Jill Gallaher

First order phase transition and hysteresis in a cell's maintenance of the membrane potential: An essential role for the inward potassium rectifiers

Hysteretic behavior is found experimentally in the transmembrane potential at low extracellular potassium in mouse lumbrical muscle cells. Adding isoprenaline to the external medium eliminates the bistable, hysteretic region. The system can be modeled mathematically and understood analytically with and without isoprenaline. Inward rectifying potassium channels appear to be essential for the bistability. Relations are derived to express the dimensions of the bistable area in terms of system parameters. The selective advantage and evolutionary origin of inward rectifying channels and hysteretic behavior is discussed.

Evolution of intratumoral phenotypic heterogeneity: the role of trait inheritance

A tumour is a heterogeneous population of cells that competes for limited resources. In the clinic, we typically probe the tumour by biopsy, and then characterize it by the dominant genetic clone. But genotypes are only the first link in the chain of hierarchical events that leads to a specific cell phenotype. The relationship between genotype and phenotype is not simple, and the so-called genotype to phenotype map is poorly understood. Many genotypes can produce the same phenotype, so genetic heterogeneity may not translate directly to phenotypic heterogeneity. We therefore choose to focus on the functional endpoint, the phenotype as defined by a collection of cellular traits (e.g. proliferative and migratory ability). Here, we will examine how phenotypic heterogeneity evolves in space and time and how the way in which phenotypes are inherited will drive this evolution. A tumour can be thought of as an ecosystem, which critically means that we cannot just consider it as a collection of mutated cells but more as a complex system of many interacting cellular and microenvironmental elements. At its simplest, a growing tumour with increased proliferation capacity must compete for space as a limited resource. Hypercellularity leads to a contact-inhibited core with a competitive proliferating rim. Evolution and selection occurs, and an individual cells capacity to survive and propagate is determined by its combination of traits and interaction with the environment. With heterogeneity in phenotypes, the clone that will dominate is not always obvious as there are both local interactions and global pressures. Several combinations of phenotypes can coexist, changing the fitness of the whole. To understand some aspects of heterogeneity in a growing tumour, we build an off-lattice agent-based model consisting of individual cells with assigned trait values for proliferation and migration rates. We represent heterogeneity in these traits with frequency distributions and combinations of traits with density maps. How the distributions change over time is dependent on how traits are passed on to progeny cells, which is our main enquiry. We bypass the translation of genetics to behaviour by focusing on the functional end result of inheritance of the phenotype combined with the environmental influence of limited space.

Bridging Population and Tissue Scale Tumor Dynamics: A New Paradigm for Understanding Differences in Tumor Growth and Metastatic Disease

To provide a better understanding of the relationship between primary tumor growth rates and metastatic burden, we present a method that bridges tumor growth dynamics at the population level, extracted from the SEER database, to those at the tissue level. Specifically, with this method, we are able to relate estimates of tumor growth rates and metastatic burden derived from a population-level model to estimates of the primary tumor vascular response and the circulating tumor cell (CTC) fraction derived from a tissue-level model. Variation in the population-level model parameters produces differences in cancer-specific survival and cure fraction. Variation in the tissue-level model parameters produces different primary tumor dynamics that subsequently lead to different growth dynamics of the CTCs. Our method to bridge the population and tissue scales was applied to lung and breast cancer separately, and the results were compared. The population model suggests that lung tumors grow faster and shed a significant number of lethal metastatic cells at small sizes, whereas breast tumors grow slower and do not significantly shed lethal metastatic cells until becoming larger. Although the tissue-level model does not explicitly model the metastatic population, we are able to disengage the direct dependency of the metastatic burden on primary tumor growth by introducing the CTC population as an intermediary and assuming dependency. We calibrate the tissue-level model to produce results consistent with the population model while also revealing a more dynamic relationship between the primary tumor and the CTCs. This leads to exponential tumor growth in lung and power law tumor growth in breast. We conclude that the vascular response of the primary tumor is a major player in the dynamics of both the primary tumor and the CTCs, and is significantly different in breast and lung cancer.

