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.

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.

Role of social interactions in dynamic patterns of resource patches and forager aggregation.

The dynamics of resource patches and species that exploit such patches are of interest to ecologists, conservation biologists, modelers, and mathematicians. Here we consider how social interactions can create unique, evolving patterns in space and time. Whereas simple prey taxis (with consumable prey) promotes spatial uniform distributions, here we show that taxis in producer-scrounger groups can lead to pattern formation. We consider two types of foragers: those that search directly ("producers") and those that exploit other foragers to find food ("scroungers" or exploiters). We show that such groups can sustain fluctuating spatiotemporal patterns, akin to "waves of pursuit." Investigating the relative benefits to the individuals, we observed conditions under which either strategy leads to enhanced success, defined as net food consumption. Foragers that search for food directly have an advantage when food patches are localized. Those that seek aggregations of group mates do better when their ability to track group mates exceeds the foragers' food-sensing acuity. When behavioral switching or reproductive success of the strategies is included, the relative abundance of foragers and exploiters is dynamic over time, in contrast with classic models that predict stable frequencies. Our work shows the importance of considering two-way interaction--i.e., how food distribution both influences and is influenced by social foraging and aggregation of predators.

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.

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 temporal model of cofilin regulation and the early peak of actin barbed ends in invasive tumor cells.

Cofilin is an important regulator of actin polymerization, cell migration, and chemotaxis. Recent experimental data on mammary carcinoma cells reveal that stimulation by epidermal growth factor (EGF) generates a pool of active cofilin that results in a peak of actin filament barbed ends on the timescale of 1 min. Here, we present results of a mathematical model for the dynamics of cofilin and its transition between several pools in response to EGF stimulation. We describe the interactions of phospholipase C, membrane lipids (PIP(2)), and cofilin bound to PIP(2) and to F-actin, as well as diffusible cofilin in active G-actin-monomer-bound or phosphorylated states. We consider a simplified representation in which the thin cell edge (lamellipod) and the cell interior are represented by two compartments that are linked by diffusion. We demonstrate that a high basal level of active cofilin stored by binding to PIP(2), as well as the highly enriched local milieu of F-actin at the cell edge, is essential to capture the EGF-induced barbed-end amplification observed experimentally.

A Prototype QSP Model of the Immune Response to SARS-CoV-2 for Community Development.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic requires the rapid development of efficacious treatments for patients with life-threatening coronavirus disease 2019 (COVID-19). Quantitative systems pharmacology (QSP) models are mathematical representations of pathophysiology for simulating and predicting the effects of existing or putative therapies. The application of model-based approaches, including QSP, have accelerated the development of some novel therapeutics. Nevertheless, the development of disease-scale mechanistic models can be a slow process, often taking years to be validated and considered mature. Furthermore, emerging data may make any QSP model quickly obsolete. We present a prototype QSP model to facilitate further development by the scientific community. The model accounts for the interactions between viral dynamics, the major host immune response mediators and tissue damage and regeneration. The immune response is determined by viral activation of innate and adaptive immune processes that regulate viral clearance and cell damage. The prototype model captures two physiologically relevant outcomes following infection: a "healthy" immune response that appropriately defends against the virus, and an uncontrolled alveolar inflammatory response that is characteristic of acute respiratory distress syndrome. We aim to significantly shorten the typical QSP model development and validation timeline by encouraging community use, testing, and refinement of this prototype model. It is our expectation that the model will be further advanced in an open science approach (i.e., by multiple contributions toward a validated quantitative platform in an open forum), with the ultimate goal of informing and accelerating the development of safe and effective treatment options for patients.

Calsequestrin mediates changes in spontaneous calcium release profiles.

Calsequestrin (CSQ) is the primary calcium buffer within the sarcoplasmic reticulum (SR) of cardiac cells. It has also been identified as a regulator of Ryanodine receptor (RyR) calcium release channels by serving as a SR luminal sensor. When calsequestrin is free and unbound to calcium, it can bind to RyR and desensitize the channel from cytoplasmic calcium activation. In this paper, we study the role of CSQ as a buffer and RyR luminal sensor using a mechanistic model of RyR-CSQ interaction. By using various asymptotic approximations and mean first exit time calculation, we derive a minimal model of a calcium release unit which includes CSQ dependence. Using this model, we then analyze the effect of changing CSQ expression on the calcium release profile and the rate of spontaneous calcium release. We show that because of its buffering capability, increasing CSQ increases the spark duration and size. However, because of luminal sensing effects, increasing CSQ depresses the basal spark rate and increases the critical SR level for calcium release termination. Finally, we show that with increased bulk cytoplasmic calcium concentration, the CRU model exhibits deterministic oscillations.

A mathematical model of airway and pulmonary arteriole smooth muscle.

Airway hyperresponsiveness is a major characteristic of asthma and is believed to result from the excessive contraction of airway smooth muscle cells (SMCs). However, the identification of the mechanisms responsible for airway hyperresponsiveness is hindered by our limited understanding of how calcium (Ca2+), myosin light chain kinase (MLCK), and myosin light chain phosphatase (MLCP) interact to regulate airway SMC contraction. In this work, we present a modified Hai-Murphy cross-bridge model of SMC contraction that incorporates Ca2+ regulation of MLCK and MLCP. A comparative fit of the model simulations to experimental data predicts 1), that airway and arteriole SMC contraction is initiated by fast activation by Ca2+ of MLCK; 2), that airway SMC, but not arteriole SMC, is inhibited by a slower activation by Ca2+ of MLCP; and 3), that the presence of a contractile agonist inhibits MLCP to enhance the Ca2+ sensitivity of airway and arteriole SMCs. The implication of these findings is that murine airway SMCs exploit a Ca2+-dependent mechanism to favor a default state of relaxation. The rate of SMC relaxation is determined principally by the rate of release of the latch-bridge state, which is predicted to be faster in airway than in arteriole. In addition, the model also predicts that oscillations in calcium concentration, commonly observed during agonist-induced smooth muscle contraction, cause a significantly greater contraction than an elevated steady calcium concentration.

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.

Integrated Model of Chemical Perturbations of a Biological Pathway Using 18 In Vitro High-Throughput Screening Assays for the Estrogen Receptor.

We demonstrate a computational network model that integrates 18 in vitro, high-throughput screening assays measuring estrogen receptor (ER) binding, dimerization, chromatin binding, transcriptional activation, and ER-dependent cell proliferation. The network model uses activity patterns across the in vitro assays to predict whether a chemical is an ER agonist or antagonist, or is otherwise influencing the assays through a manner dependent on the physics and chemistry of the technology platform ("assay interference"). The method is applied to a library of 1812 commercial and environmental chemicals, including 45 ER positive and negative reference chemicals. Among the reference chemicals, the network model correctly identified the agonists and antagonists with the exception of very weak compounds whose activity was outside the concentration range tested. The model agonist score also correlated with the expected potency class of the active reference chemicals. Of the 1812 chemicals evaluated, 111 (6.1%) were predicted to be strongly ER active in agonist or antagonist mode. This dataset and model were also used to begin a systematic investigation of assay interference. The most prominent cause of false-positive activity (activity in an assay that is likely not due to interaction of the chemical with ER) is cytotoxicity. The model provides the ability to prioritize a large set of important environmental chemicals with human exposure potential for additional in vivo endocrine testing. Finally, this model is generalizable to any molecular pathway for which there are multiple upstream and downstream assays available.

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.