Using theoretical models to analyse neural development

A one-dimensional moving-boundary model for tubulin-driven axonal growth

A one-dimensional continuum-mechanical model of axonal elongation due to assembly of tubulin dimers in the growth cone is presented. The conservation of mass leads to a coupled system of three differential equations. A partial differential equation models the dynamic and the spatial behaviour of the concentration of tubulin that is transported along the axon from the soma to the growth cone. Two ordinary differential equations describe the time-variation of the concentration of free tubulin in the growth cone and the speed of elongation. All steady-state solutions of the model are categorized. Given a set of the biological parameter values, it is shown how one easily can infer whether there exist zero, one or two steady-state solutions and directly determine the possible steady-state lengths of the axon. Explicit expressions are given for each stationary concentration distribution. It is thereby easy to examine the influence of each biological parameter on a steady state. Numerical simulations indicate that when there exist two steady states, the one with shorter axon length is unstable and the longer is stable. Another result is that, for nominal parameter values extracted from the literature, in a large portion of a fully grown axon the concentration of free tubulin is lower than both concentrations in the soma and in the growth cone.

Oscillations in a neurite growth model with extracellular feedback

We consider the influence of extracellular signalling on neurite elongation in a model of neurite growth mediated by building proteins (e.g., tubulin). The tubulin production dynamics were supplied by a function describing the influence of extracellular signalling, which can promote or depress neurite elongation. We found that this extracellular feedback could generate neurite length oscillations consisting of a periodic sequence of elongations and retractions. The oscillations prevent further outgrowth of the neurite, which becomes trapped in the non-uniform extracellular field. We analysed the characteristics of the elongation process for different distributions of attracting and repelling sources of the extracellular signalling molecules. The model predicts three different scenarios of neurite development in the extracellular field, including monotonic and oscillatory outgrowth, localised limit cycle oscillations and complete growth depression.

Computational modeling of neural plasticity for self-organization of neural networks

Self-organization in biological nervous systems during the lifetime is known to largely occur through a process of plasticity that is dependent upon the spike-timing activity in connected neurons. In the field of computational neuroscience, much effort has been dedicated to building up computational models of neural plasticity to replicate experimental data. Most recently, increasing attention has been paid to understanding the role of neural plasticity in functional and structural neural self-organization, as well as its influence on the learning performance of neural networks for accomplishing machine learning tasks such as classification and regression. Although many ideas and hypothesis have been suggested, the relationship between the structure, dynamics and learning performance of neural networks remains elusive. The purpose of this article is to review the most important computational models for neural plasticity and discuss various ideas about neural plasticity's role. Finally, we suggest a few promising research directions, in particular those along the line that combines findings in computational neuroscience and systems biology, and their synergetic roles in understanding learning, memory and cognition, thereby bridging the gap between computational neuroscience, systems biology and computational intelligence.

Homeostatic structural plasticity increases the efficiency of small-world networks

In networks with small-world topology, which are characterized by a high clustering coefficient and a short characteristic path length, information can be transmitted efficiently and at relatively low costs. The brain is composed of small-world networks, and evolution may have optimized brain connectivity for efficient information processing. Despite many studies on the impact of topology on information processing in neuronal networks, little is known about the development of network topology and the emergence of efficient small-world networks. We investigated how a simple growth process that favors short-range connections over long-range connections in combination with a synapse formation rule that generates homeostasis in post-synaptic firing rates shapes neuronal network topology. Interestingly, we found that small-world networks benefited from homeostasis by an increase in efficiency, defined as the averaged inverse of the shortest paths through the network. Efficiency particularly increased as small-world networks approached the desired level of electrical activity. Ultimately, homeostatic small-world networks became almost as efficient as random networks. The increase in efficiency was caused by the emergent property of the homeostatic growth process that neurons started forming more long-range connections, albeit at a low rate, when their electrical activity was close to the homeostatic set-point. Although global network topology continued to change when neuronal activities were around the homeostatic equilibrium, the small-world property of the network was maintained over the entire course of development. Our results may help understand how complex systems such as the brain could set up an efficient network topology in a self-organizing manner. Insights from our work may also lead to novel techniques for constructing large-scale neuronal networks by self-organization.

