On the Role of Theory and Modeling in Neuroscience.

In recent years, the field of neuroscience has gone through rapid experimental advances and a significant increase in the use of quantitative and computational methods. This growth has created a need for clearer analyses of the theory and modeling approaches used in the field. This issue is particularly complex in neuroscience because the field studies phenomena that cross a wide range of scales and often require consideration at varying degrees of abstraction, from precise biophysical interactions to the computations they implement. We argue that a pragmatic perspective of science, in which descriptive, mechanistic, and normative models and theories each play a distinct role in defining and bridging levels of abstraction, will facilitate neuroscientific practice. This analysis leads to methodological suggestions, including selecting a level of abstraction that is appropriate for a given problem, identifying transfer functions to connect models and data, and the use of models themselves as a form of experiment.

Monosynaptic inference via finely-timed spikes.

Observations of finely-timed spike relationships in population recordings have been used to support partial reconstruction of neural microcircuit diagrams. In this approach, fine-timescale components of paired spike train interactions are isolated and subsequently attributed to synaptic parameters. Recent perturbation studies strengthen the case for such an inference, yet the complete set of measurements needed to calibrate statistical models is unavailable. To address this gap, we study features of pairwise spiking in a large-scale in vivo dataset where presynaptic neurons were explicitly decoupled from network activity by juxtacellular stimulation. We then construct biophysical models of paired spike trains to reproduce the observed phenomenology of in vivo monosynaptic interactions, including both fine-timescale spike-spike correlations and firing irregularity. A key characteristic of these models is that the paired neurons are coupled by rapidly-fluctuating background inputs. We quantify a monosynapse's causal effect by comparing the postsynaptic train with its counterfactual, when the monosynapse is removed. Subsequently, we develop statistical techniques for estimating this causal effect from the pre- and post-synaptic spike trains. A particular focus is the justification and application of a nonparametric separation of timescale principle to implement synaptic inference. Using simulated data generated from the biophysical models, we characterize the regimes in which the estimators accurately identify the monosynaptic effect. A secondary goal is to initiate a critical exploration of neurostatistical assumptions in terms of biophysical mechanisms, particularly with regards to the challenging but arguably fundamental issue of fast, unobservable nonstationarities in background dynamics.

Spike-Centered Jitter Can Mistake Temporal Structure.

Jitter-type spike resampling methods are routinely applied in neurophysiology for detecting temporal structure in spike trains (point processes). Several variations have been proposed. The concern has been raised, based on numerical experiments involving Poisson spike processes, that such procedures can be conservative. We study the issue and find it can be resolved by reemphasizing the distinction between spike-centered (basic) jitter and interval jitter. Focusing on spiking processes with no temporal structure, interval jitter generates an exact hypothesis test, guaranteeing valid conclusions. In contrast, such a guarantee is not available for spike-centered jitter. We construct explicit examples in which spike-centered jitter hallucinates temporal structure, in the sense of exaggerated false-positive rates. Finally, we illustrate numerically that Poisson approximations to jitter computations, while computationally efficient, can also result in inaccurate hypothesis tests. We highlight the value of classical statistical frameworks for guiding the design and interpretation of spike resampling methods.

Ambiguity and nonidentifiability in the statistical analysis of neural codes.

Many experimental studies of neural coding rely on a statistical interpretation of the theoretical notion of the rate at which a neuron fires spikes. For example, neuroscientists often ask, "Does a population of neurons exhibit more synchronous spiking than one would expect from the covariability of their instantaneous firing rates?" For another example, "How much of a neuron's observed spiking variability is caused by the variability of its instantaneous firing rate, and how much is caused by spike timing variability?" However, a neuron's theoretical firing rate is not necessarily well-defined. Consequently, neuroscientific questions involving the theoretical firing rate do not have a meaning in isolation but can only be interpreted in light of additional statistical modeling choices. Ignoring this ambiguity can lead to inconsistent reasoning or wayward conclusions. We illustrate these issues with examples drawn from the neural-coding literature.

Spatiotemporal conditional inference and hypothesis tests for neural ensemble spiking precision.

The collective dynamics of neural ensembles create complex spike patterns with many spatial and temporal scales. Understanding the statistical structure of these patterns can help resolve fundamental questions about neural computation and neural dynamics. Spatiotemporal conditional inference (STCI) is introduced here as a semiparametric statistical framework for investigating the nature of precise spiking patterns from collections of neurons that is robust to arbitrarily complex and nonstationary coarse spiking dynamics. The main idea is to focus statistical modeling and inference not on the full distribution of the data, but rather on families of conditional distributions of precise spiking given different types of coarse spiking. The framework is then used to develop families of hypothesis tests for probing the spatiotemporal precision of spiking patterns. Relationships among different conditional distributions are used to improve multiple hypothesis-testing adjustments and design novel Monte Carlo spike resampling algorithms. Of special note are algorithms that can locally jitter spike times while still preserving the instantaneous peristimulus time histogram or the instantaneous total spike count from a group of recorded neurons. The framework can also be used to test whether first-order maximum entropy models with possibly random and time-varying parameters can account for observed patterns of spiking. STCI provides a detailed example of the generic principle of conditional inference, which may be applicable to other areas of neurostatistical analysis.

