A model of fasciculation and sorting in mixed populations of axons

We extend a recently proposed model (Chaudhuri et al., EPL 87, 20003 (2009)) aiming to describe the formation of fascicles of axons during neural development. The growing axons are represented as paths of interacting directed random walkers in two spatial dimensions. To mimic turnover of axons, whole paths are removed and new walkers are injected with specified rates. In the simplest version of the model, we use strongly adhesive short-range inter-axon interactions that are identical for all pairs of axons. We generalize the model to adhesive interactions of finite strengths and to multiple types of axons with type-specific interactions. The dynamic steady state is characterized by the position-dependent distribution of fascicle sizes. With distance in the direction of axon growth, the mean fascicle size and emergent time scales grow monotonically, while the degree of sorting of fascicles by axon type has a maximum at a finite distance. To understand the emergence of slow time scales, we develop an analytical framework to analyze the interaction between neighboring fascicles.Comment: 19 pages, 13 figures; version accepted for publication in Phys Rev

Physiology of spontaneous [Ca2+]i oscillations in the isolated vasopressin and oxytocin neurones of the rat supraoptic nucleus

AbstractThe magnocellular vasopressin (AVP) and oxytocin (OT) neurones exhibit specific electrophysiological behaviour, synthesise AVP and OT peptides and secrete them into the neurohypophysial system in response to various physiological stimulations. The activity of these neurones is regulated by the very same peptides released either somato-dendritically or when applied to supraoptic nucleus (SON) preparations in vitro. The AVP and OT, secreted somato-dendritically (i.e. in the SON proper) act through specific autoreceptors, induce distinct Ca2+ signals and regulate cellular events. Here, we demonstrate that about 70% of freshly isolated individual SON neurones from the adult non-transgenic or transgenic rats bearing AVP (AVP-eGFP) or OT (OT-mRFP1) markers, produce distinct spontaneous [Ca2+]i oscillations. In the neurones identified (through specific fluorescence), about 80% of AVP neurones and about 60% of OT neurones exhibited these oscillations. Exposure to AVP triggered [Ca2+]i oscillations in silent AVP neurones, or modified the oscillatory pattern in spontaneously active cells. Hyper- and hypo-osmotic stimuli (325 or 275 mOsmol/l) respectively intensified or inhibited spontaneous [Ca2+]i dynamics. In rats dehydrated for 3 or 5days almost 90% of neurones displayed spontaneous [Ca2+]i oscillations. More than 80% of OT-mRFP1 neurones from 3 to 6-day-lactating rats were oscillatory vs. about 44% (OT-mRFP1 neurones) in virgins. Together, these results unveil for the first time that both AVP and OT neurones maintain, via Ca2+ signals, their remarkable intrinsic in vivo physiological properties in an isolated condition

Dynamics of path aggregation in the presence of turnover

We investigate the slow time scales that arise from aging of the paths during the process of path aggregation. This is studied using Monte-Carlo simulations of a model aiming to describe the formation of fascicles of axons mediated by contact axon-axon interactions. The growing axons are represented as interacting directed random walks in two spatial dimensions. To mimic axonal turnover, random walkers are injected and whole paths of individual walkers are removed at specified rates. We identify several distinct time scales that emerge from the system dynamics and can exceed the average axonal lifetime by orders of magnitude. In the dynamical steady state, the position-dependent distribution of fascicle sizes obeys a scaling law. We discuss our findings in terms of an analytically tractable, effective model of fascicle dynamics.Comment: 6 pages, 5 figures; changed the order of presentation, rewritten the abstract and introduction, changed the title, expanded discussions; the main results remain the sam

Induction of non-d-wave order-parameter components by currents in d-wave superconductors

It is shown, within the framework of the Ginzburg-Landau theory for a superconductor with d_{x^2-y^2} symmetry, that the passing of a supercurrent through the sample results, in general, in the induction of order-parameter components of distinct symmetry. The induction of s-wave and d_{xy(x^2-y^2)-wave components are considered in detail. It is shown that in both cases the order parameter remains gapless; however, the structure of the lines of nodes and the lobes of the order parameter are modified in distinct ways, and the magnitudes of these modifications differ in their dependence on the (a-b plane) current direction. The magnitude of the induced s-wave component is estimated using the results of the calculations of Ren et al. [Phys. Rev. Lett. 74, 3680 (1995)], which are based on a microscopic approach.Comment: 15 pages, includes 2 figures. To appear in Phys. Rev.

