Mean First Passage Time in Periodic Attractors

The properties of the mean first passage time in a system characterized by multiple periodic attractors are studied. Using a transformation from a high dimensional space to 1D, the problem is reduced to a stochastic process along the path from the fixed point attractor to a saddle point located between two neighboring attractors. It is found that the time to switch between attractors depends on the effective size of the attractors, $\tau$, the noise, $\epsilon$, and the potential difference between the attractor and an adjacent saddle point as: $~T = {c \over \tau} \exp({\tau \over \epsilon} \Delta {\cal{U}})~$; the ratio between the sizes of the two attractors affects $\Delta {\cal{U}}$. The result is obtained analytically for small $\tau$ and confirmed by numerical simulations. Possible implications that may arise from the model and results are discussed.Comment: 14 pages, 3 figures, submitted to journal of physics

Network Representation of T-Cell Repertoire— A Novel Tool to Analyze Immune Response to Cancer Formation

The T cell repertoire potentially presents complexity compatible, or greater than, that of the human brain. T cell based immune response is involved with practically every part of human physiology, and high-throughput biology needed to follow the T-cell repertoire has made great leaps with the advent of massive parallel sequencing [1]. Nevertheless, tools to handle and observe the dynamics of this complexity have only recently started to emerge [e.g., 2, 3, 4] in parallel with sequencing technologies. Here, we present a network-based view of the dynamics of the T cell repertoire, during the course of mammary tumors development in a mouse model. The transition from the T cell receptor as a feature, to network-based clustering, followed by network-based temporal analyses, provides novel insights to the workings of the system and provides novel tools to observe cancer progression via the perspective of the immune system. The crux of the approach here is at the network-motivated clustering. The purpose of the clustering step is not merely data reduction and exposing structures, but rather to detect hubs, or attractors, within the T cell receptor repertoire that might shed light on the behavior of the immune system as a dynamic network. The Clone-Attractor is in fact an extension of the clone concept, i.e., instead of looking at particular clones we observe the extended clonal network by assigning clusters to graph nodes and edges to adjacent clusters (editing distance metric). Viewing the system as dynamical brings to the fore the notion of an attractors landscape, hence the possibility to chart this space and map the sample state at a given time to a vector in this large space. Based on this representation we applied two different methods to demonstrate its effectiveness in identifying changes in the repertoire that correlate with changes in the phenotype: (1) network analysis of the TCR repertoire in which two measures were calculated and demonstrated the ability to differentiate control from transgenic samples, and, (2) machine learning classifier capable of both stratifying control and trangenic samples, as well as to stratify pre-cancer and cancer samples

Model of ionic currents through microtubule nanopores and the lumen

It has been suggested that microtubules and other cytoskeletal filaments may act as electrical transmission lines. An electrical circuit model of the microtubule is constructed incorporating features of its cylindrical structure with nanopores in its walls. This model is used to study how ionic conductance along the lumen is affected by flux through the nanopores when an external potential is applied across its two ends. Based on the results of Brownian dynamics simulations, the nanopores were found to have asymmetric inner and outer conductances, manifested as nonlinear IV curves. Our simulations indicate that a combination of this asymmetry and an internal voltage source arising from the motion of the C-terminal tails causes a net current to be pumped across the microtubule wall and propagate down the microtubule through the lumen. This effect is demonstrated to enhance and add directly to the longitudinal current through the lumen resulting from an external voltage source, and could be significant in amplifying low-intensity endogenous currents within the cellular environment or as a nano-bioelectronic device.Comment: 43 pages, 6 figures, revised versio

Electrical recordings from dendritic spines of adult mouse hippocampus and effect of the actin cytoskeleton