Spatial Heterogeneity and Evolutionary Dynamics Modulate Time to Recurrence in Continuous and Adaptive Cancer Therapies

Treatment of advanced cancers has benefited from new agents that supplement or bypass conventional therapies. However, even effective therapies fail as cancer cells deploy a wide range of resistance strategies. We propose that evolutionary dynamics ultimately determine survival and proliferation of resistant cells. Therefore, evolutionary strategies should be used with conventional therapies to delay or prevent resistance. Using an agent-based framework to model spatial competition among sensitive and resistant populations, we applied antiproliferative drug treatments to varying ratios of sensitive and resistant cells. We compared a continuous maximum-tolerated dose schedule with an adaptive schedule aimed at tumor control via competition between sensitive and resistant cells. Continuous treatment cured mostly sensitive tumors, but with any resistant cells, recurrence was inevitable. We identified two adaptive strategies that control heterogeneous tumors: dose modulation controls most tumors with less drug, while a more vacation-oriented schedule can control more invasive tumors. These findings offer potential modifications to treatment regimens that may improve outcomes and reduce resistance and recurrence.Significance: By using drug dose modulation or treatment vacations, adaptive therapy strategies control the emergence of tumor drug resistance by spatially suppressing less fit resistant populations in favor of treatment sensitive ones. Cancer Res; 78(8); 2127-39. ©2018 AACR.

The role of chloride transport in the control of the membrane potential in skeletal muscle — Theory and experiment

We present a model for the control of the transmembrane potential of mammalian skeletal muscle cell. The model involves active and passive transport of Na(+), K(+), and Cl(-). As we check the model against experimental measurements on murine skeletal muscle cells, we find that the model can account for the observed bistability of the transmembrane potential at low extracellular potassium concentration. The effect of bumetanide, a blocker of the Na,K,2Cl-cotransporter, is measured and modeled. A hyperosmotic medium is known to stimulate the Na,K,2Cl-cotransporter and we also measure and model the effects of such a medium. Increased chloride transport has two effects on the interval along the extracellular potassium concentration axis where the system is bistable: the interval is shifted towards higher potassium concentrations and the length of the interval is reduced. Finally, we also obtain estimates for the chloride permeability (P(Cl)=2x10(-5) cm/s), for the transmembrane chemical potential of chloride, and for the steady state flux through the Na,K,2Cl-cotransporter (2x10(-11) mol/cm(2) s for chloride).

ION TRAFFIC THROUGH A CELL MEMBRANE — AND HOW ITS 1/f NOISE CONNECTS TO GAMBLER'S RUIN, CATALAN NUMBERS AND ZIPF'S LAW

1/f Noise has been observed in currents through ion channels, in currents through pores in lipid bilayers, and in the voltage noise of live cells. In the case of the ion channels and bilayer pores, a mechanism has been proposed and corroborated. The mechanism appears robust and may share an underlying logic with Zipfs Law and Gamblers Ruin.

Comparative dynamics of microglial and glioma cell motility at the infiltrative margin of brain tumours

Microglia are a major cellular component of gliomas, and abundant in the centre of the tumour and at the infiltrative margins. While glioma is a notoriously infiltrative disease, the dynamics of microglia and glioma migratory patterns have not been well characterized. To investigate the migratory behaviour of microglia and glioma cells at the infiltrative edge, we performed two-colour time-lapse fluorescence microscopy of brain slices generated from a platelet-derived growth factor-B (PDGFB)-driven rat model of glioma, in which glioma cells and microglia were each labelled with one of two different fluorescent markers. We used mathematical techniques to analyse glioma cells and microglia motility with both single cell tracking and particle image velocimetry (PIV). Our results show microglia motility is strongly correlated with the presence of glioma, while the correlation of the speeds of glioma cells and microglia was variable and weak. Additionally, we showed that microglia and glioma cells exhibit different types of diffusive migratory behaviour. Microglia movement fit a simple random walk, while glioma cell movement fits a super diffusion pattern. These results show that glioma cells stimulate microglia motility at the infiltrative margins, creating a correlation between the spatial distribution of glioma cells and the pattern of microglia motility.

