Intrinsic Dynamics in Neuronal Networks. I. Theory

Abstract

in the mammalian nervous system remain active in the absence of stimuli. This activity falls into two main patterns: steady firing at low rates and rhythmic bursting. How are these firing patterns generated? Specifically, how do dynamic interactions between excitatory and inhibitory neurons produce these firing patterns, and how do networks switch from one firing pattern to the other? We investigated these questions theoretically by examining the intrinsic dynamics of large networks of neurons. Using both a semianalytic model based on mean firing rate dynamics and simulations with large neuronal networks, we found that the dynamics, and thus the firing patterns, are controlled largely by one parameter, the fraction of endogenously active cells. When no endogenously active cells are present, networks are either silent or fire at a high rate; as the number of endogenously active cells increases, there is a transition to bursting; and, with a further increase, there is a second transition to steady firing at a low rate. A secondary role is played by network connectivity, which determines whether activity occurs at a constant mean firing rate or oscillates around that mean. These conclusions require only conventional assumptions: excitatory input to a neuron increases its firing rate, inhibitory input decreases it, and neurons exhibit spike-frequency adaptation. These conclusions also lead to two experimentally testable predictions: 1) isolated networks that fire at low rates must contain endogenously active cells and 2) a reduction in the fraction of endogenously active cells in such networks must lead to bursting.

Added astroglia promote greater synapse density and higher activity in neuronal networks

“…In cultures without added astroglia, the addition of glutamate eliminates the lower slope response type, converting the network to the higher slope type. This conversion was described previously, both theoretically (Latham et al, 2000a) and experimentally (Latham et al, 2000b), in terms of transition from a small fraction of endogenously active cells in a bursting network to a larger fraction of activity that produces the more steady firing that we see after glutamate stimulation, especially the higher rates in networks with added astroglia. Waagenar et al (2005) also find less bursting with more stimulation of the network.…”

Gamma oscillations as a mechanism for selective information transmission

“…The quadratic integrate and fire neuron (QIF neuron) is described in detail in Latham et al (2000). It is formally equivalent to the Theta neuron (Ermentrout and Kopell 1986) and has been often used in computational studies because it has analytical solutions for many input signals.…”

Is there a brainstem substrate for action selection?

“…Instead, we follow a tradition of capturing the global dynamic properties of a neural system using what have been variously called 'macroscopic', 'meanfield' or 'population' models ( Wilson & Cowan 1972;Tsodyks et al 1997;Latham et al 2000;Yousif & Denham 2005). In this approach, populations of neurons are treated as a statistical ensemble, assuming that the connections between populations are such that functionally meaningful subgroups of neurons cannot be further distinguished.…”

“…Thus, the model is a set of simplified ordinary differential equations describing the change in the normalized mean firing rate of each population over time; in other words, it is only concerned with temporal dynamics. Nevertheless, if the parameter values and the populations are carefully chosen, then this approach can both reveal similar dynamics to more complex models with individual neural elements and match recorded changes in neural activity (Latham et al 2000;Yousif & Denham 2005). Moreover, the simplicity of the resulting models allows for a more thorough exploration of their dynamic properties, via both simulation and analysis.…”