Estimation of synaptic conductances in presence of nonlinear effects caused by subthreshold ionic currents

Subthreshold fluctuations in neuronal membrane potential traces contain nonlinear components, and employing nonlinear models might improve the statistical inference. We propose a new strategy to estimate synaptic conductances, which has been tested using in silico data and applied to in vivo recordings. The model is constructed to capture the nonlinearities caused by subthreshold activated currents, and the estimation procedure can discern between excitatory and inhibitory conductances using only one membrane potential trace. More precisely, we perform second order approximations of biophysical models to capture the subthreshold nonlinearities, resulting in quadratic integrate-and-fire models, and apply approximate maximum likelihood estimation where we only suppose that conductances are stationary in a 50–100 ms time window. The results show an improvement compared to existent procedures for the models tested here.Peer ReviewedPostprint (published version

Detecting and Estimating Signals in Noisy Cable Structures, I: Neuronal Noise Sources

In recent theoretical approaches addressing the problem of neural coding, tools from statistical estimation and information theory have been applied to quantify the ability of neurons to transmit information through their spike outputs. These techniques, though fairly general, ignore the specific nature of neuronal processing in terms of its known biophysical properties. However, a systematic study of processing at various stages in a biophysically faithful model of a single neuron can identify the role of each stage in information transfer. Toward this end, we carry out a theoretical analysis of the information loss of a synaptic signal propagating along a linear, one-dimensional, weakly active cable due to neuronal noise sources along the way, using both a signal reconstruction and a signal detection paradigm. Here we begin such an analysis by quantitatively characterizing three sources of membrane noise: (1) thermal noise due to the passive membrane resistance, (2) noise due to stochastic openings and closings of voltage-gated membrane channels (Na^+ and K^+), and (3) noise due to random, background synaptic activity. Using analytical expressions for the power spectral densities of these noise sources, we compare their magnitudes in the case of a patch of membrane from a cortical pyramidal cell and explore their dependence on different biophysical parameters

Stochastic Differential Equation Model for Cerebellar Granule Cell Excitability

Neurons in the brain express intrinsic dynamic behavior which is known to be stochastic in nature. A crucial question in building models of neuronal excitability is how to be able to mimic the dynamic behavior of the biological counterpart accurately and how to perform simulations in the fastest possible way. The well-established Hodgkin-Huxley formalism has formed to a large extent the basis for building biophysically and anatomically detailed models of neurons. However, the deterministic Hodgkin-Huxley formalism does not take into account the stochastic behavior of voltage-dependent ion channels. Ion channel stochasticity is shown to be important in adjusting the transmembrane voltage dynamics at or close to the threshold of action potential firing, at the very least in small neurons. In order to achieve a better understanding of the dynamic behavior of a neuron, a new modeling and simulation approach based on stochastic differential equations and Brownian motion is developed. The basis of the work is a deterministic one-compartmental multi-conductance model of the cerebellar granule cell. This model includes six different types of voltage-dependent conductances described by Hodgkin-Huxley formalism and simple calcium dynamics. A new model for the granule cell is developed by incorporating stochasticity inherently present in the ion channel function into the gating variables of conductances. With the new stochastic model, the irregular electrophysiological activity of an in vitro granule cell is reproduced accurately, with the same parameter values for which the membrane potential of the original deterministic model exhibits regular behavior. The irregular electrophysiological activity includes experimentally observed random subthreshold oscillations, occasional spontaneous spikes, and clusters of action potentials. As a conclusion, the new stochastic differential equation model of the cerebellar granule cell excitability is found to expand the range of dynamics in comparison to the original deterministic model. Inclusion of stochastic elements in the operation of voltage-dependent conductances should thus be emphasized more in modeling the dynamic behavior of small neurons. Furthermore, the presented approach is valuable in providing faster computation times compared to the Markov chain type of modeling approaches and more sophisticated theoretical analysis tools compared to previously presented stochastic modeling approaches

Effects of short-term plasticity in UP-DOWN cortical dynamics

Neuronal dynamics are strongly influenced by short-term plasticity (STP), that is, changes in synaptic efficacy that occur on a short (from milliseconds to seconds) time scale. Depending on the brain areas considered, STP can be dominated by short-term depression (STD), short-term facilitation (STF), or both mechanisms can coexist simultaneously. These two plasticity mechanisms modulate particular patterns of electrophysiological activity characterized by alternating UP and DOWN states. In this work, we develop a network model made up of excitatory and inhibitory multi-compartment neurons endowed with both mechanisms (STD and STF), spatially arranged to emulate the connectivity circuitry observed experimentally in the visual cortex. Our results reveal that both depression and facilitation can be involved in the switching process between different activity patterns, from an alternation of UP and DOWN states (for relatively low levels of depression and high levels of facilitation) to an asynchronous firing regime (for relatively high levels of depression and low levels of facilitation). For STD and STF, we identify the critical levels of depression and facilitation that push the network into the different regimes. Furthermore, we also find that these critical levels separate different growth rates of the mean synaptic conductances of the whole network with respect to the depression levels. This latter data is paramount to understanding how excitation and inhibition are organized to generate different brain activity regimes. Finally, after observing the changes in the trajectories of excitatory and inhibitory instantaneous firing rates near these critical boundaries, we identify dynamic patterns that shed light on the type of bifurcations that should arise in a rate model for this complex network"AG has been funded by Catalan Research Agency (AGAUR) grant 2017-SGR-1049, by the Spanish Ministerio de Ciencia e Innovación grant PID2021-122954-I00 and by the Spanish State Research Agency through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M)."Peer ReviewedPostprint (published version

