Neuritic growth rate described by modeling microtubule dynamics

Modeling neuron growth using isogeometric collocation based phase field method

We present a new computational framework of neuron growth based on the phase field method and develop an open-source software package called “NeuronGrowth_IGAcollocation”. Neurons consist of a cell body, dendrites, and axons. Axons and dendrites are long processes extending from the cell body and enabling information transfer to and from other neurons. There is high variation in neuron morphology based on their location and function, thus increasing the complexity in mathematical modeling of neuron growth. In this paper, we propose a novel phase field model with isogeometric collocation to simulate different stages of neuron growth by considering the effect of tubulin. The stages modeled include lamellipodia formation, initial neurite outgrowth, axon differentiation, and dendrite formation considering the effect of intracellular transport of tubulin on neurite outgrowth. Through comparison with experimental observations, we can demonstrate qualitatively and quantitatively similar reproduction of neuron morphologies at different stages of growth and allow extension towards the formation of neurite networks.

A computational model of bidirectional axonal growth in micro-tissue engineered neuronal networks (micro-TENNs)

Micro-Tissue Engineered Neural Networks (Micro-TENNs) are living three-dimensional constructs designed to replicate the neuroanatomy of white matter pathways in the brain and are being developed as implantable micro-tissue for axon tract reconstruction, or as anatomically-relevant in vitro experimental platforms. Micro-TENNs are composed of discrete neuronal aggregates connected by bundles of long-projecting axonal tracts within miniature tubular hydrogels. In order to help design and optimize micro-TENN performance, we have created a new computational model including geometric and functional properties. The model is built upon the three-dimensional diffusion equation and incorporates large-scale uni- and bi-directional growth that simulates realistic neuron morphologies. The model captures unique features of 3D axonal tract development that are not apparent in planar outgrowth and may be insightful for how white matter pathways form during brain development. The processes of axonal outgrowth, branching, turning and aggregation/bundling from each neuron are described through functions built on concentration equations and growth time distributed across the growth segments. Once developed we conducted multiple parametric studies to explore the applicability of the method and conducted preliminary validation via comparisons to experimentally grown micro-TENNs for a range of growth conditions. Using this framework, the model can be applied to study micro-TENN growth processes and functional characteristics using spiking network or compartmental network modeling. This model may be applied to improve our understanding of axonal tract development and functionality, as well as to optimize the fabrication of implantable tissue engineered brain pathways for nervous system reconstruction and/or modulation.

A model for stretch growth of neurons

In the first phase of axon growth, axons sprout from neuron bodies and are extended by the pull of the migrating growth cones towards their targets. Thereafter, once the target is reached, a lesser known second phase of axon growth ensues as the mechanical forces from the growth of the animal induce extension of the integrated axons in the process of forming tracts and nerves. Although there are several microscopic physics based models of the first phase of axon growth, to date, there are no models of the very different second phase. Here we propose a mathematical model for stretch growth of axon tracts in which the rate of production of proteins required for growth is dependent on the membrane tension. We assume that growth occurs all along the axon, and are able to predict the increase in axon cross-sectional area after they are rapidly stretched and held at a constant length for several hours. We show that there is a length dependent maximum stretching rate that an axon can sustain without disconnection in steady state when the axon length is primarily increased near the cell body. Our results could inform better design of stretch growth protocols to create transplantable axon tracts to repair the nervous system.

Growth, collapse, and stalling in a mechanical model for neurite motility

Neurites, the long cellular protrusions that form the routes of the neuronal network, are capable of actively extending during early morphogenesis or regenerating after trauma. To perform this task, they rely on their cytoskeleton for mechanical support. In this paper, we present a three-component active gel model that describes neurites in the three robust mechanical states observed experimentally: collapsed, static, and motile. These states arise from an interplay between the physical forces driven by the growth of the microtubule-rich inner core of the neurite and the acto-myosin contractility of its surrounding cortical membrane. In particular, static states appear as a mechanical balance between traction and compression of these two parallel structures. The model predicts how the response of a neurite to a towing force depends on the force magnitude and recovers the response of neurites to several drug treatments that modulate the cytoskeleton active and passive properties.

