Extracellular electrical signals in a neuron-surface junction: model of heterogeneous membrane conductivity

Signals recorded from neurons with extracellular planar sensors have a wide range of waveforms and amplitudes. This variety is a result of different physical conditions affecting the ion currents through a cellular membrane. The transmembrane currents are often considered by macroscopic membrane models as essentially a homogeneous process. However, this assumption is doubtful, since ions move through ion channels, which are scattered within the membrane. Accounting for this fact, the present work proposes a theoretical model of heterogeneous membrane conductivity. The model is based on the hypothesis that both potential and charge are distributed inhomogeneously on the membrane surface, concentrated near channel pores, as the direct consequence of the inhomogeneous transmembrane current. A system of continuity equations having non-stationary and quasi-stationary forms expresses this fact mathematically. The present work performs mathematical analysis of the proposed equations, following by the synthesis of the equivalent electric element of a heterogeneous membrane current. This element is further used to construct a model of the cell-surface electric junction in a form of the equivalent electrical circuit. After that a study of how the heterogeneous membrane conductivity affects parameters of the extracellular electrical signal is performed. As the result it was found that variation of the passive characteristics of the cell-surface junction, conductivity of the cleft and the cleft height, could lead to different shapes of the extracellular signals

Glycosylation of Erythrocyte Spectrin and Its Modification in Visceral Leishmaniasis

Using a lectin, Achatinin-H, having preferential specificity for glycoproteins with terminal 9-O-acetyl sialic acid derivatives linked in α2-6 linkages to subterminal N-acetylgalactosamine, eight distinct disease-associated 9-O-acetylated sialoglycoproteins was purified from erythrocytes of visceral leishmaniaisis (VL) patients (RBCVL). Analyses of tryptic fragments by mass spectrometry led to the identification of two high-molecular weight 9-O-acetylated sialoglycoproteins as human erythrocytic α- and β-spectrin. Total spectrin purified from erythrocytes of VL patients (spectrinVL) was reactive with Achatinin-H. Interestingly, along with two high molecular weight bands corresponding to α- and β-spectrin another low molecular weight 60 kDa band was observed. Total spectrin was also purified from normal human erythrocytes (spectrinN) and insignificant binding with Achatinin-H was demonstrated. Additionally, this 60 kDa fragment was totally absent in spectrinN. Although the presence of both N- and O-glycosylations was found both in spectrinN and spectrinVL, enhanced sialylation was predominantly induced in spectrinVL. Sialic acids accounted for approximately 1.25 kDa mass of the 60 kDa polypeptide. The demonstration of a few identified sialylated tryptic fragments of α- and β-spectrinVL confirmed the presence of terminal sialic acids. Molecular modelling studies of spectrin suggest that a sugar moiety can fit into the potential glycosylation sites. Interestingly, highly sialylated spectrinVL showed decreased binding with spectrin-depleted inside-out membrane vesicles of normal erythrocytes compared to spectrinN suggesting functional abnormality. Taken together this is the first report of glycosylated eythrocytic spectrin in normal erythrocytes and its enhanced sialylation in RBCVL. The enhanced sialylation of this cytoskeleton protein is possibly related to the fragmentation of spectrinVL as evidenced by the presence of an additional 60 kDa fragment, absent in spectrinN which possibly affects the biology of RBCVL linked to both severe distortion of erythrocyte development and impairment of erythrocyte membrane integrity and may provide an explanation for their sensitivity to hemolysis and anemia in VL patients

Метод определения скрытых параметров синаптической передачи на основе данных ингибиторного анализа