Modelling and analysis of neurons coupled by electrical synapses

The objective of this thesis is to analyze the role of the intrinsic properties of neurons in the communication through electrical synapses. Mesencephalic trigeminal neurons constitute an excellent experimental model to study the communication between neurons, because of its easy experimental access experimental and simple to model and analyze a biological system. Among the contributions of this thesis are: the complete modeling of the sodium currents and other ionic current (and its modulation); the explanation preference subthreshold frequency transfer between neuronfor example and its coupling. Some preliminary results of this work have been presented at international conferences.morphology. However, the analysis of real neurons is limited by experimental constraints that do not allow to explore all aspects of the model. Within the context of this thesis, a mathematical model is built, based on electrophysiological recordings made by Sebastián Curti at the School of Medicine of Universidad de la República. The model consists of a set of differential equations, which can be represented by a nonlinear electrical circuit. Some of the differential equations are obtained from literature and only some minor parameters’ adjustments are made. Moreover, during the thesis we have found that more data was needed in order to explain some of the most important features of the behavior of neurons, such as the duration of the action potential. Therefore, more experimental recordings were made, allowing to refine the model. The model allows to evaluate the response of the neuron to different stimuli (currents or voltages imposed by an electrode), making possible to make new “experiments” that are not possible in a laboratory. Alternatives models are analyzed (varying ionic currents and morphology) using experimental information to validate them. Then the model is used to understand some unusual features of the communication between neurons. First, it is studied the subthreshold transfer function (i.e. without action potentials) between neurons coupled by electrical synapses. A reduced model is used and then linearized, in order to derive an analytical expression of the transfer function, whose behaviour is consistent with experimental results. Moreover, numerical simulations are performed to analyze the rol of the intrinsic properties of neurons in their synchronization. It is shown that the same properties that determine the subthreshold behavior are relevant to improve synchronization between neurons too. Finally, this thesis contributes not only with new models and answers, but with new questions, which should be studied using experimental models as well. This thesis applies several tools used for electrical engineering (frequency response of systems, cable equation, Markov chains, evolutionary algorithms, etc.) to model and analyze a biological system. Among the contributions of this thesis are: the complete modeling of the sodium currents and other ionic current (and its modulation); the explanation preference subthreshold frequency transfer between neuronfor example and its coupling. Some preliminary results of this work have been presented at international conferences.El objetivo de esta tesis es analizar el rol de las propiedades intrínsecas de las neuronas en la comunicación a través de sinapsis eléctricas. Las neuronas del nervio trigeminal del mesencéfalo constituyen un excelente modelo experimental para estudiar la comunicación entre neuronas, debido a su fácil acceso experimental y su sencilla morfología. Sin embargo, el análisis de neuronas reales está limitado por restricciones experimentales que impiden explorar todos los aspectos del modelo. En el marco de esta tesis, se construye un modelo matemático basado en registros electrofisiológicos realizados por Sebastián Curti en la Facultad de Medicina de la Universidad de la República. El modelo consiste en un sistema de ecuaciones diferenciales, que puede ser representado por un circuito eléctrico con componentes no lineales. Algunas de las ecuaciones diferenciales son obtenidas de bibliografía y se realizan algunos ajustes menores de parámetros. Por otro lado, durante la tesis evaluamos que se necesitaba más información para reproducir algunas de las características más importantes del comportamientos de las neuronas, como la duración del potencial de acción. Por eso, se debieron realizar nuevos registros experimentales, que permitieron refinar el modelo. El modelo permite evaluar la respuesta de la neurona ante diferentes estímulos (corrientes o voltajes impuestos por un electrodo), posibilitando nuevos “experimentos” que no son posibles en un laboratorio. Se analizan diversas alternativas de modelado (variando corrientes iónicas y morfología) usando información experimental para validarlos. Luego, el modelo es utilizado para entender algunas características inusuales de la comunicación entre neuronas. En primer lugar, se estudia la transferencia subumbral (i.e.: sin potenciales de acción) entre neuronas acopladas por sinapsis eléctricas. Se utiliza un modelo reducido, que es linealizado para obtener una expresión analítica de la transferencia, cuyo comportamiento es coherente con los resultados experimentales. Asimismo, se realizan simulaciones numéricas para analizar el rol en la sincronización de las propiedades intrínsecas de las neuronas. Se muestra que las mismas propiedades que determinan el comportamiento subumbral son relevantes para mejorar la sincronización entre neuronas. Finalmente, esta tesis no sólo contribuye con nuevos modelos y respuestas, sino con nuevas preguntas, que deberán ser estudiadas usando modelos experimentales también. Esta tesis hace uso de diversas herramientas utilizadas por la ingeniería eléctrica (comportamiento en frecuencia de sistemas, ecuación del cable, cadenas de Markov, algoritmos evolutivos, etc) para modelar y analizar un sistema biológico. Se realizan diversos aportes, por ejemplo: modelado completo de las corrientes de sodio, así como de la modulación de otra corriente; explicación de la preferencia en frecuencia de la transferencia subumbral entre neuronas; estudio de la sincronización en función de las propiedades de los osciladores y de su acople. Algunos resultados preliminares de este trabajo han sido presentados en congresos internacionales