Rac1 and Aurora A regulate MCAK to polarize microtubule growth in migrating endothelial cells

A Rac1–Aurora A–MCAK signaling pathway mediates endothelial cell polarization and directional migration by promoting regional differences in microtubule dynamics in the leading and trailing cell edges.

Endothelial cells (ECs) migrate directionally during angiogenesis and wound healing by polarizing to extracellular cues to guide directional movement. EC polarization is controlled by microtubule (MT) growth dynamics, which are regulated by MT-associated proteins (MAPs) that alter MT stability. Mitotic centromere-associated kinesin (MCAK) is a MAP that promotes MT disassembly within the mitotic spindle, yet its function in regulating MT dynamics to promote EC polarity and migration has not been investigated. We used high-resolution fluorescence microscopy coupled with computational image analysis to elucidate the role of MCAK in regulating MT growth dynamics, morphology, and directional migration of ECs. Our results show that MCAK-mediated depolymerization of MTs is specifically targeted to the trailing edge of polarized wound-edge ECs. Regulation of MCAK function is dependent on Aurora A kinase, which is regionally enhanced by signaling from the small guanosine triphosphatase, Rac1. Thus, a Rac1–Aurora A–MCAK signaling pathway mediates EC polarization and directional migration by promoting regional differences in MT dynamics in the leading and trailing cell edges.

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.

Tension-induced neurite growth in microfluidic channels

The generation of an effective method for stimulating neuronal growth in specific directions, along well-defined geometries, and in numerous cells could impact areas ranging from fundamental studies of neuronal evolution and morphogenesis, to applications in biomedical diagnostics and nerve regeneration. Applied mechanical stress can regulate neurite growth. Indeed, previous studies have shown that neuronal cells can develop and extend neurites with rapid growth rates under applied "towing" tensions imparted by micropipettes. Yet, such methods are complex and exhibit low throughputs, as the tension is applied serially to individual cells. Here we present a novel approach to inducing neurite growth in multiple cells in parallel, by using a miniaturized platform with numerous microchannels. Upon connection of a vacuum to these microchannels, tension can be applied on multiple cells simultaneously to induce the growth of neurites. A theoretical model was also developed to understand the effect of tension on the dynamics of neurite development.

Spatial and temporal sensing limits of microtubule polarization in neuronal growth cones by intracellular gradients and forces

Neuronal growth cones are the most sensitive among eukaryotic cells in responding to directional chemical cues. Although a dynamic microtubule cytoskeleton has been shown to be essential for growth-cone turning, the precise nature of coupling of the spatial cue with microtubule polarization is less understood. Here we present a computational model of microtubule polarization in a turning neuronal growth cone. We explore the limits of directional cues in modifying the spatial polarization of microtubules by testing the role of microtubule dynamics, gradients of regulators, and retrograde forces along filopodia. We analyze the steady state and transition behavior of microtubules on being presented with a directional stimulus. Our model makes novel, to our knowledge, predictions about the minimal angular spread of the chemical signal at the growth cone and the fastest polarization times. A regulatory reaction-diffusion network based on the cyclic phosphorylation-dephosphorylation of a regulator predicts that the receptor-signal magnitude can generate the maximal polarization of microtubules and not feedback loops or amplifications in the network. Using both the phenomenological and network models, we have demonstrated some of the physical limits within which the microtubule polarization system works in turning the neuron.

Numerical study of axonal outgrowth in grooved nerve conduits

Nerve conduits with grooved inner texture, working as a topographical guidance cue, have been experimentally proved to play a significant role in axonal alignment. How grooved conduits guide axonal outgrowth is of particular interest for studying nerve regeneration. A viscoelastic model of axonal outgrowth in a conduit with a defined grooved geometry characterized by its width in the circumferential direction and its height in the radial direction is developed in this work. In this model, the axon is considered as an elastic beam and the axonal deformation and motion, including stretching, bending and torsion, are described using a Cosserat rod theory. The friction between axon and substrate is also considered in this model as well as the tip outgrowth. It is found that the directional outgrowth of the axon can be significantly improved by the grooved texture: when the groove width decreases or the groove height increases, the axonal elongation in the longitudinal direction of the conduit can be increased, which is in good agreement with experimental observations. This work is the first numerical model to study the effect of the substrate geometry on axonal outgrowth.

