Reanalysis of EphA3 Knock-In Double Maps in Mouse Suggests That Stochasticity in Topographic Map Formation Acts at the Retina Rather than between Competing Mechanisms at the Colliculus.

It has been suggested that stochasticity acts in the formation of topographically ordered maps in the visual system through the opposing chemoaffinity and neural activity forces acting on the innervating nerve fibers being held in an unstable equilibrium. Evidence comes from the Islet2-EphA3 knock-in mouse, in which ∼50% of the retinal ganglion cells, distributed across the retina, acquire the EphA3 receptor, thus having an enhanced density of EphA which specifies retinotopic order along the rostrocaudal (RC) axis of the colliculus. Sampling EphA3 knock-in maps in heterozygotes at different positions along the mediolateral (ML) extent of the colliculus had found single 1D maps [as in wild types (WTs)], double maps (as in homozygous knock-ins) or both single and double maps. We constructed full 2D maps from the same mouse dataset. We found either single maps or maps where the visual field projects rostrally, with a part-projection more caudally to form a double map, the extent and location of this duplication varying considerably. Contrary to previous analyses, there was no strict demarcation between heterozygous and homozygous maps. These maps were replicated in a computational model where, as the level of EphA3 was increased, there was a smooth transition from single to double maps. Our results suggest that the diversity in these retinotopic maps has its origin in a variability over the retina in the effective amount of EphA3, such as through variability in gene expression or the proportion of EphA3+ retinal ganglion cells, rather than the result of competing mechanisms acting at the colliculus.

Modelling Feedback Excitation, Pacemaker Properties and Sensory Switching of Electrically Coupled Brainstem Neurons Controlling Rhythmic Activity.

What cellular and network properties allow reliable neuronal rhythm generation or firing that can be started and stopped by brief synaptic inputs? We investigate rhythmic activity in an electrically-coupled population of brainstem neurons driving swimming locomotion in young frog tadpoles, and how activity is switched on and off by brief sensory stimulation. We build a computational model of 30 electrically-coupled conditional pacemaker neurons on one side of the tadpole hindbrain and spinal cord. Based on experimental estimates for neuron properties, population sizes, synapse strengths and connections, we show that: long-lasting, mutual, glutamatergic excitation between the neurons allows the network to sustain rhythmic pacemaker firing at swimming frequencies following brief synaptic excitation; activity persists but rhythm breaks down without electrical coupling; NMDA voltage-dependency doubles the range of synaptic feedback strengths generating sustained rhythm. The network can be switched on and off at short latency by brief synaptic excitation and inhibition. We demonstrate that a population of generic Hodgkin-Huxley type neurons coupled by glutamatergic excitatory feedback can generate sustained asynchronous firing switched on and off synaptically. We conclude that networks of neurons with NMDAR mediated feedback excitation can generate self-sustained activity following brief synaptic excitation. The frequency of activity is limited by the kinetics of the neuron membrane channels and can be stopped by brief inhibitory input. Network activity can be rhythmic at lower frequencies if the neurons are electrically coupled. Our key finding is that excitatory synaptic feedback within a population of neurons can produce switchable, stable, sustained firing without synaptic inhibition.

Grey matter networks in people at increased familial risk for schizophrenia.

Grey matter brain networks are disrupted in schizophrenia, but it is still unclear at which point during the development of the illness these disruptions arise and whether these can be associated with behavioural predictors of schizophrenia. We investigated if single-subject grey matter networks were disrupted in a sample of people at familial risk of schizophrenia. Single-subject grey matter networks were extracted from structural MRI scans of 144 high risk subjects, 32 recent-onset patients and 36 healthy controls. The following network properties were calculated: size, connectivity density, degree, path length, clustering coefficient, betweenness centrality and small world properties. People at risk of schizophrenia showed decreased path length and clustering in mostly prefrontal and temporal areas. Within the high risk sample, the path length of the posterior cingulate cortex and the betweenness centrality of the left inferior frontal operculum explained 81% of the variance in schizotypal cognitions, which was previously shown to be the strongest behavioural predictor of schizophrenia in the study. In contrast, local grey matter volume measurements explained 48% of variance in schizotypy. The present results suggest that single-subject grey matter networks can quantify behaviourally relevant biological alterations in people at increased risk for schizophrenia before disease onset.

