Biologically plausible models of neurite outgrowth

The potential protective effects of melatonin and omega-3 on the male rat optic nerve exposed to 900 MHz electromagnetic radiation during the prenatal period

BACKGROUND

Due to children and adolescents' widespread use of electronic devices, researchers have focused on pre-and early postnatal electromagnetic field (EMF) exposure. However, little is known about the effects of EMF exposure on the optic nerve. The aim of study was to investigate the changes occurring in the optic nerve and the protective effects of melatonin (mel) and omega 3 (ω-3) in rats.

METHODS

Thirty-five pregnant rats were divided into seven groups, Cont, Sham, EMF, EMF + melatonin (EMF + Mel), EMF + ω3, Mel, and ω3. The EMF groups were exposed to 900 megahertz (MHz) EMF daily for two hours during pregnancy. After the experiment, the right optic nerve of each offspring rat was removed and fixed in glutaraldehyde. Thin and semi-thin sections were taken for electron microscopic and stereological analyses. Myelinated axon numbers, myelin sheath thicknesses, and axonal areas were estimated using stereological methods.

RESULTS

The groups had no significant differences regarding mean numbers of axons, mean axonal areas, or mean myelin sheath thicknesses (p > 0.05). Histological observations revealed impaired lamellae in the myelin sheath of most axons, and vacuolization was frequently observed between the myelin sheath and axon in the EMF-exposed group. The Mel and ω-3-treated EMF groups exhibited well-preserved myelinated nerve fibers and intact astrocytes and oligodendrocytes.

CONCLUSIONS

At the ultrastructural level, Mel and ω3 exhibits a neuroprotective effect on the optic nerve exposed to prenatal EMF. The protective effects of these antioxidants on oligodendrocytes, which play an essential role in myelin formation in the central nervous system, now require detailed investigation.

Mathematical models of neuronal growth

The establishment of a functioning neuronal network is a crucial step in neural development. During this process, neurons extend neurites—axons and dendrites—to meet other neurons and interconnect. Therefore, these neurites need to migrate, grow, branch and find the correct path to their target by processing sensory cues from their environment. These processes rely on many coupled biophysical effects including elasticity, viscosity, growth, active forces, chemical signaling, adhesion and cellular transport. Mathematical models offer a direct way to test hypotheses and understand the underlying mechanisms responsible for neuron development. Here, we critically review the main models of neurite growth and morphogenesis from a mathematical viewpoint. We present different models for growth, guidance and morphogenesis, with a particular emphasis on mechanics and mechanisms, and on simple mathematical models that can be partially treated analytically.

Quantifying scaling exponents for neurite morphology of in vitro-cultured human iPSC-derived neurons using discrete Loewner evolution: A statistical-physical approach to the neuropathology in Alzheimer's disease

Defining the morphological disorders causing neurodegenerative diseases is an unresolved problem. In this study, we propose a statistical-physical approach to quantify neurite morphology and evaluate the pathological states induced by Alzheimer's disease (AD). We analyzed the two-dimensional morphologies of neurites of in vitro-cultured human induced-pluripotent stem cell-derived neurons, reprogrammed from both a healthy person and a patient with AD, using discrete chordal Loewner evolution. For the numerically calculated Loewner driving forces, detrended fluctuation analysis was performed, and the morphological characteristics of the neurites were quantified using short-range and long-range scaling exponents. The day in vitro (DIV)-dependent behaviors of the scaling exponents and the associated neurite-type categorizations suggested that differences between healthy and AD neurites can be observed from the early stage (DIV3) of their development. Notably, AD neurites have less long-range autocorrelations than healthy neurites, particularly in the earlier stages (DIV3-10). Immunofluorescence-staining results suggested that these differences precede significant expressions of β-amyloid and phosphorylated tau, which are known as biological factors causing AD. We expect that these results will lead to a theoretical interpretation of the neurogenerative disease, providing the physical properties of individual neurites with different morphologies.

