Mathematical Modeling seminars

Intelligent behavior depends on the brain’s ability to anticipate future events. However, the learning rules that enable neurons to predict and fire ahead of sensory inputs remain largely unknown. We propose a plasticity rule based on pre-dictive processing, where the neuron learns a low-rank model of the synaptic input dynamics in its membrane potential. Neurons thereby amplify those synapses that maximally predict other synaptic inputs based on their temporal relations, which provide a solution to an optimization problem that can be implemented at the single-neuron level using only local information. Consequently, neurons learn sequences over long timescales and shift their spikes towards the first inputs in a sequence. We show that this mechanism can explain the development of anticipatory motion signaling and recall in the visual system. Furthermore, we demonstrate that the learning rule gives rise to several experimentally observed STDP (spike-timing-dependent plasticity) mechanisms. These findings suggest prediction as a guiding principle to orchestrate learning and synaptic plasticity in single neurons.

Rajanlab designs neural network models constrained by experimental data, and reverse engineers them to figure out how brain circuits function in health and disease. Recently, we have been developing a powerful new theory-based framework for “in-vivo tract tracing” from multi-regional neural activity collected experimentally. We call this framework CURrent-Based Decomposition (CURBD). CURBD employs recurrent neural networks (RNNs) directly constrained, from the outset, by time series measurements acquired experimentally, such as Ca2+ imaging or electrophysiological data. Once trained, these data-constrained RNNs let us infer matrices quantifying the interactions between all pairs of modeled units. Such model-derived “directed interaction matrices” can then be used to separately compute excitatory and inhibitory input currents that drive a given neuron from all other neurons. Therefore different current sources can be de-mixed – either within the same region or from other regions, potentially brain-wide – which collectively give rise to the population dynamics observed experimentally. Source de-mixed currents obtained through CURBD allow an unprecedented view into multi-region mechanisms inaccessible from measurements alone. We have applied this method successfully to several types of neural data from our experimental collaborators, e.g., zebrafish (Deisseroth lab, Stanford), mice (Harvey lab, Harvard), monkeys (Rudebeck lab, Sinai), and humans (Rutishauser lab, Cedars Sinai), where we have discovered both directed interactions brain wide and inter-area currents during different types of behaviors. With this powerful framework based on data-constrained multi-region RNNs and CURrent Based Decomposition (CURBD), we ask if there are conserved multi-region mechanisms across different species, as well as identify key divergences.

Birdsong emerges when a set of highly interconnected brain areas manage to generate a complex output. The similarities between birdsong production and human speech have positioned songbirds as unique animal models for studying learning and production of this complex motor skill. In this work, we developed a low dimensional model for a neural network in which the variables were the average activities of different neural populations within the nuclei of the song system. This neural network is active during production, perception and learning of birdsong. We performed electrophysiological experiments to record neural activity from one of these nuclei and found that the low dimensional model could reproduce the neural dynamics observed during the experiments. Also, this model could reproduce the respiratory motor patterns used to generate song. We showed that sparse activity in one of the neural nuclei could drive a more complex activity downstream in the neural network. This interdisciplinary work shows how low dimensional neural models can be a valuable tool for studying the emergence of complex motor tasks