Reciprocal stabilization of glycine receptors and gephyrin scaffold proteins at inhibitory synapses.

Postsynaptic scaffold proteins immobilize neurotransmitter receptors in the synaptic membrane opposite to presynaptic vesicle release sites, thus ensuring efficient synaptic transmission. At inhibitory synapses in the spinal cord, the main scaffold protein gephyrin assembles in dense molecule clusters that provide binding sites for glycine receptors (GlyRs). Gephyrin and GlyRs can also interact outside of synapses, where they form receptor-scaffold complexes. Although several models for the formation of postsynaptic scaffold domains in the presence of receptor-scaffold interactions have been advanced, a clear picture of the coupled dynamics of receptors and scaffold proteins at synapses is lacking. To characterize the GlyR and gephyrin dynamics at inhibitory synapses, we performed fluorescence time-lapse imaging after photoconversion to directly visualize the exchange kinetics of recombinant Dendra2-gephyrin in cultured spinal cord neurons. Immuno-immobilization of endogenous GlyRs with specific antibodies abolished their lateral diffusion in the plasma membrane, as judged by the lack of fluorescence recovery after photobleaching. Moreover, the cross-linking of GlyRs significantly reduced the exchange of Dendra2-gephyrin compared with control conditions, suggesting that the kinetics of the synaptic gephyrin pool is strongly dependent on GlyR-gephyrin interactions. We did not observe any change in the total synaptic gephyrin levels after GlyR cross-linking, however, indicating that the number of gephyrin molecules at synapses is not primarily dependent on the exchange of GlyR-gephyrin complexes. We further show that our experimental data can be quantitatively accounted for by a model of receptor-scaffold dynamics that includes a tightly interacting receptor-scaffold domain, as well as more loosely bound receptor and scaffold populations that exchange with extrasynaptic pools. The model can make predictions for single-molecule data such as typical dwell times of synaptic proteins. Taken together, our data demonstrate the reciprocal stabilization of GlyRs and gephyrin at inhibitory synapses and provide a quantitative understanding of their dynamic organization.

An aggregation-removal model for the formation and size determination of post-synaptic scaffold domains.

The formation and stability of synapses are key questions in neuroscience. Post-synaptic domains have been classically conceived as resulting from local insertion and turnover of proteins at the synapse. However, insertion is likely to occur outside the post-synaptic domains and advances in single-molecule imaging have shown that proteins diffuse in the plane of the membrane prior to their accumulation at synapses. We quantitatively investigated this scenario using computer simulations and mathematical analysis, taking for definiteness the specific case of inhibitory synapse components, i.e., the glycine receptor (GlyR) and the associated gephyrin scaffolding protein. The observed domain sizes of scaffold clusters can be explained by a dynamic balance between the aggregation of gephyrin proteins diffusing while bound to GlyR and their turnover at the neuron membrane. We also predict the existence of extrasynaptic clusters with a characteristic size distribution that significantly contribute to the size fluctuations of synaptic domains. New super-resolution data for gephyrin proteins established the existence of extrasynaptic clusters the sizes of which are consistent with the model predictions in a range of model parameters. At a general level, our results highlight aggregation with removal as a non-equilibrium phase separation which produces structures of tunable size.

MyoD reprogramming requires Six1 and Six4 homeoproteins: genome-wide cis-regulatory module analysis.

Myogenic regulatory factors of the MyoD family have the ability to reprogram differentiated cells toward a myogenic fate. In this study, we demonstrate that Six1 or Six4 are required for the reprogramming by MyoD of mouse embryonic fibroblasts (MEFs). Using microarray experiments, we found 761 genes under the control of both Six and MyoD. Using MyoD ChIPseq data and a genome-wide search for Six1/4 MEF3 binding sites, we found significant co-localization of binding sites for MyoD and Six proteins on over a thousand mouse genomic DNA regions. The combination of both datasets yielded 82 genes which are synergistically activated by Six and MyoD, with 96 associated MyoD+MEF3 putative cis-regulatory modules (CRMs). Fourteen out of 19 of the CRMs that we tested demonstrated in Luciferase assays a synergistic action also observed for their cognate gene. We searched putative binding sites on these CRMs using available databases and de novo search of conserved motifs and demonstrated that the Six/MyoD synergistic activation takes place in a feedforward way. It involves the recruitment of these two families of transcription factors to their targets, together with partner transcription factors, encoded by genes that are themselves activated by Six and MyoD, including Mef2, Pbx-Meis and EBF.