Large-scale analysis of neurite growth dynamics on micropatterned substrates

During both development and regeneration of the nervous system, neurons display complex growth dynamics, and several neurites compete to become the neuron's single axon. Numerous mathematical and biophysical models have been proposed to explain this competition, which remain experimentally unverified. Large-scale, precise, and repeatable measurements of neurite dynamics have been difficult to perform, since neurons have varying numbers of neurites, which themselves have complex morphologies. To overcome these challenges using a minimal number of primary neurons, we generated repeatable neuronal morphologies on a large scale using laser-patterned micron-wide stripes of adhesive proteins on an otherwise highly non-adherent substrate. By analyzing thousands of quantitative time-lapse measurements of highly reproducible neurite growth dynamics, we show that total neurite growth accelerates until neurons polarize, that immature neurites compete even at very short lengths, and that neuronal polarity exhibits a distinct transition as neurites grow. Proposed neurite growth models agree only partially with our experimental observations. We further show that simple yet specific modifications can significantly improve these models, but still do not fully predict the complex neurite growth behavior. Our high-content analysis puts significant and nontrivial constraints on possible mechanistic models of neurite growth and specification. The methodology presented here could also be employed in large-scale chemical and target-based screens on a variety of complex and subtle phenotypes for therapeutic discoveries using minimal numbers of primary neurons.

Regulation of katanin-P60 levels by LECT2 adjusts microtubular morphology

Leukocyte cell-derived chemotaxin 2 (LECT2) facilitates neuritic extension in cultured hippocampal neurons during initial development. However, the functions of LECT2 in neuritic extension are poorly understood. To elucidate these functions, we examined microtubular morphology and levels of katanin-P60, a microtubule-severing enzyme, in cultured hippocampal neurons from wild-type mice and LECT2 knockout (KO) mice. Microtubules in LECT2-KO mice exhibited fragmentation and were shorter than those of wild-type mice. Furthermore, the expression of katanin-P60 in LECT2-KO mice was significantly elevated when compared with wild-type mice at 1 day in vitro (DIV1) and 4. Our results suggest that LECT2 regulates neuritic extension through microtubular morphallaxis through the control of katanin-P60 levels.

Theoretical models of neural circuit development

Proper wiring up of the nervous system is critical to the development of organisms capable of complex and adaptable behaviors. Besides the many experimental advances in determining the cellular and molecular machinery that carries out this remarkable task precisely and robustly, theoretical approaches have also proven to be useful tools in analyzing this machinery. A quantitative understanding of these processes can allow us to make predictions, test hypotheses, and appraise established concepts in a new light. Three areas that have been fruitful in this regard are axon guidance, retinotectal mapping, and activity-dependent development. This chapter reviews some of the contributions made by mathematical modeling in these areas, illustrated by important examples of models in each section. For axon guidance, we discuss models of how growth cones respond to their environment, and how this environment can place constraints on growth cone behavior. Retinotectal mapping looks at computational models for how topography can be generated in populations of neurons based on molecular gradients and other mechanisms such as competition. In activity-dependent development, we discuss theoretical approaches largely based on Hebbian synaptic plasticity rules, and how they can generate maps in the visual cortex very similar to those seen in vivo. We show how theoretical approaches have substantially contributed to the advancement of developmental neuroscience, and discuss future directions for mathematical modeling in the field.

Modeling mitochondrial dynamics during in vivo axonal elongation

Many models of axonal elongation are based on the assumption that the rate of lengthening is driven by the production of cellular materials in the soma. These models make specific predictions about transport and concentration gradients of proteins both over time and along the length of the axon. In vivo, it is well accepted that for a particular neuron the length and rate of growth are controlled by the body size and rate of growth of the animal. In terms of modeling axonal elongation this radically changes the relationships between key variables. It raises fundamental questions. For example, during in vivo lengthening is the production of material constant or does it change over time? What is the density profile of material along the nerve during in vivo elongation? Does density change over time or vary along the nerve? To answer these questions we measured the length, mitochondrial density, and estimated the half-life of mitochondria in the axons of the medial segmental nerves of 1st, 2nd, and 3rd instar Drosophila larvae. The nerves were found to linearly increase in length at an average rate of 9.24 microm h(-1) over the 96 h period of larval life. Further, mitochondrial density increases over this period at an average rate of 4.49x10(-3) (mitochondria microm(-1))h(-1). Mitochondria in the nerves had a half-life of 35.2h. To account for the distribution of the mitochondria we observe, we derived a mathematical model which suggests that cellular production of mitochondria increases quadratically over time and that a homeostatic mechanism maintains a constant density of mitochondria along the nerve. These data suggest a complex relationship between axonal length and mass production and that the neuron may have an "axonal length sensor."