Nowadays neuroscience strongly demands application of the mathematical methods for description of many neurophysiological and neurochemical processes among which the synaptic transmission outstands. One of the main problems in synaptic transmission modelling is the lack of the accurate values of dynamic parameters of biomolecules and complexes taking part in this process.The goal of this study is to elaborate the method for evaluation of synaptic transmission parameters that cannot be measured directly (so-called hidden parameters) and apply its results for investigation of the main stages of synaptic transmission in neuronets of hippocampus.The method is based on the parametric identification of the synaptic transmission deterministic model, which includes equations for description of inhibitors action on the main biochemical participants. We used three inhibitors: cilnidipine, 1.2-        bis(2-aminophenoxy)ethane-N,N,N',N'-tetraacetic acid tetrakis(acetoxymethyl ester) (BAPTA-AM), 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX). The parametric identification was performed by minimization of deviation of modeled field excitatory postsynaptic potential from those measured in rat hippocampus slices with microelectrode technique when inhibitors were applied.The results of the parametric identification of proposed model show that the model can adequately describe the generation of field excitatory postsynaptic potentials and their inhibition. The elaborated method afforded to evaluate the numerical meanings of eleven synaptic transmission hidden parameters. Using these parameters we have modelled the key synaptic transmission stages and got the time courses of the main biochemical participants: calcium ions in presynaptic bouton, SNARE complexes, synaptic vesicles in different states, glutamate in the synaptic cleft and open channels of AMPA receptor on the postsynaptic membrane. Thus, we propose method of hidden parameters evaluation that can be applied for different synaptic contacts in the brain of mammalians.Математическое описание передачи сигнала в синапсах открывает широкие перспективы в изучении деятельности головного мозга, позволяя собрать результаты многочисленных экспериментальных исследований в единую модель. Существенные затруднения при таком подходе возникают вследствие не только многоэтапности синаптической передачи, но и отсутствия точных численных характеристик динамики многих ее участников.Цель работы - разработать метод определения параметров синаптической передачи, недоступных для прямого измерения (скрытых параметров), и апробировать его в процессе изучения динамики основных этапов данного процесса в нейронных сетях гиппокампа.Предлагаемый в данной работе метод основан на построении детерминистической модели, описывающей генерацию полевого возбуждающего постсинаптического потенциала в условиях действия ингибиторов (цилнидипина, 1.2-  бис(2-аминофенокси) этан- N,N,N′,N′ тетрауксусной кислоты тетракис(ацетоксиметилового эфира), 6-циано-7-ни-трокиноксалин-2,3-диона), и параметрической идентификации данной модели на зарегистрированных с помощью микроэлектродной техники полевых возбуждающих постсинаптических потенциалах в срезах гиппокампа крысы. Параметрическая идентификация проводилась путем минимизации отклонения моделируемого сигнала от экспериментально зарегистрированного. Для минимизации целевой функции использовали генетический алгоритм.В результате проведенного исследования было показано, что параметрическая идентификация модели позволяет с высокой степенью соответствия воспроизводить формирование полевых возбуждающих постсинаптических потенциалов и оказываемое на них действие ингибиторов. Установлены численные значения одиннадцати скрытых параметров синаптической передачи. С помощью данных значений получены временные зависимости содержания ключевых участников синаптической передачи: ионов Ca2+ в пресинаптическом окончании, SNARE-комплексов, синаптических везикул в различных состояниях, глутамата в синаптической щели, доли открытых каналов АМРА-рецепторов на постсинаптической мембране. Таким образом, предложен метод, который целесообразно использовать для определения скрытых параметров различных типов синаптических контактов в головном мозге млекопитающих

Роль потенциал-зависимых калиевых каналов в формировании клеточного отклика на электрическую стимуляцию клеток в культуре