Modelling the Effects of Electrical Coupling between Unmyelinated Axons of Brainstem Neurons Controlling Rhythmic Activity.

Gap junctions between fine unmyelinated axons can electrically couple groups of brain neurons to synchronise firing and contribute to rhythmic activity. To explore the distribution and significance of electrical coupling, we modelled a well analysed, small population of brainstem neurons which drive swimming in young frog tadpoles. A passive network of 30 multicompartmental neurons with unmyelinated axons was used to infer that: axon-axon gap junctions close to the soma gave the best match to experimentally measured coupling coefficients; axon diameter had a strong influence on coupling; most neurons were coupled indirectly via the axons of other neurons. When active channels were added, gap junctions could make action potential propagation along the thin axons unreliable. Increased sodium and decreased potassium channel densities in the initial axon segment improved action potential propagation. Modelling suggested that the single spike firing to step current injection observed in whole-cell recordings is not a cellular property but a dynamic consequence of shunting resulting from electrical coupling. Without electrical coupling, firing of the population during depolarising current was unsynchronised; with coupling, the population showed synchronous recruitment and rhythmic firing. When activated instead by increasing levels of modelled sensory pathway input, the population without electrical coupling was recruited incrementally to unpatterned activity. However, when coupled, the population was recruited all-or-none at threshold into a rhythmic swimming pattern: the tadpole "decided" to swim. Modelling emphasises uncertainties about fine unmyelinated axon physiology but, when informed by biological data, makes general predictions about gap junctions: locations close to the soma; relatively small numbers; many indirect connections between neurons; cause of action potential propagation failure in fine axons; misleading alteration of intrinsic firing properties. Modelling also indicates that electrical coupling within a population can synchronize recruitment of neurons and their pacemaker firing during rhythmic activity.

Quantitative assessment of computational models for retinotopic map formation.

Molecular and activity-based cues acting together are thought to guide retinal axons to their terminal sites in vertebrate optic tectum or superior colliculus (SC) to form an ordered map of connections. The details of mechanisms involved, and the degree to which they might interact, are still not well understood. We have developed a framework within which existing computational models can be assessed in an unbiased and quantitative manner against a set of experimental data curated from the mouse retinocollicular system. Our framework facilitates comparison between models, testing new models against known phenotypes and simulating new phenotypes in existing models. We have used this framework to assess four representative models that combine Eph/ephrin gradients and/or activity-based mechanisms and competition. Two of the models were updated from their original form to fit into our framework. The models were tested against five different phenotypes: wild type, Isl2-EphA3(ki/ki), Isl2-EphA3(ki/+), ephrin-A2,A3,A5 triple knock-out (TKO), and Math5(-/-) (Atoh7). Two models successfully reproduced the extent of the Math5(-/-) anteromedial projection, but only one of those could account for the collapse point in Isl2-EphA3(ki/+). The models needed a weak anteroposterior gradient in the SC to reproduce the residual order in the ephrin-A2,A3,A5 TKO phenotype, suggesting either an incomplete knock-out or the presence of another guidance molecule. Our article demonstrates the importance of testing retinotopic models against as full a range of phenotypes as possible, and we have made available MATLAB software, we wrote to facilitate this process.

Analysis of local and global topographic order in mouse retinocollicular maps.

