Biology subjects

Newton, P. K.

Publications and source records attributed to Newton, P. K..

9 recordsLinked to original sources

bioRxiv2018

On the design of treatment schedules that avoid chemotherapeutic resistance

We introduce a method of designing treatment schedules for a model three-component replicator dynamical system that avoids chemotherapeutic resistance by controlling and managing the competitive release of resistant cells in the tumor. We use an evolutionary game theory model with prisoners dilemma payoff matrix that governs the competition among healthy cells, chemo-sensitive cells, and chemo-resistant cells and the goal is to control the evolution of chemo-resistance via the competitive release mechanism. The method is based on nonlinear trajectory design and energy transfer methods first introduced in the orbital mechanics literature for Hamiltonian systems. By using the structure of the trajectories defined by solutions of the replicator system for different constant chemotherapeutic concentrations (which produces a curvilinear coordinate system spanning the full region), we construct periodic (closed) orbits by switching the chemo-dose at carefully chosen times and appropriate levels to design schedules that are superior to both maximum tolerated dose (MTD) schedules and low-dose metronomic (LDM) schedules, both of which ultimately lead to fixation of either sensitive cells or resistant cells. By keeping the three sub-populations of cells in competition with each other, neither the sensitive cell population nor the resitant cell population are able to dominate as we balance the populations indefinitely (closed periodic orbits), thereby avoiding fixation of the cancer cell population and re-growth of a resistant tumor. The schedules we design have the feature that they maintain a higher average population fitness than either the MTD or the LDM schedules.\n\nPACS numbers: 87.23.Kg; 87.55.de; 87.19.Xj; 87.19.lr

cancer biology↗

bioRxiv2018

Cellular cooperation shapes tumor growth: a statistical mechanics mathematical model

A tumor is made up of a heterogeneous collection of cell types all competing on a fitness landscape mediated by micro-environmental conditions that dictate their interactions. Despite the fact that much is known about cell signaling and cellular cooperation, the specifics of how the cell-to-cell coupling and the range over which this coupling acts affect the macroscopic tumor growth laws that govern total volume, mass, and carrying capacity remain poorly understood. We develop a statistical mechanics approach that focuses on the total number of possible states each cell can occupy, and show how different assumptions on correlations of these states gives rise to the many different macroscopic tumor growth laws used in the literature. Although it is widely understood that molecular and cellular heterogeneity within a tumor is a driver of growth, here we emphasize that focusing on the functional coupling of these states at the cellular level is what determines macroscopic growth characteristics.\n\nSignificance statementA mathematical model relating tumor heterogeneity at the cellular level to tumor growth at the macroscopic level is described based on a statistical mechanics framework. The model takes into account the number of accessible states available to each cell as well as their long-range coupling (population cooperation) to other cells. We show that the degree to which cell populations cooperate determine the number of independent cell states, which in turn dictates the macroscopic (volumetric) growth law. It follows that targeting cell-to-cell interactions could be a way of mitigating and controlling tumor growth.

cancer biology↗

bioRxiv2018

Markov chain models of cancer metastasis

Abstract.We describe the use of Markov chain models for the purpose of quantitative forecasting of metastatic cancer progression. Each site (node) in the Markov network (directed graph) is an organ site where a secondary tumor could develop with some probability. The Markov matrix is an N x N matrix where each entry represents a transition probability of the disease progressing from one site to another during the course of the disease. The initial state-vector has a 1 at the position corresponding to the primary tumor, and 0s elsewhere (no initial metastases). The spread of the disease to other sites (metastases) is modeled as a directed random walk on the Markov network, moving from site to site with the estimated transition probabilities obtained from longitudinal data. The stochastic model produces probabilistic predictions of the likelihood of each metastatic pathway and corresponding time sequences obtained from computer Monte Carlo simulations. The main challenge is to empirically estimate the N^2 transition probabilities in the Markov matrix using appropriate longitudinal data.

cancer biology↗

bioRxiv2018

Optimizing chemo-scheduling based on tumor growth rates

We review the classic tumor growth and regression laws of Skipper and Schable based on fixed exponential growth assumptions, and Norton and Simons law based on a Gompertzian growth assumption. We then discuss ways to optimize chemotherapeutic scheduling using a Moran process evolutionary game-theory model of tumor growth that incorporates more general dynamical and evolutionary features of tumor cell kinetics. Using this model, and employing the quantitative notion of Shannon entropy which assigns high values to low-dose metronomic (LDM) therapies, and low values to maximum tolerated dose (MTD) therapies, we show that low-dose metronomic strategies can outperform maximum tolerated dose strategies, particularly for faster growing tumors. The general concept of designing different chemotherapeutic strategies for tumors with different growth characteristics is discussed.

cancer biology↗

bioRxiv2018

Competitive release in tumors

Competitive release is a bedrock principle of coevolutionary ecology and population dynamics. It is also the main mechanism by which heterogeneous tumors develop chemotherapeutic resistance. Understanding, controlling, and exploiting this important mechanism represents one of the key challenges and potential opportunities of current medical oncology. The development of sophisticated mathematical and computational models of coevolution among clonal and sub-clonal cell populations in the tumor ecosystem can guide us in predicting and shaping various responses to perturbations in the fitness landscape which is altered by chemo-toxic agents. This in turn can help us design adaptive chemotherapeutic strategies to combat the release resistant cells.

