene regulation networks use internal states to map sensory input to an adaptive repertoire of behavior. Characterizing this mapping is a major challenge for systems biology, and though experiments that probe internal states are developing rapidly, organismal complexity presents a fundamental obstacle given the many possible ways internal states could map to behavior. Using C. elegans as an example, we propose a protocol for systematic perturbation of neural states that limits experimental complexity but still characterizes collective aspects of the neural-behavioral map. We consider experimentally motivated small perturbations -- ones that are most likely to preserve natural dynamics and are closer to internal control mechanisms -- to neural states and their impact on collective neural behavior. Then, we connect such perturbations to the local information geometry of collective statistics, which can be fully characterized using pairwise perturbations. Applying the protocol to a minimal model of C. elegans neural activity, we find that collective neural statistics are most sensitive to a few principal perturbative modes. Dominant eigenvalues decay initially as a power law, unveiling a hierarchy that arises from variation in individual neural activity and pairwise interactions. Highest-ranking modes tend to be dominated by a few, "pivotal" neurons that account for most of the system's sensitivity, suggesting a sparse mechanism for control of collective behavior.

Most of animal and human behavior occurs on time scales much longer than the response times of individual neurons. In many cases it is plausible that these long time scales emerge from the recurrent dynamics of electrical activity in networks of neurons. In linear models, time scales are set by the eigenvalues of a dynamical matrix whose elements measure the strengths of synaptic connections between neurons. It is not clear to what extent these matrix elements need to be tuned in order to generate long time scales; in some cases, one needs not just a single long time scale but a whole range. Starting from the simplest case of random symmetric connections, we combine maximum entropy and random matrix theory methods to construct ensembles of networks, exploring the constraints required for long time scales to become generic. We argue that a single long time scale can emerge generically from realistic constraints, but a full spectrum of slow modes requires more tuning. Langevin dynamics that will generate patterns of synaptic connections drawn from these ensembles involve a combination of Hebbian learning and activity-dependent synaptic scaling., Comment: 13 pages, 5 figures

In large neuronal networks, it is believed that functions emerge through the collective behavior of many interconnected neurons. Recently, the development of experimental techniques that allow simultaneous recording of calcium concentration from a large fraction of all neurons in Caenorhabditis elegans - a nematode with 302 neurons - creates the opportunity to ask if such emergence is universal, reaching down to even the smallest brains. Here, we measure the activity of 50+ neurons in C. elegans, and analyze the data by building the maximum entropy model that matches the mean activity and pairwise correlations among these neurons. To capture the graded nature of the cells' responses, we assign each cell multiple states. These models, which are equivalent to a family of Potts glasses, successfully predict higher statistical structure in the network. In addition, these models exhibit signatures of collective behavior: the state of single cells can be predicted from the state of the rest of the network; the network, despite being sparse in a way similar to the structural connectome, distributes its response globally when locally perturbed; the distribution over network states has multiple local maxima, as in models for memory; and the parameters that describe the real network are close to a critical surface in this family of models., Comment: 14 pages, 12 figures