Related papers: A stochastic version of the Hopfield-Ninio kinetic…

This paper is concerned with the modeling and analysis of two of the most commonly used recurrent neural network models (i.e., Hopfield neural network and firing-rate neural network) with dynamic recurrent connections undergoing Hebbian…

T cell receptor signaling must operate reliably under tight time constraints. While assuming quite different mechanisms, two prominent models of T cell receptor activation, kinetic segregation and kinetic proofreading, both introduce a…

Cells use surface receptors to estimate the concentration of external ligands. Limits on the accuracy of such estimations have been well studied for pairs of ligand and receptor species. However, the environment typically contains many…

Receptor-ligand interactions are essential for biological function and their binding strength is commonly explained in terms of static lock-and-key models based on molecular complementarity. However, detailed information of the full…

The Hopfield model is a paradigmatic model of neural networks that has been analyzed for many decades in the statistical physics, neuroscience, and machine learning communities. Inspired by the manifold hypothesis in machine learning, we…

Protein sequence generation via stochastic attention produces plausible family members from small alignments without training, but treats all stored sequences equally and cannot direct generation toward a functional subset of interest. We…

We consider the problem of inferring the interactions between a set of N binary variables from the knowledge of their frequencies and pairwise correlations. The inference framework is based on the Hopfield model, a special case of the Ising…

We investigate the computational limits of the memory retrieval dynamics of modern Hopfield models from the fine-grained complexity analysis. Our key contribution is the characterization of a phase transition behavior in the efficiency of…

Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic…

The response of the Hodgkin-Huxley neuronal model subjected to stochastic uncorrelated spike trains originating from a large number of inhibitory and excitatory post-synaptic potentials is analyzed in detail. The model is examined in its…

We discuss prototype formation in the Hopfield network. Typically, Hebbian learning with highly correlated states leads to degraded memory performance. We show this type of learning can lead to prototype formation, where unlearned states…

After discussing the relevance of statistical physics in molecular recognition processes, we present a schematic model for ligand-receptor association based on an Ising chain. We discuss the possible behaviors of the affinity when the…

In this paper we study the relation between the property of detailed balance and the ability of discriminating between different ligands for a class of stochastic models of kinetic proofreading. We prove the existence of a critical amount…

Molecular motors walk along filaments until they detach stochastically with a force-dependent unbinding rate. Here, we show that this unbinding rate can be obtained from the analysis of experimental data of molecular motors moving in…

Priming is the ability of the brain to more quickly activate a target concept in response to a related stimulus (prime). Experiments point to the existence of an overlap between the populations of the neurons coding for different stimuli.…

We consider the problem of estimating parameter sensitivity for Markovian models of reaction networks. Sensitivity values measure the responsiveness of an output to the model parameters. They help in analyzing the network, understanding its…

In this work we introduce and investigate the properties of the "relativistic" Hopfield model endowed with temporally correlated patterns. First, we review the "relativistic" Hopfield model and we briefly describe the experimental evidence…

Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by…

Stochastic modeling of transcription is a classic yet long-standing problem in theoretical biophysics. The lack of unified results and a computationally efficient approach for a general, fine-grained transcription model has confined…

In this article, we study the kinetics of reversible ligand binding to receptors on a spherical cell surface using a self-consistent stochastic theory. Binding, dissociation, diffusion and rebinding of ligands are incorporated into the…