Dl-3-n-butylphthalide promotes neurite outgrowth of primary cortical neurons by Sonic Hedgehog signaling via upregulating Gap43

Neurite outgrowth is the basis for wiring during the development of the nervous system. Dl-3-n-butylphthalide (NBP) has been recognized as a promising treatment to improve behavioral, neurological and cognitive outcomes in ischemic stroke. However, little is known about the effect and mechanism of NBP on the neurite outgrowth. In this study, we used different methods to investigate the potential effects of NBP on the neurite extension and plasticity of immature and mature primary cortical neurons and explored the underlying mechanisms. Our results demonstrated that in immature and mature cortical neurons, NBP promoted the neurite length and intersections, increased neuritic arborization, elevated numbers of neurite branch and terminal points and improved neurite complexity and plasticity of neuronal development processes. Besides, our data revealed that NBP promoted neurite extension and branching partly by activating Shh signaling pathway via increasing Gap43 expression both in immature and mature primary cortical neurons. The present study provided new insights into the contribution of NBP in neuronal plasticity and unveiled a novel pathway to induce Gap43 expression in primary cortical neurons.

Temporal ordering of input modulates connectivity formation in a developmental neuronal network model of the cortex

Preterm infant brain activity is discontinuous; bursts of activity recorded using EEG (electroencephalography), thought to be driven by subcortical regions, display scale free properties and exhibit a complex temporal ordering known as long-range temporal correlations (LRTCs). During brain development, activity-dependent mechanisms are essential for synaptic connectivity formation, and abolishing burst activity in animal models leads to weak disorganised synaptic connectivity. Moreover, synaptic pruning shares similar mechanisms to spike-timing dependent plasticity (STDP), suggesting that the timing of activity may play a critical role in connectivity formation. We investigated, in a computational model of leaky integrate-and-fire neurones, whether the temporal ordering of burst activity within an external driving input could modulate connectivity formation in the network. Connectivity evolved across the course of simulations using an approach analogous to STDP, from networks with initial random connectivity. Small-world connectivity and hub neurones emerged in the network structure—characteristic properties of mature brain networks. Notably, driving the network with an external input which exhibited LRTCs in the temporal ordering of burst activity facilitated the emergence of these network properties, increasing the speed with which they emerged compared with when the network was driven by the same input with the bursts randomly ordered in time. Moreover, the emergence of small-world properties was dependent on the strength of the LRTCs. These results suggest that the temporal ordering of burst activity could play an important role in synaptic connectivity formation and the emergence of small-world topology in the developing brain.

Dynamic balance between vesicle transport and microtubule growth enables neurite outgrowth

Whole cell responses involve multiple subcellular processes (SCPs). To understand how balance between SCPs controls the dynamics of whole cell responses we studied neurite outgrowth in rat primary cortical neurons in culture. We used a combination of dynamical models and experiments to understand the conditions that permitted growth at a specified velocity and when aberrant growth could lead to the formation of dystrophic bulbs. We hypothesized that dystrophic bulb formation is due to quantitative imbalances between SCPs. Simulations predict redundancies between lower level sibling SCPs within each type of high level SCP. In contrast, higher level SCPs, such as vesicle transport and exocytosis or microtubule growth characteristic of each type need to be strictly coordinated with each other and imbalances result in stalling of neurite outgrowth. From these simulations, we predicted the effect of changing the activities of SCPs involved in vesicle exocytosis or microtubule growth could lead to formation of dystrophic bulbs. siRNA ablation experiments verified these predictions. We conclude that whole cell dynamics requires balance between the higher-level SCPs involved and imbalances can terminate whole cell responses such as neurite outgrowth.

Mechanisms that cause a change of state of a cell arise from unique patterns of interactions between multiple subcellular processes (SCPs). Neurite outgrowth (NOG) is such a change of cell state where a neuron puts out a long process that eventually becomes the axon. We used a top-down based approach to mathematically model interactions between SCPs involved in NOG. These include membrane production at the cell body, membrane delivery from the cell body to the neurite tip and microtubule growth within the neurite. Our analyses show how the different SCPs interact with each other to enable NOG at a given velocity under physiological conditions. This approach is different from the commonly used bottom-up approaches that focus on predicting cell functions based on the activity of molecular interaction networks. Our simulations predict that lower-level sibling SCPs (e.g. vesicle tethering at and vesicle fusion with the plasma membrane) within a group can compensate for each other under physiological conditions, while such simple relationships do not exist between higher level SCPs (e.g. vesicle exocytosis and vesicle transport along microtubules). We predicted that imbalances of activities between higher-level SCPs induce dystrophic bulbs (a pathological response) and validated these predictions via siRNA ablation experiments.

Theoretical Models of Neural Development

Constructing a functioning nervous system requires the precise orchestration of a vast array of mechanical, molecular, and neural-activity-dependent cues. Theoretical models can play a vital role in helping to frame quantitative issues, reveal mathematical commonalities between apparently diverse systems, identify what is and what is not possible in principle, and test the abilities of specific mechanisms to explain the data. This review focuses on the progress that has been made over the last decade in our theoretical understanding of neural development.

