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Adrian Joseph Alva – Dual Degree CNS

Adrian Joseph Alva received his MS Dual Degree in Computational Natural Sciences (CNS). His research work was supervised by Prof. Harjinder Singh. Here’s a summary of  his research work on The Dynamics of Neurons in a Minimal Model for Synaptic Integration:

Biological neurons are prototypical examples of nonlinear excitable systems. Nonlinear dynamics and a strong coupling of the relevant variables allows neurons to function in an array of different physiological modes. Such complexity at the single neuron level is ultimately responsible for the immense complexity of the mammalian nervous system. From a mathematical standpoint as well, neuron models are highly of interest as they provide opportunities to explore the larger domain of excitable systems and threshold phenomena. As a result, theoretical and computational studies of neuron models have in the last few decades, explained and predicted interesting and unexpected phenomena, as seen for instance when external noise interacts with the dynamics of an excitable system. The most prominent aspect of neuronal information processing is the phenomenon of synaptic integration. The detailed mechanisms that modulate synaptic inputs determine the computational properties of any given neuron. In this thesis, we study a simple model for the summation of excitatory inputs from synapses and illustrate its use by characterizing some functional properties of postsynaptic neurons. Our experiments are based on the well studied FitzHugh-Nagumo (FHN) model for action potential generation. The FHN equations have been investigated extensively since their introduction in the early 1960s. In particular, a number of insights into the dynamics of excitation thresholds have been gained from this model as well how these thresholds change as bifurcations are approached. The FHN model is also well known for its ability to exhibit interesting noise driven properties like stochastic resonance. By applying minimal perturbations to the FHN system, we provide a simple framework to study the dynamics of postsynaptic neurons. The model is based on a first order approximation of dendritic currents as identical rectangular current pulses. Using this, we obtain firing threshold curves of postsynaptic neurons as a function of the average time gap between successive dendritic current pulses. Furthermore, we explain the features of these threshold curves using an analysis based on nullclines and a class of trajectories known as Canards. A realistic simulation of an individual neuron involves different spatial and temporal scales: propagation of currents across passive dendrites modelled with partial differential equations has to be coupled to the excitable dynamics of the cell body modelled with FHN type ordinary differential equations. This results in computationally intensive requirements even for a modestly small number of dendrites especially if we want to investigate long-time statistical properties of the firings. This is what motivates us to introduce a minimal model for synaptic integration. Although not biophysically realistic on finer scales, we try to show that a simple model can nonetheless highlight the general statistical features of spike timings in neural processes where the active properties of dendrites do not play a major role. In particular, our model postsynaptic neurons are especially suited to study how a simple integration mechanism such as the spatial summation of dendritic currents can lead to nontrivial dynamics. Noise is a ubiquitous presence in neuronal processes and has been shown to play important functional roles in sensory physiology among other things. To study the functional aspects of noise in sensory information processing, we obtain the firing statistics of postsynaptic neurons when their corresponding presynaptic neurons are subjected to two well known noise driven processes: stochastic and coherence resonance. These phenomena have been observed in a variety of models as well as experimental systems. By subjecting the model to the conditions of these processes, we propose some advantages of postsynaptic neurons towards processing weak or irregular sensory stimuli. Interspike interval histograms are employed to demonstrate the contrast between presynaptic and postsynaptic neurons in biological scenarios such as the transmission of sensory information. Biologically relevant implications of the results are highlighted throughout and further experiments suggested. The model requires a small number of parameters and is especially useful to isolate the role of integration mechanisms that rely on summation of inputs with little dendritic processing. Simple extensions/modifications to include more aspects of synaptic integration such as inhibitory synapses, bursting dynamics, etc are also dealt with. The simplicity of the model establishes a base case in a bottom-up modelling hierarchy while maintaining the ability to explore new functional roles of postsynaptic neurons.