Biology subjects

Newton, P. K.

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

18 recordsLinked to original sources

bioRxiv2026

Generation-Establishment Tradeoffs Shape the Temporal Window of Recombinant Evolution

Recent viral coinfection experiments show that recombinant genomes are generated readily and depend strongly on infection timing and order, yet only a small fraction give rise to persistent lineages. We develop a hybrid deterministic-stochastic framework that resolves this discrepancy by coupling density-dependent recombinant generation with stochastic establishment of rare lineages. The resulting hazard of successful lineage formation is generically non-monotonic, increasing with parental abundance through enhanced generation while decreasing under competitive suppression, and exhibits a unique interior maximum in parental-density space. As parental populations evolve, their trajectory across this hazard landscape defines a sharply localized temporal window of evolutionary opportunity. These results reveal a general principle: evolutionary success is determined not only by intrinsic fitness, but by when variants arise within a dynamically changing ecological context.

biophysics↗

bioRxiv2025

Chemotherapy dose scheduling via Q-learning in a Markov tumor model

We describe a Q-learning approach to optimized chemotherapy dose scheduling in a stochastic finite-cell Markov process that models tumor cell natural selection dynamics. The three competing subpopulations comprising our virtual tumor are a chemo-sensitive population (S), and two chemo-resistant populations, R1 and R2, each resistant to one of two drugs, C1 and C2. The two drugs are toggled off or on which constitute the actions (selection pressure) imposed on our state-variables (S, R1, R2), measured as proportions in our finite state-space of N cancer cells (S + R1 + R2 = N). After the converged chemo-dosing policies are obtained, corresponding to a given reward structure, we focus on three important aspects of chemotherapy dose scheduling. First, we identify the most likely evolutionary paths of the tumor cell populations in response to the optimized (converged) policies. Second, we quantify the robustness in the ability to reach our target of balanced co-existence in light of incomplete information in both the initial cell-populations as well as the state-variables at each step. Third, we evaluate the efficacy of simplified policies which exploit the symmetries uncovered from an examination of the full policy. Our reward structure is designed to delay the onset of chemo-resistance in the tumor by rewarding a well-balanced mix of co-existing states, while punishing unbalanced subpopulations to avoid extinction.

systems biology↗

bioRxiv2024

Gaming the cancer-immunity cycle by synchronizing the dose schedules

We introduce a mathematical model of the cancer-immunity cycle and use it to test several hypotheses regarding the combination, timing, and optimization associated with chemotherapy and immunotherapy dosing schedules in the context of competition and selection pressure. A key conceptual idea is the value of synchronizing the dosing schedules with the fundamental period of the cancer-immunity cycle. The competitors in the population dynamics evolutionary game are the cancer cells, healthy cells, and T-cells, which form a non-transitive rock-paper-scissor chain, mediated by the tumor microenvironment. The chemotherapy and immunotherapy dosing schedules each act as control functions whose timing we synchronize with the fundamental period of the underlying nonlinear dynamical system. With the model, we show among other more detailed results, that chemotherapy and immunotherapy schedules are non-transitive; the best duration of the chemotherapy is around one-quarter of the cancer-immunity cycle, whereas for immunotherapy it is one-half cycle; immunotherapy dosing should preceed chemotherapy dosing. A general conclusion is that optimized timing of the dosing schedules can make up for lower total dose, opening up new possibilities for designing less toxic and more efficacious dosing regimens with drugs currently in use. Obtaining and calibrating more accurate measurements of the cycle-period across patient populations would be an important step in making some of these ideas clinically actionable.

systems biology↗

bioRxiv2024

Design of two-stage multi-drug chemotherapy schedules using replicator game dynamics