In SilicoModeling of Axonal Reconnection within A Discrete Fiber Tract after Spinal Cord Injury

Following spinal cord injury (SCI), descending axons that carry motor commands from the brain to the spinal cord are injured or transected, producing chronic motor dysfunction and paralysis. Reconnection of these axons is a major prerequisite for restoration of function after SCI. Thus far, only modest gains in motor function have been achieved experimentally or in the clinic after SCI, identifying the practical limitations of current treatment approaches. In this paper, we use an ordinary differential equation (ODE) to simulate the relative and synergistic contributions of several experimentally-established biological factors related to inhibition or promotion of axonal repair and restoration of function after SCI. The factors were mathematically modeled by the ODE. The results of our simulation show that in a model system, many factors influenced the achievability of axonal reconnection. Certain factors more strongly affected axonal reconnection in isolation, and some factors interacted in a synergistic fashion to produce further improvements in axonal reconnection. Our data suggest that mathematical modeling may be useful in evaluating the complex interactions of discrete therapeutic factors not possible in experimental preparations, and highlight the benefit of a combinatorial therapeutic approach focused on promoting axonal sprouting, attraction of cut ends, and removal of growth inhibition for achieving axonal reconnection. Predictions of this simulation may be of utility in guiding future experiments aimed at restoring function after SCI.

Mathematical modelling and numerical simulation of the morphological development of neurons

Background

The morphological development of neurons is a very complex process involving both genetic and environmental components. Mathematical modelling and numerical simulation are valuable tools in helping us unravel particular aspects of how individual neurons grow their characteristic morphologies and eventually form appropriate networks with each other.

Methods

A variety of mathematical models that consider (1) neurite initiation (2) neurite elongation (3) axon pathfinding, and (4) neurite branching and dendritic shape formation are reviewed. The different mathematical techniques employed are also described.

Results

Some comparison of modelling results with experimental data is made. A critique of different modelling techniques is given, leading to a proposal for a unified modelling environment for models of neuronal development.

Conclusion

A unified mathematical and numerical simulation framework should lead to an expansion of work on models of neuronal development, as has occurred with compartmental models of neuronal electrical activity.

Dynamics of outgrowth in a continuum model of neurite elongation

Neurite outgrowth (dendrites and axons) should be a stable, but easily regulated process to enable a neuron to make its appropriate network connections during development. We explore the dynamics of outgrowth in a mathematical continuum model of neurite elongation. The model describes the construction of the internal microtubule cytoskeleton, which results from the production and transport of tubulin dimers and their assembly into microtubules at the growing neurite tip. Tubulin is assumed to be largely synthesised in the cell body from where it is transported by active mechanisms and by diffusion along the neurite. It is argued that this construction process is a fundamental limiting factor in neurite elongation. In the model, elongation is highly stable when tubulin transport is dominated by either active transport or diffusion, but oscillations in length may occur when both active transport and diffusion contribute. Autoregulation of tubulin production can eliminate these oscillations. In all cases a stable steady-state length is reached, provided there is intrinsic decay of tubulin. Small changes in growth parameters, such as the tubulin production rate, can lead to large changes in length. Thus cytoskeleton construction can be both stable and easily regulated, as seems necessary for neurite outgrowth during nervous system development.