A developmental approach to predicting neuronal connectivity from small biological datasets: a gradient-based neuron growth model

Relating structure and function of neuronal circuits is a challenging problem. It requires demonstrating how dynamical patterns of spiking activity lead to functions like cognitive behaviour and identifying the neurons and connections that lead to appropriate activity of a circuit. We apply a “developmental approach” to define the connectome of a simple nervous system, where connections between neurons are not prescribed but appear as a result of neuron growth. A gradient based mathematical model of two-dimensional axon growth from rows of undifferentiated neurons is derived for the different types of neurons in the brainstem and spinal cord of young tadpoles of the frog Xenopus. Model parameters define a two-dimensional CNS growth environment with three gradient cues and the specific responsiveness of the axons of each neuron type to these cues. The model is described by a nonlinear system of three difference equations; it includes a random variable, and takes specific neuron characteristics into account. Anatomical measurements are first used to position cell bodies in rows and define axon origins. Then a generalization procedure allows information on the axons of individual neurons from small anatomical datasets to be used to generate larger artificial datasets. To specify parameters in the axon growth model we use a stochastic optimization procedure, derive a cost function and find the optimal parameters for each type of neuron. Our biologically realistic model of axon growth starts from axon outgrowth from the cell body and generates multiple axons for each different neuron type with statistical properties matching those of real axons. We illustrate how the axon growth model works for neurons with axons which grow to the same and the opposite side of the CNS. We then show how, by adding a simple specification for dendrite morphology, our model “developmental approach” allows us to generate biologically-realistic connectomes.

A software tool for the analysis of neuronal morphology data

Anatomy plays a fundamental role in supporting and shaping nervous system activity. The remarkable progress of computer processing power within the last two decades has enabled the generation of electronic databases of complete three-dimensional (3D) dendritic and axonal morphology for neuroanatomical studies. Several laboratories are freely posting their reconstructions online after result publication v.gr. NeuroMorpho.Org (Nat Rev Neurosci7:318-324, 2006). These neuroanatomical archives represent a crucial resource to explore the relationship between structure and function in the brain (Front Neurosci6:49, 2012). However, such 'Cartesian' descriptions bear little intuitive information for neuroscientists. Here, we developed a simple prototype of a MATLAB-based software tool to quantitatively describe the 3D neuronal structures from public repositories. The program imports neuronal reconstructions and quantifies statistical distributions of basic morphological parameters such as branch length, tortuosity, branch's genealogy and bifurcation angles. Using these morphological distributions, our algorithm can generate a set of virtual neurons readily usable for network simulations.

Competitive dynamics during resource-driven neurite outgrowth

Neurons form networks by growing out neurites that synaptically connect to other neurons. During this process, neurites develop complex branched trees. Interestingly, the outgrowth of neurite branches is often accompanied by the simultaneous withdrawal of other branches belonging to the same tree. This apparent competitive outgrowth between branches of the same neuron is relevant for the formation of synaptic connectivity, but the underlying mechanisms are unknown. An essential component of neurites is the cytoskeleton of microtubules, long polymers of tubulin dimers running throughout the entire neurite. To investigate whether competition between neurites can emerge from the dynamics of a resource such as tubulin, we developed a multi-compartmental model of neurite growth. In the model, tubulin is produced in the soma and transported by diffusion and active transport to the growth cones at the tip of the neurites, where it is assembled into microtubules to elongate the neurite. Just as in experimental studies, we find that the outgrowth of a neurite branch can lead to the simultaneous retraction of its neighboring branches. We show that these competitive interactions occur in simple neurite morphologies as well as in complex neurite arborizations and that in developing neurons competition for a growth resource such as tubulin can account for the differential outgrowth of neurite branches. The model predicts that competition between neurite branches decreases with path distance between growth cones, increases with path distance from growth cone to soma, and decreases with a higher rate of active transport. Together, our results suggest that competition between outgrowing neurites can already emerge from relatively simple and basic dynamics of a growth resource. Our findings point to the need to test the model predictions and to determine, by monitoring tubulin concentrations in outgrowing neurons, whether tubulin is the resource for which neurites compete.

The use and abuse of large-scale brain models

We provide an overview and comparison of several recent large-scale brain models. In addition to discussing challenges involved with building large neural models, we identify several expected benefits of pursuing such a research program. We argue that these benefits are only likely to be realized if two basic guidelines are made central to the pursuit. The first is that such models need to be intimately tied to behavior. The second is that models, and more importantly their underlying methods, should provide mechanisms for varying the level of simulated detail. Consequently, we express concerns with models that insist on a 'correct' amount of detail while expecting interesting behavior to simply emerge.