We use a replicator evolutionary game in conjunction with control theory to design a two-stage multidrug chemotherapy schedule where each stage has a specific design objective. In the first stage, we use optimal control theory that minimizes a cost function to design a transfer orbit which takes any initial tumor-cell frequency composition and steers it to a state-space region of three competing clonal subpopulations in which the three populations co-exist with a relatively equal abundance (high-entropy co-existence region). In the second stage, we use adaptive control with continuous monitoring of the subpopulation balance to design a maintenance orbit which keeps the subpopulations trapped in the favorable co-existence region to suppress the competitive release of a resistant cell population in order to avoid the onset of chemoresistance. Our controlled replicator dynamics model consists of a chemo-sensitive cell phenotype S, which is sensitive to both drugs, and two resistant cell phenotypes, R1 and R2, which are sensitive to drugs 1 and 2 respectively, but resistant to drug 2 and 1. The 3 x 3 payoff matrix used to define the fitness function associated with the interactions of the competing populations is a prisoners dilemma matrix which ensures that in the absence of chemotherapy, the S population (defectors) has higher fitness (reproductive prowess) than the two resistant cell populations, reflecting an inherent cost of resistance which our chemotherapy design methodology seeks to exploit. In our model, the two drugs C1 and C2 can act synergistically, additively, or antagonistically on the populations of cells as they compete and evolve under natural and artifical selection dynamics. Our model brings to light the inherent trade-offs between navigating to the maintenance orbit in minimal time vs. arriving there using the least total drug dose and also that the optimal balance of synergystic or antagonistic drug combinations depends the frequency balance of the populations of cells.

evolutionary biology↗

bioRxiv2022

Stochastic competitive release and adaptive chemotherapy

We develop a finite-cell model of tumor natural selection dynamics to investigate the stochastic fluctuations associated with multiple rounds of adaptive chemotherapy. The adaptive cycles are designed to avoid chemo-resistance in the tumor by managing the ecological mechanism of competitive release of a resistant sub-population. Our model is based on a three-component evolutionary game played among healthy (H), sensitive (S), and resistant (R) populations of N cells, with a chemotherapy control parameter, C(t), used to dynamically impose selection pressure on the sensitive sub-population to slow tumor growth but manage competitive release of the resistant population. The adaptive chemo-schedule is designed based on the deterministic (N [->] {infty}) adjusted replicator dynamical system, then implemented using the finite-cell stochastic frequency dependent Moran process model (N = 10K - 50K) to ascertain the size and variations of the stochastic fluctuations associated with the adaptive schedules. We quantify the stochastic fixation probability regions of the R and S populations in the HSR tri-linear phase plane as a function of the control parameter C [isin] [0, 1], showing that the size of the R region increases with increasing C. We then implement an adaptive time-dependent schedule C(t) for the stochastic model and quantify the variances (using principal component coordinates) associated with the evolutionary cycles for multiple rounds of adaptive therapy, showing they grow according to power-law scaling. The simplified low-dimensional model provides some insights on how well multiple rounds of adaptive therapies are likely to perform over a range of tumor sizes if the goal is to maintain a sustained balance among competing sub-populations of cells so as to avoid chemo-resistance via competitive release in a stochastic environment.

cancer biology↗

bioRxiv2021

Optimal dynamic incentive scheduling for Hawk-Dove evolutionary games

The Hawk-Dove mathematical game offers a paradigm of the trade-offs associated with aggressive and passive behaviors. When two (or more) populations of players (animals, insect populations, countries in military conflict, economic competitors, microbial communities, populations of co-evolving tumor cells, or reinforcement learners adopting different strategies) compete, their success or failure can be measured by their frequency in the population (successful behavior is reinforced, unsuccessful behavior is not), and the system is governed by the replicator dynamical system. We develop a time-dependent optimal-adaptive control theory for this nonlinear dynamical system in which the payoffs of the Hawk-Dove payoff matrix are dynamically altered (dynamic incentives) to produce (bang-bang) control schedules that (i) maximize the aggressive population at the end of time T, and (ii) minimize the aggressive population at the end of time T. These two distinct time-dependent strategies produce upper and lower bounds on the outcomes from all strategies since they represent two extremizers of the cost function using the Pontryagin maximum (minimum) principle. We extend the results forward to times nT (n = 1, ..., 5) in an adaptive way that uses the optimal value at the end of time nT to produce the new schedule for time (n + 1)T. Two special schedules and initial conditions are identified that produce absolute maximizers and minimizers over an arbitrary number of cycles for 0 [≤] T [≤] 3. For T > 3, our optimum schedules can drive either population to extinction or fixation. The method described can be used to produce optimal dynamic incentive schedules for many different applications in which the 2 x 2 replicator dynamics is used as a governing model.

evolutionary biology↗

bioRxiv2021

Are adaptive chemotherapy schedules robust? A three-strategy stochastic evolutionary game theory model

