Study of a two-state model for a membrane channel

Màster en Biofísica Part II, 2008-2009. Part I la trobareu a: http://hdl.handle.net/2445/5801We explore biological transport across membrane channels from a physical point of view. The main objective is to use the tools available to a physicist from non-equilibrium thermodynamics and apply them to a concrete biological problem. In this case, we focus our attention in trying to build simple physical models, yet not trivial, that match the behavior of real channels, or ones that can be synthetically accomplished. We start with a brief review of the results we obtained for a model with multiplicative noise and proceed to study a dichotomous model, introducing a more realistic description of channel gating, both analytically and numerically. We also introduce a new different simulation framework that allows more flexibility in parameter exploration than the one previously used

Noise, coherent activity and network structure in neuronal cultures

In this thesis we apply a multidisciplinary approach, based on statistical physics and complex systems, to the study of neuronal dynamics. We focus on understanding, using theoretical and computational tools, how collective neuronal activity emerges in a controlled system, a neuronal culture. We show how the interplay between noise and network structure defines the emergent collective behavior of the system. We build, using theory and simulation, a framework that takes carefully describes spontaneous activity in neuronal cultures by taking into account the underlying network structure of neuronal cultures and use an accurate, yet simple, model for the individual neuronal dynamics. We show that the collective behavior of young cultures is dominated by the nucleation and propagations of activity fronts (bursts) throughout the system. These bursts nucleate at specific sites of the culture, called nucleation points, which result in a highly heterogeneous probability distribution of nucleation. We are able to explain the nucleation mechanism theoretically as a mechanism of noise propagation and amplification called noise focusing. We also explore the internal structure of activity avalanches by using well--defined regular networks, in which all the neurons have the same connectivity rules (motifs). Within these networks, we are able to associate to the avalanches an effective velocity and topological size and relate it to specific motifs. We also devise a continuum description of a neuronal culture at the mesoscale, i.e., we move away from the single neuron dynamics into a coarse--grained description that is able to capture most of the characteristic observables presented in previous chapters. This thesis also studies the spontaneous activity of neuronal cultures within the framework of quorum percolation. We study the effect of network structure within quorum percolation and propose a new model, called stochastic quorum percolation, that includes dynamics and the effect of internal noise. Finally, we use tools from information theory, namely transfer entropy, to show how to reliably infer the connectivity of a neuronal network from its activity, and how to distinguish between different excitatory and inhibitory connections purely from the activity, with no prior knowledge of the different neuronal types. The technique works directly on the fluorescence traces obtained in calcium imaging experiments, without the need to infer the underlying spike trains

Unraveling the hidden complexity of quasideterministic ratchets: random walks, graphs, and circle maps

Brownian ratchets are shown to feature a nontrivial vanishing-noise limit where the dynamics is reduced to a stochastic alternation between two deterministic circle maps (quasideterministic ratchets). Motivated by cooperative dynamics of molecular motors, here we solve exactly the problem of two interacting quasideterministic ratchets. We show that the dynamics can be described as a random walk on a graph that is specific to each set of parameters. We compute point by point the exact velocity-force V ( f ) function as a summation over all paths in the specific graph for each f , revealing a complex structure that features self-similarity and nontrivial continuity properties. From a general perspective, we unveil that the alternation of two simple piecewise linear circle maps unfolds a very rich variety of dynamical complexity, in particular the phenomenon of piecewise chaos, where chaos emerges from the combination of nonchaotic maps. We show convergence of the finite-noise case to our exact solution

Noise focusing in neuronal tissues: Symmetry breaking and localization in excitable networks with quenched disorder