We introduce the Lattice Method for the quantitative assessment of the topographic order within the pattern of connections between two structures. We apply this method to published visuocollicular mapping data obtained by Fourier-based intrinsic imaging of mouse colliculus. We find that, in maps from wild types and ß2 knock-outs, at least 150 points on the colliculus are represented in the visual field in the correct relative order. In maps from animals with knock-out of the three ephrinA ligands (TKO), thought to specify the rostrocaudal axis of the map, the projection on the colliculus of each small circular area of visual field is elongated approximately rostrocaudally. Of these projections, 9% are made up of two distinct regions lying along the direction of ingrowth of retinal fibers. These are similar to the ectopic projections found in other ephrinA knock-out data. Coexisting with the ectopic projections, each TKO map contains a submap where neighbor-neighbor relations are preserved, which is ordered along both rostrocaudal and mediolateral axes, in the orientation found in wild-type maps. The submaps vary in size with order well above chance level, which can approach the order in wild-type maps. Knock-out of both ß2 and two of the three ephrinAs yields maps with some order. The ordered TKO maps cannot be produced by correlated neural activity acting alone, as this mechanism is unable to specify map orientation. These results invite reassessment of the role of molecular signaling, particularly that of ephrinAs, in the formation of ordered nerve connections.

Standard anatomical and visual space for the mouse retina: computational reconstruction and transformation of flattened retinae with the Retistruct package.

The concept of topographic mapping is central to the understanding of the visual system at many levels, from the developmental to the computational. It is important to be able to relate different coordinate systems, e.g. maps of the visual field and maps of the retina. Retinal maps are frequently based on flat-mount preparations. These use dissection and relaxing cuts to render the quasi-spherical retina into a 2D preparation. The variable nature of relaxing cuts and associated tears limits quantitative cross-animal comparisons. We present an algorithm, "Retistruct," that reconstructs retinal flat-mounts by mapping them into a standard, spherical retinal space. This is achieved by: stitching the marked-up cuts of the flat-mount outline; dividing the stitched outline into a mesh whose vertices then are mapped onto a curtailed sphere; and finally moving the vertices so as to minimise a physically-inspired deformation energy function. Our validation studies indicate that the algorithm can estimate the position of a point on the intact adult retina to within 8° of arc (3.6% of nasotemporal axis). The coordinates in reconstructed retinae can be transformed to visuotopic coordinates. Retistruct is used to investigate the organisation of the adult mouse visual system. We orient the retina relative to the nictitating membrane and compare this to eye muscle insertions. To align the retinotopic and visuotopic coordinate systems in the mouse, we utilised the geometry of binocular vision. In standard retinal space, the composite decussation line for the uncrossed retinal projection is located 64° away from the retinal pole. Projecting anatomically defined uncrossed retinal projections into visual space gives binocular congruence if the optical axis of the mouse eye is oriented at 64° azimuth and 22° elevation, in concordance with previous results. Moreover, using these coordinates, the dorsoventral boundary for S-opsin expressing cones closely matches the horizontal meridian.

Steerable-filter based quantification of axonal populations at the developing optic chiasm reveal significant defects in Slit2(-/-) as well as Slit1(-/-)Slit2(-/-) embryos.

BACKGROUND: Previous studies have suggested that the axon guidance proteins Slit1 and Slit2 co-operate to establish the optic chiasm in its correct position at the ventral diencephalic midline. This is based on the observation that, although both Slit1 and Slit2 are expressed around the ventral midline, mice defective in either gene alone exhibit few or no axon guidance defects at the optic chiasm whereas embryos lacking both Slit1 and Slit2 develop a large additional chiasm anterior to the chiasm's normal position. Here we used steerable-filters to quantify key properties of the population of axons at the chiasm in wild-type, Slit1(-/-), Slit2(-/-) and Slit1(-/-)Slit2(-/-) embryos. RESULTS: We applied the steerable-filter algorithm successfully to images of embryonic retinal axons labelled from a single eye shortly after they have crossed the midline. We combined data from multiple embryos of the same genotype and made statistical comparisons of axonal distributions, orientations and curvatures between genotype groups. We compared data from the analysis of axons with data on the expression of Slit1 and Slit2. The results showed a misorientation and a corresponding anterior shift in the position of many axons at the chiasm of both Slit2(-/-) and Slit1(-/-)Slit2(-/-) mutants. There were very few axon defects at the chiasm of Slit1(-/-) mutants. CONCLUSIONS: We found defects of the chiasms of Slit1(-/-)Slit2(-/-) and Slit1(-/-) mutants similar to those reported previously. In addition, we discovered previously unreported defects resulting from loss of Slit2 alone. This indicates the value of a quantitative approach to complex pathway analysis and shows that Slit2 can act alone to control aspects of retinal axon routing across the ventral diencephalic midline.

morphforge: a toolbox for simulating small networks of biologically detailed neurons in Python.

