Effects of neuronal noise on neural communication

In this work, we propose an approach to better understand the effects of neuronal noise on neural communication systems. Here, we extend the fundamental Hodgkin-Huxley (HH) model by adding synaptic couplings to represent the statistical dependencies among different neurons under the effect of additional noise. We estimate directional information-theoretic quantities, such as the Transfer Entropy (TE), to infer the couplings between neurons under the effect of different noise levels. Based on our computational simulations, we demonstrate that these nonlinear systems can behave beyond our predictions and TE is an ideal tool to extract such dependencies from data.No sponso

Computational bifurcation analysis to find dynamic transitions of the corticotroph model

The corticotroph model is a 7th order nonlinear differential equation system derived for representing the action potential dynamics of corticotrophs; one of the endocrine cells that are responsible for stress regulation. Here we use numerical continuation methods to perform bifurcation analysis since controlling bifurcations in the hormonal dynamics may bring some new insights in the treatment of stress-related disorders. We study the bifurcation structure of the system as a function of the BK-channel dynamic parameters and all maximal conductances. We identify the regions of bistability and bifurcations that shape the transitions between resting, bursting, and spiking behaviors, and which lead to the appearance of bursting which is directly connected to stress regulation. Furthermore, we find that there are two routes to bursting, one is the experimentally observed BK-channel dynamics and the other is Ca2+ channel conductance only. Finally, we discuss how some of the described bifurcations affect the dynamic behavior and can be tested experimentally.No sponso

Analysis of parameter changes of a neuronal network model using transfer entropy

Understanding the dynamics of coupled neurons is one of the fundamental problems in the analysis of neuronal model dynamics. The transfer entropy (TE) method is one of the primary analyses to explore the information flow between the neuronal populations. We perform the TE analysis on the two-neuron conductance-based Hodgkin-Huxley (HH) neuronal network to analyze how their connectivity changes due to conductances. We find that the information flow due to underlying synaptic connectivity changes direction by changing conductances individually and/or simultaneously as a result of TE analysis through numerical simulations.No sponso

Quantitative roles of ion channel dynamics on ventricular action potential

Mathematical models for the action potential (AP) generation of the electrically excitable cells including the heart are involved different mechanisms including the voltage-dependent currents with nonlinear time- and voltage-gating properties. From the shape of the AP waveforms to the duration of the refractory periods or heart rhythms are greatly affected by the functions describing the features or the quantities of these ion channels. In this work, a mathematical measure to analyze the regional contributions of voltage-gated channels is defined by dividing the AP into phases, epochs, and intervals of interest. The contribution of each time-dependent current for the newly defined cardiomyocyte model is successfully calculated and it is found that the contribution of dominant ion channels changes substantially not only for each phase but also for different regions of the cardiac AP. Besides, the defined method can also be applied in all Hodgkin–Huxley types of electrically excitable cell models to be able to understand the underlying dynamics better.No sponso

Statistical approaches for the analysis of dependency among neurons under noise

Neuronal noise is a major factor affecting the communication between coupled neurons. In this work, we propose a statistical toolset to infer the coupling between two neurons under noise. We estimate these statistical dependencies from data which are generated by a coupled Hodgkin–Huxley (HH) model with additive noise. To infer the coupling using observation data, we employ copulas and information-theoretic quantities, such as the mutual information (MI) and the transfer entropy (TE). Copulas and MI between two variables are symmetric quantities, whereas TE is asymmetric. We demonstrate the performances of copulas and MI as functions of different noise levels and show that they are effective in the identification of the interactions due to coupling and noise. Moreover, we analyze the inference of TE values between neurons as a function of noise and conclude that TE is an effective tool for finding out the direction of coupling between neurons under the effects of noise.No sponso

Modeling and analyzing Ca2+ channel dynamics during cardiac action potential

International Conference on Applied Analysis and Mathematical Modeling (2019 : Istanbul, Turkey)We have studied the cardiac action potential model which consists of 26 nonlinear first-order differential equations in a detailed manner computationally. Later, it has been discussed what is the role of the Ca2+ ion channel to the cardiac action potential by applying a mathematical measure called contribution analysis. Computational simulations are done to analyze the roles of Ca2+ gating variables and detailed analysis showed the changing dynamics of Ca2+ channel during a cardiac action potential.No sponso

Sulfur dioxide derivative prevents the prolongation of action potential during the isoproterenol-induced hypertrophy of rat cardiomyocytes

