A biochemical description of postsynaptic plasticity-with timescales ranging from milliseconds to seconds.

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.

Causal connectivity measures for pulse-output network reconstruction: Analysis and applications.

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.

Modeling the role of gap junctions between excitatory neurons in the developing visual cortex.

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.

Dendritic computations captured by an effective point neuron model.

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.

Mechanisms underlying contrast-dependent orientation selectivity in mouse V1.

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).

Neural networks of different species, brain areas and states can be characterized by the probability polling state.

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.

Ring models of binocular rivalry and fusion.

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.

Spatiotemporal dynamics of neuronal population response in the primary visual cortex.

One of the fundamental questions in system neuroscience is how the brain encodes external stimuli in the early sensory cortex. It has been found in experiments that even some simple sensory stimuli can activate large populations of neurons. It is believed that information can be encoded in the spatiotemporal profile of these collective neuronal responses. Here, we use a large-scale computational model of the primary visual cortex (V1) to study the population responses in V1 as observed in experiments in which monkeys performed visual detection tasks. We show that our model can capture very well spatiotemporal activities measured by voltage-sensitive-dye-based optical imaging in V1 of the awake state. In our model, the properties of horizontal long-range connections with NMDA conductance play an important role in the correlated population responses and have strong implications for spatiotemporal coding of neuronal populations. Our computational modeling approach allows us to reveal intrinsic cortical dynamics, separating them from those statistical effects arising from averaging procedures in experiment. For example, in experiments, it was shown that there was a spatially antagonistic center-surround structure in optimal weights in signal detection theory, which was believed to underlie the efficiency of population coding. However, our study shows that this feature is an artifact of data processing.

Quantifying neuronal network dynamics through coarse-grained event trees.

Animals process information about many stimulus features simultaneously, swiftly (in a few 100 ms), and robustly (even when individual neurons do not themselves respond reliably). When the brain carries, codes, and certainly when it decodes information, it must do so through some coarse-grained projection mechanism. How can a projection retain information about network dynamics that covers multiple features, swiftly and robustly? Here, by a coarse-grained projection to event trees and to the event chains that comprise these trees, we propose a method of characterizing dynamic information of neuronal networks by using a statistical collection of spatial-temporal sequences of relevant physiological observables (such as sequences of spiking multiple neurons). We demonstrate, through idealized point neuron simulations in small networks, that this event tree analysis can reveal, with high reliability, information about multiple stimulus features within short realistic observation times. Then, with a large-scale realistic computational model of V1, we show that coarse-grained event trees contain sufficient information, again over short observation times, for fine discrimination of orientation, with results consistent with recent experimental observation.

Estimation of synaptic conductances.

In order to identify and understand mechanistically the cortical circuitry of sensory information processing estimates are needed of synaptic input fields that drive neurons. From intracellular in vivo recordings one would like to estimate net synaptic conductance time courses for excitation and inhibition, g(E)(t) and g(I)(t), during time-varying stimulus presentations. However, the intrinsic conductance transients associated with neuronal spiking can confound such estimates, and thereby jeopardize functional interpretations. Here, using a conductance-based pyramidal neuron model we illustrate errors in estimates when the influence of spike-generating conductances are not reduced or avoided. A typical estimation procedure involves approximating the current-voltage relation at each time point during repeated stimuli. The repeated presentations are done in a few sets, each with a different steady bias current. From the trial-averaged smoothed membrane potential one estimates total membrane conductance and then dissects out estimates for g(E)(t) and g(I)(t). Simulations show that estimates obtained during phases without spikes are good but those obtained from phases with spiking should be viewed with skeptism. For the simulations, we consider two different synaptic input scenarios, each corresponding to computational network models of orientation tuning in visual cortex. One input scenario mimics a push-pull arrangement for g(E)(t) and g(I)(t) and idealized as specified smooth time courses. The other is taken directly from a large-scale network simulation of stochastically spiking neurons in a slab of cortex with recurrent excitation and inhibition. For both, we show that spike-generating conductances cause serious errors in the estimates of g(E) and g(I). In some phases for the push-pull examples even the polarity of g(I) is mis-estimated, indicating significant increase when g(I) is actually decreased. Our primary message is to be cautious about forming interpretations based on estimates developed during spiking phases.

