Mark S. Goldman

Global Structure, Robustness, and Modulation of Neuronal Models

The electrical characteristics of many neurons are remarkably robust in the face of changing internal and external conditions. At the same time, neurons can be highly sensitive to neuromodulators. We find correlates of this dual robustness and sensitivity in a global analysis of the structure of a conductance-based model neuron. We vary the maximal conductance parameters of the model neuron and, for each set of parameters tested, characterize the activity pattern generated by the cell as silent, tonically firing, or bursting. Within the parameter space of the five maximal conductances of the model, we find directions, representing concerted changes in multiple conductances, along which the basic pattern of neural activity does not change. In other directions, relatively small concurrent changes in a few conductances can induce transitions between these activity patterns. The global structure of the conductance-space maps implies that neuromodulators that alter a sensitive set of conductances will have powerful, and possibly state-dependent, effects. Other modulators that may have no direct impact on the activity of the neuron may nevertheless change the effects of such direct modulators via this state dependence. Some of the results and predictions arising from the model studies are replicated and verified in recordings of stomatogastric ganglion neurons using the dynamic clamp.

Memory without Feedback in a Neural Network

Memory storage on short timescales is thought to be maintained by neuronal activity that persists after the remembered stimulus is removed. Although previous work suggested that positive feedback is necessary to maintain persistent activity, here it is demonstrated how neuronal responses can instead be maintained by a purely feedforward mechanism in which activity is passed sequentially through a chain of network states. This feedforward form of memory storage is shown to occur both in architecturally feedforward networks and in recurrent networks that nevertheless function in a feedforward manner. The networks can be tuned to be perfect integrators of their inputs or to reproduce the time-varying firing patterns observed during some working memory tasks but not easily reproduced by feedback-based attractor models. This work illustrates a mechanism for maintaining short-term memory in which both feedforward and feedback processes interact to govern network behavior.

Tuning Curves, Neuronal Variability, and Sensory Coding

Tuning curves are widely used to characterize the responses of sensory neurons to external stimuli, but there is an ongoing debate as to their role in sensory processing. Commonly, it is assumed that a neurons role is to encode the stimulus at the tuning curve peak, because high firing rates are the neurons most distinct responses. In contrast, many theoretical and empirical studies have noted that nearby stimuli are most easily discriminated in high-slope regions of the tuning curve. Here, we demonstrate that both intuitions are correct, but that their relative importance depends on the experimental context and the level of variability in the neuronal response. Using three different information-based measures of encoding applied to experimentally measured sensory neurons, we show how the best-encoded stimulus can transition from high-slope to high-firing-rate regions of the tuning curve with increasing noise level. We further show that our results are consistent with recent experimental findings that correlate neuronal sensitivities with perception and behavior. This study illustrates the importance of the noise level in determining the encoding properties of sensory neurons and provides a unified framework for interpreting how the tuning curve and neuronal variability relate to the overall role of the neuron in sensory encoding.

Functional dissection of circuitry in a neural integrator

In neural integrators, transient inputs are accumulated into persistent firing rates that are a neural correlate of short-term memory. Integrators often contain two opposing cell populations that increase and decrease sustained firing as a stored parameter value rises. A leading hypothesis for the mechanism of persistence is positive feedback through mutual inhibition between these opposing populations. We tested predictions of this hypothesis in the goldfish oculomotor velocity-to-position integrator by measuring the eye position and firing rates of one population, while pharmacologically silencing the opposing one. In complementary experiments, we measured responses in a partially silenced single population. Contrary to predictions, induced drifts in neural firing were limited to half of the oculomotor range. We built network models with synaptic-input thresholds to demonstrate a new hypothesis suggested by these data: mutual inhibition between the populations does not provide positive feedback in support of integration, but rather coordinates persistent activity intrinsic to each population.

Balanced cortical microcircuitry for maintaining information in working memory

Persistent neural activity in the absence of a stimulus has been identified as a neural correlate of working memory, but how such activity is maintained by neocortical circuits remains unknown. We used a computational approach to show that the inhibitory and excitatory microcircuitry of neocortical memory-storing regions is sufficient to implement a corrective feedback mechanism that enables persistent activity to be maintained stably for prolonged durations. When recurrent excitatory and inhibitory inputs to memory neurons were balanced in strength and offset in time, drifts in activity triggered a corrective signal that counteracted memory decay. Circuits containing this mechanism temporally integrated their inputs, generated the irregular neural firing observed during persistent activity and were robust against common perturbations that severely disrupted previous models of short-term memory storage. These results reveal a mechanism for the accumulation and storage of memories in neocortical circuits based on principles of corrective negative feedback that are widely used in engineering applications.