Biophysical mechanisms of frequency-dependence and its neuromodulation in neurons in oscillatory networks

In response to oscillatory input, many isolated neurons exhibit a preferred frequency response in their voltage amplitude and phase shift. Membrane potential resonance (MPR), a maximum amplitude in a neuron’s input impedance at a non-zero frequency, captures the essential subthreshold properties of a neuron, which may provide a coordinating mechanism for organizing the activity of oscillatory neuronal networks around a given frequency. In the pyloric central pattern generator network of the crab Cancer borealis, for example, the pacemaker group pyloric dilator neurons show MPR at a frequency that is correlated with the network frequency. This dissertation uses the crab pyloric CPG to examine how, in one neuron type, interactions of ionic currents, even when expressed at different levels, can produce consistent MPR properties, how MPR properties are modified by neuromodulators and how such modifications may lead to distinct functional effects at different network frequencies. In the first part of this dissertation it is demonstrated that, despite the extensive variability of individual ionic currents in a neuron type such as PD, these currents can generate a consistent impedance profile as a function of input frequency and therefore result in stable MPR properties. Correlated changes in ionic current parameters are associated with the dependence of MPR on the membrane potential range. Synaptic inputs or neuromodulators that shift the membrane potential range can modify the interaction of multiple resonant currents and therefore shift the MPR frequency. Neuromodulators change the properties of voltage-dependent ionic currents. Since ionic current interactions are nonlinear, the modulation of excitability and the impedance profile may depend on all ionic current types expressed by the neuron. MPR is generated by the interaction of positive and negative feedback effects due to fast amplifying and slower resonant currents. Neuromodulators can modify existing MPR properties to generate antiresonance (a minimum amplitude response). In the second part of this dissertation, it is shown that the neuropeptide proctolin produces antiresonance in the follower lateral pyloric neuron, but not in the PD neuron. This finding is inconsistent with the known influences of proctolin. However, a novel proctolin-activated ionic current is shown to produce the antiresonance. Using linear models, antiresonance is then demonstrated to amplify MPR in synaptic partner neurons, indicating a potential function in the pyloric network. Neuromodulators are state dependent, so that their action may depend on the prior activity history of the network. It is shown that state-dependence may arise in part from the time-dependence of an inactivating inward current targeted by the neuromodulator proctolin. Due to the kinetics of inactivation, this current advances the burst phase and increases the duty cycle of the neuron, but mainly at higher network frequencies. These results demonstrate that the effect of neuromodulators on MPR in individual neuron types depends on the nonlinear interaction of modulator-activated and other ionic currents as well as the activation of currents with frequency-dependent properties. Consequently, the action of neuromodulators on the output of oscillatory networks may depend on the frequency of oscillations and be predictable from the MPR properties of the network neurons

Mechanisms of Multistability in Neuronal Models

Multistability is a fundamental attribute of the dynamics of neuronal systems under normal and pathological conditions. The mechanism of bistability of bursting and silence is not well understood and to our knowledge has not been experimentally recorded in single neurons. We considered four models. Two of them described the dynamics of a leech heart interneuron: the canonical model and a low-dimensional model. The other two models described mammalian pacemakers from the respiratory center. We investigated the low-dimensional model and identified six different types of multistability of dynamical regimes. We described six generic mechanisms underlying the co-existence of oscillatory and silent regimes. The mechanisms are based either on a saddle equilibrium or a saddle periodic orbit. The stable manifold of the saddle equilibrium or the saddle orbit sets the threshold between the regimes. In the two models of the leech interneuron the range of the controlling parameters supporting the co-existence of bursting and silence is limited by the Andronov-Hopf and homoclinic bifurcations (Malashchenko, Master Thesis 2007). The bistability was found in a narrow range of the leak currents\u27 parameters. Here, we introduced a propensity index to bistability as the width of the range on a bifurcation diagram; we investigated how the propensity index was affected by modifications of the ionic currents, and found that conductances of only two currents substantially affected the index. The increase of the conductance of the hyperpolarization-activated current, Ih, and the reduction of the fast Ca2+ current, ICaF, notably increased the propensity index. These findings define modulatory conditions under which we suggest the bistability of bursting and silence could be experimentally revealed in leech heart interneurons. We hypothesize that this mechanism could be commonly found in a large variety of neuronal models. We applied our techniques to models of vertebrate neurons controlling respiratory rhythm, which represent two types of inspiratory pacemakers of the Pre-Bӧtzinger Complex. We showed that both types of neurons could exhibit bistability of bursting and silence in accordance with the mechanism which we described