Nonuniformity in the linear network model of the oculomotor integrator produces approximately fractional-order dynamics and more realistic neuron behavior

Abstract

The oculomotor integrator is a network that is composed of neurons in the medial vestibular nuclei and nuclei prepositus hypoglossi in the brainstem. Those neurons act approximately as fractional integrators of various orders, converting eye velocity commands into signals that are intermediate between velocity and position. The oculomotor integrator has been modeled as a network of linear neural elements, the time constants of which are lengthened by positive feedback through reciprocal inhibition. In this model, in which each neuron reciprocally inhibits its neighbors with the same Gaussian profile, all model neurons behave as identical, first-order, low-pass filters with dynamics that do not match the variable, approximately fractional-order dynamics of the neurons that compose the actual oculomotor integrator. Fractional-order integrators can be approximated by weighted sums of first-order, low-pass filters with diverse, broadly distributed time constants. Dynamic systems analysis reveals that the model integrator indeed has many broadly distributed time constants. However, only one time constant is expressed in the model due to the uniformity of its network connections. If the model network is made nonuniform by removing the reciprocal connections to and from a small number of neurons, then many more time constants are expressed. The dynamics of the neurons in the nonuniform network model are variable, approximately fractional-order, and resemble those of the neurons that compose the actual oculomotor integrator. Completely removing the connections to and from a neuron is equivalent to eliminating it, an operation done previously to demonstrate the robustness of the integrator network model. Ironically, the resulting nonuniform network model, previously supposed to represent a pathological integrator, may in fact represent a healthy integrator containing neurons with realistically variable, approximately fractional-order dynamics.

Oscillatory and Intrinsic Membrane Properties of Guinea Pig Nucleus Prepositus Hypoglossi Neurons In Vitro

“…The PHN is in the rostral medulla (McCrea and Horn 2005), near the medial vestibular nucleus (MVN), which is one of its major inputs. Theoretical models based on intrinsic cellular properties (Egorov et al 2002;Loewenstein and Sompolinsky 2003;Marder et al 1996), the finding of rostrocaudal gradients for neurons showing position versus velocity signals (Delgado-Garcia et al 1989) and extensive studies related to the oculomotor integrator of goldfish (Aksay et al 2000(Aksay et al , 2001(Aksay et al , 2003aMajor et al 2004a,b;Seung et al 2000) suggest that the stability and robustness of the neuronal integrator (Galiana and Outerbridge 1984;Goldman et al 2003;Koulakov et al 2002) require both intrinsic properties and network interconnections (Anastasio 1998;Robinson 1991, 1997;Blazquez et al 2003;Cannon et al 1983).…”

Neural network simulations of the primate oculomotor system IV. A distributed bilateral stochastic model of the neural integrator of the vertical saccadic system

“…In the ®rst one, non-uniformities were introduced either with the help of a learning algorithm leading to clusters of interconnected cells (Draye et al 1997) or after disconnecting a small number of units (Anastasio 1998). Although the ensuing fractional-order dynamics of model units presumably endow them with burst±tonic activity pro®les, their similarity to the discharge pattern of NIC cells has not been established.…”

Sparse cerebellar innervation can morph the dynamics of a model oculomotor neural integrator

“…Previous models of the mammalian neural integrator focused only on the brainstem (Cannon et al, 1983;Arnold and Robinson, 1991;Anastasio, 1998) and did not consider the effects of the cerebellar contribution. No previous modeling studies have addressed the issue of the sparseness of cerebellar innervation of brainstem neurons.…”