Usage of electric fields for forming a certain cellular response finds application in various fields of biology and medicine. The efficiency of the methods based on the electric field action was discussed repeatedly. However, the process of developing stimulation protocols is being complicated by the absence of the specification of the precise mechanism of the electric stimulation action upon cells in the culture. Thus, the identification of signal transduction mechanism in cells under the electric field action is of current interest. The objective of this work is to investigate the role of potassium potential-dependent channels in forming the cellular response at long-term electrical stimulation. Studies were carried out using glioma cells C6. The pulsed electric field with the strength of 3-20 V/m, with 2 ms biphase pulses and with a frequency of 10 Hz was used for electric stimulation. 4-Aminopyridine was used for inhibitory analysis. It was shown that the change in the membrane potential under the electric field action takes place involving the potassium potential-dependent ion channels. It was revealed that the use of a potassium potential-dependent ion channels inhibitor partially levels the field effects. Thus, potassium potential-dependent channels play a significant role in the processes of signal transduction in cells at long-term electrical stimulation of the culture of cells.Применение электрических полей для формирования определенного клеточного отклика находит применение в различных областях биологии и медицины. Неоднократно обсуждалась эффективность методов, основанных на действии электрических полей. Однако отсутствие описания точного механизма действия электрической стимуляции на клетки в культуре осложняет процесс разработки протоколов стимуляции. Таким образом, установление механизма трансдукции сигнала в клетках при действии электрических полей является актуальным. Цель работы - изучение роли калиевых потенциал-зависимых каналов в формировании клеточного отклика в условиях долговременной электрической стимуляции. Исследования проводили на культуре клеток глиомы С6. Для проведения электрической стимуляции использовали импульсное электрическое поле с напряженностью 3-20 В/м с длительностью бифазных импульсов 2 мс и частотой 10 Гц. Для проведения ингибиторного анализа использовали 4-аминопиридин. Установлено, что изменение мембранного потенциала при действии электрического поля происходит при участии калиевых потенциал-зависимых ионных каналов. Выявлено, что применение ингибитора калиевых потен-циал-зависимых ионных каналов частично нивелирует эффекты действия поля. Таким образом, калиевые потенци-ал-зависимые каналы играют важную роль в процессах трансдукции сигнала в клетках при долговременной электрической стимуляции культуры клеток

Aromatic polymers obtained by precipitation polycondensation, 2a) Synthesis of poly(ether ketone ether ketone ketone) (PEKEKK)

A high molecular weight, linear aromatic poly(ether ketone ether ketone ketone) (PEKEKK) has been synthesized by electrophilic Friedel-Crafts acylation condensation of 1,4-diphenoxybenzophenone with terephthaloyl chloride. The syntheses were performed as precipitation polycondensations, and the polyketones were obtained in particle form. The viscosity (molecular weight), shape and size of these particles were found to be strongly dependent on the reaction conditions. For low monomer concentration, highly ordered needle-like particles were also obtained. The chemical structure of the polymers obtained was confirmed by 1H and 13C NMR spectroscopy, and para-substitution in aryl fragments of the main chain was identified. Analysis of the expanded 1H NMR spectra for the ring proton resonances reveals defect mefa- and ortho-structures. The amount and isomer ratio of these defect structures depend on the monomer concentration used.Peer reviewe

Aromatic polymers obtained by precipitation polycondensation: 5*. 1H and 13C n.m.r. study of poly(ether ketone ketone)s

High molecular weight, linear aromatic poly(etherketoneketone)s with differentiso-/tere-isomer repeating unit ratio (100/0,50/50/0,0/100) have been studied by 1H and 13Cn.m.r.spectroscopy. The polymers were obtained in particle form by precipitation electrophilic Friedel–Crafts acylation condensation of iso-and terephthaloyclhlorideswithdiphenyl ether,1,4-and l,3-bis(4-phenoxybenzoyl) benze.ConvwentionallH and 13Cn.m.r. spectroscoy shows para-substitution in the diphenylether fragments of the mainchain. Analysis of th eexpanded 1Hn.m.r.spectra for the ring proton resonances reveals defect meta-and orthostructures. The amount and isomer ratio of these defect structures depend on the polymer structure and preparationp ath.Thelow field of 1Hn.m.r.spectra of polyketones based on ‘small monomers’(diphenylether and iso- and terephthaloylchlorides)were found to show additional minor signals corresponding to a different type of defect structure.A possible mechanism of formation of these defec tstructures is discussed.Peer reviewe

