Error-induced extinction in a multi-type critical birth-death process.

Extreme mutation rates in microbes and cancer cells can result in error-induced extinction (EEX), where every descendant cell eventually acquires a lethal mutation. In this work, we investigate critical birth-death processes with n distinct types as a birth-death model of EEX in a growing population. Each type-i cell divides independently or mutates at the same rate.

Learning spatio-temporal patterns with Neural Cellular Automata.

Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and Partial Differential Equation (PDE) trajectories. Our method is designed to identify underlying local rules that govern large scale dynamic emergent behaviours.

Sequential mutations in exponentially growing populations.

Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with n alterations, and how long will it take for these cells to appear. For exponentially growing populations, these questions have been tackled only in special cases so far.

Interference with HIV infection of the first cell is essential for viral clearance at sub-optimal levels of drug inhibition.

HIV infection can be cleared with antiretroviral drugs if they are administered before exposure, where exposure occurs at low viral doses which infect one or few cells. However, infection clearance does not happen once infection is established, and this may be because of the very early formation of a reservoir of latently infected cells. Here we investigated whether initial low dose infection could be cleared with sub-optimal drug inhibition which allows ongoing viral replication, and hence does not require latency for viral persistence.

Competing evolutionary paths in growing populations with applications to multidrug resistance.

Investigating the emergence of a particular cell type is a recurring theme in models of growing cellular populations. The evolution of resistance to therapy is a classic example. Common questions are: when does the cell type first occur, and via which sequence of steps is it most likely to emerge? For growing populations, these questions can be formulated in a general framework of branching processes spreading through a graph from a root to a target vertex.

Universal Asymptotic Clone Size Distribution for General Population Growth.

Deterministically growing (wild-type) populations which seed stochastically developing mutant clones have found an expanding number of applications from microbial populations to cancer. The special case of exponential wild-type population growth, usually termed the Luria-Delbrück or Lea-Coulson model, is often assumed but seldom realistic. In this article, we generalise this model to different types of wild-type population growth, with mutants evolving as a birth-death branching process.

Spatial evolution of tumors with successive driver mutations.

We study the influence of driver mutations on the spatial evolutionary dynamics of solid tumors. We start with a cancer clone that expands uniformly in three dimensions giving rise to a spherical shape. We assume that cell division occurs on the surface of the growing tumor.

Evolutionary dynamics of cancer in response to targeted combination therapy.

In solid tumors, targeted treatments can lead to dramatic regressions, but responses are often short-lived because resistant cancer cells arise. The major strategy proposed for overcoming resistance is combination therapy. We present a mathematical model describing the evolutionary dynamics of lesions in response to treatment.

Molecular spiders on a plane.

Synthetic biomolecular spiders with "legs" made of single-stranded segments of DNA can move on a surface covered by single-stranded segments of DNA called substrates when the substrate DNA is complementary to the leg DNA. If the motion of a spider does not affect the substrates, the spider behaves asymptotically as a random walk. We study the diffusion coefficient and the number of visited sites for spiders moving on the square lattice with a substrate in each lattice site.

Distant metastasis occurs late during the genetic evolution of pancreatic cancer.

Metastasis, the dissemination and growth of neoplastic cells in an organ distinct from that in which they originated, is the most common cause of death in cancer patients. This is particularly true for pancreatic cancers, where most patients are diagnosed with metastatic disease and few show a sustained response to chemotherapy or radiation therapy. Whether the dismal prognosis of patients with pancreatic cancer compared to patients with other types of cancer is a result of late diagnosis or early dissemination of disease to distant organs is not known.

Accumulation of driver and passenger mutations during tumor progression.

Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. In the current study, we provide a mathematical model that begins to address this challenge.

Effect of stalling after mismatches on the error catastrophe in nonenzymatic nucleic acid replication.

The frequency of errors during genome replication limits the amount of functionally important information that can be passed on from generation to generation. During the origin of life, mutation rates are thought to have been quite high, raising a classic chicken-and-egg paradox: could nonenzymatic replication propagate sequences accurately enough to allow for the emergence of heritable function? Here we show that the theoretical limit on genomic information content may increase substantially as a consequence of dramatically slowed polymerization after mismatches. As a result of postmismatch stalling, accurate copies of a template tend to be completed more rapidly than mutant copies and the accurate copies can therefore begin a second round of replication more quickly.

