Strength Of Synaptic Connections Research Articles

Balancing the critical period of spiking neurons with attractor-less STDP

Attractor-based (multiplicative) STDP has been called a biologically more realistic form of spike timing dependent plasticity than attractor-less (additive) variants [1-4], as it produces unimodal distributions of synaptic weights [5,6] when given poisson-distributed random input spike trains [1,2,4,7-9]. While unimodal weight distributions have been observed as an outcome in some in vitro experiments [5], the actual biochemical process that changes synaptic connection strengths has yet to be fully understood. Unfortunately, attractor-based STDP has been repeatedly shown to be computationally less powerful than attractor-less STDP [9] and successful implementations of attractor-based STDP used attractors that were either very weak [8] or very close to some minimum weight [2,3], causing a more additive-like [2,8] behaviour of the plasticity rule. We therefore examined possible biological interpretations of attractor-less STDP rules while keeping in mind that any STDP rule is just an abstraction from the hidden biophysical reality. We show how unimodal weight distributions can reliably result from attractor-less STDP when negative synaptic drift is combined with activity-independent synaptic growth. A bimodal distribution is then only formed when non-random (polychromous [10]) poisson-distributed inputs are presented to a neuron [11]. In practice, this produces a plasticity rule that keeps the postsynaptic neuron unselective and responsive to a broad range of inputs while receiving only random spikes, but quickly allows the neuron's receptive field to become highly selective as soon as some inputs start repeating a non-random ordering of spikes. This stabilization procedure preserves STDP's sensitivity to temporally shifted correlations in input spike data, which in turn gives us several beneficial features for biologically more realistic and computationally more powerful [12] implementations of plasticity in spiking neural networks.

Postsynaptic VAMP/Synaptobrevin Facilitates Differential Vesicle Trafficking of GluA1 and GluA2 AMPA Receptor Subunits.

Vertebrate organisms adapt to a continuously changing environment by regulating the strength of synaptic connections between brain cells. Excitatory synapses are believed to increase their strength by vesicular insertion of transmitter glutamate receptors into the postsynaptic plasma membrane. These vesicles, however, have never been demonstrated or characterized. For the first time, we show the presence of small vesicles in postsynaptic spines, often closely adjacent to the plasma membrane and PSD (postsynaptic density). We demonstrate that they harbor vesicle-associated membrane protein 2 (VAMP2/synaptobrevin-2) and glutamate receptor subunit 1 (GluA1). Disrupting VAMP2 by tetanus toxin treatment reduces the concentration of GluA1 in the postsynaptic plasma membrane. GluA1/VAMP2-containing vesicles, but not GluA2/VAMP2-vesicles, are concentrated in postsynaptic spines relative to dendrites. Our results indicate that small postsynaptic vesicles containing GluA1 are inserted directly into the spine plasma membrane through a VAMP2-dependent mechanism.

Noise promotes independent control of gamma oscillations and grid firing within recurrent attractor networks.

Neural computations underlying cognitive functions require calibration of the strength of excitatory and inhibitory synaptic connections and are associated with modulation of gamma frequency oscillations in network activity. However, principles relating gamma oscillations, synaptic strength and circuit computations are unclear. We address this in attractor network models that account for grid firing and theta-nested gamma oscillations in the medial entorhinal cortex. We show that moderate intrinsic noise massively increases the range of synaptic strengths supporting gamma oscillations and grid computation. With moderate noise, variation in excitatory or inhibitory synaptic strength tunes the amplitude and frequency of gamma activity without disrupting grid firing. This beneficial role for noise results from disruption of epileptic-like network states. Thus, moderate noise promotes independent control of multiplexed firing rate- and gamma-based computational mechanisms. Our results have implications for tuning of normal circuit function and for disorders associated with changes in gamma oscillations and synaptic strength.