A simple rule for dendritic spine and axonal bouton formation can account for cortical reorganization after focal retinal lesions

Lasting alterations in sensory input trigger massive structural and functional adaptations in cortical networks. The principles governing these experience-dependent changes are, however, poorly understood. Here, we examine whether a simple rule based on the neurons' need for homeostasis in electrical activity may serve as driving force for cortical reorganization. According to this rule, a neuron creates new spines and boutons when its level of electrical activity is below a homeostatic set-point and decreases the number of spines and boutons when its activity exceeds this set-point. In addition, neurons need a minimum level of activity to form spines and boutons. Spine and bouton formation depends solely on the neuron's own activity level, and synapses are formed by merging spines and boutons independently of activity. Using a novel computational model, we show that this simple growth rule produces neuron and network changes as observed in the visual cortex after focal retinal lesions. In the model, as in the cortex, the turnover of dendritic spines was increased strongest in the center of the lesion projection zone, while axonal boutons displayed a marked overshoot followed by pruning. Moreover, the decrease in external input was compensated for by the formation of new horizontal connections, which caused a retinotopic remapping. Homeostatic regulation may provide a unifying framework for understanding cortical reorganization, including network repair in degenerative diseases or following focal stroke.

The adult brain is less hard-wired than traditionally thought. About ten percent of synapses in the mature visual cortex is continually replaced by new ones (structural plasticity). This percentage greatly increases after lasting changes in visual input. Due to the topographically organized nerve connections from the retina in the eye to the primary visual cortex in the brain, a small circumscribed lesion in the retina leads to a defined area in the cortex that is deprived of input. Recent experimental studies have revealed that axonal sprouting and dendritic spine turnover are massively increased in and around the cortical area that is deprived of input. However, the driving forces for this structural plasticity remain unclear. Using a novel computational model, we examine whether the need for activity homeostasis of individual neurons may drive cortical reorganization after lasting changes in input activity. We show that homeostatic growth rules indeed give rise to structural and functional reorganization of neuronal networks similar to the cortical reorganization observed experimentally. Understanding the principles of structural plasticity may eventually lead to novel treatment strategies for stimulating functional reorganization after brain damage and neurodegeneration.

Simulating cortical development as a self constructing process: a novel multi-scale approach combining molecular and physical aspects

Current models of embryological development focus on intracellular processes such as gene expression and protein networks, rather than on the complex relationship between subcellular processes and the collective cellular organization these processes support. We have explored this collective behavior in the context of neocortical development, by modeling the expansion of a small number of progenitor cells into a laminated cortex with layer and cell type specific projections. The developmental process is steered by a formal language analogous to genomic instructions, and takes place in a physically realistic three-dimensional environment. A common genome inserted into individual cells control their individual behaviors, and thereby gives rise to collective developmental sequences in a biologically plausible manner. The simulation begins with a single progenitor cell containing the artificial genome. This progenitor then gives rise through a lineage of offspring to distinct populations of neuronal precursors that migrate to form the cortical laminae. The precursors differentiate by extending dendrites and axons, which reproduce the experimentally determined branching patterns of a number of different neuronal cell types observed in the cat visual cortex. This result is the first comprehensive demonstration of the principles of self-construction whereby the cortical architecture develops. In addition, our model makes several testable predictions concerning cell migration and branching mechanisms.

The proper operation of the brain depends on the correct developmental wiring of billions of neurons. Understanding this process of living self-construction is crucial not only for biological explanation and medical therapy, but could also provide an entirely new approach to industrial fabrication. We are approaching this problem through detailed simulation of cortical development. We have previously presented a software package that allows for simulation of cellular growth in a 3D space that respects physical forces and diffusion of substances, as well as an instruction language for specifying biologically plausible ‘genetic codes’. Here we apply this novel formalism to understanding the principles of cortical development in the context of multiple, spatially distributed agents that communicate only by local metabolic messages.

Ultrasound can modulate neuronal development: impact on neurite growth and cell body morphology