Adaptive Therapy For Heterogeneous Cancer: Exploiting Space And Trade-Offs In Drug Scheduling

The treatment of advanced cancers has greatly benefited from the introduction of new agents, such as targeted therapy and checkpoint inhibitors, to supplement or bypass conventional therapies. However, even the most effective therapy usually fails over time as cancer cells are able to deploy a wide range of molecular and micro environmental resistance strategies. Here we propose that, while molecular dynamics largely govern response and resistance to therapy, evolutionary dynamics determine survival and proliferation of treatment-resistant cells. We hypothesize that understanding these evolutionary interactions may identify strategies to delay or prevent proliferation of the resistant population using conventional therapies thus prolonging time to recurrence. Here we use an off-lattice, agent-based framework to model competition among sensitive and resistant populations during therapy in a spatially competitive resource-limited tumor micro environment. Our model applies a classic evolutionary trade-off between fecundity (cellular proliferation) and survivorship (drug sensitivity). We simulate the application of an anti-proliferative drug on varying ratios of mixed sensitive and resistant cells using two general treatment strategies: a continuous schedule of maximum tolerated dose or an evolution-informed schedule that incorporates dose modulation and treatment vacations to sustain control of the tumor through competition between sensitive and resistant cell populations. We find tumors consisting only of sensitive cells can be cured with continuous treatment, but the presence of any significant population of resistant cells will lead to eventual recurrence. We identify two treatment strategies that control heterogeneous tumors: one emphasizes continuous dose modulation, and the other relies on treatment vacations. Both strategies control tumors over a wide range of resistant/sensitive population ratios but the average dose given is significantly lower with dose modulation while a more vacation-oriented schedule can control more aggressive tumors.Treatment of advanced cancers has benefited from new agents that supplement or bypass conventional therapies. However, even effective therapies fail as cancer cells deploy a wide range of resistance strategies. We propose that evolutionary dynamics ultimately determine survival and proliferation of resistant cells, therefore evolutionary strategies should be used with conventional therapies to delay or prevent resistance. Using an agent-based framework to model spatial competition among sensitive and resistant populations, we apply anti-proliferative drug treatments to varying ratios of sensitive and resistant cells. We compare a continuous maximum tolerated dose schedule with an adaptive schedule aimed at tumor control through competition between sensitive and resistant cells. We find that continuous treatment cures mostly sensitive tumors, but with any resistant cells, recurrence is inevitable. We identify two adaptive strategies that control heterogeneous tumors: dose modulation controls most tumors with less drug, while a more vacation-oriented schedule can control more invasive tumors.

The dynamic tumor ecosystem: how cell turnover and trade-offs affect cancer evolution

Tumors are not static masses of cells but rather dynamic ecosystems where cancer cells experience constant turnover and evolve fitness-enhancing phenotypes. Selection for different phenotypes may vary with 1) the tumor niche (edge or core), 2) cell turnover rates, 3) the nature of the tradeoff between traits (proliferation vs migration), and 4) whether deaths occur in response to demographic or environmental stochasticity. In an agent based, spatially-explicit model, we observe how two traits (proliferation rate and migration speed) evolve under different trade-off conditions with different turnover rates. Migration rate is favored over proliferation at the tumor’s edge and vice-versa for the interior. Increasing cell turnover rates only slightly slows the growth of the tumor, but accelerates the rate of evolution for both proliferation and migration. The absence of a tradeoff favors ever higher values for proliferation and migration. A convex tradeoff tends to favor proliferation over migration while often promoting the coexistence of a generalist and specialist phenotype. A concave tradeoff slows the rate of evolution, and favors migration at low death rates and proliferation at higher death rates. Mortality via demographic stochasticity favors proliferation at the expense of migration; and vice-versa for environmental stochasticity. All of these factors and their interactions contribute to the ecology of the tumor, tumor heterogeneity, trait evolution, and phenotypic variation. While diverse, these effects may be predictable and empirically accessible.

Connecting the Microenvironmental Niche to Treatment Response in Ovarian Cancer

Ovarian cancer has the highest mortality rate of all gynecologic cancers, which may be attributed to an often late stage diagnosis, when the cancer is already metastatic, and rapid development of treatment resistance. We propose that the metastatic disease could be better characterized by observing interactions within the microenvironmental niche of the primary site that shapes the tumor’s early phenotypic progression. We present a mechanistic mathematical model of ovarian cancer that considers spatial interactions between tumor cells and several key stromal components. We demonstrate how spatial biomarker imaging data from the primary tumor can be analyzed to define a patient-specific microenvironment in the mathematical model. We then show preliminary results, using this model, that demonstrate how differences in the niche composition of a tumor affects phenotypic evolution and treatment response.