Melatonin prevents mitochondrial dysfunction and promotes neuroprotection by inducing autophagy during oxaliplatin-evoked peripheral neuropathy

Oxaliplatin, an organoplatinum compound, is used in the treatment of colorectal cancer, but its clinical use can be limited due to the development of peripheral neuropathy. Whilst mitochondrial dysfunction has been implicated as a major pathomechanism for oxaliplatin-induced neurotoxicity, the prevention of autophagy may also aggravate neuronal cell death. Melatonin, a well-known mitoprotectant and autophagy inducer, was used to examine its neuroprotective role in oxaliplatin-induced peripheral neuropathy (OIPN). Melatonin prevented the loss of mitochondrial membrane potential (Ψm) and promoted neuritogenesis in oxaliplatin-challenged neuro-2a cells. It did not interfere with the cytotoxic activity of oxaliplatin in human colon cancer cell line, HT-29. Melatonin treatment significantly alleviated oxaliplatin-induced pain behavior and neuropathic deficits in rats. It also ameliorated nitro-oxidative stress mediated by oxaliplatin, thus prevented nitrosylation of proteins and loss of antioxidant enzymes, and therefore, it improved mitochondrial electron transport chain function and maintained cellular bioenergetics by improving the ATP levels. The protective effects of melatonin were attributed to preventing oxaliplatin-induced neuronal apoptosis by increasing the autophagy pathway (via LC3A/3B) in peripheral nerves and dorsal root ganglion (DRG). Hence, it preserved the epidermal nerve fiber density in oxaliplatin-induced neuropathic rats. Taken together, we provide detailed molecular mechanisms for the neuroprotective effect of melatonin and suggest it has translational potential for oxaliplatin-induced neuropathy.

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.

Dendrite and Axon Specific Geometrical Transformation in Neurite Development

We propose a model of neurite growth to explain the differences in dendrite and axon specific neurite development. The model implements basic molecular kinetics, e.g., building protein synthesis and transport to the growth cone, and includes explicit dependence of the building kinetics on the geometry of the neurite. The basic assumption was that the radius of the neurite decreases with length. We found that the neurite dynamics crucially depended on the relationship between the rate of active transport and the rate of morphological changes. If these rates were in the balance, then the neurite displayed axon specific development with a constant elongation speed. For dendrite specific growth, the maximal length was rapidly saturated by degradation of building protein structures or limited by proximal part expansion reaching the characteristic cell size.

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.

Neuroprotective copper bis(thiosemicarbazonato) complexes promote neurite elongation

Abnormal biometal homeostasis is a central feature of many neurodegenerative disorders including Alzheimer's disease (AD), Parkinson's disease (PD), and motor neuron disease. Recent studies have shown that metal complexing compounds behaving as ionophores such as clioquinol and PBT2 have robust therapeutic activity in animal models of neurodegenerative disease; however, the mechanism of neuroprotective action remains unclear. These neuroprotective or neurogenerative processes may be related to the delivery or redistribution of biometals, such as copper and zinc, by metal ionophores. To investigate this further, we examined the effect of the bis(thiosemicarbazonato)-copper complex, Cu(II)(gtsm) on neuritogenesis and neurite elongation (neurogenerative outcomes) in PC12 neuronal-related cultures. We found that Cu(II)(gtsm) induced robust neurite elongation in PC12 cells when delivered at concentrations of 25 or 50 nM overnight. Analogous effects were observed with an alternative copper bis(thiosemicarbazonato) complex, Cu(II)(atsm), but at a higher concentration. Induction of neurite elongation by Cu(II)(gtsm) was restricted to neurites within the length range of 75-99 µm with a 2.3-fold increase in numbers of neurites in this length range with 50 nM Cu(II)(gtsm) treatment. The mechanism of neurogenerative action was investigated and revealed that Cu(II)(gtsm) inhibited cellular phosphatase activity. Treatment of cultures with 5 nM FK506 (calcineurin phosphatase inhibitor) resulted in analogous elongation of neurites compared to 50 nM Cu(II)(gtsm), suggesting a potential link between Cu(II)(gtsm)-mediated phosphatase inhibition and neurogenerative outcomes.

