On the properties of input-to-output transformations in neuronal networks.

Information processing in neuronal networks in certain important cases can be considered as maps of binary vectors, where ones (spikes) and zeros (no spikes) of input neurons are transformed into spikes and no spikes of output neurons. A simple but fundamental characteristic of such a map is how it transforms distances between input vectors into distances between output vectors. We advanced earlier known results by finding an exact solution to this problem for McCulloch-Pitts neurons. The obtained explicit formulas allow for detailed analysis of how the network connectivity and neuronal excitability affect the transformation of distances in neurons. As an application, we explored a simple model of information processing in the hippocampus, a brain area critically implicated in learning and memory. We found network connectivity and neuronal excitability parameter values that optimize discrimination between similar and distinct inputs. A decrease of neuronal excitability, which in biological neurons may be associated with decreased inhibition, impaired the optimality of discrimination.

Input-to-output transformation in a model of the rat hippocampal CA1 network.

Here we use computational modeling to gain new insights into the transformation of inputs in hippocampal field CA1. We considered input-output transformation in CA1 principal cells of the rat hippocampus, with activity synchronized by population gamma oscillations. Prior experiments have shown that such synchronization is especially strong for cells within one millimeter of each other. We therefore simulated a one-millimeter it patch of CA1 with 23,500 principal cells. We used morphologically and biophysically detailed neuronal models, each with more than 1000 compartments and thousands of synaptic inputs. Inputs came from binary patterns of spiking neurons from field CA3 and entorhinal cortex (EC). On average, each presynaptic pattern initiated action potentials in the same number of CA1 principal cells in the patch. We considered pairs of similar and pairs of distinct patterns. In all the cases CA1 strongly separated input patterns. However, CA1 cells were considerably more sensitive to small alterations in EC patterns compared to CA3 patterns. Our results can be used for comparison of input-to-output transformations in normal and pathological hippocampal networks.

Measuring the quality of neuronal identification in ensemble recordings.

Technological advances in electrode construction and digital signal processing now allow recording simultaneous extracellular action potential discharges from many single neurons, with the potential to revolutionize understanding of the neural codes for sensory, motor, and cognitive variables. Such studies have revealed the importance of ensemble neural codes, encoding information in the dynamic relationships among the action potential spike trains of multiple single neurons. Although the success of this research depends on the accurate classification of extracellular action potentials to individual neurons, there are no widely used quantitative methods for assessing the quality of the classifications. Here we describe information theoretic measures of action potential waveform isolation applicable to any dataset that have an intuitive, universal interpretation, that are not dependent on the methods or choice of parameters for single-unit isolation, and that have been validated using a dataset of simultaneous intracellular and extracellular neuronal recordings from Sprague Dawley rats.

Attention-like modulation of hippocampus place cell discharge.

Hippocampus place cell discharge is an important model system for understanding cognition, but evidence is missing that the place code is under the kind of dynamic attentional control characterized in primates as selective activation of one neural representation and suppression of another, competing representation. We investigated the apparent noise ("overdispersion") in the CA1 place code, hypothesizing that overdispersion results from discharge fluctuations as spatial attention alternates between distal cues and local/self-motion cues. The hypothesis predicts that: (1) preferential use of distal cues will decrease overdispersion; (2) global, attention-like states can be decoded from ensemble discharge such that both the discharge rates and the spatial firing patterns of individual cells will be distinct in the two states; (3) identifying attention-like states improves reconstructions of the rat's path from ensemble discharge. These predictions were confirmed, implying that a covert, dynamic attention-like process modulates discharge on a approximately 1 s time scale. We conclude the hippocampus place code is a dynamic representation of the spatial information in the immediate focus of attention.

Geometry and dynamics of activity-dependent homeostatic regulation in neurons.

