The dynamics of biological neural networks are of great interest to neuroscientists and are frequently studied using conductance-based compartmental neuron models. For speed and ease of use, neuron models are often reduced in morphological complexity. This reduction may affect input processing and prevent the accurate reproduction of neural dynamics. However, such effects are not yet well understood. Therefore, for my first aim I analyzed the processing capabilities of 'branched' or 'unbranched' reduced models by collapsing the dendritic tree of a morphologically realistic 'full' globus pallidus neuron model while maintaining all other model parameters. Branched models maintained the original detailed branching structure of the full model while the unbranched models did not. I found that full model responses to somatic inputs were generally preserved by both types of reduced model but that branched reduced models were better able to maintain responses to dendritic inputs. However, inputs that caused dendritic sodium spikes, for instance, could not be accurately reproduced by any reduced model. Based on my analyses, I provide recommendations on how to construct reduced models and indicate suitable applications for different levels of reduction. In particular, I recommend that unbranched reduced models be used for fast searches of parameter space given somatic input output data. The intrinsic electrical properties of neurons depend on the modifiable behavior of their ion channels. Obtaining a quality match between recorded voltage traces and the output of a conductance based compartmental neuron model depends on accurate estimates of the kinetic parameters of the channels in the biological neuron. Indeed, mismatches in channel kinetics may be detectable as failures to match somatic neural recordings when tuning model conductance densities. In my first aim, I showed that this is a task for which unbranched reduced models are ideally suited. Therefore, for my second aim I optimized unbranched reduced model parameters to match three experimentally characterized globus pallidus neurons by performing two stages of automated searches. In the first stage, I set conductance densities free and found that even the best matches to experimental data exhibited unavoidable problems. I hypothesized that these mismatches were due to limitations in channel model kinetics. To test this hypothesis, I performed a second stage of searches with free channel kinetics and observed decreases in the mismatches from the first stage. Additionally, some kinetic parameters consistently shifted to new values in multiple cells, suggesting the possibility for tailored improvements to channel models. Given my results and the potential for cell specific modulation of channel kinetics, I recommend that experimental kinetic data be considered as a starting point rather than as a gold standard for the development of neuron models.

Submitted by (ana.araujo@ufrpe.br) on 2016-07-06T14:22:48Z No. of bitstreams: 1 Heliovanio Torres Bandeira.pdf: 959027 bytes, checksum: 9873348980adb3c73410a63f86c250d6 (MD5) / Made available in DSpace on 2016-07-06T14:22:48Z (GMT). No. of bitstreams: 1 Heliovanio Torres Bandeira.pdf: 959027 bytes, checksum: 9873348980adb3c73410a63f86c250d6 (MD5) Previous issue date: 2006-06-19 / Ionic channels are formed by one or few protein molecules found in biological membranes and constitute one of the possible ways for the transport of ions through these membranes. These proteins can assume different conformational open and closed states, phenomenon named ion channel kinetics. The transitions from one state to another are dependent on the potential energy barrier that separates them and can be controlled by electric field, ions, chemical substances and other physical agents. The dwell times in which the proteinchannel stays in one these conformational states have been modeled assuming that the process is Markovian. A chaotic model also was proposed for modeling the ion channel kinetics (LIEBOVITCH e TÓTH., 1991).In this work we use the R/S Hurst analysis to test the long-range correlation found in calcium-activated potassium channel kinetics in Leydig cells. The Hurst coefficient H, a parameter that show the memory existent in a kinetic process (NOGUEIRA et al., 1995), was calculated to a calcium-activated potassium channel in Leydig cells recording and it was equal to H = 0,66±0,044 (n=4), disclosing that the system presents a persistent memory. The R/S analysis when applied to the opening and closing dwell time series obtained from ion channel simulated data using a chaotic model was inadequate to describe the long-term correlation previously found in the experimental data. As conclusion, this work shows that: (i) really, opening and closing dwell times for the single calciumactivated potassium channel of Leydig cells present long-term correlation and (ii) the chaotic model, proposed by Liebovitch and Thót (1991), is not adequate to describe the memory found in the kinetic of this channel. / Canais iônicos são compostos de uma ou poucas moléculas de proteínas que se encontram nas membranas biológicas e constituem uma das vias possíveis para o transporte de íons através dessas membranas. Essas proteínas podem assumir diferentes estados conformacionais, abertos