Differential regulation of proliferation and neuronal differentiation in adult rat spinal cord neural stem/progenitors by ERK1/2, Akt, and PLCγ

Proliferation of endogenous neural stem/progenitor cells (NSPCs) has been identified in both normal and injured adult mammalian spinal cord. Yet the signaling mechanisms underlying the regulation of adult spinal cord NSPCs proliferation and commitment toward a neuronal lineage remain undefined. In this study, the role of three growth factor-mediated signaling pathways in proliferation and neuronal differentiation was examined. Adult spinal cord NSPCs were enriched in the presence of fibroblast growth factor 2 (FGF2). We observed an increase in the number of cells expressing the microtubule-associated protein 2 (MAP2) over time, indicating neuronal differentiation in the culture. Inhibition of the mitogen-activated protein kinase or extracellular signal-regulated kinase (ERK) kinase 1 and 2/ERK 1 and 2 (MEK/ERK1/2) or the phosphoinositide 3-kinase (PI3K)/Akt pathways suppressed active proliferation in adult spinal cord NSPC cultures; whereas neuronal differentiation was negatively affected only when the ERK1/2 pathway was inhibited. Inhibition of the phospholipase Cγ (PLCγ) pathway did not affect proliferation or neuronal differentiation. Finally, we demonstrated that the blockade of either the ERK1/2 or PLCγ signaling pathways reduced neurite branching of MAP2+ cells derived from the NSPC cultures. Many of the MAP2+ cells expressed synaptophysin and had a glutamatergic phenotype, indicating that over time adult spinal cord NSPCs had differentiated into mostly glutamatergic neurons. Our work provides new information regarding the contribution of these pathways to the proliferation and neuronal differentiation of NSPCs derived from adult spinal cord cultures, and emphasizes that the contribution of these pathways is dependent on the origin of the NSPCs.

Biofunctionalized carbon nanotubes in neural regeneration: a mini-review

Carbon nanotubes (CNTs) have become an intriguing and promising biomaterial platform for the regeneration and functional recovery of damaged nerve tissues. The unique electrical, structural and mechanical properties, diversity of available surface chemistry and cell-penetrating ability of CNTs have made them useful implantable matrices or carriers for the delivery of therapeutic molecules. Although there are still challenges being faced in the clinical applications of CNTs mainly due to their toxicity, many studies to overcome this issue have been published. Modification of CNTs with chemical groups to ensure their dissolution in aqueous media is one possible solution. Functionalization of CNTs with biologically relevant and effective molecules (biofunctionalization) is also a promising strategy to provide better biocompatibility and selectivity for neural regeneration. Here, we review recent advances in the use of CNTs to promote neural regeneration.

Morphological assessment of neurite outgrowth in hippocampal neuron-astrocyte co-cultures

Neurite outgrowth is a fundamental event in brain development, as well as in regeneration of damaged neurons. Astrocytes play a major role in neuritogenesis, by expressing and releasing factors that facilitate neurite outgrowth, such as extracellular matrix proteins, and factors that can inhibit neuritogenesis, such as the chondroitin sulfate proteoglycan neurocan. In this unit we describe a noncontact co-culture system of hippocampal neurons and cortical (or hippocampal) astrocytes for measurement of neurite outgrowth. Hippocampal pyramidal neurons are plated on glass coverslips, which are inverted onto an astrocyte feeder layer, allowing exposure of neurons to astrocyte-derived factors without direct contact between these two cell types. After co-culture, neurons are stained and photographed, and processes are assessed morphologically using Metamorph software. This method allows exposing astrocytes to various agents before co-culture in order to assess how these exposures may influence the ability of astrocytes to foster neurite outgrowth.

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.

Modeling of Neuronal Growth In Vitro: Comparison of Simulation Tools NETMORPH and CX3D

We simulate the growth of neuronal networks using the two recently published tools, NETMORPH and CX3D. The goals of the work are (1) to examine and compare the simulation tools, (2) to construct a model of growth of neocortical cultures, and (3) to characterize the changes in network connectivity during growth, using standard graph theoretic methods. Parameters for the neocortical culture are chosen after consulting both the experimental and the computational work presented in the literature. The first (three) weeks in culture are known to be a time of development of extensive dendritic and axonal arbors and establishment of synaptic connections between the neurons. We simulate the growth of networks from day 1 to day 21. It is shown that for the properly selected parameters, the simulators can reproduce the experimentally obtained connectivity. The selected graph theoretic methods can capture the structural changes during growth.

