A Stochastic Compartmental Model for Fast Axonal Transport

In this paper we develop a probabilistic micro-scale compartmental model and use it to study macro-scale properties of axonal transport, the process by which intracellular cargo is moved in the axons of neurons. By directly modeling the smallest scale interactions, we can use recent microscopic experimental observations to infer all the parameters of the model. Then, using techniques from probability theory, we compute asymptotic limits of the stochastic behavior of individual motor-cargo complexes, while also characterizing both equilibrium and non-equilibrium ensemble behavior. We use these results in order to investigate three important biological questions: (1) How homogeneous are axons at stochastic equilibrium? (2) How quickly can axons return to stochastic equilibrium after large local perturbations? (3) How is our understanding of delivery time to a depleted target region changed by taking the whole cell point-of-view

Distribution and regulation of ion channels in neurons: Quantitative studies of global ion channel transport and homeostatic synaptic scaling

A healthy neuron must continually produce millions of proteins and distribute them to function-specific regions of the cell. Among these proteins are ion channels that modulate neuronal excitability, allowing neurons to fulfill their primary role of information transfer. Neurons are unique among cells in their morphology, with projections that extend hundreds to thousands of microns. Neuron size and asymmetry pose a challenge for autoregulation of properties that require cargo transport across the cell. Homeostasis of ion channel localization has strong implications for neural excitability. This thesis concerns the intracellular distribution of ion channels in the context of longitudinal transport and global neuron regulation. The principal contributions are experimental measurements, data analysis, and modeling in the study of longitudinal neurite transport. Empirical investigations focus on the distribution and trafficking kinetics of ion channel Kv4.2, including quantitative measurements of both passive diffusion and active microtubule-based transport in both axons and dendrites (Chapters 3 and 5). Mass action models reveal that measured transport profiles corroborate discrepancies in Kv4.2 localization both between neurite types and along the somatodendritic axis (Chapter 4). Exchange between mobile and immobile fractions, inferred from analysis of repeated photobleaching, shapes intracellular distribution of Kv4.2 (Chapter 5). Further, the ensuing theoretical study surveys global regulation of ion channels, specifically for synaptic scaling, which requires cell-wide modulation of AMPA receptors for normalization of neural excitability. A unified model of synaptic potentiation, transport, and feedback reveals limitations imposed on synaptic scaling by neuron morphology. A neuron balances the stability, accuracy, and efficiency of synaptic scaling (Chapter 6).National Institutes of Health Oxford-Cambridge Scholars Gates Cambridge University of North Carolina Medical Scientist Training Progra

The function of NaV1.8 clusters in lipid rafts

NaV1.8 is a voltage gated sodium channel mainly expressed on the membrane of thin diameter c-fibre neurons involved in the transmission of pain signals. In these neurons NaV1.8 is essential for the propagation of action potentials. NaV1.8 is located in lipid rafts along the axons of sensory neurons and disruption of these lipid rafts leads to NaV1.8 dependant conduction failure. Using computational modelling, I show that the clustering of NaV1.8 channels in lipid rafts along the axon of thin diameter neurons is energetically advantageous and requires fewer channels to conduct action potentials. During an action potential NaV1.8 currents across the membrane in these thin axons are large enough to dramatically change the sodium ion concentration gradient and thereby void the assumptions upon which the cable equation is based. Using scanning electron microscopy NaV1.8 is seen to be clustered, as are lipid raft marker proteins, on neurites at scales below 200nm. FRET signals show that the lipid raft marker protein Flotillin is densely packed on the membrane however disruption of rafts does not reduce the FRET signal from dense protein packing. Using mass spectrometry I investigated the population of proteins found in the lipid rafts of sensory neurons. I found that the membrane pump NaK-ATPase, which restores the ion concentrations across the membrane, is also contained in lipid rafts. NaK-ATPase may help to offset concentration changes due to NaV1.8 currents enabling the repeated firing of c-fibres, which is associated with spontaneous pain in chronic pain disorders.Open Acces

Entorhinal Denervation Induces Homeostatic Synaptic Scaling of Excitatory Postsynapses of Dentate Granule Cells in Mouse Organotypic Slice Cultures

