Giancarlo La Camera

Minimal Models of Adapted Neuronal Response to In Vivo &#8211lLike Input Currents

Rate models are often used to study the behavior of large networks of spiking neurons. Here we propose a procedure to derive rate models that take into account the fluctuations of the input current and firing-rate adaptation, two ubiquitous features in the central nervous system that have been previously overlooked in constructing rate models. The procedure is general and applies to any model of firing unit. As examples, we apply it to the leaky integrate-and-fire (IF) neuron, the leaky IF neuron with reversal potentials, and to the quadratic IF neuron. Two mechanisms of adaptation are considered, one due to an after hyperpolarization current and the other to an adapting threshold for spike emission. The parameters of these simple models can be tuned to match experimental data obtained from neocortical pyramidal neurons. Finally, we show how the stationary model can be used to predict the time-varying activity of a large population of adapting neurons.

Measuring and Modeling the Interaction Among Reward Size, Delay to Reward, and Satiation Level on Motivation in Monkeys

Motivation is usually inferred from the likelihood or the intensity with which behavior is carried out. It is sensitive to external factors (e.g., the identity, amount, and timing of a rewarding outcome) and internal factors (e.g., hunger or thirst). We trained macaque monkeys to perform a nonchoice instrumental task (a sequential red-green color discrimination) while manipulating two external factors: reward size and delay-to-reward. We also inferred the state of one internal factor, level of satiation, by monitoring the accumulated reward. A visual cue indicated the forthcoming reward size and delay-to-reward in each trial. The fraction of trials completed correctly by the monkeys increased linearly with reward size and was hyperbolically discounted by delay-to-reward duration, relations that are similar to those found in free operant and choice tasks. The fraction of correct trials also decreased progressively as a function of the satiation level. Similar (albeit noiser) relations were obtained for reaction times. The combined effect of reward size, delay-to-reward, and satiation level on the proportion of correct trials is well described as a multiplication of the effects of the single factors when each factor is examined alone. These results provide a quantitative account of the interaction of external and internal factors on instrumental behavior, and allow us to extend the concept of subjective value of a rewarding outcome, usually confined to external factors, to account also for slow changes in the internal drive of the subject.

The response of cortical neurons to in vivo-like input current: theory and experiment: I. Noisy inputs with stationary statistics

The study of several aspects of the collective dynamics of interacting neurons can be highly simplified if one assumes that the statistics of the synaptic input is the same for a large population of similarly behaving neurons (mean field approach). In particular, under such an assumption, it is possible to determine and study all the equilibrium points of the network dynamics when the neuronal response to noisy, in vivo-like, synaptic currents is known. The response function can be computed analytically for simple integrate-and-fire neuron models and it can be measured directly in experiments in vitro. Here we review theoretical and experimental results about the neural response to noisy inputs with stationary statistics. These response functions are important to characterize the collective neural dynamics that are proposed to be the neural substrate of working memory, decision making and other cognitive functions. Applications to the case of time-varying inputs are reviewed in a companion paper (Giugliano et al. in Biol Cybern, 2008). We conclude that modified integrate-and-fire neuron models are good enough to reproduce faithfully many of the relevant dynamical aspects of the neuronal response measured in experiments on real neurons in vitro.

Mean Field and Capacity in Realistic Networks of Spiking Neurons Storing Sparsely Coded Random Memories

Mean-field (MF) theory is extended to realistic networks of spiking neurons storing in synaptic couplings of randomly chosen stimuli of a given low coding level. The underlying synaptic matrix is the result of a generic, slow, long-term synaptic plasticity of two-state synapses, upon repeated presentation of the fixed set of the stimuli to be stored. The neural populations subtending the MF description are classified by the number of stimuli to which their neurons are responsive (multiplicity). This involves 2p + 1 populations for a network storing p memories. The computational complexity of the MF description is then significantly reduced by observing that at low coding levels (f), only a few populations remain relevant: the population of mean multiplicity pf and those of multiplicity of order pf around the mean. The theory is used to produce (predict) bifurcation diagrams (the onset of selective delay activity and the rates in its various stationary states) and to compute the storage capacity of the network (the maximal number of single items used in training for each of which the network can sustain a persistent, selective activity state). This is done in various regions of the space of constitutive parameters for the neurons and for the learning process. The capacity is computed in MF versus potentiation amplitude, ratio of potentiation to depression probability and coding level f. The MF results compare well with recordings of delay activity rate distributions in simulations of the underlying microscopic network of 10,000 neurons.