Collective cell migration: a physics perspective.

Cells have traditionally been viewed either as independently moving entities or as somewhat static parts of tissues. However, it is now clear that in many cases, multiple cells coordinate their motions and move as collective entities. Well-studied examples comprise development events, as well as physiological and pathological situations. Different ex vivo model systems have also been investigated. Several recent advances have taken place at the interface between biology and physics, and have benefitted from progress in imaging and microscopy, from the use of microfabrication techniques, as well as from the introduction of quantitative tools and models. We review these interesting developments in quantitative cell biology that also provide rich examples of collective out-of-equilibrium motion.

Six homeoproteins and a Iinc-RNA at the fast MYH locus lock fast myofiber terminal phenotype.

Thousands of long intergenic non-coding RNAs (lincRNAs) are encoded by the mammalian genome. However, the function of most of these lincRNAs has not been identified in vivo. Here, we demonstrate a role for a novel lincRNA, linc-MYH, in adult fast-type myofiber specialization. Fast myosin heavy chain (MYH) genes and linc-MYH share a common enhancer, located in the fast MYH gene locus and regulated by Six1 homeoproteins. linc-MYH in nuclei of fast-type myofibers prevents slow-type and enhances fast-type gene expression. Functional fast-sarcomeric unit formation is achieved by the coordinate expression of fast MYHs and linc-MYH, under the control of a common Six-bound enhancer.

Neuronal morphology generates high-frequency firing resonance.

The attenuation of neuronal voltage responses to high-frequency current inputs by the membrane capacitance is believed to limit single-cell bandwidth. However, neuronal populations subject to stochastic fluctuations can follow inputs beyond this limit. We investigated this apparent paradox theoretically and experimentally using Purkinje cells in the cerebellum, a motor structure that benefits from rapid information transfer. We analyzed the modulation of firing in response to the somatic injection of sinusoidal currents. Computational modeling suggested that, instead of decreasing with frequency, modulation amplitude can increase up to high frequencies because of cellular morphology. Electrophysiological measurements in adult rat slices confirmed this prediction and displayed a marked resonance at 200 Hz. We elucidated the underlying mechanism, showing that the two-compartment morphology of the Purkinje cell, interacting with a simple spiking mechanism and dendritic fluctuations, is sufficient to create high-frequency signal amplification. This mechanism, which we term morphology-induced resonance, is selective for somatic inputs, which in the Purkinje cell are exclusively inhibitory. The resonance sensitizes Purkinje cells in the frequency range of population oscillations observed in vivo.

Time-invariant feed-forward inhibition of Purkinje cells in the cerebellar cortex in vivo.

KEY POINTS: We performed extracellular recording of pairs of interneuron-Purkinje cells in vivo. A single interneuron produces a substantial, short-lasting, inhibition of Purkinje cells. Feed-forward inhibition is associated with characteristic asymmetric cross-correlograms. In vivo, Purkinje cell spikes only depend on the most recent synaptic activity. ABSTRACT: Cerebellar molecular layer interneurons are considered to control the firing rate and spike timing of Purkinje cells. However, interactions between these cell types are largely unexplored in vivo. Using tetrodes, we performed simultaneous extracellular recordings of neighbouring Purkinje cells and molecular layer interneurons, presumably basket cells, in adult rats in vivo. The high levels of afferent synaptic activity encountered in vivo yield irregular spiking and reveal discharge patterns characteristic of feed-forward inhibition, thus suggesting an overlap of the afferent excitatory inputs between Purkinje cells and basket cells. Under conditions of intense background synaptic inputs, interneuron spikes exert a short-lasting inhibitory effect, delaying the following Purkinje cell spike by an amount remarkably independent of the Purkinje cell firing cycle. This effect can be explained by the short memory time of the Purkinje cell potential as a result of the intense incoming synaptic activity. Finally, we found little evidence for any involvement of the interneurons that we recorded with the cerebellar high-frequency oscillations promoting Purkinje cell synchrony. The rapid interactions between interneurons and Purkinje cells might be of particular importance in fine motor control because the inhibitory action of interneurons on Purkinje cells leads to deep cerebellar nuclear disinhibition and hence increased cerebellar output.