Dendritic spines (DS) are tiny protrusions implicated in excitatory postsynaptic responses in the CNS. To achieve their function, DS concentrate a high density of ion channels and dynamic actin networks in a tiny specialized compartment. However, to date there is no direct information on DS ionic conductances. Here, we used several experimental techniques to obtain direct electrical information from DS of the adult mouse hippocampus. First, we optimized a method to isolate DS from the dissected hippocampus. Second, we used the lipid bilayer membrane (BLM) reconstitution and patch clamping techniques and obtained heretofore unavailable electrical phenotypes on ion channels present in the DS membrane. Third, we also patch clamped DS directly in cultured adult mouse hippocampal neurons, to validate the electrical information observed with the isolated preparation. Electron microscopy and immunochemistry of PDS-95 and NMDA receptors and intrinsic actin networks confirmed the enrichment of the isolated DS preparation, showing open and closed DS, and multi-headed DS. The preparation was used to identify single channel activities and “whole-DS” electrical conductance. We identified NMDA and Ca2+-dependent intrinsic electrical activity in isolated DS and in situ DS of cultured adult mouse hippocampal neurons. In situ recordings in the presence of local NMDA, showed that individual DS intrinsic electrical activity often back-propagated to the dendrite from which it sprouted. The DS electrical oscillations were modulated by changes in actin cytoskeleton dynamics by addition of the F-actin disrupter agent, cytochalasin D, and exogenous actin-binding proteins. The data indicate that DS are elaborate excitable electrical devices, whose activity is a functional interplay between ion channels and the underlying actin networks. The data argue in favor of the active contribution of individual DS to the electrical activity of neurons at the level of both the membrane conductance and cytoskeletal signaling.Fil: Priel, Avner. Bar-Ilan University; IsraelFil: Dai, Xiao Qing. University of Alberta; CanadáFil: Chen, Xing-Zhen. University of Alberta; CanadáFil: Scarinci, María Noelia. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet Noa Sur. Instituto Multidisciplinario de Salud, Tecnologia y Desarrollo. - Universidad Nacional de Santiago del Estero. Instituto Multidisciplinario de Salud, Tecnologia y Desarrollo.; ArgentinaFil: Cantero, Maria del Rocio. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet Noa Sur. Instituto Multidisciplinario de Salud, Tecnologia y Desarrollo. - Universidad Nacional de Santiago del Estero. Instituto Multidisciplinario de Salud, Tecnologia y Desarrollo.; ArgentinaFil: Cantiello, Horacio Fabio. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet Noa Sur. Instituto Multidisciplinario de Salud, Tecnologia y Desarrollo. - Universidad Nacional de Santiago del Estero. Instituto Multidisciplinario de Salud, Tecnologia y Desarrollo.; Argentin

A Bio-Polymer Transistor: Electrical Amplification by Microtubules

Microtubules (MTs) are important cytoskeletal structures, engaged in a number of specific cellular activities, including vesicular traffic, cell cyto-architecture and motility, cell division, and information processing within neuronal processes. MTs have also been implicated in higher neuronal functions, including memory, and the emergence of "consciousness". How MTs handle and process electrical information, however, is heretofore unknown. Here we show new electrodynamic properties of MTs. Isolated, taxol-stabilized microtubules behave as bio-molecular transistors capable of amplifying electrical information. Electrical amplification by MTs can lead to the enhancement of dynamic information, and processivity in neurons can be conceptualized as an "ionic-based" transistor, which may impact among other known functions, neuronal computational capabilities.Comment: This is the final submitted version. The published version should be downloaded from Biophysical Journa

Neural cytoskeleton capabilities for learning and memory

This paper proposes a physical model involving the key structures within the neural cytoskeleton as major players in molecular-level processing of information required for learning and memory storage. In particular, actin filaments and microtubules are macromolecules having highly charged surfaces that enable them to conduct electric signals. The biophysical properties of these filaments relevant to the conduction of ionic current include a condensation of counterions on the filament surface and a nonlinear complex physical structure conducive to the generation of modulated waves. Cytoskeletal filaments are often directly connected with both ionotropic and metabotropic types of membrane-embedded receptors, thereby linking synaptic inputs to intracellular functions. Possible roles for cable-like, conductive filaments in neurons include intracellular information processing, regulating developmental plasticity, and mediating transport. The cytoskeletal proteins form a complex network capable of emergent information processing, and they stand to intervene between inputs to and outputs from neurons. In this manner, the cytoskeletal matrix is proposed to work with neuronal membrane and its intrinsic components (e.g., ion channels, scaffolding proteins, and adaptor proteins), especially at sites of synaptic contacts and spines. An information processing model based on cytoskeletal networks is proposed that may underlie certain types of learning and memory

Analytical Study of the Interplay Between Architecture and Predictability

We study model feed forward networks as time series predictors in the stationary limit. The focus is on complex, yet non-chaotic, behavior. The main question we address is whether the asymptotic behavior is governed by the architecture, regardless the details of the weights. We find hierarchies among classes of architectures with respect to the attractor dimension of the long term sequence they are capable of generating; larger number of hidden units can generate higher dimensional attractors. In the case of a perceptron, we develop the stationary solution for general weights, and show that the flow is typically one dimensional. The relaxation time from an arbitrary initial condition to the stationary solution is found to scale linearly with the size of the network. In multilayer networks, the number of hidden units gives bounds on the number and dimension of the possible attractors. We conclude that long term prediction (in the non-chaotic regime) with such models is governed by attra..