The broad structure of a modeling study can often be explained over a cup of coffee, but converting this high-level conceptual idea into graphs of the final simulation results may require many weeks of sitting at a computer. Although models themselves can be complex, often many mental resources are wasted working around complexities of the software ecosystem such as fighting to manage files, interfacing between tools and data formats, finding mistakes in code or working out the units of variables. morphforge is a high-level, Python toolbox for building and managing simulations of small populations of multicompartmental biophysical model neurons. An entire in silico experiment, including the definition of neuronal morphologies, channel descriptions, stimuli, visualization and analysis of results can be written within a single short Python script using high-level objects. Multiple independent simulations can be created and run from a single script, allowing parameter spaces to be investigated. Consideration has been given to the reuse of both algorithmic and parameterizable components to allow both specific and stochastic parameter variations. Some other features of the toolbox include: the automatic generation of human-readable documentation (e.g., PDF files) about a simulation; the transparent handling of different biophysical units; a novel mechanism for plotting simulation results based on a system of tags; and an architecture that supports both the use of established formats for defining channels and synapses (e.g., MODL files), and the possibility to support other libraries and standards easily. We hope that this toolbox will allow scientists to quickly build simulations of multicompartmental model neurons for research and serve as a platform for further tool development.

Prevalence and elimination of sibling neurite convergence in motor units supplying neonatal and adult mouse skeletal muscle.

During development, neurons form supernumerary synapses, most of which are selectively pruned leading to stereotyped patterns of innervation. During the development of skeletal muscle innervation, or its regeneration after nerve injury, each muscle fiber is transiently innervated by multiple motor axon branches but eventually by a single branch. The selective elimination of all but one branch is the result of competition between the converging arbors. It is thought that motor neurons initially innervate muscle fibers randomly, but that axon branches from the same neuron (sibling branches) do not converge to innervate the same muscle fiber. However, random innervation would result in many neonatal endplates that are co-innervated by sibling branches. To investigate whether this occurs we examined neonatal levator auris longus (LAL) and 4th deep lumbrical (4DL) muscles, as well as adult reinnervated deep lumbrical muscles (1-4) in transgenic mice expressing yellow fluorescent protein (YFP) as a reporter. We provide direct evidence of convergence of sibling neurites within single fluorescent motor units, both during development and during regeneration after nerve crush. The incidence of sibling neurite convergence was 40% lower in regeneration and at least 75% lower during development than expected by chance. Therefore, there must be a mechanism that decreases the probability of its occurrence. As sibling neurite convergence is not seen in normal adults, or at later timepoints in regeneration, synapse elimination must also remove convergent synaptic inputs derived from the same motor neuron. Mechanistic theories of synaptic competition should now accommodate this form of isoaxonal plasticity.

The importance of combinatorial gene expression in early Mammalian thalamic patterning and thalamocortical axonal guidance.