Physicochemical characterisation and biological evaluation of hydrogel-poly(epsilon-caprolactone) interpenetrating polymer networks as novel urinary biomaterials.

Hydrogels are frequently employed as medical device biomaterials due to their advantageous biological properties, e.g. resistance to infection and encrustation, biocompatibility; however, their poor mechanical properties generally limit the scope of application to coatings of medical devices. To address this limitation, this study described the formulation of sequential interpenetrating polymer networks (IPN) of poly(-caprolactone) (PCL) and poly(hydroxyethylmethacrylate) (p(HEMA)). IPN containing 20% w/w PCL, p(HEMA), both in the presence or absence of ethyleneglycol dimethacrylate (EGDMA 1% w/w), were prepared by free radical polymerisation. Following preparation the degradation and the mechanical and surface properties of the biomaterials and, in addition, the resistances to microbial adherence and encrustation in vitro were examined. In comparison to p(HEMA) the various IPN exhibited substantially greater tensile properties (ultimate tensile strength, % elongation, Young's modulus) that were accredited to the discrete distribution of PCL within the hydrogel network. The IPN exhibited two glass transition temperatures that were statistically similar to those of the individual components, thereby providing evidence of the immiscible nature of the two polymers. The IPN possessed higher receding contact angles and lower equilibrium water contents in comparison to p(HEMA), whereas the limited degradation of the IPN at both pH 7 and 9 was deemed suitable for clinical usage for periods of at least 4 weeks. The resistances of the various IPN to bacterial adherence and urinary encrustation were examined using in vitro models. Importantly the resistance of the IPN to encrustation was, in general, similar to that of p(HEMA) but greater than that of PCL whereas, the resistance of the IPN to bacterial adherence was frequently greater than that of p(HEMA) and PCL. Therefore, this study has shown that the mechanical properties of p(HEMA) may be substantially increased by the formation of IPN with PCL whilst maintaining other appropriate physicochemical properties and resistances to urinary encrustation and bacterial adherence. It is suggested that these IPN may be suitable for device fabrication thereby expanding the manufacturing application of hydrogels without compromising their potential clinical efficacy.

Orientation selectivity in visual cortex by fluctuation-controlled criticality.

Within a large-scale neuronal network model of macaque primary visual cortex, we examined how intrinsic dynamic fluctuations in synaptic currents modify the effect of strong recurrent excitation on orientation selectivity. Previously, we showed that, using a strong network inhibition countered by feedforward and recurrent excitation, the cortical model reproduced many observed properties of simple and complex cells. However, that network's complex cells were poorly selective for orientation, and increasing cortical self-excitation led to network instabilities and unrealistically high firing rates. Here, we show that a sparsity of connections in the network produces large, intrinsic fluctuations in the cortico-cortical conductances that can stabilize the network and that there is a critical level of fluctuations (controllable by sparsity) that allows strong cortical gain and the emergence of orientation-selective complex cells. The resultant sparse network also shows near contrast invariance in its selectivity and, in agreement with recent experiments, has extracellular tuning properties that are similar in pinwheel center and iso-orientation regions, whereas intracellular conductances show positional dependencies. Varying the strength of synaptic fluctuations by adjusting the sparsity of network connectivity, we identified a transition between the dynamics of bistability and without bistability. In a network with strong recurrent excitation, this transition is characterized by a near hysteretic behavior and a rapid rise of network firing rates as the synaptic drive or stimulus input is increased. We discuss the connection between this transition and orientation selectivity in our model of primary visual cortex.

Modeling the spatiotemporal cortical activity associated with the line-motion illusion in primary visual cortex.