Processing of Hedonic and Chemosensory Features of Taste in Medial Prefrontal and Insular Networks

Most of the research on cortical processing of taste has focused on either the primary gustatory cortex (GC) or the orbitofrontal cortex (OFC). However, these are not the only areas involved in taste processing. Gustatory information can also reach another frontal region, the medial prefrontal cortex (mPFC), via direct projections from GC. mPFC has been studied extensively in relation to its role in controlling goal-directed action and reward-guided behaviors, yet very little is known about its involvement in taste coding. The experiments presented here address this important point and test whether neurons in mPFC can significantly process the physiochemical and hedonic dimensions of taste. Spiking responses to intraorally delivered tastants were recorded from rats implanted with bundles of electrodes in mPFC and GC. Analysis of single-neuron and ensemble activity revealed similarities and differences between the two areas. Neurons in mPFC can encode the chemosensory identity of gustatory stimuli. However, responses in mPFC are sparser, more narrowly tuned, and have a later onset than in GC. Although taste quality is more robustly represented in GC, taste palatability is coded equally well in the two areas. Additional analysis of responses in neurons processing the hedonic value of taste revealed differences between the two areas in temporal dynamics and sensitivities to palatability. These results add mPFC to the network of areas involved in processing gustatory stimuli and demonstrate significant differences in taste-coding between GC and mPFC.

Dynamics of multistable states during ongoing and evoked cortical activity.

Single-trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory, and decision-making. Yet, very little is known about the network mechanisms responsible for its genesis. It is often assumed that the onset of state sequences is triggered by an external stimulus. Here we show that state sequences can be observed also in the absence of overt sensory stimulation. Analysis of multielectrode recordings from the gustatory cortex of alert rats revealed ongoing sequences of states, where single neurons spontaneously attain several firing rates across different states. This single-neuron multistability represents a challenge to existing spiking network models, where typically each neuron is at most bistable. We present a recurrent spiking network model that accounts for both the spontaneous generation of state sequences and the multistability in single-neuron firing rates. Each state results from the activation of neural clusters with potentiated intracluster connections, with the firing rate in each cluster depending on the number of active clusters. Simulations show that the models ensemble activity hops among the different states, reproducing the ongoing dynamics observed in the data. When probed with external stimuli, the model predicts the quenching of single-neuron multistability into bistability and the reduction of trial-by-trial variability. Both predictions were confirmed in the data. Together, these results provide a theoretical framework that captures both ongoing and evoked network dynamics in a single mechanistic model.

Stimuli Reduce the Dimensionality of Cortical Activity.

The activity of ensembles of simultaneously recorded neurons can be represented as a set of points in the space of firing rates. Even though the dimension of this space is equal to the ensemble size, neural activity can be effectively localized on smaller subspaces. The dimensionality of the neural space is an important determinant of the computational tasks supported by the neural activity. Here, we investigate the dimensionality of neural ensembles from the sensory cortex of alert rats during periods of ongoing (inter-trial) and stimulus-evoked activity. We find that dimensionality grows linearly with ensemble size, and grows significantly faster during ongoing activity compared to evoked activity. We explain these results using a spiking network model based on a clustered architecture. The model captures the difference in growth rate between ongoing and evoked activity and predicts a characteristic scaling with ensemble size that could be tested in high-density multi-electrode recordings. Moreover, we present a simple theory that predicts the existence of an upper bound on dimensionality. This upper bound is inversely proportional to the amount of pair-wise correlations and, compared to a homogeneous network without clusters, it is larger by a factor equal to the number of clusters. The empirical estimation of such bounds depends on the number and duration of trials and is well predicted by the theory. Together, these results provide a framework to analyze neural dimensionality in alert animals, its behavior under stimulus presentation, and its theoretical dependence on ensemble size, number of clusters, and correlations in spiking network models.