Imogene: identification of motifs and cis-regulatory modules underlying gene co-regulation.

Cis-regulatory modules (CRMs) and motifs play a central role in tissue and condition-specific gene expression. Here we present Imogene, an ensemble of statistical tools that we have developed to facilitate their identification and implemented in a publicly available software. Starting from a small training set of mammalian or fly CRMs that drive similar gene expression profiles, Imogene determines de novo cis-regulatory motifs that underlie this co-expression. It can then predict on a genome-wide scale other CRMs with a regulatory potential similar to the training set. Imogene bypasses the need of large datasets for statistical analyses by making central use of the information provided by the sequenced genomes of multiple species, based on the developed statistical tools and explicit models for transcription factor binding site evolution. We test Imogene on characterized tissue-specific mouse developmental CRMs. Its ability to identify CRMs with the same specificity based on its de novo created motifs is comparable to that of previously evaluated 'motif-blind' methods. We further show, both in flies and in mammals, that Imogene de novo generated motifs are sufficient to discriminate CRMs related to different developmental programs. Notably, purely relying on sequence data, Imogene performs as well in this discrimination task as a previously reported learning algorithm based on Chromatin Immunoprecipitation (ChIP) data for multiple transcription factors at multiple developmental stages.

From discrete to continuum models of three-dimensional deformations in epithelial sheets.

Epithelial tissue, in which cells adhere tightly to each other and to the underlying substrate, is one of the four major tissue types in adult organisms. In embryos, epithelial sheets serve as versatile substrates during the formation of developing organs. Some aspects of epithelial morphogenesis can be adequately described using vertex models, in which the two-dimensional arrangement of epithelial cells is approximated by a polygonal lattice with an energy that has contributions reflecting the properties of individual cells and their interactions. Previous studies with such models have largely focused on dynamics confined to two spatial dimensions and analyzed them numerically. We show how these models can be extended to account for three-dimensional deformations and studied analytically. Starting from the extended model, we derive a continuum plate description of cell sheets, in which the effective tissue properties, such as bending rigidity, are related explicitly to the parameters of the vertex model. To derive the continuum plate model, we duly take into account a microscopic shift between the two sublattices of the hexagonal network, which has been ignored in previous work. As an application of the continuum model, we analyze tissue buckling by a line tension applied along a circular contour, a simplified set-up relevant to several situations in the developmental contexts. The buckling thresholds predicted by the continuum description are in good agreement with the results of stability calculations based on the vertex model. Our results establish a direct connection between discrete and continuum descriptions of cell sheets and can be used to probe a wide range of morphogenetic processes in epithelial tissues.

Collective cell motion in an epithelial sheet can be quantitatively described by a stochastic interacting particle model.

Modelling the displacement of thousands of cells that move in a collective way is required for the simulation and the theoretical analysis of various biological processes. Here, we tackle this question in the controlled setting where the motion of Madin-Darby Canine Kidney (MDCK) cells in a confluent epithelium is triggered by the unmasking of free surface. We develop a simple model in which cells are described as point particles with a dynamic based on the two premises that, first, cells move in a stochastic manner and, second, tend to adapt their motion to that of their neighbors. Detailed comparison to experimental data show that the model provides a quantitatively accurate description of cell motion in the epithelium bulk at early times. In addition, inclusion of model "leader" cells with modified characteristics, accounts for the digitated shape of the interface which develops over the subsequent hours, providing that leader cells invade free surface more easily than other cells and coordinate their motion with their followers. The previously-described progression of the epithelium border is reproduced by the model and quantitatively explained.