Soft and non-soft structural transitions in disordered nematic networks

Properties of disordered nematic elastomers and gels are theoretically investigated with emphasis on the roles of non-local elastic interactions and crosslinking conditions. Networks originally crosslinked in the isotropic phase lose their long-range orientational order by the action of quenched random stresses, which we incorporate into the affine-deformation model of nematic rubber elasticity. We present a detailed picture of mechanical quasi-Goldstone modes, which accounts for an almost completely soft polydomain-monodomain (P-M) transition under strain as well as a ``four-leaf clover'' pattern in depolarized light scattering intensity. Dynamical relaxation of the domain structure is studied using a simple model. The peak wavenumber of the structure factor obeys a power-law-type slow kinetics and goes to zero in true mechanical equilibrium. The effect of quenched disorder on director fluctuation in the monodomain state is analyzed. The random frozen contribution to the fluctuation amplitude dominates the thermal one, at long wavelengths and near the P-M transition threshold. We also study networks obtained by crosslinking polydomain nematic polymer melts. The memory of initial director configuration acts as correlated and strong quenched disorder, which renders the P-M transition non-soft. The spatial distribution of the elastic free energy is strongly dehomogenized by external strain, in contrast to the case of isotropically crosslinked networks.Comment: 19 pages, 15 EPS figure

26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 - Meeting Abstracts - Antwerp, Belgium. 15–20 July 2017

This work was produced as part of the activities of FAPESP Research,\ud Disseminations and Innovation Center for Neuromathematics (grant\ud 2013/07699-0, S. Paulo Research Foundation). NLK is supported by a\ud FAPESP postdoctoral fellowship (grant 2016/03855-5). ACR is partially\ud supported by a CNPq fellowship (grant 306251/2014-0)

The role of topological defects and textures in the kinetics of phase ordering

In this thesis, I present the results of a theoretical investigation of ordering processes induced by symmetry-breaking quenches in two physical systems. Both systems investigated possess a rich homotopy structure of the order-parameter space, which results in numerous topologically stable objects being generated during the quench, and influencing the properties of the system during the subsequent approach to equilibrium. The results reported are mostly computational in nature. The two systems investigated are (i) nematic liquid crystals, which support topologically stable abelian (in the uniaxial nematic case) and non-abelian (in the biaxial nematic case) singular defects, and (ii) the 0(3)-symmetric vector (i.e., Heisenberg-type) system in 2 spatial dimensions, which supports topologically stable, but non-singular objectstopological textures. In the case of nematic systems, the numerical investigation concentrates on the phase-ordering proceSs and point defect dynamics following a quench into both the uniaxial and biaxial nematiC phases of a quasi-2-dimensionalliquid crystalline system. The time dependences of the correlation function, structure factor, energy density, and number densities of topological defects are computed. By comparing the growth laws for the characteristic length scales extracted from the order-parameter correlations and from the total number of topological defects in the system, it is determined that weak violations of dynamical scaling occur in the system, even at the latest times studied. The observed scaling violations ~~ attributed to the presence of a logarithmic correction to the asymptotic power-law growth. of the average inter:defect separation. Following the quench to the biaxial nematic phase, there are four topologically distinct defect species ptesent in the system, the populations of which are studied in detail. It is found that only two types of defect are observed in large numbers at late times, and a mechanism for the selection of the prevailing defect species is proposed. In addition to the computational investigation of the phase ordering process in 2-d.imensional nematic systems, analytical derivations of the singular (power-law) short-distance behavior of the contribution to the structure factor (i.e., the light scattering intensity) for all types of topologically stable defects encountered in 2- and 3-d.imensional uniaxial and biaxial nematics are presented. The second system studied-the Heisenberg-type model in 2 spatial dimensionsis first implemented numerically as the discretized 0(3) nonlinear u-model with the standard form of free energy and with purely dissipative dynamics. Two distinct mechanisms for the decay of the order-parameter variations-single texture unwinding, and topological charge annihi1ation-are identified and characterized in this system. It is found that whereas at early times after the quench the annibi1ation process dominates, the unwinding processes become of comparable importance at later times. By·examining the correlations in the order parameter and in the topological charge density, it is shown that dynamical scaling is strongly violated during the phase-ordering process, and multiple characteristic length-scales growing as distinct power-laws in time are identified. In order to study in detail the origins of the observed multi-scaling behavior, the phase-ordering process is then studied within a modified 0(3) nonlinear u-model with an additional free energy term {analogous.to the· so-called Sk:yrme term, familiar in high-energy physics) that stabilizes the textures against shrinking and unwinding. It is found that this modification influences the multi-scaling properties of the system in a dramatic way, and that with single-texture u.n windings suppressed, the form of the spectrum of exponents characterizing the decay or the moments of the topological charge density distribution can be predicted successfully by a simple two-length-scale argument.U of I OnlyThesi

Information transfer through a signaling module with feedback: A perturbative approach

Signal transduction in biological cells is effected by signaling pathways that typically include multiple feedback loops. Here we analyze information transfer through a prototypical signaling module with biochemical feedback. The module switches stochastically between an inactive and active state; the input to the module governs the activation rate while the output (i.e., the product concentration) perturbs the inactivation rate. Using a novel perturbative approach, we compute the rate with which information about the input is gained from observation of the output. We obtain an explicit analytical result valid to first order in feedback strength and to second order in the strength of input. The total information gained during an extended time interval is found to depend on the feedback strength only through the total number of activation/inactivation events