The thalamus is essential for sensory perception. In mammals, work on the mouse has taught us most of what we know about how it develops and connects to the cortex. The mature thalamus of all mammalian species comprises numerous anatomically distinct collections of neurons called nuclei that differ in function, connectivity, and molecular constitution. At the time of its initial appearance as a distinct structure following neural tube closure, the thalamus is already patterned by the regional expression of numerous regulatory genes. This patterning, which lays down the blueprint for later development of thalamic nuclei, predates the development of thalamocortical projections. In this review we apply novel analytical methods to gene expression data available in the Allen Developing Mouse Brain Atlas to highlight the complex organized molecular heterogeneity already present among cells in the thalamus from the earliest stages at which it contains differentiating neurons. This early patterning is likely to invest in axons growing from different parts of the thalamus the ability to navigate in an ordered way to their appropriate area in the cerebral cortex. We review the mechanisms and cues that thalamic axons use, encounter, and interpret to attain the cortex. Mechanisms include guidance by previously generated guidepost cells, such as those in the subpallium that maintain thalamic axonal order and direction, and axons such as those of reciprocal projections from intermediate structures or from the cortex itself back toward the thalamus. We show how thalamocortical pathfinding involves numerous guidance cues operating at a series of steps along their route. We stress the importance of the combinatorial actions of multiple genes for the development of the numerous specific identities and functions of cells in this exquisitely complex system and their orderly innervation of the cortex.

Similarity-based extraction of individual networks from gray matter MRI scans.

The characterization of gray matter morphology of individual brains is an important issue in neuroscience. Graph theory has been used to describe cortical morphology, with networks based on covariation of gray matter volume or thickness between cortical areas across people. Here, we extend this research by proposing a new method that describes the gray matter morphology of an individual cortex as a network. In these large-scale morphological networks, nodes represent small cortical regions, and edges connect regions that have a statistically similar structure. The method was applied to a healthy sample (n = 14, scanned at 2 different time points). For all networks, we described the spatial degree distribution, average minimum path length, average clustering coefficient, small world property, and betweenness centrality (BC). Finally, we studied the reproducibility of all these properties. The networks showed more clustering than random networks and a similar minimum path length, indicating that they were "small world." The spatial degree and BC distributions corresponded closely to those from group-derived networks. All network property values were reproducible over the 2 time points examined. Our results demonstrate that intracortical similarities can be used to provide a robust statistical description of individual gray matter morphology.

Spike-timing-dependent plasticity with weight dependence evoked from physical constraints.

Analogue and mixed-signal VLSI implementations of Spike-Timing-Dependent Plasticity (STDP) are reviewed. A circuit is presented with a compact implementation of STDP suitable for parallel integration in large synaptic arrays. In contrast to previously published circuits, it uses the limitations of the silicon substrate to achieve various forms and degrees of weight dependence of STDP. It also uses reverse-biased transistors to reduce leakage from a capacitance representing weight. Chip results are presented showing: various ways in which the learning rule may be shaped; how synaptic weights may retain some indication of their learned values over periods of minutes; and how distributions of weights for synapses convergent on single neurons may shift between more or less extreme bimodality according to the strength of correlational cues in their inputs.

Synaptic rewiring for topographic mapping and receptive field development.

A model of topographic map refinement is presented which combines both weight plasticity and the formation and elimination of synapses, as well as both activity-dependent and activity-independent processes. The question of whether an activity-dependent process can refine a mapping created by an activity-independent process is addressed statistically. A new method of evaluating the quality of topographic projections is presented which allows independent consideration of the development of the centres and spatial variances of receptive fields for a projection. Synapse formation and elimination embed in the network topology changes in the weight distributions of synapses due to the activity-dependent learning rule used (spike-timing-dependent plasticity). In this model, the spatial variance of receptive fields can be reduced by an activity-dependent mechanism with or without spatially correlated inputs, but the accuracy of receptive field centres will not necessarily improve when synapses are formed based on distributions with on-average perfect topography.

Large developing receptive fields using a distributed and locally reprogrammable address-event receiver.

A distributed and locally reprogrammable address-event receiver has been designed, in which incoming address-events are monitored simultaneously by all synapses, allowing for arbitrarily large axonal fan-out without reducing channel capacity. Synapses can change the address of their presynaptic neuron, allowing the distributed implementation of a biologically realistic learning rule, with both synapse formation and elimination (synaptic rewiring). Probabilistic synapse formation leads to topographic map development, made possible by a cross-chip current-mode calculation of Euclidean distance. As well as synaptic plasticity in rewiring, synapses change weights using a competitive Hebbian learning rule (spike-timing-dependent plasticity). The weight plasticity allows receptive fields to be modified based on spatio-temporal correlations in the inputs, and the rewiring plasticity allows these modifications to become embedded in the network topology.