Genome-wide identification of cis-regulatory motifs and modules underlying gene coregulation using statistics and phylogeny.

Cell fate determination depends in part on the establishment of specific transcriptional programs of gene expression. These programs result from the interpretation of the genomic cis-regulatory information by sequence-specific factors. Decoding this information in sequenced genomes is an important issue. Here, we developed statistical analysis tools to computationally identify the cis-regulatory elements that control gene expression in a set of coregulated genes. Starting with a small number of validated and/or predicted cis-regulatory modules (CRMs) in a reference species as a training set, but with no a priori knowledge of the factors acting in trans, we computationally predicted transcription factor binding sites (TFBSs) and genomic CRMs underlying coregulation. This method was applied to the gene expression program active in Drosophila melanogaster sensory organ precursor cells (SOPs), a specific type of neural progenitor cells. Mutational analysis showed that four, including one newly characterized, out of the five top-ranked families of predicted TFBSs were required for SOP-specific gene expression. Additionaly, 19 out of the 29 top-ranked predicted CRMs directed gene expression in neural progenitor cells, i.e., SOPs or larval brain neuroblasts, with a notable fraction active in SOPs (11/29). We further identified the lola gene as the target of two SOP-specific CRMs and found that the lola gene contributed to SOP specification. The statistics and phylogeny-based tools described here can be more generally applied to identify the cis-regulatory elements of specific gene regulatory networks in any family of related species with sequenced genomes.

Beta oscillations and waves in motor cortex can be accounted for by the interplay of spatially structured connectivity and fluctuating inputs.

The beta rhythm (13-30 Hz) is a prominent brain rhythm. Recordings in primates during instructed-delay reaching tasks have shown that different types of traveling waves of oscillatory activity are associated with episodes of beta oscillations in motor cortex during movement preparation. We propose here a simple model of motor cortex based on local excitatory-inhibitory neuronal populations coupled by long-range excitation, where additionally inputs to the motor cortex from other neural structures are represented by stochastic inputs on the different model populations. We show that the model accurately reproduces the statistics of recording data when these external inputs are correlated on a short time scale (25 ms) and have two different components, one that targets the motor cortex locally and another one that targets it in a global and synchronized way. The model reproduces the distribution of beta burst durations, the proportion of the different observed wave types, and wave speeds, which we show not to be linked to axonal propagation speed. When the long-range connectivity or the local input targets are anisotropic, traveling waves are found to preferentially propagate along the axis where connectivity decays the fastest. Different from previously proposed mechanistic explanations, the model suggests that traveling waves in motor cortex are the reflection of the dephasing by external inputs, putatively of thalamic origin, of an oscillatory activity that would otherwise be spatially synchronized by recurrent connectivity.

Different cell fates from cell-cell interactions: core architectures of two-cell bistable networks.

The acquisition of different fates by cells that are initially in the same state is central to development. Here, we investigate the possible structures of bistable genetic networks that can allow two identical cells to acquire different fates through cell-cell interactions. Cell-autonomous bistable networks have been previously sampled using an evolutionary algorithm. We extend this evolutionary procedure to take into account interactions between cells. We obtain a variety of simple bistable networks that we classify into major subtypes. Some have long been proposed in the context of lateral inhibition through the Notch-Delta pathway, some have been more recently considered and others appear to be new and based on mechanisms not previously considered. The results highlight the role of posttranscriptional interactions and particularly of protein complexation and sequestration, which can replace cooperativity in transcriptional interactions. Some bistable networks are entirely based on posttranscriptional interactions and the simplest of these is found to lead, upon a single parameter change, to oscillations in the two cells with opposite phases. We provide qualitative explanations as well as mathematical analyses of the dynamical behaviors of various created networks. The results should help to identify and understand genetic structures implicated in cell-cell interactions and differentiation.