Denervation-induced changes in excitatory synaptic strength were studied following entorhinal deafferentation of hippocampal granule cells in mature (≥3 weeks old) mouse organotypic entorhino-hippocampal slice cultures. Whole-cell patch-clamp recordings revealed an increase in excitatory synaptic strength in response to denervation during the first week after denervation. By the end of the second week synaptic strength had returned to baseline. Because these adaptations occurred in response to the loss of excitatory afferents, they appeared to be in line with a homeostatic adjustment of excitatory synaptic strength. To test whether denervation-induced changes in synaptic strength exploit similar mechanisms as homeostatic synaptic scaling following pharmacological activity blockade, we treated denervated cultures at 2 days post lesion for 2 days with tetrodotoxin. In these cultures, the effects of denervation and activity blockade were not additive, suggesting that similar mechanisms are involved. Finally, we investigated whether entorhinal denervation, which removes afferents from the distal dendrites of granule cells while leaving the associational afferents to the proximal dendrites of granule cells intact, results in a global or a local up-scaling of granule cell synapses. By using computational modeling and local electrical stimulations in Strontium (Sr2+)-containing bath solution, we found evidence for a lamina-specific increase in excitatory synaptic strength in the denervated outer molecular layer at 3–4 days post lesion. Taken together, our data show that entorhinal denervation results in homeostatic functional changes of excitatory postsynapses of denervated dentate granule cells in vitro

Queuing model of axonal transport

The motor-driven intracellular transport of vesicles to synaptic targets in the axons and dendrites of neurons plays a crucial role in normal cell function. Moreover, stimulus-dependent regulation of active transport is an important component of long-term synaptic plasticity, whereas the disruption of vesicular transport can lead to the onset of various neurodegenerative diseases. In this paper we investigate how the discrete and stochastic nature of vesicular transport in axons contributes to fluctuations in the accumulation of resources within synaptic targets. We begin by solving the first passage time problem of a single motor-cargo complex (particle) searching for synaptic targets distributed along a one-dimensional axonal cable. We then use queuing theory to analyze the accumulation of synaptic resources under the combined effects of multiple search-and-capture events and degradation. In particular, we determine the steady-state mean and variance of the distribution of synaptic resources along the axon in response to the periodic insertion of particles. The mean distribution recovers the spatially decaying distribution of resources familiar from deterministic population models. However, the discrete nature of vesicular transport can lead to Fano factors that are greater than unity (non-Poissonian) across the array of synapses, resulting in significant fluctuation bursts. We also find that each synaptic Fano factor is independent of the rate of particle insertion but increases monotonically with the amount of protein cargo in each vesicle. This implies that fluctuations can be reduced by increasing the injection rate while decreasing the cargo load of each vesicle

Doctor of Philosophy

dissertationWe formulate and analyze three spatio-temporal models for cell polarization in budding yeast, fission yeast, and the neuronal growth cone, respectively. We focus on the roles of diffusion and active transport of cytosolic molecules along cytoskeletal filaments on the establishment of a polarized distribution of membrane-bound molecules. Our first model couples the diffusion equation on a finite interval to a pair of delay differential equations at the boundaries. The model is used to study the oscillatory dynamics of the signaling molecule Cdc42 in fission yeast. We explore the effect of diffusion by performing a bifurcation analysis and find that the critical time delay for the onset of oscillations increases as the diffusion coefficient decreases. We then extend the model to a growing domain and show that there is a transition from asymmetric to symmetric oscillations as the cell grows. This is consistent with the experimental findings of “new-end-takeoff†in fission yeast. In our second model, we study the active transport of signaling molecules along a two-dimensional microtubule (MT) network in the neuronal growth cone. We consider a Rac1-stathmin-MT pathway and use a modified Dogteromâ€"Leibler model for the microtubule growth. In the presence of a nonuniform Rac1 concentration, we derive the resulting nonuniform length distribution of MTs and couple it to the active transport model. We calculate the polarized distribution of signaling molecules at the membrane using perturbation analysis and numerical simulation. We find the distribution is sensitive to the explicit Rac1 distribution and the stahmin-MT pathway. Our third model is a stochastic active transport model for vesicles containing signaling molecules in a filament network. We first derive the corresponding advection-diffusion model by a quasi-steady-state analysis. We find the diffusion is anisotropic and depends on the local density of filaments. The stability of the homogeneous steady state is sensitive to the geometry of filaments. For a parallelMTnetwork, the homogeneous steady state is linearly stable. For a network with filaments nucleated from the membrane (actin cytoskeleton), the homogeneous steady state is linearly unstable and a polarized distribution can occur

Probing brain microstructure with multidimensional diffusion MRI: Encoding, interpretation, and the role of exchange