Millisecond timescale synchrony among hippocampal neurons.

Inhibitory neurons in cortical circuits play critical roles in composing spike timing and oscillatory patterns in neuronal activity. These roles in turn require coherent activation of interneurons at different timescales. To investigate how the local circuitry provides for these activities, we applied resampled cross-correlation analyses to large-scale recordings of neuronal populations in the cornu ammonis 1 (CA1) and CA3 regions of the hippocampus of freely moving rats. Significant counts in the cross-correlation of cell pairs, relative to jittered surrogate spike-trains, allowed us to identify the effective couplings between neurons in CA1 and CA3 hippocampal regions on the timescale of milliseconds. In addition to putative excitatory and inhibitory monosynaptic connections, we uncovered prominent millisecond timescale synchrony between cell pairs, observed as peaks in the central 0 ms bin of cross-correlograms. This millisecond timescale synchrony appeared to be independent of network state, excitatory input, and γ oscillations. Moreover, it was frequently observed between cells of differing putative interneuronal type, arguing against gap junctions as the sole underlying source. Our observations corroborate recent in vitro findings suggesting that inhibition alone is sufficient to synchronize interneurons at such fast timescales. Moreover, we show that this synchronous spiking may cause stronger inhibition and rebound spiking in target neurons, pointing toward a potential function for millisecond synchrony of interneurons in shaping and affecting timing in pyramidal populations within and downstream from the circuit.

Conditional modeling and the jitter method of spike resampling.

The existence and role of fine-temporal structure in the spiking activity of central neurons is the subject of an enduring debate among physiologists. To a large extent, the problem is a statistical one: what inferences can be drawn from neurons monitored in the absence of full control over their presynaptic environments? In principle, properly crafted resampling methods can still produce statistically correct hypothesis tests. We focus on the approach to resampling known as jitter. We review a wide range of jitter techniques, illustrated by both simulation experiments and selected analyses of spike data from motor cortical neurons. We rely on an intuitive and rigorous statistical framework known as conditional modeling to reveal otherwise hidden assumptions and to support precise conclusions. Among other applications, we review statistical tests for exploring any proposed limit on the rate of change of spiking probabilities, exact tests for the significance of repeated fine-temporal patterns of spikes, and the construction of acceptance bands for testing any purported relationship between sensory or motor variables and synchrony or other fine-temporal events.

Internally generated cell assembly sequences in the rat hippocampus.

A long-standing conjecture in neuroscience is that aspects of cognition depend on the brain's ability to self-generate sequential neuronal activity. We found that reliably and continually changing cell assemblies in the rat hippocampus appeared not only during spatial navigation but also in the absence of changing environmental or body-derived inputs. During the delay period of a memory task, each moment in time was characterized by the activity of a particular assembly of neurons. Identical initial conditions triggered a similar assembly sequence, whereas different conditions gave rise to different sequences, thereby predicting behavioral choices, including errors. Such sequences were not formed in control (nonmemory) tasks. We hypothesize that neuronal representations, evolved for encoding distance in spatial navigation, also support episodic recall and the planning of action sequences.

Behavior-dependent short-term assembly dynamics in the medial prefrontal cortex.

Although short-term plasticity is believed to play a fundamental role in cortical computation, empirical evidence bearing on its role during behavior is scarce. Here we looked for the signature of short-term plasticity in the fine-timescale spiking relationships of a simultaneously recorded population of physiologically identified pyramidal cells and interneurons, in the medial prefrontal cortex of the rat, in a working memory task. On broader timescales, sequentially organized and transiently active neurons reliably differentiated between different trajectories of the rat in the maze. On finer timescales, putative monosynaptic interactions reflected short-term plasticity in their dynamic and predictable modulation across various aspects of the task, beyond a statistical accounting for the effect of the neurons' co-varying firing rates. Seeking potential mechanisms for such effects, we found evidence for both firing pattern-dependent facilitation and depression, as well as for a supralinear effect of presynaptic coincidence on the firing of postsynaptic targets.

Spike count reliability and the Poisson hypothesis.

The variability of cortical activity in response to repeated presentations of a stimulus has been an area of controversy in the ongoing debate regarding the evidence for fine temporal structure in nervous system activity. We present a new statistical technique for assessing the significance of observed variability in the neural spike counts with respect to a minimal Poisson hypothesis, which avoids the conventional but troubling assumption that the spiking process is identically distributed across trials. We apply the method to recordings of inferotemporal cortical neurons of primates presented with complex visual stimuli. On this data, the minimal Poisson hypothesis is rejected: the neuronal responses are too reliable to be fit by a typical firing-rate model, even allowing for sudden, time-varying, and trial-dependent rate changes after stimulus onset. The statistical evidence favors a tightly regulated stimulus response in these neurons, close to stimulus onset, although not further away.