Nessy Tania

Coagulation under Flow: The Influence of Flow-Mediated Transport on the Initiation and Inhibition of Coagulation

A mathematical model of intravascular coagulation is presented; it encompasses the biochemistry of the tissue factor pathway, platelet activation and deposition on the subendothelium, and flow- and diffusion-mediated transport of coagulation proteins and platelets. Simulation experiments carried out with the model indicate the predominant role played by the physical processes of platelet deposition and flow-mediated removal of enzymes in inhibiting coagulation in the vicinity of vascular injury. Sufficiently rapid production of factors IXa and Xa by the TF:VIIa complex can overcome this inhibition and lead to formation of significant amounts of the tenase complex on the surface of activated platelets and, as a consequence, to substantial thrombin production. Chemical inhibitors are seen to play almost no (TFPI) or little (AT-III and APC) role in determining whether substantial thrombin production will occur. The role of APC is limited by the necessity for diffusion of thrombin from the site of injury to nearby endothelial cells to form the thrombomodulin-thrombin complex and for diffusion in the reverse direction of the APC made by this complex. TFPI plays an insignificant part in inhibiting the TF:VIIa complex under the conditions studied whether its action involves sequential binding of TFPI to Xa and then TFPI:Xa to TF:VIIa, or direct binding of TFPI to Xa already bound to the TF:VIIa complex.

Modeling the Synergy of Cofilin and Arp2/3 in Lamellipodial Protrusive Activity

Rapid polymerization of actin filament barbed ends generates protrusive forces at the cell edge, leading to cell migration. Two important regulators of free barbed ends, cofilin and Arp2/3, have been shown to work in synergy (net effect greater than additive). To explore this synergy, we model the dynamics of F-actin at the leading edge, motivated by data from EGF-stimulated mammary carcinoma cells. We study how synergy depends on the localized rates and relative timing of cofilin and Arp2/3 activation at the cell edge. The model incorporates diffusion of cofilin, membrane protrusion, F-actin capping, aging, and severing by cofilin and branch nucleation by Arp2/3 (but not G-actin recycling). In a well-mixed system, cofilin and Arp2/3 can each generate a large pulse of barbed ends on their own, but have little synergy; high synergy occurs only at low activation rates, when few barbed ends are produced. In the full spatially distributed model, both synergy and barbed-end production are significant over a range of activation rates. Furthermore, barbed-end production is greatest when Arp2/3 activation is delayed relative to cofilin. Our model supports a direct role for cofilin-mediated actin polymerization in stimulated cell migration, including chemotaxis and cancer invasion.

Kif11 dependent cell cycle progression in radial glial cells is required for proper neurogenesis in the zebrafish neural tube

Radial glia serve as the resident neural stem cells in the embryonic vertebrate nervous system, and their proliferation must be tightly regulated to generate the correct number of neuronal and glial cell progeny in the neural tube. During a forward genetic screen, we recently identified a zebrafish mutant in the kif11 loci that displayed a significant increase in radial glial cell bodies at the ventricular zone of the spinal cord. Kif11, also known as Eg5, is a kinesin-related, plus-end directed motor protein responsible for stabilizing and separating the bipolar mitotic spindle. We show here that Gfap+ radial glial cells express kif11 in the ventricular zone and floor plate. Loss of Kif11 by mutation or pharmacological inhibition with S-trityl-L-cysteine (STLC) results in monoastral spindle formation in radial glial cells, which is characteristic of mitotic arrest. We show that M-phase radial glia accumulate over time at the ventricular zone in kif11 mutants and STLC treated embryos. Mathematical modeling of the radial glial accumulation in kif11 mutants not only confirmed an ~226× delay in mitotic exit (likely a mitotic arrest), but also predicted two modes of increased cell death. These modeling predictions were supported by an increase in the apoptosis marker, anti-activated Caspase-3, which was also found to be inversely proportional to a decrease in cell proliferation. In addition, treatment with STLC at different stages of neural development uncovered two critical periods that most significantly require Kif11 function for stem cell progression through mitosis. We also show that loss of Kif11 function causes specific reductions in oligodendroglia and secondary interneurons and motorneurons, suggesting these later born populations require proper radial glia division. Despite these alterations to cell cycle dynamics, survival, and neurogenesis, we document unchanged cell densities within the neural tube in kif11 mutants, suggesting that a mechanism of compensatory regulation may exist to maintain overall proportions in the neural tube. We propose a model in which Kif11 normally functions during mitotic spindle formation to facilitate the progression of radial glia through mitosis, which leads to the maturation of progeny into specific secondary neuronal and glial lineages in the developing neural tube.

The effects of facilitation and competition on group foraging in patches

Significant progress has been made towards understanding the social behaviour of animal groups, but the patch model, a foundation of foraging theory, has received little attention in a social context. The effect of competition on the optimal time to leave a foraging patch was considered as early as the original formulation of the marginal value theorem, but surprisingly, the role of facilitation (where foraging in groups decreases the time to find food in patches), has not been incorporated. Here we adapt the classic patch model to consider how the trade-off between facilitation and competition influences optimal group size. Using simple assumptions about the effect of group size on the food-finding time and the sharing of resources, we find conditions for existence of optima in patch residence time and in group size. When patches are close together (low travel times), larger group sizes are optimal. Groups are predicted to exploit patches differently than individual foragers and the degree of patch depletion at departure depends on the details of the trade-off between competition and facilitation. A variety of currencies and group-size effects are also considered and compared. Using our simple formulation, we also study the effects of social foraging on patch exploitation which to date have received little empirical study.