How connectivity, background activity, and synaptic properties shape the cross-correlation between spike trains.

Functional interactions between neurons in vivo are often quantified by cross-correlation functions (CCFs) between their spike trains. It is therefore essential to understand quantitatively how CCFs are shaped by different factors, such as connectivity, synaptic parameters, and background activity. Here, we study the CCF between two neurons using analytical calculations and numerical simulations. We quantify the role of synaptic parameters, such as peak conductance, decay time, and reversal potential, and analyze how various patterns of connectivity influence CCF shapes. In particular, we find that the symmetry of the CCF distinguishes in general, but not always, the case of shared inputs between two neurons from the case in which they are directly synaptically connected. We systematically examine the influence of background synaptic inputs from the surrounding network that set the baseline firing statistics of the neurons and modulate their response properties. We find that variations in the background noise modify the amplitude of the cross-correlation function as strongly as variations of synaptic strength. In particular, we show that the postsynaptic neuron spiking regularity has a pronounced influence on CCF amplitude. This suggests an efficient and flexible mechanism for modulating functional interactions.

Lifetime of a structure evolving by cluster aggregation and particle loss, and application to postsynaptic scaffold domains.

The dynamics of several mesoscopic biological structures depend on the interplay of growth through the incorporation of components of different sizes laterally diffusing along the cell membrane, and loss by component turnover. In particular, a model of such an out-of-equilibrium dynamics has recently been proposed for postsynaptic scaffold domains, which are key structures of neuronal synapses. It is of interest to estimate the lifetime of these mesoscopic structures, especially in the context of synapses where this time is related to memory retention. The lifetime of a structure can be very long as compared to the turnover time of its components and it can be difficult to estimate it by direct numerical simulations. Here, in the context of the model proposed for postsynaptic scaffold domains, we approximate the aggregation-turnover dynamics by a shot-noise process. This enables us to analytically compute the quasistationary distribution describing the sizes of the surviving structures as well as their characteristic lifetime. We show that our analytical estimate agrees with numerical simulations of a full spatial model, in a regime of parameters where a direct assessment is computationally feasible. We then use our approach to estimate the lifetime of mesoscopic structures in parameter regimes where computer simulations would be prohibitively long. For gephyrin, the scaffolding protein specific to inhibitory synapses, we estimate a lifetime longer than several months for a scaffold domain when the single gephyrin protein turnover time is about half an hour, as experimentally measured. While our focus is on postsynaptic domains, our formalism and techniques should be applicable to other biological structures that are also formed by a balance of condensation and turnover.

Synchronization, Stochasticity, and Phase Waves in Neuronal Networks With Spatially-Structured Connectivity.

Oscillations in the beta/low gamma range (10-45 Hz) are recorded in diverse neural structures. They have successfully been modeled as sparsely synchronized oscillations arising from reciprocal interactions between randomly connected excitatory (E) pyramidal cells and local interneurons (I). The synchronization of spatially distant oscillatory spiking E-I modules has been well-studied in the rate model framework but less so for modules of spiking neurons. Here, we first show that previously proposed modifications of rate models provide a quantitative description of spiking E-I modules of Exponential Integrate-and-Fire (EIF) neurons. This allows us to analyze the dynamical regimes of sparsely synchronized oscillatory E-I modules connected by long-range excitatory interactions, for two modules, as well as for a chain of such modules. For modules with a large number of neurons (> 105), we obtain results similar to previously obtained ones based on the classic deterministic Wilson-Cowan rate model, with the added bonus that the results quantitatively describe simulations of spiking EIF neurons. However, for modules with a moderate (~ 104) number of neurons, stochastic variations in the spike emission of neurons are important and need to be taken into account. On the one hand, they modify the oscillations in a way that tends to promote synchronization between different modules. On the other hand, independent fluctuations on different modules tend to disrupt synchronization. The correlations between distant oscillatory modules can be described by stochastic equations for the oscillator phases that have been intensely studied in other contexts. On shorter distances, we develop a description that also takes into account amplitude modes and that quantitatively accounts for our simulation data. Stochastic dephasing of neighboring modules produces transient phase gradients and the transient appearance of phase waves. We propose that these stochastically-induced phase waves provide an explanative framework for the observations of traveling waves in the cortex during beta oscillations.