cancer biology↗

bioRxiv2017

Nonlinear dynamical shaping of the fitness landscape of an evolving tumor to combat competitive release

The development of chemotherapeutic resistance resulting in tumor relapse is largely the consequence of the mechanism of competitive release of pre-existing resistant tumor cells selected for regrowth after chemotherapeutic agents attack the previously dominant chemo-sensitive population. We introduce a prisoners dilemma mathematical model based on the replicator of three competing cell populations: healthy (cooperators), sensitive (defectors), and resistant (defectors) cells. The model is shown to recapitulate prostate-specific antigen measurement data from three clinical trials for metastatic castration-resistant prostate cancer patients treated with 1) prednisone, 2) mitoxantrone and prednisone and 3) docetaxel and prednisone. Continuous maximum tolerated dose schedules reduce the sensitive cell population, initially shrinking tumor volume, but subsequently \"release\" the resistant cells to re-populate and re-grow the tumor in a resistant form. Importantly, a model fit of prostate data shows the emergence of a positive fitness cost associated with a majority of patients for each drug, without predetermining a cost in the model a priori. While the specific mechanism associated with this cost may be very different for each of the drugs, a measurable fitness cost emerges in each. The evolutionary model allows us to quantify responses to conventional therapeutic strategies as well as to design adaptive strategies.

cancer biology↗

bioRxiv2017

Chemotherapeutic dose scheduling based on tumor growth rates: the case for low dose metronomic high entropy therapies

We extend classical tumor regression models, such as the Norton-Simon hypothesis, from instantaneous regression rates (i.e. the derivative) to the cumulative effect (i.e. the integral) over one (or many) cycles of chemotherapy. To achieve this end, we use a stochastic Moran process model of tumor cell kinetics, coupled with a prisoners dilemma game-theoretic cell-cell interaction model to design chemotherapeutic strategies tailored to different tumor growth characteristics. Using the Shannon entropy as a novel tool to quantify the success of dosing strategies, we contrast maximum tolerated dose (MTD) strategies as compared with low dose, high density metronomic strategies (LDM) for tumors with different growth rates. Our results show that LDM strategies can outperform MTD strategies in total tumor cell reduction (TCR). The advantage is magnified for fast growing tumors that thrive on long periods of unhindered growth without chemotherapy drugs present and is not evident after a single cycle of chemotherapy, but grows after each subsequent cycle of repeated chemotherapy. The model supports the concept of designing different chemotherapeutic schedules for tumors with different growth rates and develops quantitative tools to optimize these schedules for maintaining low volume tumors. The evolutionary model we introduce in this paper is compared with regression data from murine models and shown to be in good agreement.\n\nMajor FindingsModel simulations show that metronomic (low dose, high density) therapies can outperform maximum tolerated dose (high dose, low density) therapies. This is due to the fact that tumor cell reduction is more sensitive to changes in dose density than changes in dose concentration, especially for faster growing tumors. This effect is negligible after a single cycle of chemotherapy, but magnified after many cycles. The model also allows for novel chemotherapeutic schedules and quantifies their performance according to tumor growth rate.

cancer biology↗

bioRxiv2016

MultiCellDS: a standard and a community for sharing multicellular data

Cell biology is increasingly focused on cellular heterogeneity and multicellular systems. To make the fullest use of experimental, clinical, and computational efforts, we need standardized data formats, community-curated \"public data libraries\", and tools to combine and analyze shared data. To address these needs, our multidisciplinary community created MultiCellDS (MultiCellular Data Standard): an extensible standard, a library of digital cell lines and tissue snapshots, and support software. With the help of experimentalists, clinicians, modelers, and data and library scientists, we can grow this seed into a community-owned ecosystem of shared data and tools, to the benefit of basic science, engineering, and human health.

systems biology↗

bioRxiv2016

MultiCellDS: a community-developed standard for curating microenvironment-dependent multicellular data

Exchanging and understanding scientific data and their context represents a significant barrier to advancing research, especially with respect to information siloing. Maintaining information provenance and providing data curation and quality control help overcome common concerns and barriers to the effective sharing of scientific data. To address these problems in and the unique challenges of multicellular systems, we assembled a panel composed of investigators from several disciplines to create the MultiCellular Data Standard (MultiCellDS) with a use-case driven development process. The standard includes (1) digital cell lines, which are analogous to traditional biological cell lines, to record metadata, cellular microenvironment, and cellular phenotype variables of a biological cell line, (2) digital snapshots to consistently record simulation, experimental, and clinical data for multicellular systems, and (3) collections that can logically group digital cell lines and snapshots. We have created a MultiCellular DataBase (MultiCellDB) to store digital snapshots and the 200+ digital cell lines we have generated. MultiCellDS, by having a fixed standard, enables discoverability, extensibility, maintainability, searchability, and sustainability of data, creating biological applicability and clinical utility that permits us to identify upcoming challenges to uplift biology and strategies and therapies for improving human health.

systems biology↗