Neuronal development is known to be a dynamic process that can be modulated by presenting guidance cues to neuronal cells. We show that ultrasound, when applied at pulsed settings and with intensities slightly greater than clinical diagnosis levels, can potentially act as a repulsive cue for modulating neuronal growth dynamics. Using differentiated Neuro-2a cells as the model, we have examined in vitro how neuronal development can change during and after exposure to 1-MHz ultrasound for different acoustic settings. Neurite retraction and cell body shrinkage were found in neuronal cells over a 10-min exposure period with 1.168 W/cm(2) spatial-peak, time-averaged intensity (based on 0.84 MPa peak acoustic pressure, 100-cycle pulse duration, and 500-Hz pulse repetition frequency). These effects were found to result in instances of neuronal cell body displacement. The extent of the effects was dependent on acoustic intensity, with peak acoustic pressure being a more important contributing factor compared with pulse duration. The morphological changes were found to be non-destructive, in that post-exposure neurite outgrowth and neuritogenesis were respectively observed in neurite-bearing and neurite-less neuronal cells. Our results also showed that mechanotransduction might be involved in mediating ultrasound-neuron interactions, as the morphological changes were suppressed if stretch-activated ion channels were blocked or if calcium messenger ions were chelated. Overall, these findings suggest that ultrasound can potentially influence how neuronal cells develop through modifying their cytomechanical characteristics.

Neuronal morphology goes digital: a research hub for cellular and system neuroscience

The importance of neuronal morphology in brain function has been recognized for over a century. The broad applicability of "digital reconstructions" of neuron morphology across neuroscience subdisciplines has stimulated the rapid development of numerous synergistic tools for data acquisition, anatomical analysis, three-dimensional rendering, electrophysiological simulation, growth models, and data sharing. Here we discuss the processes of histological labeling, microscopic imaging, and semiautomated tracing. Moreover, we provide an annotated compilation of currently available resources in this rich research "ecosystem" as a central reference for experimental and computational neuroscience.

Time scales of memory, learning, and plasticity

After only about 10 days would the storage capacity of our nervous system be reached if we stored every bit of input. The nervous system relies on at least two mechanisms that counteract this capacity limit: compression and forgetting. But the latter mechanism needs to know how long an entity should be stored: some memories are relevant only for the next few minutes, some are important even after the passage of several years. Psychology and physiology have found and described many different memory mechanisms, and these mechanisms indeed use different time scales. In this prospect we review these mechanisms with respect to their time scale and propose relations between mechanisms in learning and memory and their underlying physiological basis.

Growth dynamics explain the development of spatiotemporal burst activity of young cultured neuronal networks in detail

A typical property of isolated cultured neuronal networks of dissociated rat cortical cells is synchronized spiking, called bursting, starting about one week after plating, when the dissociated cells have sufficiently sent out their neurites and formed enough synaptic connections. This paper is the third in a series of three on simulation models of cultured networks. Our two previous studies [26], [27] have shown that random recurrent network activity models generate intra- and inter-bursting patterns similar to experimental data. The networks were noise or pacemaker-driven and had Izhikevich-neuronal elements with only short-term plastic (STP) synapses (so, no long-term potentiation, LTP, or depression, LTD, was included). However, elevated pre-phases (burst leaders) and after-phases of burst main shapes, that usually arise during the development of the network, were not yet simulated in sufficient detail. This lack of detail may be due to the fact that the random models completely missed network topology .and a growth model. Therefore, the present paper adds, for the first time, a growth model to the activity model, to give the network a time dependent topology and to explain burst shapes in more detail. Again, without LTP or LTD mechanisms. The integrated growth-activity model yielded realistic bursting patterns. The automatic adjustment of various mutually interdependent network parameters is one of the major advantages of our current approach. Spatio-temporal bursting activity was validated against experiment. Depending on network size, wave reverberation mechanisms were seen along the network boundaries, which may explain the generation of phases of elevated firing before and after the main phase of the burst shape.In summary, the results show that adding topology and growth explain burst shapes in great detail and suggest that young networks still lack/do not need LTP or LTD mechanisms.

Calcium and cAMP levels interact to determine attraction versus repulsion in axon guidance

Correct guidance of axons to their targets depends on an intricate network of signaling molecules in the growth cone. Calcium and cAMP are two key regulators of whether axons are attracted or repelled by molecular gradients, but how these molecules interact to determine guidance responses remains unclear. Here, we constructed a mathematical model for the relevant signaling network, which explained a large range of previous biological data and made predictions for when axons will be attracted or repelled. We then confirmed these predictions experimentally, in particular showing that while small increases in cAMP levels promote attraction large increases do not, and that under some circumstances reducing cAMP levels promotes attraction. Together, these results show that a relatively simple mathematical model can quantitatively predict guidance decisions across a wide range of conditions, and that calcium and cAMP levels play a more complex role in these decisions than previously determined.

