Evolutionary models on graphs, as an extension of the Moran process, have two major implementations: birth–death (BD) models (or the invasion process) and death–birth (DB) models (or voter models). The isothermal theorem states that the fixation probability of mutants in a large group of graph structures (known as isothermal graphs, which include regular graphs) coincides with that for the mixed population. This result has been proved by Lieberman et al. (2005 Nature 433, 312–316. (doi:10.1038/nature0320410.1038/nature03204)) in the case of BD processes, where mutants differ from the wild-types by their birth rate (and not by their death rate). In this paper, we discuss to what extent the isothermal theorem can be formulated for DB processes, proving that it only holds for mutants that differ from the wild-type by their death rate (and not by their birth rate). For more general BD and DB processes with arbitrary birth and death rates of mutants, we show that the fixation probabilities of mutants are different from those obtained in the mass-action populations. We focus on spatial lattices and show that the difference between BD and DB processes on one- and two-dimensional lattices is non-small even for large population sizes. We support these results with a generating function approach that can be generalized to arbitrary graph structures. Finally, we discuss several biological applications of the results.

Understanding intrinsic and acquired resistance is crucial to overcoming cancer chemotherapy failure. While it is well-established that intratumor, subclonal genetic and phenotypic heterogeneity significantly contribute to resistance, it is not fully understood how tumor sub-clones interact with each other to withstand therapy pressure. Here, we report a previously unrecognized behavior in heterogeneous tumors: cooperative adaptation to therapy (CAT), in which cancer cells induce co-resistant phenotypes in neighboring cancer cells when exposed to cancer therapy. Using a CRISPR/Cas9 toolkit we engineered phenotypically diverse non-small cell lung cancer (NSCLC) cells by conferring mutations in Dicer1, a type III cytoplasmic endoribonuclease involved in small non-coding RNA genesis. We monitored three-dimensional growth dynamics of fluorescently-labeled mutant and/or wild-type cells individually or in co-culture using a substrate-free NanoCulture system under unstimulated or drug pressure conditions. By integrating mathematical modeling with flow cytometry, we characterized the growth patterns of mono- and co-cultures using a mathematical model of intra- and interspecies competition. Leveraging the flow cytometry data, we estimated the model’s parameters to reveal that the combination of WT and mutants in co-cultures allowed for beneficial growth in previously drug sensitive cells despite drug pressure via induction of cell state transitions described by a cooperative game theoretic change in the fitness values. Finally, we used an ex vivo human tumor model that predicts clinical response through drug sensitivity analyses and determined that cellular and morphologic heterogeneity correlates to prognostic failure of multiple clinically-approved and off-label drugs in individual NSCLC patient samples. Together, these findings present a new paradox in drug resistance implicating non-genetic cooperation among tumor cells to thwart drug pressure, suggesting that profiling for druggable targets (i.e. mutations) alone may be insufficient to assign effective therapy.

To explore the effects of the combination of tryptophan (Trp) and arginine (Arg) on growth performance, serum parameters and immune response of broiler chickens challenged with intermediate plus strain of infectious bursal disease virus vaccine, an in vivo experiment was conducted. A corn-soybean meal-based diet containing different levels of Arg and Trp was used. Cobb500 male broiler chickens from 0 to 49 days of age were subjected to a diet supplemented with the combination of Trp and Arg. Growth performance parameters and serum parameters were measured at 27 and 49 days of age. To evaluate the immunomodulatory effects of the combination of Trp and Arg on the challenged chickens, we measured the serum levels of interferon-α, interferon-γ and immunoglobulin G at 27, 35, 42, and 49 days of age. The results showed that the three evaluated immune system parameters including interferon-α, interferon-γ and immunoglobulin G were significantly enhanced after treatment. This enhancement resulted in the recovery of infectious bursal disease virus-infected chickens compared with controls as confirmed by histopathological examinations. Moreover, serum parameters such as albumin and total protein increased, whereas the treatment decreased (P<0.05) the feed:gain ratio, aspartate amino-transferase, alkaline phosphatase, lactic dehydrogenase, triglyceride and cholesterol. These findings suggest that the combination of Arg and Trp has a regulatory effect on growth performance. Moreover, it modulates the systemic immune response against infectious bursal disease.

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