Faculty Bibliography

The causal connectivity of a network is often inferred to understand network function. It is arguably acknowledged that the inferred causal connectivity relies on the causality measure one applies, and it may differ from the network's underlying structural connectivity. However, the interpretation of causal connectivity remains to be fully clarified, in particular, how causal connectivity depends on causality measures and how causal connectivity relates to structural connectivity. Here, we focus on nonlinear networks with pulse signals as measured output, e.g., neural networks with spike output, and address the above issues based on four commonly utilized causality measures, i.e., time-delayed correlation coefficient, time-delayed mutual information, Granger causality, and transfer entropy. We theoretically show how these causality measures are related to one another when applied to pulse signals. Taking a simulated Hodgkin-Huxley network and a real mouse brain network as two illustrative examples, we further verify the quantitative relations among the four causality measures and demonstrate that the causal connectivity inferred by any of the four well coincides with the underlying network structural connectivity, therefore illustrating a direct link between the causal and structural connectivity. We stress that the structural connectivity of pulse-output networks can be reconstructed pairwise without conditioning on the global information of all other nodes in a network, thus circumventing the curse of dimensionality. Our framework provides a practical and effective approach for pulse-output network reconstruction.

Synaptic plasticity [long-term potentiation/depression (LTP/D)], is a cellular mechanism underlying learning. Two distinct types of early LTP/D (E-LTP/D), acting on very different time scales, have been observed experimentally-spike timing dependent plasticity (STDP), on time scales of tens of ms; and behavioral time scale synaptic plasticity (BTSP), on time scales of seconds. BTSP is a candidate for a mechanism underlying rapid learning of spatial location by place cells. Here, a computational model of the induction of E-LTP/D at a spine head of a synapse of a hippocampal pyramidal neuron is developed. The single-compartment model represents two interacting biochemical pathways for the activation (phosphorylation) of the kinase (CaMKII) with a phosphatase, with ion inflow through channels (NMDAR, CaV1,Na). The biochemical reactions are represented by a deterministic system of differential equations, with a detailed description of the activation of CaMKII that includes the opening of the compact state of CaMKII. This single model captures realistic responses (temporal profiles with the differing timescales) of STDP and BTSP and their asymmetries. The simulations distinguish several mechanisms underlying STDP vs. BTSP, including i) the flow of [Formula: see text] through NMDAR vs. CaV1 channels, and ii) the origin of several time scales in the activation of CaMKII. The model also realizes a priming mechanism for E-LTP that is induced by [Formula: see text] flow through CaV1.3 channels. Once in the spine head, this small additional [Formula: see text] opens the compact state of CaMKII, placing CaMKII ready for subsequent induction of LTP.

Recent experiments in the developing mammalian visual cortex have revealed that gap junctions couple excitatory cells and potentially influence the formation of chemical synapses. In particular, cells that were coupled by a gap junction during development tend to share an orientation preference and are preferentially coupled by a chemical synapse in the adult cortex, a property that is diminished when gap junctions are blocked. In this work, we construct a simplified model of the developing mouse visual cortex including spike-timing-dependent plasticity of both the feedforward synaptic inputs and recurrent cortical synapses. We use this model to show that synchrony among gap-junction-coupled cells underlies their preference to form strong recurrent synapses and develop similar orientation preference; this effect decreases with an increase in coupling density. Additionally, we demonstrate that gap-junction coupling works, together with the relative timing of synaptic development of the feedforward and recurrent synapses, to determine the resulting cortical map of orientation preference.

Cortical networks are complex systems of a great many interconnected neurons that operate from collective dynamical states. To understand how cortical neural networks function, it is important to identify their common dynamical operating states from the probabilistic viewpoint. Probabilistic characteristics of these operating states often underlie network functions. Here, using multi-electrode data from three separate experiments, we identify and characterize a cortical operating state (the "probability polling" or "p-polling" state), common across mouse and monkey with different behaviors. If the interaction among neurons is weak, the p-polling state provides a quantitative understanding of how the high dimensional probability distribution of firing patterns can be obtained by the low-order maximum entropy formulation, effectively utilizing a low dimensional stimulus-coding structure. These results show evidence for generality of the p-polling state and in certain situations its advantage of providing a mathematical validation for the low-order maximum entropy principle as a coding strategy.

When similar visual stimuli are presented binocularly to both eyes, one perceives a fused single image. However, when the two stimuli are distinct, one does not perceive a single image; instead, one perceives binocular rivalry. That is, one perceives one of the stimulated patterns for a few seconds, then the other for few seconds, and so on - with random transitions between the two percepts. Most theoretical studies focus on rivalry, with few considering the coexistence of fusion and rivalry. Here we develop three distinct computational neuronal network models which capture binocular rivalry with realistic stochastic properties, fusion, and the hysteretic transition between. Each is a conductance-based point neuron model, which is multi-layer with two ocular dominance columns (L & R) and with an idealized "ring" architecture where the orientation preference of each neuron labels its location on a ring. In each model, the primary mechanism initiating binocular rivalry is cross-column inhibition, with firing rate adaptation governing the temporal properties of the transitions between percepts. Under stimulation by similar visual patterns, each of three models uses its own mechanism to overcome cross-column inhibition, and thus to prevent rivalry and allow the fusion of similar images: The first model uses cross-column feedforward inhibition from the opposite eye to "shut off" the cross-column feedback inhibition; the second model "turns on" a second layer of monocular neurons as a parallel pathway to the binocular neurons, rivaling out of phase with the first layer, and together these two pathways represent fusion; and the third model uses cross-column excitation to overcome the cross-column inhibition and enable fusion. Thus, each of the idealized ring models depends upon a different mechanism for fusion that might emerge as an underlying mechanism present in real visual cortex.