A mathematical model for selective differentiation of neural progenitor cells on micropatterned polymer substrates

The biological hypothesis that the astrocyte-secreted cytokine, interleukin-6 (IL6), stimulates differentiation of adult rat hippocampal progenitor cells (AHPCs) is considered from a mathematical perspective. The proposed mathematical model includes two different mechanisms for stimulation and is based on mass-action kinetics. Both biological mechanisms involve sequential binding, with one pathway solely utilizing surface receptors while the other pathway also involves soluble receptors. Choosing biologically-reasonable values for parameters, simulations of the mathematical model show good agreement with experimental results. A global sensitivity analysis is also conducted to determine both the most influential and non-influential parameters on cellular differentiation, providing additional insights into the biological mechanisms.

An instruction language for self-construction in the context of neural networks

Biological systems are based on an entirely different concept of construction than human artifacts. They construct themselves by a process of self-organization that is a systematic spatio-temporal generation of, and interaction between, various specialized cell types. We propose a framework for designing gene-like codes for guiding the self-construction of neural networks. The description of neural development is formalized by defining a set of primitive actions taken locally by neural precursors during corticogenesis. These primitives can be combined into networks of instructions similar to biochemical pathways, capable of reproducing complex developmental sequences in a biologically plausible way. Moreover, the conditional activation and deactivation of these instruction networks can also be controlled by these primitives, allowing for the design of a "genetic code" containing both coding and regulating elements. We demonstrate in a simulation of physical cell development how this code can be incorporated into a single progenitor, which then by replication and differentiation, reproduces important aspects of corticogenesis.

Balancing of ephrin/Eph forward and reverse signaling as the driving force of adaptive topographic mapping

The retinotectal projection, which topographically maps retinal axons onto the tectum of the midbrain, is an ideal model system with which to investigate the molecular genetics of embryonic brain wiring. Corroborating Sperry's seminal hypothesis, ephrin/Eph counter-gradients on both retina and tectum were found to represent matching chemospecificity markers. Intriguingly, however, it has never been possible to reconstitute topographically appropriate fiber growth in vitro with these cues. Moreover, experimentally derived molecular mechanisms have failed to provide explanations as to why the mapping adapts to grossly diverse targets in some experiments, while displaying strict point-to-point specificity in others. In vitro, ephrin-A/EphA forward, as well as reverse, signaling mediate differential repulsion to retinal fibers, instead of providing topographic guidance. We argue that those responses are indicative of ephrin-A and EphA being members of a guidance system that requires two counteracting cues per axis. Experimentally, we demonstrate by introducing novel double-cue stripe assays that the simultaneous presence of both cues indeed suffices to elicit topographically appropriate guidance. The peculiar mechanism, which uses forward and reverse signaling through a single receptor/ligand combination, entails fiber/fiber interactions. We therefore propose to extend Sperry's model to include ephrin-A/EphA-based fiber/fiber chemospecificity, eventually out-competing fiber/target interactions. By computational simulation, we show that our model is consistent with stripe assay results. More importantly, however, it not only accounts for classical in vivo evidence of point-to-point and adaptive topographic mapping, but also for the map duplication found in retinal EphA knock-in mice. Nonetheless, it is based on a single constraint of topographic growth cone navigation: the balancing of ephrin-A/EphA forward and reverse signaling.

Language development after cochlear implantation: an epigenetic model

Growing evidence supports the notion that dynamic gene expression, subject to epigenetic control, organizes multiple influences to enable a child to learn to listen and to talk. Here, we review neurobiological and genetic influences on spoken language development in the context of results of a longitudinal trial of cochlear implantation of young children with severe to profound sensorineural hearing loss in the Childhood Development after Cochlear Implantation study. We specifically examine the results of cochlear implantation in participants who were congenitally deaf (N = 116). Prior to intervention, these participants were subject to naturally imposed constraints in sensory (acoustic-phonologic) inputs during critical phases of development when spoken language skills are typically achieved rapidly. Their candidacy for a cochlear implant was prompted by delays (n = 20) or an essential absence of spoken language acquisition (n = 96). Observations thus present an opportunity to evaluate the impact of factors that influence the emergence of spoken language, particularly in the context of hearing restoration in sensitive periods for language acquisition. Outcomes demonstrate considerable variation in spoken language learning, although significant advantages exist for the congenitally deaf children implanted prior to 18 months of age. While age at implantation carries high predictive value in forecasting performance on measures of spoken language, several factors show significant association, particularly those related to parent-child interactions. Importantly, the significance of environmental variables in their predictive value for language development varies with age at implantation. These observations are considered in the context of an epigenetic model in which dynamic genomic expression can modulate aspects of auditory learning, offering insights into factors that can influence a child's acquisition of spoken language after cochlear implantation. Increased understanding of these interactions could lead to targeted interventions that interact with the epigenome to influence language outcomes with intervention, particularly in periods in which development is subject to time-sensitive experience.