Exogenous SO2 is toxic especially to the pulmonary and cardiovascular system, similar to nitric-oxide, carbon-monoxide, and hydrogen-sulfide. Endogenous SO2 is produced in many cell types. The SO2 content of the rat heart has been observed to substantially decrease during isoproterenol-induced hypertrophy. This study sought to determine whether an SO2 derivative could inhibit the prolongation of action potentials during the isoproterenol-induced hypertrophy of rat cardiomyocytes and explore the ionic currents. Alongside electrocardiogram recordings, the voltage and current- clamped measurements were conducted in the enzymatically isolated left ventricular cardiomyocytes of Wistar rats. The consistency of the results was evaluated by the novel mathematical electrophysiology model. Our results show that SO2 significantly blocked the prolongation of QT-interval and action potential duration. Furthermore, SO2 did not substantially affect the Na+ currents and did not improve the decreased steady- state and transient outward K+ currents, but it reverted the reduced L-type Ca2+ currents (ICaL) to the physiological levels. Altered inactivation of ICaL was remarkably recovered by SO2. Interestingly, SO2 significantly increased the Ca2+ transients in hypertrophic rat hearts. Our mathematical model also confirmed the mechanism of the SO2 effect. Our findings suggest that the shortening mechanism of SO2 is related to the Ca2+ dependent inactivation kinetics of the Ca2+ current.This study was supported in part by Akdeniz University Scientific Research Coordination Unit (Project No: 2012.02.0122.009) and The Scientific and Technological Research Council of Turkey (TUBITAK, Project No: 117F020). These funding sources had no involvement in study design, writing of the report, decision to publish, or the collection, analysis, and interpretation of data

Nöronlardaki enerji tüketiminin sıcaklık bağımlılığının iki bölmeli matematiksel modelde analiz edilmesi

No sponso

Matematiksel modelleme ve dinamik-kenetleme yöntemleri ile ventrikül kardiyomiyosit aksiyon potansiyeli dinamiklerinin incelenmesi

No sponso

Examining the electrochemical energy consumption of model neurons through the use of differential equation systems

Nöronlar tarafından aksiyon potansiyeli üretimi, enerji gerektiren yoğun bir süreçtir ve nöronların sinyal iletim aktivitesini korumak için ne kadar metabolik enerjinin gerekli olduğunu belirlemek, oldukça pratik öneme sahip bir problemdir. Diferansiyel denklem modelleri, gerçek nöronların dinamiklerini göstermek için yaygın olarak kullanılır, ancak bu dinamiklerin devam etmesini sağlamak için gereken elektrokimyasal enerji miktarını tahmin etmek için nadiren kullanılırlar. Kortikal piramidal hücreler, hem zaman alıcı hem de metabolik harcama açısından maliyetli olan gelen sinyalleri işleme konusunda olağanüstü yeteneklere sahiptir. Sinyal molekülleri, sinapslar ve iyon kanallarının tümü hücreler tarafından kullanılır ve her birinin çeşitli ölçeklerde nöronal anatomi ve fizyoloji üzerinde önemli bir etkisi vardır. Sonuç olarak, piramidal hücrelerde aksiyon potansiyelleri üretmek için metabolik enerjinin nasıl etkin bir şekilde kullanıldığını anlamak, bunların hesaplanması ve işleyişi hakkında kapsamlı bir anlayışkazanmak için kritik öneme sahiptir. Dendritler, kortikal piramidal hücrelerde sinyal alımı için başlıca yerlerdir ve ayrıca diğer nöronlara sinyallerin iletilmesinden sorumludurlar. Dendritik entegrasyonun çıktısı, aksiyon potansiyellerinin başlatılmasında doğrudan bir rol oynar ve nihai çıktı üzerinde bir etkiye sahiptir. Dendritler tarafından sağlanan doğrusal olmayan dönüşüm, piramidal nöron ağlarının matematiksel yeteneğini önemli ölçüde geliştirme potansiyeline sahiptir. Çalışmamız, dendritlerin somatik/aksonal aksiyon potansiyelinin metabolik verimliliğini nasıl etkilediğini matematiksel model ve analizler ile incelemektedir. Bu çalışmada, biyofiziksel ilkelere dayalı diferansiyel denklem modellerinin sayısal simülasyonları aracılığıyla soma-dendrit arasındaki enerji tüketimi analizi yapılmıştır. Pasif ve aktif dendritleri tanımlamak için iki bölmeli bir soma dendrit modeli geliştirilmiştir. Elektrokimyasal enerji tüketimi hesaplanmış ve hücrelerin dendritik ve somatik özellikleri araştırılmıştır. Pasif ve aktif dendritlerin, aksiyon potansiyeli oluşumu sırasındaki enerji verimliliğinde nasıl aktif bir rol oynadıkları açıklanarak kortikal piramidal nöronlardaki iletişimin enerji tüketimine nasıl katkıda bulunduğu gösterilmiştir. Sinaptik simülasyonun metabolik enerjiyi nasıl kullandığını anlamak için gerekli olan somadan dendrite akışla ilgili model parametrelerini değiştirerek iyonik akım dinamiklerinin soma-dendrit örtüşmesi üzerinde farklı etkileri olduğu araştırılmıştır.No sponso