Modeling neuronal activity and synaptic transmission
I - Neuronal genesis
collaboration Thierry Galli
Our group is interested in neurite growth, which is a fundamental step of neuronal development. To study neurite outgrowth, we constructed a model based on vesicle trafficking and microtubule dynamics. In our model, neurite growth is induced by vesicular delivery of membrane at the leading edge of the neurite. We find that neurite growth occurs into two main phases: one early phase characterized by the absence of microtubules in the nascent neurite, while in the second phase, microtubules interact with vesicles. The first phase is initiated by vesicular delivery at the neurite base. During the second phase, the coupling between vesicles and microtubule dynamics can give rise to various growth regimes, dominated by fast or slow transition between growing and shrinking. Microtubule dynamics plays a major role in neurite stabilization, especially during the transition between an initial neuritic protrusion (phase 1) and a long neurite leading to dendrites or axons (phase 2). The different regimes in phase 2 can characterize dendritic and axonal growth in normal, and pathological conditions or during regeneration.
II - Small neural ensemble: up and Down states
collaboration M. Tsodyks, WIS
Small ensemble of neurons might process information in a very efficient way. We have modeled the emergence of the Up and Down states occurring in cortical neurons. Up and Down states are presented experimentally as a fluctuation of the membrane potential between two stages. The origin of such phenomena is still unknown.
To identify the Up-state dynamics we have derived a stochastic dynamical system, modeling the neural network interconnected by excitatory synapses, where depression can occur. The model reveals that there exists a certain threshold for the total synaptic connection strength: when it is reached, the dynamical system has exactly two attractors, interpreted as an Up and Down state. In that case, the transition between the states is due to the synaptic noise. The analysis reveals that the transitions between the states are not symmetric. Moreover an external stimuli increases the time spent in the Up state, as observed experimentally. The Up and Down state is thus a fundamental and inherent property of a noisy neural ensemble, with sufficient synaptic connection.
The analysis and the simulations of the equations reveals that the noise is able to drive the dynamics (Voltage) from the Up to the down state and conversely, as described in the following figure below (upper curve). The second figure corresponds to the depression dynamics.
D. Holcman, M. Tsodyks, Emergence of the Up and Down States in cortical networks, PloS Computational Biology, 3,2, 2006
E. Bart, S. Bao, D. Holcman. Modeling the spontaneous activity in the auditory cortex, of Computational Neuroscience,2004.