Wastewater bioremediation using white rot fungi: Validation of a dynamical system with real data obtained in laboratory

Nowadays, wastewater treatment has become an important issue in view of the ever increasing worldwide paucity of abundant and clean water supplies. In this work, we propose a mathematical model describing the process of decolorization of textile industry wastewater and validate it using data from a laboratory experiment. To this aim, a selected white rot fungus, capable of degrading a wide range of recalcitrant compounds, is used against Remazol Brilliant Blue Reactive dye. The real data obtained in laboratory are use to fit the parameters of our model. The qualitative analysis is performed to study the behavior of the wastewater and of the fungus as functions of time. In the present study the, carbon (glucose) has an important role in the system since it can sustain the fungal metabolism and growth. Furthermore a more general mathematical model is studied, considering an open system where there is a constant input and output of pollutant and nutrients respectively

Interacting With COVID-19: How Population Behavior, Feedback and Memory Shaped Recurrent Waves of the Epidemic

Until the approval of vaccines at the end of 2020, societies relied on non-pharmaceutical interventions (NPIs) in order to control the COVID-19 pandemic. Spontaneous changes in individual behavior might have contributed to or counteracted epidemic control due to NPIs. For example, the population compliance to NPIs may have varied over time as people developed 'epidemic fatigue' or altered their perception of the risk and severity of COVID-19. Whereas official measures are well documented, the behavioral response of the citizens is harder to capture. We propose a mathematical model of the societal response, taking into account three main effects: the citizen response dynamics, the authorities' NPIs, and the occurrence of unpreventable events that significantly alter the virus transmission rate. A key assumption is that a society has a waning memory of the epidemic effects, which reflects on both the severity of the authorities' NPIs and on the citizens' compliance to the prescribed rules. This, in turn, feeds back onto the transmission rate of the disease, such that a higher number of hospitalizations decreases the probability of transmission. We show that the model is able to reproduce the COVID-19 dynamics in terms of hospital admissions for several European countries during 2020 over surprisingly long time scales. Also, it is capable of capturing the effects of disturbances (for example the emergence of new virus variants) and can be exploited for implementing control actions to limit such effects. A possible application, illustrated in this letter, consists of exploiting the estimations based on the data of one country, to predict and control the evolution in another country, where the virus spreading is still in an earlier phase

Interacting with COVID-19: How population behavior, feedback and memory shaped recurrent waves of the epidemic

Until the approval of vaccines at the end of 2020, societies relied on non-pharmaceutical interventions (NPIs) in order to control the COVID-19 pandemic. Spontaneous changes in individual behavior might have contributed to or counteracted epidemic control due to NPIs. For example, the population compliance to NPIs may have varied over time as people developed "epidemic fatigue" or altered their perception of the risk and severity of COVID-19. Whereas official measures are well documented, the behavioral response of the citizens is harder to capture. We propose a mathematical model of the societal response, taking into account three main effects: the citizen response dynamics, the authorities' NPIs, and the occurrence of unpreventable events that significantly alter the virus transmission rate. A key assumption is that a society has a waning memory of the epidemic effects, which reflects on both the severity of the authorities' NPIs and on the citizens' compliance to the prescribed rules. This, in turn, feeds back onto the transmission rate of the disease, such that a higher number of hospitalizations decreases the probability of transmission. We show that the model is able to reproduce the COVID-19 dynamics in terms of hospital admissions for several European countries during 2020 over surprisingly long time scales. Also, it is capable of capturing the effects of disturbances (for example the emergence of new virus variants) and can be exploited for implementing control actions to limit such effects. A possible application, illustrated in this letter, consists of exploiting the estimations based on the data of one country, to predict and control the evolution in another country, where the virus spreading is still in an earlier phase