To maintain activity in a functional range, neurons constantly adjust membrane excitability to changing intra- and extracellular conditions. Such activity-dependent homeostatic regulation (ADHR) is critical for normal processing of the nervous system and avoiding pathological conditions. Here, we posed a homeostatic regulation problem for the classical Morris-Lecar (ML) model. The problem was motivated by the phenomenon of the functional recovery of stomatogastric neurons in crustaceans in the absence of neuromodulation. In our study, the regulation of the ionic conductances in the ML model depended on the calcium current or the intracellular calcium concentration. We found an asymptotic solution to the problem under the assumption of slow regulation. The solution provides a full account of the regulation in the case of correlated or anticorrelated changes of the maximal conductances of the calcium and potassium currents. In particular, the solution shows how the target and parameters of the regulation determine which perturbations of the conductances can be compensated by the ADHR. In some cases, the sets of compensated initial perturbations are not convex. On the basis of our analysis we formulated specific questions for subsequent experimental and theoretical studies of ADHR.

How does maintenance of network activity depend on endogenous dynamics of isolated neurons?

Robust activity of some networks, such as central pattern generators, suggests the existence of physiological mechanisms that maintain the most important characteristics, for example, the period and spike frequency of the pattern. Whatever these mechanisms are, they change the appropriate model parameters to or along the isomanifolds on which the characteristics of the pattern are constant, while their sensitivities to parameters may be different. Setting synaptic connections to zero at the points of isomanifolds allows for dissecting the maintenance mechanisms into components involving synaptic transmission and components involving intrinsic currents. The physiological meaning of the intrinsic current changes might be revealed by analysis of their impact on endogenous neuronal dynamics. Here, we sought answers to two questions: (1) Do parameter variations in insensitive directions (along isomanifolds) change endogenous dynamics of the network neurons? (2) Do sensitive and insensitive directions for network pattern characteristics depend on endogenous dynamics of the network neurons? We considered a leech heartbeat half-center oscillator model network and analyzed isomanifolds on which the burst period or spike frequency of the model, or both, are constant. Based on our analysis, we hypothesize that the dependence on endogenous dynamics of the isolated neurons is the stronger the more characteristics of the pattern have to be maintained. We also found that in general, the network was more flexible when it consisted of endogenously tonically spiking rather than bursting or silent neurons. Finally, we discuss the physiological implications of our findings.

Unmasking the CA1 ensemble place code by exposures to small and large environments: more place cells and multiple, irregularly arranged, and expanded place fields in the larger space.

In standard experimental environments, a constant proportion of CA1 principal cells are place cells, each with a spatial receptive field called a place field. Although the properties of place cells are a basis for understanding the mammalian representation of spatial knowledge, there is no consensus on which of the two fundamental neural-coding hypotheses correctly accounts for how place cells encode spatial information. Within the dedicated-coding hypothesis, the current activity of each cell is an independent estimate of the location with respect to its place field. The average of the location estimates from many cells represents current location, so a dedicated place code would degrade if single cells had multiple place fields. Within the alternative, ensemble-coding hypothesis, the concurrent discharge of many place cells is a vector that represents current location. An ensemble place code is not degraded if single cells have multiple place fields as long as the discharge vector at each location is unique. Place cells with multiple place fields might be required to represent the substantially larger space in more natural environments. To distinguish between the dedicated-coding and ensemble-coding hypotheses, we compared the characteristics of CA1 place fields in a standard cylinder and an approximately six times larger chamber. Compared with the cylinder, in the chamber, more CA1 neurons were place cells, each with multiple, irregularly arranged, and enlarged place fields. The results indicate that multiple place fields is a fundamental feature of CA1 place cell activity and that, consequently, an ensemble place code is required for CA1 discharge to accurately signal location.

Using constraints on neuronal activity to reveal compensatory changes in neuronal parameters.