Stochastic continuous time neurite branching models with tree and segment dependent rates

In this paper we introduce a continuous time stochastic neurite branching model closely related to the discrete time stochastic BES-model. The discrete time BES-model is underlying current attempts to simulate cortical development, but is difficult to analyze. The new continuous time formulation facilitates analytical treatment thus allowing us to examine the structure of the model more closely. We derive explicit expressions for the time dependent probabilities p(γ,t) for finding a tree γ at time t, valid for arbitrary continuous time branching models with tree and segment dependent branching rates. We show, for the specific case of the continuous time BES-model, that as expected from our model formulation, the sums needed to evaluate expectation values of functions of the terminal segment number μ(f(n),t) do not depend on the distribution of the total branching probability over the terminal segments. In addition, we derive a system of differential equations for the probabilities p(n,t) of finding n terminal segments at time t. For the continuous BES-model, this system of differential equations gives direct numerical access to functions only depending on the number of terminal segments, and we use this to evaluate the development of the mean and standard deviation of the number of terminal segments at a time t. For comparison we discuss two cases where mean and variance of the number of terminal segments are exactly solvable. Then we discuss the numerical evaluation of the S-dependence of the solutions for the continuous time BES-model. The numerical results show clearly that higher S values, i.e. values such that more proximal terminal segments have higher branching rates than more distal terminal segments, lead to more symmetrical trees as measured by three tree symmetry indicators.

Distance dependence of neuronal growth on nanopatterned gold surfaces

Understanding network development in the brain is of tremendous fundamental importance, but it is immensely challenging because of the complexity of both its architecture and function. The mechanisms of axonal navigation to target regions and the specific interactions with guidance factors such as membrane-bound proteins, chemical gradients, mechanical guidance cues, etc., are largely unknown. A current limitation for the study of neural network formation is the ability to control precisely the connectivity of small groups of neurons. A first step in designing such networks is to understand the "rules" central nervous system (CNS) neurons use to form functional connections with one another. Here we begin to delineate novel rules for growth and connectivity of small numbers of neurons patterned on Au substrates in simplified geometries. These studies yield new insights into the mechanisms determining the organizational features present in intact systems. We use a previously reported atomic force microscopy (AFM) nanolithography method to control precisely the location and growth of neurons on these surfaces. By examining a series of systems with different geometrical parameters, we quantitatively and systematically analyze how neuronal growth depends on these parameters.

Proteomic analysis of an alpha7 nicotinic acetylcholine receptor interactome

The alpha7 nicotinic acetylcholine receptor (nAChR) is well established as the principal high-affinity alpha-bungarotoxin-binding protein in the mammalian brain. We isolated carbachol-sensitive alpha-bungarotoxin-binding complexes from total mouse brain tissue by affinity immobilization followed by selective elution, and these proteins were fractionated by SDS-PAGE. The proteins in subdivided gel lane segments were tryptically digested, and the resulting peptides were analyzed by standard mass spectrometry. We identified 55 proteins in wild-type samples that were not present in comparable brain samples from alpha7 nAChR knockout mice that had been processed in a parallel fashion. Many of these 55 proteins are novel proteomic candidates for interaction partners of the alpha7 nAChR, and many are associated with multiple signaling pathways that may be implicated in alpha7 function in the central nervous system. The newly identified potential protein interactions, together with the general methodology that we introduce for alpha-bungarotoxin-binding protein complexes, form a new platform for many interesting follow-up studies aimed at elucidating the physiological role of neuronal alpha7 nAChRs.

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.

Sharpening of neurite morphology using complex coherence enhanced diffusion

The study of the molecular mechanisms involved in neurite outgrowth and differentiation, requires essential accurate and reproducible segmentation and quantification of neuronal processes. The common method used in this study is to detect and trace individual neurites, i.e. neurite tracing. The challenge comes mainly from the morphological problem in which these images contains ambiguities such as neurites discontinuities and intensity differences. In our work, we encounter a bigger challenge as the neurites in our images have a higher density of neurites. In this paper, we present a hybrid complex coherence-enhanced method for sharpening the morphology of neurons from such images. Coherence-enhanced diffusion (CED) is used to enhance the flowlike structures of the neurites, while the imaginary part of the complex nonlinear diffusion of the image cancels the appearance of 'clouds'. We also describe an elementary method for estimating the density of neuritis based on the obtained images. Our preliminary results show that the proposed methodology is a step ahead toward an effective neuronal morphology algorithm.