Early-stage waves in the retinal network emerge close to a critical state transition between local and global functional connectivity.

A novel, biophysically realistic model for early-stage, acetylcholine-mediated retinal waves is presented. In this model, neural excitability is regulated through a slow after-hyperpolarization (sAHP) operating on two different temporal scales. As a result, the simulated network exhibits competition between a desynchronizing effect of spontaneous, cell-intrinsic bursts, and the synchronizing effect of synaptic transmission during retinal waves. Cell-intrinsic bursts decouple the retinal network through activation of the sAHP current, and we show that the network is capable of operating at a transition point between purely local and global functional connectedness, which corresponds to a percolation phase transition. Multielectrode array recordings show that, at this point, the properties of retinal waves are reliably predicted by the model. These results indicate that early spontaneous activity in the developing retina is regulated according to a very specific principle, which maximizes randomness and variability in the resulting activity patterns.

Optimal learning rules for familiarity detection.

It has been suggested that the mammalian memory system has both familiarity and recollection components. Recently, a high-capacity network to store familiarity has been proposed. Here we derive analytically the optimal learning rule for such a familiarity memory using a signal- to-noise ratio analysis. We find that in the limit of large networks the covariance rule, known to be the optimal local, linear learning rule for pattern association, is also the optimal learning rule for familiarity discrimination. In the limit of large networks, the capacity is independent of the sparseness of the patterns and the corresponding information capacity is 0.057 bits per synapse, which is somewhat less than typically found for associative networks.

Inhomogeneities in heteroassociative memories with linear learning rules.

We investigate how various inhomogeneities present in synapses and neurons affect the performance of feedforward associative memories with linear learning, a high-level network model of hippocampal circuitry and plasticity. The inhomogeneities incorporated into the model are differential input attenuation, stochastic synaptic transmission, and memories learned with varying intensity. For a class of local learning rules, we determine the memory capacity of the model by extending previous analysis. We find that the signal-to-noise ratio (SNR), a measure of fidelity of recall, depends on the coefficients of variation (CVs) of the attenuation factors, the transmission variables, and the intensity of the memories, as well as the parameters of the learning rule, pattern sparsity and the number of memories stored. To predict the effects of attenuation due to extended dendritic trees, we use distributions of attenuations appropriate to unbranched and branched dendritic trees. Biological parameters for stochastic transmission are used to determine the CV of the transmission factors. The reduction in SNR due to differential attenuation is surprisingly low compared to the reduction due to stochastic transmission. Training a network by storing memories at different intensities is equivalent to using a learning rule incorporating weight decay. In this type of network, new memories can be stored continuously at the expense of older ones being forgotten (a palimpsest). We show that there is an optimal rate of weight decay that maximizes the capacity of the network, which is a factor of e lower than its nonpalimpsest equivalent.

Neuroinformatics and modeling of the basal ganglia: bridging pharmacology and physiology.

The subthalamic nucleus (STN) is the primary target for the chronic deep brain stimulation treatment of Parkinson's disease. STN neurons exhibit a variety of characteristic properties that may play a key role in the overall population response to deep brain stimulation. Neuroinformatics techniques, in particular computational modeling, provide a method of bringing together pharmacological phenomena, such as the loss of dopamine, with electrophysiological characteristics. Developing accurate models of STN neurons plays an important part in the process of uncovering the link between the changes in STN pharmacology, physiology and synaptic input that occurs with Parkinson's disease and the effectiveness of treatments targeting the STN. We review a general procedure for developing computational models and present a model of STN neurons that reveals important membrane channel interactions. In particular, changes in these channel interactions under parkinsonian conditions may underlie changes in characteristic physiology, critical in determining the mechanisms of deep brain stimulation.