Theoretical analysis of a synaptotropic dendrite growth mechanism

It is generally believed that the genome cannot encode explicit instructions to form each synaptic connection in the nervous system, but may provide general neurite growth mechanisms which will result in proper connectivity. Recent in vivo imaging has provided evidence for a synaptotropic growth mechanism, wherein synapses could influence dendrite growth by selectively stabilizing filopodia upon which they form. We undertook a theoretical investigation into the consequences of such a growth process. Discrete stochastic simulations demonstrate that the synaptotropic mechanism can result in decreased dendritic wiring length, is capable of searching for regions of high density pre-synaptic partners, and can recapitulate specific patterns of dendrite growth and connectivity. A mean-field analysis shows that growth by selective stabilization of filopodia can be approximated as a reaction-diffusion system, with a spatially varying diffusion constant that depends on the probability of synapse formation. Thus, growth will occur faster in regions of appropriate synaptic connections, and the net growth can be shown to climb a gradient of synaptic partner density. Synaptotropic growth thus presents a mechanism for the emergent development of connectivity based on local properties of the circuit elements, rather than explicit dependence on global guidance molecules or innate predetermined branching programs.

Local diameter fully constrains dendritic size in basal but not apical trees of CA1 pyramidal neurons

Computational modeling of dendritic morphology is a powerful tool for quantitatively describing complex geometrical relationships, uncovering principles of dendritic development, and synthesizing virtual neurons to systematically investigate cellular biophysics and network dynamics. A feature common to many morphological models is a dependence of the branching probability on local diameter. Previous models of this type have been able to recreate a wide variety of dendritic morphologies. However, these diameter-dependent models have so far failed to properly constrain branching when applied to hippocampal CA1 pyramidal cells, leading to explosive growth. Here we present a simple modification of this basic approach, in which all parameter sampling, not just bifurcation probability, depends on branch diameter. This added constraint prevents explosive growth in both apical and basal trees of simulated CA1 neurons, yielding arborizations with average numbers and patterns of bifurcations extremely close to those observed in real cells. However, simulated apical trees are much more varied in size than the corresponding real dendrites. We show that, in this model, the excessive variability of simulated trees is a direct consequence of the natural variability of diameter changes at and between bifurcations observed in apical, but not basal, dendrites. Conversely, some aspects of branch distribution were better matched by virtual apical trees than by virtual basal trees. Dendritic morphometrics related to spatial position, such as path distance from the soma or branch order, may be necessary to fully constrain CA1 apical tree size and basal branching pattern.

Competition in neurite outgrowth and the development of nerve connections

During the development of the nervous system, neurons form their characteristic morphologies and become assembled into synaptically connected networks. In both neuronal morphogenesis and the development of nerve connections, competition plays an important role. Although the notion of competition is commonly used in neurobiology, there is little understanding of the nature of the competitive process and the underlying molecular and cellular mechanisms. In this chapter, we review a model of competition between outgrowing neurites, as well as various models of competition that have been proposed for the refinement of connections that takes place in the development of the neuromuscular and visual systems. We describe in detail a model that links competition in the development of nerve connections with the underlying actions and biochemistry of neurotrophic factors.

Growth cone pathfinding: a competition between deterministic and stochastic events

Background

Growth cone migratory patterns show evidence of both deterministic and stochastic search modes.

Results

We quantitatively examine how these two different migration modes affect the growth cone's pathfinding response, by simulating growth cone contact with a repulsive cue and measuring the resultant turn angle. We develop a dimensionless number, we call the determinism ratio Ψ, to define the ratio of deterministic to stochastic influences driving the growth cone's migration in response to an external guidance cue. We find that the growth cone can exhibit three distinct types of turning behaviors depending on the magnitude of Ψ.

Conclusions

We conclude, within the context of these in silico studies, that only when deterministic and stochastic migration factors are in balance (i.e. Ψ ~ 1) can the growth cone respond constructively to guidance cues.

A computational model of dendrite elongation and branching based on MAP2 phosphorylation

We introduce a new computational model of dendritic development in neurons. In contrast to previous models, our model explicitly includes cellular mechanisms involved in dendritic development. It is based on recent experimental data which indicates that the phosphorylation state of microtubule-associated protein 2 (MAP2) may play a key role in controlling dendritic elongation and branching (Audesirk et al., 1997). Dephosphorylated MAP2 favours elongation by promoting microtubule polymerization and bundling, whilst branching is more likely to occur when MAP2 is phosphorylated and microtubules are spaced apart. In the model, the rate of elongation and branching is directly determined by the ratio of phosphorylated to dephosphorylated MAP2. This is regulated by calmodulin-dependent protein kinase II (CaMKII) and calcineurin, which are both dependent on the intracellular calcium concentration. Results from computer simulations of the model suggest that the wide variety of branching patterns observed among different cell types may be generated by the same underlying mechanisms and that elongation and branching are not necessarily independent processes. The model predicts how the branching pattern will change following manipulations with calcium, CaMKII and MAP2 phosphorylation.

