Researches Of Simple Models On Neural Information Processing

Computational neuroscience is an interdisciplinary science that applies concepts andanalytical tools from physics, mathematics, and engineering to explore the underlyingmechanisms of brain functions, with a strong emphasis on the interaction of experimentsand theories. In recent years, as the development of experimental neuroscience, a hugeamount of date has been accumulated. The brain research is in urgent need of computa-tional modeling method, to investigate the working mechanisms of brain in terms of anintegrated system. Nevertheless, nervous system is an extremely complicated system, itinvolves multiple nonlinear interactions in a high-dimensional dynamical system. A goalin theoretical neuroscience is to develop simple models which, on one hand, capture thefundamental features of the real biologic systems, and on the other hand, allow us to pur-sue analytical treatment unveiling the general principle of brain function. Based on theexperimental fndings in synapses and neural circuits, we build some biophysically realis-tic simple models to theoretically investigate their roles in neural information processing.In particular, we are concentrated on answering these computational problems:1)Thebiophysical mechanisms behind experimental fndings;2)The computational meanings ofthese experimental evidences, especially in terms of neural networks. The main works inthis thesis are listed as follows:(1) The experimental study has found that the integration of excitatory and inhibito-ry currents at the soma of a neuron can be expressed as a simple arithmetic rule. Basedon this simple arithmetic rule, we carry out a biophysical motivated derivation of a singlecompartment model that integrates the nonlinear efects of shunting inhibition, wherean inhibitory input on the route of an excitatory input to the soma cancels or “shunts”the excitatory potential. Our results agree with the experimental fndings. Using ournew simplifed formulation, we devise a spiking network model where inhibitory neuronsact as global shunting gates, and show that the network exhibits persistent activity ina low fring regime. We further build a continuous attractor neural network model andshow that shunting inhibition could be well approximated as an operation of divisivenormalization in the network dynamics.(2) Systematically analyze a canonical neural circuit which is widely existed in theearly pathway of sensory systems, e.g., visual system and olfactory system. The circuit is endowed with mechanisms, namely short term synaptic depression and presynapticinhibition. We frst investigate how spatial information is processed in this circuit. Simu-lation results reveal that it can input gain control of a single neuron’s IO function, whichis observed in experiment. Moreover, the circuit could achieve concentration invariantrepresentations to odorant stimuli, while the odor concentration information is encodedin the network transient dynamics. Second, we explore the power of the circuit to processtemporal information. We fnd that the circuit could be approximated as a adaptive dif-ferentiator, with its transient response obeying the Weber-Fechner law. These propertiesare of great importance for the circuit to efciently process neural information.(3) Analyze the sparse coding network in the olfactory system of drosophila. Sparsecoding is a common coding mechanism in the brain to achieve efcient pattern separation.In the olfactory system of the fy drosopohila melangaster, projection neurons (PNs)in the antennal lobe (AL) convert a dense activation of glomeruli into a sparse fringpattern of Kenyon cells (KCs) in the mushroom body (MB). A sparse code of odorqualities has the advantage to achieve efcient decorrelation of the representation ofsimilar odors. While the sparseness of a code is directly related to its decorrelationproperties, too low fring probabilities might result in other disadvantages for the brain.We here investigate the structure of the sparse projection from the antennal lobe to themushroom body in regard to faithful information transmission and robustness to extrinsicand intrinsic noise. In particular, we emphasize on understanding the role of the highlycorrelated homotypic projection neurons found in the glomeruli of fies which receiveidentical information from their ORN input but target randomly diferent KCs. We fndthat a certain number of sister cells is crucial for the robustness of the sparse KC codeto noise. Our analysis predicts that4-5sister cells per glomerulus would be sufcient,which is in good anatomical agreement in fies. Moreover, we estimate how many PNsshould optimally connect to a single KC, and found that values around10would sufceto guarantee both, robust information transmission and a very sparse odor representationin MB.