Our large-scale computational model of the primary visual cortex that incorporates orientation-specific, long-range couplings with slow NMDA conductances operates in a fluctuating dynamic state of intermittent desuppression (IDS), which captures the behavior of coherent spontaneous cortical activity, as revealed by in vivo optical imaging based on voltage-sensitive dyes. Here, we address the functional significance of the IDS cortical operating points by investigating our model cortex response to the Hikosaka line-motion illusion (LMI) stimulus-a cue of a quickly flashed stationary square followed a few milliseconds later by a stationary bar. As revealed by voltage-sensitive dye imaging, there is an intriguing similarity between the cortical spatiotemporal activity in response to (i) the Hikosaka LMI stimulus and (ii) a small moving square. This similarity is believed to be associated with the preattentive illusory motion perception. Our numerical cortex produces similar spatiotemporal patterns in response to the two stimuli above, which are both in very good agreement with experimental results. The essential network mechanisms underpinning the LMI phenomenon in our model are (i) the spatiotemporal structure of the LMI input as sculpted by the lateral geniculate nucleus, (ii) a priming effect of the long-range NMDA-type cortical coupling, and (iii) the NMDA conductance-voltage correlation manifested in the IDS state. This mechanism in our model cortex, in turn, suggests a physiological underpinning for the LMI-associated patterns in the visual cortex of anaesthetized cat.

Architectural and synaptic mechanisms underlying coherent spontaneous activity in V1.

To investigate the existence and the characteristics of possible cortical operating points of the primary visual cortex, as manifested by the coherent spontaneous ongoing activity revealed by real-time optical imaging based on voltage-sensitive dyes, we studied numerically a very large-scale ( approximately 5 x 10(5)) conductance-based, integrate-and-fire neuronal network model of an approximately 16-mm(2) patch of 64 orientation hypercolumns, which incorporates both isotropic local couplings and lateral orientation-specific long-range connections with a slow NMDA component. A dynamic scenario of an intermittent desuppressed state (IDS) is identified in the computational model, which is a dynamic state of (i) high conductance, (ii) strong inhibition, and (iii) large fluctuations that arise from intermittent spiking events that are strongly correlated in time as well as in orientation domains, with the correlation time of the fluctuations controlled by the NMDA decay time scale. Our simulation results demonstrate that the IDS state captures numerically many aspects of experimental observation related to spontaneous ongoing activity, and the specific network mechanism of the IDS may suggest cortical mechanisms and the cortical operating point underlying observed spontaneous activity.

An embedded network approach for scale-up of fluctuation-driven systems with preservation of spike information.

To address computational "scale-up" issues in modeling large regions of the cortex, many coarse-graining procedures have been invoked to obtain effective descriptions of neuronal network dynamics. However, because of local averaging in space and time, these methods do not contain detailed spike information and, thus, cannot be used to investigate, e.g., cortical mechanisms that are encoded through detailed spike-timing statistics. To retain high-order statistical information of spikes, we develop a hybrid theoretical framework that embeds a subnetwork of point neurons within, and fully interacting with, a coarse-grained network of dynamical background. We use a newly developed kinetic theory for the description of the coarse-grained background, in combination with a Poisson spike reconstruction procedure to ensure that our method applies to the fluctuation-driven regime as well as to the mean-driven regime. This embedded-network approach is verified to be dynamically accurate and numerically efficient. As an example, we use this embedded representation to construct "reverse-time correlations" as spiked-triggered averages in a ring model of orientation-tuning dynamics.

An effective kinetic representation of fluctuation-driven neuronal networks with application to simple and complex cells in visual cortex.

A coarse-grained representation of neuronal network dynamics is developed in terms of kinetic equations, which are derived by a moment closure, directly from the original large-scale integrate-and-fire (I&F) network. This powerful kinetic theory captures the full dynamic range of neuronal networks, from the mean-driven limit (a limit such as the number of neurons N --> infinity, in which the fluctuations vanish) to the fluctuation-dominated limit (such as in small N networks). Comparison with full numerical simulations of the original I&F network establishes that the reduced dynamics is very accurate and numerically efficient over all dynamic ranges. Both analytical insights and scale-up of numerical representation can be achieved by this kinetic approach. Here, the theory is illustrated by a study of the dynamical properties of networks of various architectures, including excitatory and inhibitory neurons of both simple and complex type, which exhibit rich dynamic phenomena, such as, transitions to bistability and hysteresis, even in the presence of large fluctuations. The implication for possible connections between the structure of the bifurcations and the behavior of complex cells is discussed. Finally, I&F networks and kinetic theory are used to discuss orientation selectivity of complex cells for "ring-model" architectures that characterize changes in the response of neurons located from near "orientation pinwheel centers" to far from them.