How neurons migrate: a dynamic in-silico model of neuronal migration in the developing cortex

Background

Neuronal migration, the process by which neurons migrate from their place of origin to their final position in the brain, is a central process for normal brain development and function. Advances in experimental techniques have revealed much about many of the molecular components involved in this process. Notwithstanding these advances, how the molecular machinery works together to govern the migration process has yet to be fully understood. Here we present a computational model of neuronal migration, in which four key molecular entities, Lis1, DCX, Reelin and GABA, form a molecular program that mediates the migration process.

Results

The model simulated the dynamic migration process, consistent with in-vivo observations of morphological, cellular and population-level phenomena. Specifically, the model reproduced migration phases, cellular dynamics and population distributions that concur with experimental observations in normal neuronal development. We tested the model under reduced activity of Lis1 and DCX and found an aberrant development similar to observations in Lis1 and DCX silencing expression experiments. Analysis of the model gave rise to unforeseen insights that could guide future experimental study. Specifically: (1) the model revealed the possibility that under conditions of Lis1 reduced expression, neurons experience an oscillatory neuron-glial association prior to the multipolar stage; and (2) we hypothesized that observed morphology variations in rats and mice may be explained by a single difference in the way that Lis1 and DCX stimulate bipolar motility. From this we make the following predictions: (1) under reduced Lis1 and enhanced DCX expression, we predict a reduced bipolar migration in rats, and (2) under enhanced DCX expression in mice we predict a normal or a higher bipolar migration.

Conclusions

We present here a system-wide computational model of neuronal migration that integrates theory and data within a precise, testable framework. Our model accounts for a range of observable behaviors and affords a computational framework to study aspects of neuronal migration as a complex process that is driven by a relatively simple molecular program. Analysis of the model generated new hypotheses and yet unobserved phenomena that may guide future experimental studies. This paper thus reports a first step toward a comprehensive in-silico model of neuronal migration.

Signaling mechanisms in cortical axon growth, guidance, and branching

Precise wiring of cortical circuits during development depends upon axon extension, guidance, and branching to appropriate targets. Motile growth cones at axon tips navigate through the nervous system by responding to molecular cues, which modulate signaling pathways within axonal growth cones. Intracellular calcium signaling has emerged as a major transducer of guidance cues but exactly how calcium signaling pathways modify the actin and microtubule cytoskeleton to evoke growth cone behaviors and axon branching is still mysterious. Axons must often pause their extension in tracts while their branches extend into targets. Some evidence suggests a competition between growth of axons and branches but the mechanisms are poorly understood. Since it is difficult to study growing axons deep within the mammalian brain, much of what we know about signaling pathways and cytoskeletal dynamics of growth cones comes from tissue culture studies, in many cases, of non-mammalian species. Consequently it is not well understood how guidance cues relevant to mammalian neural development in vivo signal to the growth cone cytoskeleton during axon outgrowth and guidance. In this review we describe our recent work in dissociated cultures of developing rodent sensorimotor cortex in the context of the current literature on molecular guidance cues, calcium signaling pathways, and cytoskeletal dynamics that regulate growth cone behaviors. A major challenge is to relate findings in tissue culture to mechanisms of cortical development in vivo. Toward this goal, we describe our recent work in cortical slices, which preserve the complex cellular and molecular environment of the mammalian brain but allow direct visualization of growth cone behaviors and calcium signaling. Findings from this work suggest that mechanisms regulating axon growth and guidance in dissociated culture neurons also underlie development of cortical connectivity in vivo.

Emergence of structural patterns out of synchronization in networks with competitive interactions

Synchronization is a collective phenomenon occurring in systems of interacting units, and is ubiquitous in nature, society and technology. Recent studies have enlightened the important role played by the interaction topology on the emergence of synchronized states. However, most of these studies neglect that real world systems change their interaction patterns in time. Here, we analyze synchronization features in networks in which structural and dynamical features co-evolve. The feedback of the node dynamics on the interaction pattern is ruled by the competition of two mechanisms: homophily (reinforcing those interactions with other correlated units in the graph) and homeostasis (preserving the value of the input strength received by each unit). The competition between these two adaptive principles leads to the emergence of key structural properties observed in real world networks, such as modular and scale-free structures, together with a striking enhancement of local synchronization in systems with no global order.