Computational model provides insight into the distinct responses of neurons to chemical and topographical cues

Neuronal cell polarization (i.e., establishment of an axon) and axon guidance are mediated and controlled by mechanical and chemical signals from the environment. Unfortunately, an integrated approach to study cell-substrate interactions in a unified framework incorporating structural and chemical effects of the substrate has been lacking. In this paper, we present a new model combining experimental and computational methods to better understand the distinct behavior of E18 hippocampal neurons in response to topographical vs. immobilized chemical cues. We present results from our coarse-grain physiological computational model that correctly describes previously observed phenomena and predicts behavior that was subsequently tested through new experiments. The model differentiates topographical from chemical cues via a difference in cue spacing in these two substrates. Using the feature size spacing for topographical cues and a minimum step size, governed by the physics of filopodia protrusion, for chemical cues, the model successfully mimics the trend observed in experimental polarization probability for four different topographical feature sizes and constant chemical cue spacing. Our results not only show good agreement with experiments, but also provide novel suggestions for development of substrates for finer control of neuronal cell polarization.

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."

Analysis of cultured neuronal networks using intraburst firing characteristics

It is an open question whether neuronal networks, cultured on multielectrode arrays, retain any capability to usefully process information (learning and memory). A necessary prerequisite for learning is that stimulation can induce lasting changes in the network. To observe these changes, one needs a method to describe the network in sufficient detail, while stable in normal circumstances. We analyzed the spontaneous bursting activity that is encountered in dissociated cultures of rat neocortical cells. Burst profiles (BPs) were made by estimating the instantaneous array-wide firing frequency. The shape of the BPs was found to be stable on a time scale of hours. Spatiotemporal detail is provided by analyzing the instantaneous firing frequency per electrode. The resulting phase profiles (PPs) were estimated by aligning BPs to their peak spiking rate over a period of 15 min. The PPs reveal a stable spatiotemporal pattern of activity during bursts over a period of several hours, making them useful for plasticity and learning studies. We also show that PPs can be used to estimate conditional firing probabilities. Doing so, yields an approach in which network bursting behavior and functional connectivity can be studied.

A new stochastic tridimensional model of neonatal rat spinal motoneuron for investigating compartmentalization of neuronal conductances and their influence on firing

During postnatal development spinal motoneurons play a major role in expressing basic behaviours like reflex reactions and in allowing the onset of the locomotor programme. For this purpose it is useful to clarify how various inputs are integrated at the level of the motoneuron soma to generate phasic or rhythmic firing. Although existing models of motoneurons have indicated the distributed role of certain conductances in regulating firing, it is unclear how the spatial distribution of certain currents is ultimately shaping motoneuron output. Thus, it would be helpful to build a bridge between histological and electrophysiological data. The present report is based on the construction of a 3D motoneuron model based on available parameters applicable to the neonatal spinal cord. The presented algorithm allows building up a complex, variable dendrogram which, together with the somatic and axonic compartments, enables strategic location of certain voltage or ligand gated conductances and simulation of resulting electrical behaviour. One application of the present model has been exploring the functional location of the recently reported cystic fibrosis transmembrane conductance regulator (CFTR) which controls Cl(-) homeostasis of postnatal motoneurons. The 3D model is made available for free, user friendly use via the dedicated web site http://www.mn-morphology.org.

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.

Contribution of mGluR and Fmr1 functional pathways to neurite morphogenesis, craniofacial development and fragile X syndrome

Fragile X Syndrome is a leading heritable cause of mental retardation that results from the loss of FMR1 gene function. Studies in mouse and Drosophila model organisms have been critical in understanding many aspects of the loss of function of the FMR1 gene in the human syndrome. Here, we establish that the zebrafish is a useful model organism for the study of the human fragile X syndrome and can be used to examine phenotypes that are difficult or inaccessible to observation in other model organisms. Using morpholino knockdown of the fmr1 gene, we observed abnormal axonal branching of Rohon-Beard and trigeminal ganglion neurons and guidance and defasciculation defects in the lateral longitudinal fasciculus. We demonstrate that this axonal branching defect can be rescued by treatment with MPEP [2-methyl-6-(phenylethynyl) pyridine]. This is consistent with an interaction between mGluR signalling and fmr1 function in neurite morphogenesis. We also describe novel findings of abnormalities in the abundance of trigeminal ganglion neurons and of craniofacial abnormalities apparently due to dysmorphic cartilage formation. These abnormalities may be related to a role for fmr1 in neural crest cell specification and possibly in migration.

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.