The statistics of repeating patterns of cortical activity can be reproduced by a model network of stochastic binary neurons.

Calcium imaging of the spontaneous activity in cortical slices has revealed repeating spatiotemporal patterns of transitions between so-called down states and up states (Ikegaya et al., 2004). Here we fit a model network of stochastic binary neurons to data from these experiments, and in doing so reproduce the distributions of such patterns. We use two versions of this model: (1) an unconnected network in which neurons are activated as independent Poisson processes; and (2) a network with an interaction matrix, estimated from the data, representing effective interactions between the neurons. The unconnected model (model 1) is sufficient to account for the statistics of repeating patterns in 11 of the 15 datasets studied. Model 2, with interactions between neurons, is required to account for pattern statistics of the remaining four. Three of these four datasets are the ones that contain the largest number of transitions, suggesting that long datasets are in general necessary to render interactions statistically visible. We then study the topology of the matrix of interactions estimated for these four datasets. For three of the four datasets, we find sparse matrices with long-tailed degree distributions and an overrepresentation of certain network motifs. The remaining dataset exhibits a strongly interconnected, spatially localized subgroup of neurons. In all cases, we find that interactions between neurons facilitate the generation of long patterns that do not repeat exactly.

What can we learn from synaptic weight distributions?

Much research effort into synaptic plasticity has been motivated by the idea that modifications of synaptic weights (or strengths or efficacies) underlie learning and memory. Here, we examine the possibility of exploiting the statistics of experimentally measured synaptic weights to deduce information about the learning process. Analysing distributions of synaptic weights requires a theoretical framework to interpret the experimental measurements, but the results can be unexpectedly powerful, yielding strong constraints on possible learning theories as well as information that is difficult to obtain by other means, such as the information storage capacity of a cell. We review the available experimental and theoretical techniques as well as important open issues.

Synchronization properties of networks of electrically coupled neurons in the presence of noise and heterogeneities.

We investigate how synchrony can be generated or induced in networks of electrically coupled integrate-and-fire neurons subject to noisy and heterogeneous inputs. Using analytical tools, we find that in a network under constant external inputs, synchrony can appear via a Hopf bifurcation from the asynchronous state to an oscillatory state. In a homogeneous net work, in the oscillatory state all neurons fire in synchrony, while in a heterogeneous network synchrony is looser, many neurons skipping cycles of the oscillation. If the transmission of action potentials via the electrical synapses is effectively excitatory, the Hopf bifurcation is supercritical, while effectively inhibitory transmission due to pronounced hyperpolarization leads to a subcritical bifurcation. In the latter case, the network exhibits bistability between an asynchronous state and an oscillatory state where all the neurons fire in synchrony. Finally we show that for time-varying external inputs, electrical coupling enhances the synchronization in an asynchronous network via a resonance at the firing-rate frequency.

Optimal information storage and the distribution of synaptic weights: perceptron versus Purkinje cell.

It is widely believed that synaptic modifications underlie learning and memory. However, few studies have examined what can be deduced about the learning process from the distribution of synaptic weights. We analyze the perceptron, a prototypical feedforward neural network, and obtain the optimal synaptic weight distribution for a perceptron with excitatory synapses. It contains more than 50% silent synapses, and this fraction increases with storage reliability: silent synapses are therefore a necessary byproduct of optimizing learning and reliability. Exploiting the classical analogy between the perceptron and the cerebellar Purkinje cell, we fitted the optimal weight distribution to that measured for granule cell-Purkinje cell synapses. The two distributions agreed well, suggesting that the Purkinje cell can learn up to 5 kilobytes of information, in the form of 40,000 input-output associations.