We introduce a coarse-grained stochastic model for the spontaneous activity of neuronal cultures to explain the phenomenon of noise focusing, which entails localization of the noise activity in excitable networks with metric correlations. The system is modeled as a continuum excitable medium with a state-dependent spatial coupling that accounts for the dynamics of synaptic connections. The most salient feature is the emergence at the mesoscale of a vector field V ( r ) , which acts as an advective carrier of the noise. This entails an explicit symmetry breaking of isotropy and homogeneity that stems from the amplification of the quenched fluctuations of the network by the activity avalanches, concomitant with the excitable dynamics. We discuss the microscopic interpretation of V ( r ) and propose an explicit construction of it. The coarse-grained model shows excellent agreement with simulations at the network level. The generic nature of the observed phenomena is discussed

Dominance of metric correlations in two-dimensional neuronal cultures described through a Random Field Ising Model

We introduce a novel random field Ising model, grounded on experimental observations, to assess the importance of metric correlations in cortical circuits in vitro. Metric correlations arise from both the finite axonal length and the heterogeneity in the spatial arrangement of neurons. The experiments consider the response of neuronal cultures to an external electric stimulation for a gradually weaker connectivity strength between neurons, and in cultures with different spatial configurations. The model can be analytically solved in the metric-free, mean-field scenario. The presence of metric correlations precipitates a strong deviation from the mean field. Null models of the same networks that preserve the distribution of connections recover the mean field. Our results show that metric-inherited correlations in spatial networks dominate the connectivity blueprint, mask the actual distribution of connections, and may emerge as the asset that shapes network dynamics

Biological transport: membrane channels, a white noise flashing ratchet model

Màster en Biofísica Part I, curs 2007-2008. Part II la trobareu a: http://hdl.handle.net/2445/6722We explore biological transport across membrane channels from a physical point of view. The main objective is to use the tools available to a physicist from non-equilibrium thermodynamics and apply them to a concrete biological problem. In this case, we focus our attention in trying to build simple physical models, yet not trivial, that match the behavior of real channels, or ones that can be synthetically accomplished. The model of a channel studied in here consists on a symmetric sawtooth potential with multiplicative noise. The introduction of multiplicative noise into the system makes it dramatically change its behavior, yet it remains analytically solvable. We also present a simulation framework applicable to more complex and realistic models for channels that can be easily mapped to real experiments and does not require cumbersome theoretical developments

Evolution over Time of Ventilatory Management and Outcome of Patients with Neurologic Disease∗

OBJECTIVES: To describe the changes in ventilator management over time in patients with neurologic disease at ICU admission and to estimate factors associated with 28-day hospital mortality. DESIGN: Secondary analysis of three prospective, observational, multicenter studies. SETTING: Cohort studies conducted in 2004, 2010, and 2016. PATIENTS: Adult patients who received mechanical ventilation for more than 12 hours. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: Among the 20,929 patients enrolled, we included 4,152 (20%) mechanically ventilated patients due to different neurologic diseases. Hemorrhagic stroke and brain trauma were the most common pathologies associated with the need for mechanical ventilation. Although volume-cycled ventilation remained the preferred ventilation mode, there was a significant (p < 0.001) increment in the use of pressure support ventilation. The proportion of patients receiving a protective lung ventilation strategy was increased over time: 47% in 2004, 63% in 2010, and 65% in 2016 (p < 0.001), as well as the duration of protective ventilation strategies: 406 days per 1,000 mechanical ventilation days in 2004, 523 days per 1,000 mechanical ventilation days in 2010, and 585 days per 1,000 mechanical ventilation days in 2016 (p < 0.001). There were no differences in the length of stay in the ICU, mortality in the ICU, and mortality in hospital from 2004 to 2016. Independent risk factors for 28-day mortality were age greater than 75 years, Simplified Acute Physiology Score II greater than 50, the occurrence of organ dysfunction within first 48 hours after brain injury, and specific neurologic diseases such as hemorrhagic stroke, ischemic stroke, and brain trauma. CONCLUSIONS: More lung-protective ventilatory strategies have been implemented over years in neurologic patients with no effect on pulmonary complications or on survival. We found several prognostic factors on mortality such as advanced age, the severity of the disease, organ dysfunctions, and the etiology of neurologic disease