In this study, we developed a general description of parameter combinations for which specified characteristics of neuronal or network activity are constant. Our approach is based on the implicit function theorem and is applicable to activity characteristics that smoothly depend on parameters. Such smoothness is often intrinsic to neuronal systems when they are in stable functional states. The conclusions about how parameters compensate each other, developed in this study, can thus be used even without regard to the specific mathematical model describing a particular neuron or neuronal network. We showed that near a generic point in the parameter space there are infinitely many other points, or parameter combinations, for which specified characteristics of activity are the same as in the original point. These parameter combinations form a smooth manifold. This manifold can be extended as long as the gradients of characteristics are defined and independent. All possible variations of parameters compensating each other are simply all possible charts of the same manifold. The number of compensating parameters (but not parameters themselves) is fixed and equal to the number of the independent characteristics maintained. The algorithm that we developed shows how to find compensatory functional dependencies between parameters numerically. Our method can be used in the analysis of the homeostatic regulation, neuronal database search, model tuning and other applications.

Hybrid systems analysis of the control of burst duration by low-voltage-activated calcium current in leech heart interneurons.

The leech heartbeat CPG is paced by the alternating bursting of pairs of mutually inhibitory heart interneurons that form elemental half-center oscillators. We explore the control of burst duration in heart interneurons using a hybrid system, where a living, pharmacologically isolated, heart interneuron is connected with artificial synapses to a model heart interneuron running in real-time, by focusing on a low-voltage-activated (LVA) calcium current I(CaS). The transition from silence to bursting in this half-center oscillator occurs when the spike frequency of the bursting interneuron declines to a critical level, f(Final), at which the inhibited interneuron escapes owing to a build-up of the hyperpolarization-activated cation current, I(h). We varied I(CaS) inactivation time constant either in the living heart interneuron or in the model heart interneuron. In both cases, varying I(CaS) inactivation time constant did not affect f(Final) of either interneuron, but in the varied interneuron, the time constant of decline of spike frequency during bursts to f(Final) and thus the burst duration varied directly and nearly linearly with I(CaS) inactivation time constant. Bursts of the opposite, nonvaried interneuron did not change. We show also that control of burst duration by I(CaS) inactivation does not require synaptic interaction by reconstituting autonomous bursting in synaptically isolated living interneurons with injected I(CaS). Therefore inactivation of LVA calcium current is critically important for setting burst duration and thus period in a heart interneuron half-center oscillator and is potentially a general intrinsic mechanism for regulating burst duration in neurons.

Cognitive disorganization in hippocampus: a physiological model of the disorganization in psychosis.

Cognitive coordination refers to processes that organize the timing of activity among neurons without altering individual discharge properties. Coordinating processes allow neural networks to coactivate related representations and prevent the coactivation of unrelated representations. Impaired cognitive coordination, also called cognitive disorganization, is hypothesized to be the core deficit in the disorganized syndrome of schizophrenia (Phillips and Silverstein, 2003), a condition characterized by hallucinations, disorganization, and thought disorder. This disorganization hypothesis is based on the observation that schizophrenic subjects are impaired at segregating relevant and irrelevant stimuli and selectively using associations between relevant cues. We report that injecting the neural activity blocker tetrodotoxin (TTX) into one hippocampus persistently coactivated pyramidal cells in the uninjected hippocampus that initially discharged independently. In accord with the definition of cognitive disorganization, pyramidal cell firing rates only changed for 15 min and did not accompany the coactivation. The TTX-induced coactivity was maximal at gamma periods, consistent with altered gamma oscillations and disorganization in schizophrenia. A network model confirmed that increasing the coupling of weakly associated cells impairs the selective activation and inhibition of stored spatial representations. This TTX-induced cognitive disorganization correctly predicted that the same TTX injection selectively impaired the ability of rats to segregate relevant associations among distal spatial stimuli from irrelevant local stimuli (Wesierska et al., 2005). The TTX-induced coactivity of hippocampal pyramidal cell discharge has construct and predictive validity as a physiological model of psychosis-related disorganization.