Diffusion MRI (dMRI) is a non-invasive probe of human brain microstructure. It is a long-standing promise to use dMRI for ‘in vivo histology’ and estimate tissue quantities. However, this faces several challenges. First, the microstructure models used for dMRI data are based on assumptions that may cause erroneous interpretations. Also, probing neurites in gray matter assumes high microscopic diffusion anisotropy in both axons and dendrites, which is not supported by evidence. Furthermore, dMRI data analysis typically ignores diffusional exchange between microscopic environments. This thesis investigates and addresses these challenges using ‘multidimensional’ dMRI techniques that vary additional sequence encoding parameters to obtain new information on the tissue. In Paper I, we optimized an acquisition protocol for filter exchange imaging (FEXI). We found slow rates of diffusional exchange in normal brain tissue. In patients with gliomas and meningiomas, faster exchange was tentatively associated with higher tumor grade. In Paper II, we used tensor-valued diffusion encoding to test the NODDI microstructure model. The NODDI assumptions were contradicted by independent data and parameter estimates were found to be biased in normal brain and in gliomas. The CODIVIDE model combined data acquired with different b-tensor shapes to remove NODDI assumptions and reduce the susceptibility to bias. In Paper III, we used tensor-valued diffusion encoding with multiple echo times to investigate challenges in estimating neurite density. We found that microscopic anisotropy in the brain reflected axons but not dendrites. We could not separate the densities and T2 values of a two-component model in normal brain, but we did detect different component T2 values in white matter lesions. Microstructure models ranked regions from normal brain and white matter lesions inconsistently with respect to neurite density. In Paper IV, we optimized an acquisition protocol for tensor-valued diffusion encoding with multiple echo times. The data allowed removing all assumptions on diffusion and T2 relaxation from a two-component model. This increased the measurable parameters from two to six and reduced their susceptibility to bias. Data from the normal brain showed different component T2 values and contradicted common model assumptions. In Paper V, we used tensor-valued diffusion encoding in malformations of cortical development. Lesions that appeared gray matter-like in T1- and T2-weighted contrasts featured white matter-like regions with high microscopic diffusion anisotropy. We interpreted these regions as myelin-poor white matter with a high axonal content. By primarily reflecting axons and not dendrites or myelin, microscopic anisotropy may differentiate tissue where alterations to myelin confound conventional MRI contrasts. In Paper VI, we used SDE with multiple diffusion times in patients with acute ischemic stroke. Subacute lesions exhibited elevated diffusional exchange that predicted later infarction. MD reduction was partially reversible and did not predict infarction. Diffusional exchange may improve definition of ischemic core and identify additional patients for late revascularization

THE SYNERGISTIC INTERPLAY OF AMYLOID BETA AND TAU PROTEINS IN ALZHEIMER'S DISEASE: A COMPARTMENTAL MATHEMATICAL MODEL

The purpose of this Note is to present and discuss some mathematical results concerning a compartmental model for the synergistic interplay of Amyloid beta and tau proteins in the onset and progression of Alzheimer's disease. We model the possible mechanisms of interaction between the two proteins by a system of Smoluchowski equations for the Amyloid beta concentration, an evolution equation for the dynamics of misfolded tau and a kinetic-type transport equation for a function taking into accout the degree of malfunctioning of neurons. We provide a well-posedness results for our system of equations. This work extends results obtained in collaboration with M.Bertsch, B.Franchi and A.Tosin

A system-theoretic approach to global and local regulation in neuron morphologies

Synaptic plasticity is a crucial neuronal mechanism for learning and memory. It allows synapses to change their strength over time. This dissertation focuses on a particular form of synaptic plasticity called synaptic scaling, a homeostatic mechanism that preserves relative synaptic strengths in an activity-dependent manner. Synaptic scaling is fundamental for neuronal stability, regulating other plasticity mechanisms like Hebbian plasticity or long-term potentiation (LTP). The aims of this dissertation are to explore the implications of synaptic scaling (and other forms of plasticity, such as structural plasticity) on the overall behavior of neurons. This is done using system-theoretic tools and feedback control. We first formulate a biophysical closed loop model of synaptic scaling. We then study how synaptic scaling affect neurons’ behavior in both abstract and reconstructed morphologies. This study reveals important tradeoffs between robustness, convergence rate, and accuracy of scaling. We first look at synaptic scaling as a “global control action” whose main role is to guarantee a steady level of neural activity. We then consider activity-dependent degradation as a “local control action” whose role is to assist the neuron in fine-tuning different desirable spatial concentration profiles. We show that, in extreme scenarios, it can promote a level of competition between synapses that has a destabilizing effect on the overall behavior. At the methodological level, we use compartmental modeling and we focus on the in- teraction between feedback and transport, in linear and nonlinear settings. Using classical system-theoretic tools like Bode and Nyquist analysis and singular perturbation arguments, and more recent tools like contraction and dominance theory, we derive parameter ranges under which synaptic scaling is stable and well-behaved (slow regulation), stable and oscilla- tory (aggressive regulation), and unstable (pathological regulation). We also study the system robustness against static and dynamics uncertainties. Finally, to understand how different plasticity mechanisms simultaneously affect the neuron behavior, we study synaptic scaling in the presence of activity-dependent growth (mimicking a structural plasticity mechanism). This is a third layer of control action shaping the neuron morphology. We find that activity-dependent growth improves the neuron’s performance when synaptic scaling is insufficient