Training sensory–motor behavior in the connectome of an artificial C. elegans

The Caenorhabditis elegans nematode worm is a small well-known creature, intensely studied for decades. Its entire morphology has been mapped cell-by-cell, including its 302 neuron connectome. The connectome is a synaptic wiring diagram that also specifies neurotransmitters and junction types. It does not however specify the synaptic connection strengths. It is believed that measuring these must be done in live specimens, requiring emerging or yet to be developed techniques. Without the connection strengths, it is not known how the nematode׳s nervous system produces behaviors. Discovering these strengths as a set of weights is a challenging and important problem: an artificial worm embodying the connectome and trained to perform a set of behaviors taken from measurements of the actual C. elegans would behave realistically in its environment. This is a crucial step toward creating a functional artificial creature. Indeed, knowing the artificial weights might cast light on the actual ones. In this project a genetic algorithm was used to train the entire connectome, a large space of 3680 synapse weights, to learn behaviors defined as sensory–motor sequences. It was found that utilizing the topology of the connectome for local optimization and crossover significantly boosts the performance of the genetic algorithm. Using a network of artificial neurons, random sequences involving the entire connectome were successfully trained. Additionally, for locomotion training, sinusoidal body postures were observed when sensory touch neurons were stimulated. Locomotion training was done using a Fourier Transform fitness function. Finally, using the NEURON tool to simulate a biologically higher fidelity network, the pharyngeal assembly of neurons was successfully trained.

GluN2B-Containing NMDA Receptors Regulate AMPA Receptor Traffic through Anchoring of the Synaptic Proteasome.

NMDA receptors play a central role in shaping the strength of synaptic connections throughout development and in mediating synaptic plasticity mechanisms that underlie some forms of learning and memory formation in the CNS. In the hippocampus and the neocortex, GluN1 is combined primarily with GluN2A and GluN2B, which are differentially expressed during development and confer distinct molecular and physiological properties to NMDA receptors. The contribution of each subunit to the synaptic traffic of NMDA receptors and therefore to their role during development and in synaptic plasticity is still controversial. We report a critical role for the GluN2B subunit in regulating NMDA receptor synaptic targeting. In the absence of GluN2B, the synaptic levels of AMPA receptors are increased and accompanied by decreased constitutive endocytosis of GluA1-AMPA receptor. We used quantitative proteomic analysis to identify changes in the composition of postsynaptic densities from GluN2B(-/-) mouse primary neuronal cultures and found altered levels of several ubiquitin proteasome system components, in particular decreased levels of proteasome subunits. Enhancing the proteasome activity with a novel proteasome activator restored the synaptic levels of AMPA receptors in GluN2B(-/-) neurons and their endocytosis, revealing that GluN2B-mediated anchoring of the synaptic proteasome is responsible for fine tuning AMPA receptor synaptic levels under basal conditions.

Adaptive stochastic resonance in self-organized small-world neuronal networks with time delay

In this paper, adaptive stochastic resonance in time-delayed Newman–Watts small-world neuronal networks is studied, where the strength of synaptic connections between neurons is adaptively modulated by spike-timing-dependent plasticity (STDP). Numerical results show that, in the absence of information transmission delay, the phenomenon of stochastic resonance occurs and the efficiency of networked stochastic resonance can be slightly depressed by STDP. Due to the reduction of strong couplings induced by STDP, for a larger adjusting rate of STDP, a smaller peak value of the resonance response is obtained. In addition, the effect of stochastic resonance can be either promoted or destroyed by time delay, and multiple stochastic resonances appear intermittently at the integer multiples of periods of the subthreshold forcing. Furthermore, it is demonstrated that the networked stochastic resonance can also be dramatically affected by the small-world topology. For small and moderate adjusting rate of STDP, fine-tuning of the probability of adding links can significantly enhance the effect of stochastic resonance in adaptive neural network. Additionally, there is an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks and the location of this span depends largely on the time delay and adjusting rate.

Vibrational resonance in adaptive small-world neuronal networks with spike-timing-dependent plasticity

The phenomenon of vibrational resonance is investigated in adaptive Newman–Watts small-world neuronal networks, where the strength of synaptic connections between neurons is modulated based on spike-timing-dependent plasticity. Numerical results demonstrate that there exists appropriate amplitude of high-frequency driving which is able to optimize the neural ensemble response to the weak low-frequency periodic signal. The effect of networked vibrational resonance can be significantly affected by spike-timing-dependent plasticity. It is shown that spike-timing-dependent plasticity with dominant depression can always improve the efficiency of vibrational resonance, and a small adjusting rate can promote the transmission of weak external signal in small-world neuronal networks. In addition, the network topology plays an important role in the vibrational resonance in spike-timing-dependent plasticity-induced neural systems, where the system response to the subthreshold signal is maximized by an optimal network structure. Furthermore, it is demonstrated that the introduction of inhibitory synapses can considerably weaken the phenomenon of vibrational resonance in the hybrid small-world neuronal networks with spike-timing-dependent plasticity.