Modeling the Violation of Reward Maximization and Invariance in Reinforcement Schedules

It is often assumed that animals and people adjust their behavior to maximize reward acquisition. In visually cued reinforcement schedules, monkeys make errors in trials that are not immediately rewarded, despite having to repeat error trials. Here we show that error rates are typically smaller in trials equally distant from reward but belonging to longer schedules (referred to as “schedule length effect”). This violates the principles of reward maximization and invariance and cannot be predicted by the standard methods of Reinforcement Learning, such as the method of temporal differences. We develop a heuristic model that accounts for all of the properties of the behavior in the reinforcement schedule task but whose predictions are not different from those of the standard temporal difference model in choice tasks. In the modification of temporal difference learning introduced here, the effect of schedule length emerges spontaneously from the sensitivity to the immediately preceding trial. We also introduce a policy for general Markov Decision Processes, where the decision made at each node is conditioned on the motivation to perform an instrumental action, and show that the application of our model to the reinforcement schedule task and the choice task are special cases of this general theoretical framework. Within this framework, Reinforcement Learning can approach contextual learning with the mixture of empirical findings and principled assumptions that seem to coexist in the best descriptions of animal behavior. As examples, we discuss two phenomena observed in humans that often derive from the violation of the principle of invariance: “framing,” wherein equivalent options are treated differently depending on the context in which they are presented, and the “sunk cost” effect, the greater tendency to continue an endeavor once an investment in money, effort, or time has been made. The schedule length effect might be a manifestation of these phenomena in monkeys.

Comparison between networks of conductance- and current-driven neurons: stationary spike rates and subthreshold depolarization

Abstract The problem of an equivalence between conductance- and current-driven neurons in terms of mean stationary output rates is investigated. We show that it is possible to study a network of conductance-driven neurons by means of a mean field analysis of an equivalent network of current-driven neurons. The current drive is Gauss distributed and not voltage dependent. The equivalent network is composed by the same neurons and exhibits the same stable firing rates at the only price of having different connectivity. In addition, the differences in the subthreshold depolarization and the interspike-interval distribution can be studied at parity of output rates, providing a method to study those effects of the conductance drive which do not arise in a network of current-driven neurons.

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

The response of a population of neurons to time-varying synaptic inputs can show a rich phenomenology, hardly predictable from the dynamical properties of the membrane’s inherent time constants. For example, a network of neurons in a state of spontaneous activity can respond significantly more rapidly than each single neuron taken individually. Under the assumption that the statistics of the synaptic input is the same for a population of similarly behaving neurons (mean field approximation), it is possible to greatly simplify the study of neural circuits, both in the case in which the statistics of the input are stationary (reviewed in La Camera et al. in Biol Cybern, 2008) and in the case in which they are time varying and unevenly distributed over the dendritic tree. Here, we review theoretical and experimental results on the single-neuron properties that are relevant for the dynamical collective behavior of a population of neurons. We focus on the response of integrate-and-fire neurons and real cortical neurons to long-lasting, noisy, in vivo-like stationary inputs and show how the theory can predict the observed rhythmic activity of cultures of neurons. We then show how cortical neurons adapt on multiple time scales in response to input with stationary statistics in vitro. Next, we review how it is possible to study the general response properties of a neural circuit to time-varying inputs by estimating the response of single neurons to noisy sinusoidal currents. Finally, we address the dendrite–soma interactions in cortical neurons leading to gain modulation and spike bursts, and show how these effects can be captured by a two-compartment integrate-and-fire neuron. Most of the experimental results reviewed in this article have been successfully reproduced by simple integrate-and-fire model neurons.