A Mathematical Model for Tumor–Immune Dynamics in Multiple Myeloma

We propose a mathematical model that describes the dynamics of multiple myeloma and three distinct populations of the innate and adaptive immune system: cytotoxic T cells, natural killer cells, and regulatory T cells. The model includes significant biologically- and therapeutically-relevant pathways for inhibitory and stimulatory interactions between these populations. Due to the model complexity, we propose a reduced version that captures the principal biological aspects for advanced disease, while still including potential targets for therapeutic interventions. Analysis of the reduced two-dimensional model revealed details about long-term model behavior. In particular, theoretical results describing equilibria and their associated stability are described in detail. Consistent with the theoretical analysis, numerical results reveal parameter regions for which bistability exits. The two stable states in these cases may correspond to long-term disease control or a higher level of disease burden. This initial analysis of the dynamical system provides a foundation for later work, which will consider combination therapies, their expected outcomes, and optimization of regimens.

Mathematical Modeling and Analyses of Interspike-Intervals of Spontaneous Activity in Afferent Neurons of the Zebrafish Lateral Line

Without stimuli, hair cells spontaneously release neurotransmitter leading to spontaneous generation of action potentials (spikes) in innervating afferent neurons. We analyzed spontaneous spike patterns recorded from the lateral line of zebrafish and found that distributions of interspike intervals (ISIs) either have an exponential shape or an “L” shape that is characterized by a sharp decay but wide tail. ISI data were fitted to renewal-process models that accounted for the neuron refractory periods and hair-cell synaptic release. Modeling the timing of synaptic release using a mixture of two exponential distributions yielded the best fit for our ISI data. Additionally, lateral line ISIs displayed positive serial correlation and appeared to exhibit switching between faster and slower modes of spike generation. This pattern contrasts with previous findings from the auditory system where ISIs tended to have negative serial correlation due to synaptic depletion. We propose that afferent neuron innervation with multiple and heterogenous hair-cells synapses, each influenced by changes in calcium domains, can serve as a mechanism for the random switching behavior. Overall, our analyses provide evidence of how physiological similarities and differences between synapses and innervation patterns in the auditory, vestibular, and lateral line systems can lead to variations in spontaneous activity.

Methods for determining key components in a mathematical model for tumor–immune dynamics in multiple myeloma

In this work, we analyze a mathematical model we introduced previously for the dynamics of multiple myeloma and the immune system. We focus on four main aspects: (1) obtaining and justifying ranges and values for all parameters in the model; (2) determining a subset of parameters to which the model is most sensitive; (3) determining which parameters in this subset can be uniquely estimated given certain types of data; and (4) exploring the model numerically. Using global sensitivity analysis techniques, we found that the model is most sensitive to certain growth, loss, and efficacy parameters. This analysis provides the foundation for a future application of the model: prediction of optimal combination regimens in patients with multiple myeloma.

Mathematical Modeling and Analyses of Interspike-Intervals of Spontaneous Activity in Afferent Neurons of the Zebrafish Lateral-Line

Temporal patterns of spontaneous activity may vary between sensory systems such as the auditory, vestibular, and lateral line systems due to differences in physiology at the level of hair cells. In the absence of stimuli, hair cells display spontaneous synaptic vesicle fusion and neurotransmitter release, which lead to action potential (spike) generation in innervating afferent neurons. As a result, features of synaptic transmission and the innervation of hair cells will affect the timing of spontaneous spike trains. We analyzed spontaneous spiking recorded from the lateral line of zebrafish, and found that the distribution of interspike-intervals (ISI) had an “L-shape” that decayed faster and had a wider tail than a typical exponential distribution commonly observed in other models of spike timing. Additionally, successive ISIs in the lateral line recordings tended to have positive serial correlation, i.e., successive ISI pairs were either short/short or long/long. This pattern contrasts previous findings from the auditory system where ISIs tended to have negative serial correlation presumably due to the effects of synaptic depletion. Computational models of spike trains that included the calcium-dependency of neurotransmitter release at the ribbon synapse of hair cells were able to generate ISI distributions consistent with those we acquired experimentally. These simulations suggested that fluctuations in total calcium channel activity, including both the number and cooperativity of channels in the population, are a primary contributor to serial correlations in hair-cell evoked spike trains. Given the difference in innervation pattern between auditory and vestibular/lateral line hair cells, we further modeled the effects of single versus multiple synapses on the temporal patterns of spontaneous spike trains. Altogether, our findings provide evidence for how physiological similarities and differences between the auditory, vestibular, and lateral line systems can account for differences in spontaneous activity. Furthermore, our computational methods allow for future characterization of mechanisms that underlie spontaneous activity in these different sensory systems.