Complex dendrites in general present formidable challenges to understanding neuronal information processing. To circumvent the difficulty, a prevalent viewpoint simplifies the neuronal morphology as a point representing the soma, and the excitatory and inhibitory synaptic currents originated from the dendrites are treated as linearly summed at the soma. Despite its extensive applications, the validity of the synaptic current description remains unclear, and the existing point neuron framework fails to characterize the spatiotemporal aspects of dendritic integration supporting specific computations. Using electrophysiological experiments, realistic neuronal simulations, and theoretical analyses, we demonstrate that the traditional assumption of linear summation of synaptic currents is oversimplified and underestimates the inhibition effect. We then derive a form of synaptic integration current within the point neuron framework to capture dendritic effects. In the derived form, the interaction between each pair of synaptic inputs on the dendrites can be reliably parameterized by a single coefficient, suggesting the inherent low-dimensional structure of dendritic integration. We further generalize the form of synaptic integration current to capture the spatiotemporal interactions among multiple synaptic inputs and show that a point neuron model with the synaptic integration current incorporated possesses the computational ability of a spatial neuron with dendrites, including direction selectivity, coincidence detection, logical operation, and a bilinear dendritic integration rule discovered in experiment. Our work amends the modeling of synaptic inputs and improves the computational power of a modeling neuron within the point neuron framework.

Over the past two decades, mathematicians and neuroscientists at New York University have developed several large-scale computational models of a layer of macaque primary visual cortex. Here we provide an overview of these models, organized by the specific questions about cortical processing that each model addressed. Each model was founded upon the available anatomical and physiological data; and not by building into the model network assumptions about theoretical mechanisms specifically designed to enable the network to produce desired response properties. Also, our aim was to use one comprehensive network, with a fixed architecture and one set of parameters, to model all experiments. The response properties of individual neurons and populations of neurons then emerge from this experimentally constrained model. This overview is dedicated to Professor David Cai, who played a leading role in several of the models described here. We are very fortunate to have had the opportunity to work with him over the past two decades.

Recent experiments have shown that mouse primary visual cortex (V1) is very different from that of cat or monkey, including response properties-one of which is that contrast invariance in the orientation selectivity (OS) of the neurons' firing rates is replaced in mouse with contrast-dependent sharpening (broadening) of OS in excitatory (inhibitory) neurons. These differences indicate a different circuit design for mouse V1 than that of cat or monkey. Here we develop a large-scale computational model of an effective input layer of mouse V1. Constrained by experiment data, the model successfully reproduces experimentally observed response properties-for example, distributions of firing rates, orientation tuning widths, and response modulations of simple and complex neurons, including the contrast dependence of orientation tuning curves. Analysis of the model shows that strong feedback inhibition and strong orientation-preferential cortical excitation to the excitatory population are the predominant mechanisms underlying the contrast-sharpening of OS in excitatory neurons, while the contrast-broadening of OS in inhibitory neurons results from a strong but nonpreferential cortical excitation to these inhibitory neurons, with the resulting contrast-broadened inhibition producing a secondary enhancement on the contrast-sharpened OS of excitatory neurons. Finally, based on these mechanisms, we show that adjusting the detailed balances between the predominant mechanisms can lead to contrast invariance-providing insights for future studies on contrast dependence (invariance).

BACKGROUND: Although cognitive deficits in patients with schizophrenia are rooted early in development, the impact of psychosis on the course of cognitive functioning remains unclear. In this study a nested case-control design was used to examine the relationship between emerging psychosis and the course of cognition in individuals ascertained as clinical high-risk (CHR) who developed psychosis during the study (CHR + T). METHOD: Fifteen CHR + T subjects were administered a neurocognitive battery at baseline and post-psychosis onset (8.04 months, s.d. = 10.26). CHR + T subjects were matched on a case-by-case basis on age, gender, and time to retest with a group of healthy comparison subjects (CNTL, n = 15) and two groups of CHR subjects that did not transition: (1) subjects matched on medication treatment (i.e. antipsychotics and antidepressants) at both baseline and retesting (Meds-matched CHR + NT, n = 15); (2) subjects unmedicated at both assessments (Meds-free CHR + NT, n = 15). RESULTS: At baseline, CHR + T subjects showed large global neurocognitive and intellectual impairments, along with specific impairments in processing speed, verbal memory, sustained attention, and executive function. These impairments persisted after psychosis onset and did not further deteriorate. In contrast, CHR + NT subjects demonstrated stable mild to no impairments in neurocognitive and intellectual performance, independent of medication treatment. CONCLUSIONS: Cognition appears to be impaired prior to the emergence of psychotic symptoms, with no further deterioration associated with the onset of psychosis. Cognitive deficits represent trait risk markers, as opposed to state markers of disease status and may therefore serve as possible predictors of schizophrenia prior to the onset of the full illness.