Molecular Substrates of Altered Axonal Growth and Brain Connectivity in a Mouse Model of Schizophrenia

22q11.2 deletion carriers show specific cognitive deficits, and ∼30% of them develop schizophrenia. One of the disrupted genes is ZDHHC8, which encodes for a palmitoyltransferase. We show that Zdhhc8-deficient mice have reduced palmitoylation of proteins that regulate axonal growth and branching. Analysis of axonal projections of pyramidal neurons from both Zdhhc8-deficient and Df(16)A(+/-) mice, which model the 22q11.2 deletion, revealed deficits in axonal growth and terminal arborization, which can be prevented by reintroduction of active ZDHHC8 protein. Impaired terminal arborization is accompanied by a reduction in the strength of synaptic connections and altered functional connectivity and working memory. The effect of ZDHHC8 is mediated in part via Cdc42-dependent modulation of Akt/Gsk3β signaling at the tip of the axon and can be reversed by pharmacologically decreasing Gsk3β activity during postnatal brain development. Our findings provide valuable mechanistic insights into the cognitive and psychiatric symptoms associated with a schizophrenia-predisposing mutation.

Apoptotic self-organized electronic device using thin-film transistors for artificial neural networks with unsupervised learning functions

Artificial neural networks are promising systems for information processing with many advantages, such as self-teaching and parallel distributed computing. However, conventional networks consist of extremely intricate circuits to guarantee accurate behaviors of the neurons and synapses. We demonstrate an apoptotic self-organized electronic device using thin-film transistors for artificial neural networks with unsupervised learning functions. First, we formed a “neuron” from only eight transistors and reduced a “synapse” to only one transistor by employing the characteristic degradations of the synapse transistors to adjust the synaptic connection strength. Second, we classified the synapses into two types, “concordant” and “discordant” synapses, and composed a local interconnective network optimized for integrated electronic circuits. Finally, we confirmed that the device is feasible and can learn multiple logical operations, including AND, OR, and XOR.

Functional organization of excitatory synaptic strength in primary visual cortex.

The strength of synaptic connections fundamentally determines how neurons influence each other's firing. Excitatory connection amplitudes between pairs of cortical neurons vary over two orders of magnitude, comprising only very few strong connections among many weaker ones. Although this highly skewed distribution of connection strengths is observed in diverse cortical areas, its functional significance remains unknown: it is not clear how connection strength relates to neuronal response properties, nor how strong and weak inputs contribute to information processing in local microcircuits. Here we reveal that the strength of connections between layer 2/3 (L2/3) pyramidal neurons in mouse primary visual cortex (V1) obeys a simple rule--the few strong connections occur between neurons with most correlated responses, while only weak connections link neurons with uncorrelated responses. Moreover, we show that strong and reciprocal connections occur between cells with similar spatial receptive field structure. Although weak connections far outnumber strong connections, each neuron receives the majority of its local excitation from a small number of strong inputs provided by the few neurons with similar responses to visual features. By dominating recurrent excitation, these infrequent yet powerful inputs disproportionately contribute to feature preference and selectivity. Therefore, our results show that the apparently complex organization of excitatory connection strength reflects the similarity of neuronal responses, and suggest that rare, strong connections mediate stimulus-specific response amplification in cortical microcircuits.

A useful electroencephalography (EEG) marker of brain plasticity: delta waves.

A useful electroencephalography (EEG) marker of brain plasticity: delta waves.

Hebbian and neuromodulatory mechanisms interact to trigger associative memory formation.

A long-standing hypothesis termed "Hebbian plasticity" suggests that memories are formed through strengthening of synaptic connections between neurons with correlated activity. In contrast, other theories propose that coactivation of Hebbian and neuromodulatory processes produce the synaptic strengthening that underlies memory formation. Using optogenetics we directly tested whether Hebbian plasticity alone is both necessary and sufficient to produce physiological changes mediating actual memory formation in behaving animals. Our previous work with this method suggested that Hebbian mechanisms are sufficient to produce aversive associative learning under artificial conditions involving strong, iterative training. Here we systematically tested whether Hebbian mechanisms are necessary and sufficient to produce associative learning under more moderate training conditions that are similar to those that occur in daily life. We measured neural plasticity in the lateral amygdala, a brain region important for associative memory storage about danger. Our findings provide evidence that Hebbian mechanisms are necessary to produce neural plasticity in the lateral amygdala and behavioral memory formation. However, under these conditions Hebbian mechanisms alone were not sufficient to produce these physiological and behavioral effects unless neuromodulatory systems were coactivated. These results provide insight into how aversive experiences trigger memories and suggest that combined Hebbian and neuromodulatory processes interact to engage associative aversive learning.