We investigate the robustness of adaptive chemotherapy schedules over repeated cycles and a wide range of tumor sizes. We introduce a non-stationary stochastic three-component fitness-dependent Moran process to quantify the variance of the response to treatment associated with multidrug adaptive schedules that are designed to mitigate chemotherapeutic resistance in an idealized (well-mixed) setting. The finite cell (N tumor cells) stochastic process consists of populations of chemosensitive cells, chemoresistant cells to drug 1, and chemoresistant cells to drug 2, and the drug interactions can be synergistic, additive, or antagonistic. First, the adaptive chemoschedule is determined by using the N [->] {infty} limit of the finite-cell process (i.e. the adjusted replicator equations) which is constructed by finding closed treatment response loops (which we call evolutionary cycles) in the three component phase-space. The schedules that give rise to these cycles are designed to manage chemoresistance by avoiding competitive release of the resistant cell populations. To address the question of how these cycles are likely to perform in practice over large patient populations with tumors across a range of sizes, we then consider the statistical variances associated with the approximate stochastic cycles for finite N, repeating the idealized adaptive schedule over multiple periods. For finite cell populations, the error distributions remain approximately multi-Gaussian in the principal component coordinates through the first three cycles, with variances increasing exponentially with each cycle. As the number of cycles increases, the multi-Gaussian nature of the distribution breaks down due to the fact that one of the three subpopulations typically saturates the tumor (competitive release) resulting in treatment failure. This suggests that to design an effective and repeatable adaptive chemoschedule in practice will require a highly accurate tumor model and accurate measurements of the subpopulation frequencies or the errors will quickly (exponentially) degrade its effectiveness, particularly when the drug interactions are synergistic. Possible ways to extend the efficacy of the stochastic cycles in light of the computational simulations are discussed. Prepared for Special IssueUnderstanding the Evolutionary Dynamics and Ecology of Cancer Treatment Resistance, Ed. D. Basanta, Cancers (2021)

biophysics↗

bioRxiv2020

Maximizing cooperation in the prisoner's dilemma evolutionary game via optimal control

The prisoners dilemma (PD) game offers a simple paradigm of competition between two players who can either cooperate or defect. Since defection is a strict Nash equilibrium, it is an asymptotically stable state of the replicator dynamical system that uses the PD payoff matrix to define the fitness landscape of two interacting evolving populations. The dilemma arises from the fact that the average payoff of this asymptotically stable state is sub-optimal. Coaxing the players to cooperate would result in a higher payoff for both. Here we develop an optimal control theory for the prisoners dilemma evolutionary game in order to maximize cooperation (minimize the defector population) over a given cycle-time T, subject to constraints. Our two time-dependent controllers are applied to the off-diagonal elements of the payoff matrix in a bang-bang sequence that dynamically changes the game being played by dynamically adjusting the payoffs, with optimal timing that depends on the initial population distributions. Over multiple cycles nT (n > 1), the method is adaptive as it uses the defector population at the end of the nth cycle to calculate the optimal schedule over the n + 1st cycle. The control method, based on Pontryagins maximum principle, can be viewed as determining the optimal way to dynamically alter incentives and penalties in order to maximize the probability of cooperation in settings that track dynamic changes in the frequency of strategists, with potential applications in evolutionary biology, economics, theoretical ecology, and other fields where the replicator system is used. PACS numbers02.50.Le; 02.30.Yy; 05.45.-a; 87.23.Kg; 87.23.Cc

evolutionary biology↗

bioRxiv2018

Towards multi-drug adaptive therapy

A new ecologically inspired paradigm in cancer treatment known as \"adaptive therapy\" capitalizes on competitive interactions between drug-sensitive and drug-resistant subclones. The goal of adaptive therapy is to maintain a controllable stable tumor burden by allowing a significant population of treatment sensitive cells to survive. These, in turn, suppress proliferation of the less fit resistant populations. However, there remain several open challenges in designing adaptive therapies, particularly in extending these therapeutic concepts to multiple treatments. We present a cancer treatment case study (metastatic castrate resistant prostate cancer) as a point of departure to illustrate three novel concepts to aid the design of multi-drug adaptive therapies. First, frequency-dependent \"cycles\" of tumor evolution can trap tumor evolution in a periodic, controllable loop. Second, the availability and selection of treatments may limit the evolutionary \"absorbing region\" reachable by the tumor. Third, the velocity of evolution significantly influences the optimal timing of drug sequences.

cancer biology↗

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↗