Enhancement of information transmission efficiency by synaptic failures

Many synapses have a high percentage of synaptic transmission failures. I consider the hypothesis that synaptic failures can increase the efficiency of information transmission across the synapse. I use the information transmitted per vesicle release about the presynaptic spike train as a measure of synaptic transmission efficiency and show that this measure can increase with the synaptic failure probability. I analytically calculate the Shannon mutual information transmitted across two model synapses with probabilistic transmission: one with a constant probability of vesicle release and one with vesicle release probabilities governed by the dynamics of synaptic depression. For inputs generated by a non-Poisson process with positive autocorrelations, both synapses can transmit more information per vesicle release than a synapse with perfect transmission, although the information increases are greater for the depressing synapse than for a constant-probability synapse with the same average transmission probability. The enhanced performance of the depressing synapse over the constant-release-probability synapse primarily reflects a decrease in noise entropy rather than an increase in the total transmission entropy. This indicates alimitation of analysis methods, such as decorrelation, that consider only the total response entropy. My results suggest that synaptic transmission failures governed by appropriately tuned synaptic dynamics can increase the information-carrying efficiency of a synapse.

A modeling framework for deriving the structural and functional architecture of a short-term memory microcircuit.

Although many studies have identified neural correlates of memory, relatively little is known about the circuit properties connecting single-neuron physiology to behavior. Here we developed a modeling framework to bridge this gap and identify circuit interactions capable of maintaining short-term memory. Unlike typical studies that construct a phenomenological model and test whether it reproduces select aspects of neuronal data, we directly fit the synaptic connectivity of an oculomotor memory circuit to a broad range of anatomical, electrophysiological, and behavioral data. Simultaneous fits to all data, combined with sensitivity analyses, revealed complementary roles of synaptic and neuronal recruitment thresholds in providing the nonlinear interactions required to generate the observed circuit behavior. This work provides a methodology for identifying the cellular and synaptic mechanisms underlying short-term memory and demonstrates how the anatomical structure of a circuit may belie its functional organization.

NMDA and GABAB (KIR) Conductances: The “Perfect Couple” for Bistability

Networks that produce persistent firing in response to novel input patterns are thought to be important in working memory and other information storage functions. One possible mechanism for maintaining persistent firing is dendritic voltage bistability in which the depolarized state depends on the voltage dependence of the NMDA conductance at recurrent synapses. In previous models, the hyperpolarized state is dependent on voltage-independent conductances, including GABAA. The interplay of these conductances leads to bistability, but its robustness is limited by the fact that the conductance ratio must be within a narrow range. The GABAB component of inhibitory transmission was not considered in previous analyses. Here, we show that the voltage dependence of the inwardly rectifying potassium (KIR) conductance activated by GABAB receptors adds substantial robustness to network simulations of bistability and the persistent firing that it underlies. The hyperpolarized state is robust because, at hyperpolarized potentials, the GABAB/KIR conductance is high and the NMDA conductance is low; the depolarized state is robust because, at depolarized potentials, the NMDA conductance is high and the GABAB/KIR conductance is low. Our results suggest that this complementary voltage dependence of GABAB/KIR and NMDA conductances makes them a “perfect couple” for producing voltage bistability.

Vitamin A and aflatoxin: Effect on liver and colon cancer

A vitamin A (retinyl acetate)-deficient diet enhanced liver cancer in rats exposed to aflatoxin B1 (AFB1) and also caused a 29% incidence of colon cancer. The following factors were considered in attempts to define conditions under which vitamin-A-deprived rats were more susceptible to colon cancer induced by AFB1: liver morphology, enterohepatic recirculation, level of reduced glutathione (GSH) in liver, and differing capacities for conjugation of aflatoxin to GSH. Enzyme concentrations in liver, in intestinal and colon mucosa, and in intestinal and colon contents suggested that AFB1 may have different metabolites and that there may be differing susceptibilities of colon mucosa to carcinogenesis. Binding studies supported this hypothesis. Previous studies have shown that colon epithelium from vitamin-A-deficient rats binds more AFB1 than colon epithelium from normal, vitamin-A-supplemented animals. In the present study, vitamin A supplementation to the vitamin-A-deficient rats before oral administration of 3H-AFB1 significantly decreased the binding capacity at 12 and 15 hours after dosing with the carcinogen. These results suggest that the effect of vitamin A on the metabolism of the carcinogen, particularly on binding of AFB1 to cellular macromolecules, may be the mechanism by which vitamin A modifies aflatoxins carcinogenic potential, influenced in part through enzymatic mechanisms.

Neural Integrator Models

Integration of information across time is a neural computation of critical importance to a variety of brain functions. Examples include oculomotor neural integrators and head direction cells that integrate velocity signals into positional or directional signals, parametric working memory circuits which convert transient input pulses into self-sustained persistent neural activity patterns, and linear ramping neural activity underlying the accumulation of information during decision making. How is integration over long timescales realized in neural circuits? This article reviews experimental and theoretical work related to this fundamental question, with a focus on the idea that recurrent synaptic or cellular mechanisms can instantiate an integration time much longer than intrinsic biophysical time constants of the system. We first introduce some basic concepts and present two types of codes used by neural integrators – the location code and the rate code. Then we summarize models that implement a variety of candidate mechanisms for neural integration in the brain, and we discuss the problem of fine-tuning of model parameters and possible solutions to this problem. Finally, we outline challenges for future research.