Development of intrinsic connectivity in the central nucleus of the mouse inferior colliculus.

The inferior colliculus (IC) in the mammalian midbrain is the major subcortical auditory integration center receiving ascending inputs from almost all auditory brainstem nuclei as well as descending inputs from the thalamus and cortex. In addition to these extrinsic inputs, the IC also contains a dense network of local, intracollicular connections, which are thought to provide gain control and contribute to the selectivity for complex acoustic features. However, in contrast to the organization of extrinsic IC afferents, the development and functional organization of intrinsic connections in the IC has remained poorly understood. Here we used laser-scanning photostimulation with caged glutamate to characterize the spatial distribution and strength of local synaptic connections in the central nucleus of the inferior colliculus of newborn mice until after hearing onset (P2-P22). We demonstrate the presence of an extensive excitatory and inhibitory intracollicular network already at P2. Excitatory and inhibitory synaptic maps to individual IC neurons formed continuous maps that largely overlapped with each other and that were aligned with the presumed isofrequency axis of the central nucleus of the IC. Although this characteristic organization was present throughout the first three postnatal weeks, the size of input maps was developmentally regulated as input maps underwent an expansion during the first week that was followed by a dramatic refinement after hearing onset. These changes occurred in parallel for excitatory and inhibitory input maps. However, the functional elimination of intrinsic connections was greater for excitatory than for inhibitory connections, resulting in a predominance of intrinsic inhibition after hearing onset.

Effects of spike-time-dependent plasticity on the stochastic resonance of small-world neuronal networks.

The phenomenon of stochastic resonance in Newman-Watts small-world neuronal networks is investigated when the strength of synaptic connections between neurons is adaptively adjusted by spike-time-dependent plasticity (STDP). It is shown that irrespective of the synaptic connectivity is fixed or adaptive, the phenomenon of stochastic resonance occurs. The efficiency of network stochastic resonance can be largely enhanced by STDP in the coupling process. Particularly, the resonance for adaptive coupling can reach a much larger value than that for fixed one when the noise intensity is small or intermediate. STDP with dominant depression and small temporal window ratio is more efficient for the transmission of weak external signal in small-world neuronal networks. In addition, we demonstrate that the effect of stochastic resonance can be further improved via fine-tuning of the average coupling strength of the adaptive network. Furthermore, the small-world topology can significantly affect stochastic resonance of excitable neuronal networks. It is found that there exists an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks.

On Stationary Distributions of Stochastic Neural Networks

The paper deals with nonlinear Poisson neuron network models with bounded memory dynamics, which can include both Hebbian learning mechanisms and refractory periods. The state of the network is described by the times elapsed since its neurons fired within the post-synaptic transfer kernel memory span, and the current strengths of synaptic connections, the state spaces of our models being hierarchies of finite-dimensional components. We prove the ergodicity of the stochastic processes describing the behaviour of the networks, establish the existence of continuously differentiable stationary distribution densities (with respect to the Lebesgue measures of corresponding dimensionality) on the components of the state space, and find upper bounds for them. For the density components, we derive a system of differential equations that can be solved in a few simplest cases only. Approaches to approximate computation of the stationary density are discussed. One approach is to reduce the dimensionality of the problem by modifying the network so that each neuron cannot fire if the number of spikes it emitted within the post-synaptic transfer kernel memory span reaches a given threshold. We show that the stationary distribution of this ‘truncated’ network converges to that of the unrestricted network as the threshold increases, and that the convergence is at a superexponential rate. A complementary approach uses discrete Markov chain approximations to the network process.

On Stationary Distributions of Stochastic Neural Networks

The paper deals with nonlinear Poisson neuron network models with bounded memory dynamics, which can include both Hebbian learning mechanisms and refractory periods. The state of the network is described by the times elapsed since its neurons fired within the post-synaptic transfer kernel memory span, and the current strengths of synaptic connections, the state spaces of our models being hierarchies of finite-dimensional components. We prove the ergodicity of the stochastic processes describing the behaviour of the networks, establish the existence of continuously differentiable stationary distribution densities (with respect to the Lebesgue measures of corresponding dimensionality) on the components of the state space, and find upper bounds for them. For the density components, we derive a system of differential equations that can be solved in a few simplest cases only. Approaches to approximate computation of the stationary density are discussed. One approach is to reduce the dimensionality of the problem by modifying the network so that each neuron cannot fire if the number of spikes it emitted within the post-synaptic transfer kernel memory span reaches a given threshold. We show that the stationary distribution of this ‘truncated’ network converges to that of the unrestricted network as the threshold increases, and that the convergence is at a superexponential rate. A complementary approach uses discrete Markov chain approximations to the network process.