Competition-colonization dynamics in an RNA virus.

During replication, RNA viruses rapidly generate diverse mutant progeny which differ in their ability to kill host cells. We report that the progeny of a single RNA viral genome diversified during hundreds of passages in cell culture and self-organized into two genetically distinct subpopulations that exhibited the competition-colonization dynamics previously recognized in many classical ecological systems. Viral colonizers alone were more efficient in killing cells than competitors in culture.

Evolutionary dynamics in structured populations.

Evolutionary dynamics shape the living world around us. At the centre of every evolutionary process is a population of reproducing individuals. The structure of that population affects evolutionary dynamics.

Shepherd model for knot-limited polymer ejection from a capsid.

We construct a tractable model to describe the rate at which a knotted polymer is ejected from a spherical capsid via a small pore. Knots are too large to fit through the pore and must reptate to the end of the polymer for ejection to occur. The reptation of knots is described by symmetric exclusion on the line, with the internal capsid pressure represented by an additional biased particle that drives knots to the end of the chain.

Mutation-selection equilibrium in games with mixed strategies.

We develop a new method for studying stochastic evolutionary game dynamics of mixed strategies. We consider the general situation: there are n pure strategies whose interactions are described by an nxn payoff matrix. Players can use mixed strategies, which are given by the vector (p(1),.

Evolutionary dynamics in set structured populations.

Evolutionary dynamics are strongly affected by population structure. The outcome of an evolutionary process in a well-mixed population can be very different from that in a structured population. We introduce a powerful method to study dynamical population structure: evolutionary set theory.

Evolution of cooperation by phenotypic similarity.

The emergence of cooperation in populations of selfish individuals is a fascinating topic that has inspired much work in theoretical biology. Here, we study the evolution of cooperation in a model where individuals are characterized by phenotypic properties that are visible to others. The population is well mixed in the sense that everyone is equally likely to interact with everyone else, but the behavioral strategies can depend on distance in phenotype space.

Strategy selection in structured populations.

Evolutionary game theory studies frequency dependent selection. The fitness of a strategy is not constant, but depends on the relative frequencies of strategies in the population. This type of evolutionary dynamics occurs in many settings of ecology, infectious disease dynamics, animal behavior and social interactions of humans.

Mutation-selection equilibrium in games with multiple strategies.

In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We explore stochastic evolutionary dynamics under weak selection, but for any mutation rate.

Strategy abundance in 2x2 games for arbitrary mutation rates.

We study evolutionary game dynamics in a well-mixed populations of finite size, N. A well-mixed population means that any two individuals are equally likely to interact. In particular we consider the average abundances of two strategies, A and B, under mutation and selection.

Cyclic neutropenia in mammals.

Cyclic neutropenia (CN) has been well documented in humans and the gray collie. A recent model of the architecture and dynamics of hematopoiesis has been used to provide insights into the mechanism of cycling of this disorder. It provides a link between the cycling period and the cells where the mutated ELA2 is expressed.

Voter models on heterogeneous networks.

We study simple interacting particle systems on heterogeneous networks, including the voter model and the invasion process. These are both two-state models in which in an update event an individual changes state to agree with a neighbor. For the voter model, an individual "imports" its state from a randomly chosen neighbor.

Comparative lesion sequencing provides insights into tumor evolution.

We show that the times separating the birth of benign, invasive, and metastatic tumor cells can be determined by analysis of the mutations they have in common. When combined with prior clinical observations, these analyses suggest the following general conclusions about colorectal tumorigenesis: (i) It takes approximately 17 years for a large benign tumor to evolve into an advanced cancer but <2 years for cells within that cancer to acquire the ability to metastasize; (ii) it requires few, if any, selective events to transform a highly invasive cancer cell into one with the capacity to metastasize; (iii) the process of cell culture ex vivo does not introduce new clonal mutations into colorectal tumor cell populations; and (iv) the rates at which point mutations develop in advanced cancers are similar to those of normal cells. These results have important implications for understanding human tumor pathogenesis, particularly those associated with metastasis.