Generic modeling of chemotactic based self-wiring of neural networks

The proper functioning of the nervous system depends critically on the intricate network of synaptic connections that are generated during the system development. During the network formation, the growth cones migrate through the embryonic environment to their targets using chemical communication. A major obstacle in the elucidation of fundamental principles underlying this self-wiring is the complexity of the system being analyzed. Hence much effort is devoted to in vitro experiments of simpler (two-dimensional) 2D model systems. In these experiments neurons are placed on Poly-L-Lysine (PLL) surfaces, so it is easier to monitor their self-wiring. We developed a model to reproduce the salient features of the 2D systems, inspired by the study of the growth of bacterial colonies and the aggregation of amoebae. We represent the neurons (each composed of cell's soma, neurites and growth cones) by active elements that capture the generic features of the real neurons. The model also incorporates stationary units representing the cells' soma and communicating walkers representing the growth cones. The stationary units send neurites one at a time, and respond to chemical signaling. The walkers migrate in response to chemotaxis substances emitted by the soma and communicate with each other and with the soma by means of chemotactic "feedback". The interplay between the chemo-repulsive and chemo-attractive responses is determined by the dynamics of the walker's internal energy which is controlled by the soma. These features enable the neurons to perform the complex task of self-wiring. We present numerical experiments of the model to demonstrate its ability to form fine structures in simple networks of few neurons. Our results raise two fundamental issues: (1) one needs to develop characterization methods (beyond number of connections per neuron) to distinguish the various possible networks; (2) what are the relations between the network organization and its computational properties and efficiency?

Growth cone dynamics and activity-dependent processes in neuronal network development

Many structural and functional properties of neuronal networks find their origin in the dynamic behavior of growth cones during development. The variation in dendritic morphologies can be traced back to random branching of growth cones. Segment length characteristics arise under random branching and steady growth cone propagation. Delayed outgrowth, as a result of competition between growth cones after splitting, is hypothesized to explain different lengths of paired terminal segments in Purkinje cells. The implications of activity-dependent neurite outgrowth were studied using an outgrowth function based on the theory of Kater et al. (1988, 1990). This theory embodies a homeostatic principle, according to which a neuron adapts its neuritic field so as to maintain a certain level bioelectric activity. It is shown that such homeostasis has many implications for neuromorphogenesis and network formation, as it may underlie phenomena such as overshoot during development, size differences among cells, differentiation between excitatory and inhibitory cells and compensatory sprouting. Finally, function-dependent regulation of development involves physiological as well as morphological variables. For instance, activity dependent regulation of ionic conductances such as to stabilize functional activity can result in a differentiation of certain neurons into, respectively, bursting and regular firing sub-types (Abbot et al., 1993; LeMasson et al., 1993). Similarly, the GABAergic phenotype comes fully to expression in hindbrain (cerebellar) and forebrain (neocortical) networks only if the level of ongoing excitatory activity during development is sufficiently high, whereas chronically intensified activity leads to a compensatory hypertrophy of inhibitory mechanisms (for review, see Corner 1994). Many of these results could only have been obtained by the use of mathematical models which allow rigorous analysis of the consequences of basic assumptions in the dynamics of neurite outgrowth. All in all, the findings further emphasize the role of spontaneous bioelectric activity during early development in neuronal network formation, the importance of which was first established in cultures of developing neural tissue.

Neuroengineering in biological and biosynthetic systems

Recent advances in restoring neural function to biological systems and incorporating neural function into bioartificial devices have been made possible by developments in biology, materials science, engineering, and physics. Further progress is being achieved in relating cellular function to overall system behavior through the application of quantitative experimental and theoretical techniques.