Memristor Crossbar Architecture for Synchronous Neural Networks

This paper focuses on suitable architecture and neural network training using crossbar connections of memristive elements. We developed a novel memristor training scheme that preserves high density of synaptic connections in the crossbar organization. We designed supporting circuits and performed time domain analog simulation of the architecture, to demonstrate that it properly adjusts memristor values during neural network training. A single sensing and winner-takes-all circuit is used to adjust strength of synaptic connections implemented by all memristors. We present results of HSPICE simulation of the developed architecture, generated control signals and resulting changes of memristor values. We used crosstalk test and Monte Carlo analysis to demonstrate robustness of the proposed architecture. Tests performed on MNIST character recognition benchmark confirmed functionality of the proposed circuit and training scheme in a practical and demanding application. The proposed approach improves available in the literature architecture and training methods for memristive neural networks.

Translational control in synaptic plasticity and cognitive dysfunction.

Activity-dependent changes in the strength of synaptic connections are fundamental to the formation and maintenance of memory. The mechanisms underlying persistent changes in synaptic strength in the hippocampus, specifically long-term potentiation and depression, depend on new protein synthesis. Such changes are thought to be orchestrated by engaging the signaling pathways that regulate mRNA translation in neurons. In this review, we discuss the key regulatory pathways that govern translational control in response to synaptic activity and the mRNA populations that are specifically targeted by these pathways. The critical contribution of regulatory control over new protein synthesis to proper cognitive function is underscored by human disorders associated with either silencing or mutation of genes encoding proteins that directly regulate translation. In light of these clinical implications, we also consider the therapeutic potential of targeting dysregulated translational control to treat cognitive disorders of synaptic dysfunction.

βCaMKII regulates bidirectional long-term plasticity in cerebellar Purkinje cells by a CaMKII/PP2B switch mechanism

It is thought that modifications in the strength of synaptic connections onto cerebellar Purkinje cells (PCs) such as long-term depression (LTD) and long-term potentiation (LTP) contribute to learning. Repeated paired stimulations of parallel fibres (PFs) and climbing fibre (CF) evoke high-amplitude calcium signals that lead to LTD in PCs, while LTP is induced by low-amplitude calcium pulses as a result of PF input alone. Although the events following these stimulation protocols are becoming clearer, the precise interactions of the molecular machinery underlying LTD and LTP induction remain something of an enigma. Calcium-calmodulin dependent protein kinase II (CaMKII) is an important component of the signalling network that is responsible for cerebellar plasticity in PCs. The CaMKII holoenzyme contains isoforms such as αCaMKII and βCaMKII. Experiments with Camk2b knockout mice that lack the β isoform of CaMKII have demonstrated that βCaMKII regulates the direction of plasticity at PF-PC synapses [1]. Stimulation protocols that induce LTD in wild-type mice, which contain both α and βCaMKII, lead to LTP in knockout mice without βCaMKII, and vice versa. In previous work, we have developed a kinetic simulation of the phosphorylation and dephosphorylation of AMPA receptors by CaMKII and protein phosphatase 2B (PP2B) to investigate how βCaMKII controls bidirectional plasticity in cerebellar PCs [2]. This bidirectional plasticity model was based on our earlier model of CaMKII activation [3,4]. Because the βCaMKII, but not αCaMKII, isoforms can bind to filamentous actin (F-actin), we have included the binding of F-actin to CaMKII to simulate plasticity induction in wild-type mice, whereas the F-actin binding was omitted in the knockout mice that lack the β isoform. Our previous simulation results have demonstrated that the binding of F-actin to βCaMKII can contribute to the regulation of bidirectional plasticity at PF-PC synapses, as suggested by Van Woerden and collaborators [1]. However, we have investigated the induction of bidirectional plasticity only in the presence of calcium signals, i.e. during the early phase of LTD and LTP. But the experimental observations in [1] have demonstrated that the bidirectional plasticity is also observed after the offset of paired PF and CF inputs and PF input alone. To analyse the persistent AMPA receptor phosphorylation after calcium stimulation protocols that last 5 min, we modified our previous model [2] because it did not simulate the CaMKII dephosphorylation, and PP2B was rapidly inactivated with the interruption of calcium signals. Here, we allow the CaMKII subunits in the autonomous form, which are not bound to calcium-calmodulin but still retain some activity levels, to be dephosphorylated and switch to the inactive state of CaMKII. The kinase is therefore gradually inactivated after calcium stimulation stops. Moreover, calcium-calmodulin slowly dissociates from PP2B, leading to a gradual deactivation of PP2B. Results of computer simulations of our mathematical model suggest that the balance of CaMKII-mediated phosphorylation and PP2B-mediated dephosphorylation of AMPA receptors determines whether LTD or LTP occurs at the PF-PC synapse. PF activity alone evokes PP2B concentration levels higher than CaMKII, leading to LTP induction. Instead, LTD occurs when the CaMKII concentration levels surpass the PP2B concentration in response to the paired activation of PF and CF. Moreover, our recent simulation results replicate the experimental observations by Van Woerden et al. [1] not only in the early phase of LTD and LTP as shown in [2], but also in their intermediate and late phases after the termination of PF and CF stimulation and PF input alone. The mechanisms observed in our previous simulations with 5 min duration are also observed in simulations that last 100 min. The loss of F-actin binding in the knockout mice enhances the availability of active CaMKII when compared to the wild-type mice at low calcium concentrations. This favours the induction of LTD rather than LTP. In contrast, the reduction in the CaMKII concentration in the knockout mice leads to AMPA receptor dephosphorylation by PP2B for high calcium concentrations, leading to the induction of LTP instead of LTD. We again demonstrate that the binding of F-actin to βCaMKII can indeed contribute to the control of bidirectional plasticity at PF-PC synapses, as suggested in [1,2].