e fechados, fenômeno denominado de cinética de canais iônicos. As transições entre os estados cinéticos dos canais dependem das barreiras de energias potenciais que separam esses estados e, que podem ser controladas por campo elétrico, íons, substâncias químicas e outros agentes. Os tempos de permanências dos canais em cada um dos estados conformacionais têm sido modelados assumindo-se que este processo é markoviano. Um modelo caótico também foi proposto para modelar a cinética de canal iônico (LIEBOVITCH e TÓTH, 1991). Neste trabalho utilizamos a análise R/S de Hurst para testar a correlação de longo alcance (memória) na cinética de um canal para potássio ativado por cálcio em células de Leydig. O coeficiente de Hurst H, um parâmetro que mostra a memória existente em um processo cinético (NOGUEIRA et al., 1995), foi calculado para um registro de um canal para potássio ativado por cálcio e foi encontrado um valor de H = 0,66 ± 0,044 (n=4), evidenciando que o sistema apresenta uma memória persistente. A análise R/S aplicada à seqüência temporal de aberturas e fechamentos obtida para um canal iônico simulado por um modelo caótico mostrou que esse modelo é inadequado para descrever a correlação de longo alcance encontrada nos dados experimentais. Como conclusão, este trabalho mostra que: (i) tempos de permanência para aberturas e fechamentos do canal para potássio ativado por cálcio em células de Leydig apresentam correlação de longo alcance (memória);(ii) o modelo caótico, proposto por Liebovitch e Tóth (1991), é inadequado para descrever a memória encontrada na cinética do canal.

Chemical reactions involving small number of reacting molecules are noisy processes. They are simulated using stochastic simulation algorithms like the Gillespie SSA, which are valid when the reaction environment is well-mixed. This is not the case in reactions occuring on biological media like cell membranes, where alternative simulation methods have to be used to account for the crowded nature of the reacting environment. Ion channels, which are membrane proteins controlling the flow of ions into and out of the cell, offer excellent single molecule conditions to test stochastic simulation schemes in crowded biological media. Single molecule reactions are of great importance in determining the functions of biological molecules. Access to their experimental data have increased the scope of com-putational modeling of biological processes. Recently, single molecule experiments have revealed the non-Markovian nature of chemical reactions, due to a phenomenon called `dynamic disorder', which makes the rate constants a deterministic function of time or a random process. This happens when there are additional slow scale conformational transitions, giving the molecule a memory of its previous states. In a previous work, the hTREK1 two pore domain potassium channel was revealed to have long term memory in its kinetics, prompting alternate non-Markovian schemes to analyze its gating. Traditionally, ion channel gating is modeled as Markovian transitions between fixed states. In this work, we have used single channel data from hTREK1 ion channel and have provided a simple diffusion model for its gating. The main assumption of this model is that the ion channel diffuses through a continuum of states on its potential energy landscape, which is derived from the steady state probability distribution of ionic current recorded from patch clamp experiments. A stochastic differential equation (SDE) driven by Gaussian white noise is proposed to model this motion in an asymmetric double well potential. The method is computationally very simple and efficient and reproduces the amplitude histogram very well. For the case when ligands are added, leading to incorporation of long term memory in the kinetics, the SDE is modified to run on coloured noise. This has been done by introducing an auxiliary variable into the equation. It has been shown that increasing the noise correlation with ligand concentration improves the fits to the experimental data. This has been validated for several datasets. These methods are more advantageous for simulation than the Markovian models as they are true to the physical picture of gating and also computationally very efficient. Reproducing the whole raw data trace takes no more than a few seconds with our scheme, with the only input being the amplitude histogram and four parameters. Finally a quantitative model based on a modified version of the Chemical Langevin equation is given, which works on random rate parameters. This model is computationally simple to implement and reproduces the catalytic activity of the channel as a function of time. From the computational analysis undertaken in this work, we can infer that ion channel activity can be modeled using the framework of non-Markovian processes, lending credence to the recent understanding that single molecule reactions are basically processes with long-term memory. Since the ion channel is basically a protein, we can also hypothesize that the some of the properties that make proteins so vital to living organ-isms could be attributed to long-term memory in their folding kinetics, giving them the ability to sample specific regions of their conformation space, which are of interest to biological functions.