Network-level effects of optogenetic stimulation in a computer model of macaque primary motor cortex

Optogenetics is a potent tool for performing precise perturbations to ongoing cortical dynamics in behaving primates. However, only small numbers of neurons can be recorded simultaneously. In this work, we present a biomimetic spiking network model of macaque primary motor cortex (M1) in order to explore network-level effects of optogenetic stimulation – namely, how synaptic connections modulate the optogenetic stimulus response, and how optogenetic stimulation affects interlaminar information flow. Experimental data were recorded from M1 in a male macaque. Optogenetic stimulation targeted excitatory neurons, likely preferentially affecting deeper layers, via the excitatory opsin C1V1TT, with either continuous (200 ms duration) or periodic (20, 40, or 80 Hz) pulses of green light (561 nm) [1]. The network model consisted of 24,800 spiking Izhikevich neurons [2], consisting of regular-firing and bursting pyramidal neurons and fast-spiking and low-threshold-spiking interneurons, with connectivities and proportions of each cell type across each cortical layer drawn from empirical mammalian M1 literature. Opsin channel properties were based on empirical estimates. The network model was calibrated to reproduce experimentally observed firing rates and dynamics. Experimentally, optogenetic stimulation was found to increase firing rates by up to 300 spikes/sec, with higher firing rates observed close to the optrode; firing returned to baseline values between 4 and 5 mm laterally from the optrode. A similar response was observed in the model. Manipulating the strength of synaptic connectivity in the model elucidated several noteworthy aspects of the response. First, the decrease in peak firing rates very near the optrode appears to be due to increased recruitment of inhibitory neurons. Second, even though all excitatory neurons in the model had identical biophysical properties and received identical current input from the opsin, heterogeneities in connectivity were sufficient to account for the broad range of observed firing rates. Third, all of the high-firing excitatory cells (>100 spikes/sec) were opsin-expressing; no indirectly activated excitatory cells fired above 60 spikes/sec. Applying spectral Granger causality to the LFPs produced by the different cortical layers of the model showed that the strongest projection without stimulation was from layer 2/3 to layer 5A, consistent with the hypothesis that descending excitation is the primary driver of dynamics in the motor cortex. Strong Granger causality from layer 5A to layer 5B was also observed. Across all layer pairs, Granger causality showed a pronounced peak in the mu rhythm band (~9 Hz), with a small, broad bump in the gamma band (~40 Hz) observed in pathways from layer 2/3 to other layers. Optogenetic stimulation in the model increased Granger causality from layer 5 to other layers in a narrow band near the stimulation frequency. It also increased the amplitude of Granger causality from layer 2/3 to other layers in the mu rhythm band, while decreasing it in the gamma band. In summary, this work demonstrates that (1) synaptic connections play an important role in determining the network-level response to optogenetic stimulation, and (2) optogenetic stimulation may be used to enhance and suppress information flow in particular frequency bands and between particular cortical layers.