Control by Viability in a Chemotherapy Cancer Model Abstract The aim of this study is to provide a feedback control, called the Chemotherapy Protocol Law, with the purpose to keep the density of tumor cells that are treated by chemotherapy below a “tolerance level” \(L_c\), while retaining the density of normal cells above a “healthy level” \(N_c\). The mathematical model is a controlled dynamical system involving three nonlinear differential equations, based on a Gompertzian law of cell growth. By evoking viability and set-valued theories, we derive sufficient conditions for the existence of a Chemotherapy Protocol Law. Thereafter, on a suitable viability domain, we build a multifunction whose selections are the required Chemotherapy Protocol Laws. Finally, we propose a design of selection that generates a Chemotherapy Protocol Law.

Robust Model Selection and Estimation for Censored Survival Data with High Dimensional Genomic Covariates Abstract When relating genomic data to survival outcomes, there are three main challenges that are the censored survival outcomes, the high-dimensionality of the genomic data, and the non-normality of data. We propose a method to tackle these challenges simultaneously and obtain a robust estimation of detecting significant genes related to survival outcomes based on Accelerated Failure Time (AFT) model. Specifically, we include a general loss function to the AFT model, adopt model regularization and shrinkage technique, cope with parameters tuning and model selection, and develop an algorithm based on unified Expectation–Maximization approach for easy implementation. Simulation results demonstrate the advantages of the proposed method compared with existing methods when the data has heavy-tailed errors and correlated covariates. Two real case studies on patients are provided to illustrate the application of the proposed method.

Walking the Line: A Tempered View of Contingency and Convergence in Life’s History

Causally Modeling Adaptation to the Environment Abstract Brandon claims that to explain adaptation one must specify fitnesses in each selective environment and specify the distribution of individuals across selective environments. Glymour claims, using an example of the adaptive evolution of costly plasticity in a symmetric environment, that there are some predictive or explanatory tasks for which Brandon’s claim is limited. In this paper, I provide necessary conditions for carrying out Brandon’s task, produce a new version of the argument for his claim, and show that Glymour’s reasons for making his claim are problematic. I provide a few interpretations of Glymour’s argument but ultimately raise worries for what I take to be the key premises.

Clearing New Ground

On the Effect of Age-Dependent Mortality on the Stability of a System of Delay-Differential Equations Modeling Erythropoiesis Abstract We present an age-structured model for erythropoiesis in which the mortality of mature cells is described empirically by a physiologically realistic probability distribution of survival times. Under some assumptions, the model can be transformed into a system of delay differential equations with both constant and distributed delays. The stability of the equilibrium of this system and possible Hopf bifurcations are described for a number of probability distributions. Physiological motivation and interpretation of our results are provided.

Formalizing Metabolic-Regulatory Networks by Hybrid Automata Abstract Computational approaches in systems biology have become a powerful tool for understanding the fundamental mechanisms of cellular metabolism and regulation. However, the interplay between the regulatory and the metabolic system is still poorly understood. In particular, there is a need for formal mathematical frameworks that allow analyzing metabolism together with dynamic enzyme resources and regulatory events. Here, we introduce a metabolic-regulatory network model (MRN) that allows integrating metabolism with transcriptional regulation, macromolecule production and enzyme resources. Using this model, we show that the dynamic interplay between these different cellular processes can be formalized by a hybrid automaton, combining continuous dynamics and discrete control.

Phylogeny and Sequence Space: A Combined Approach to Analyze the Evolutionary Trajectories of Homologous Proteins. The Case Study of Aminodeoxychorismate Synthase Abstract During the course of evolution, variations of a protein sequence is an ongoing phenomenon however limited by the need to maintain its structural and functional integrity. Deciphering the evolutionary path of a protein is thus of fundamental interest. With the development of new methods to visualize high dimension spaces and the improvement of phylogenetic analysis tools, it is possible to study the evolutionary trajectories of proteins in the sequence space. Using the data-driven high-dimensional scaling method, we show that it is possible to predict and represent potential evolutionary trajectories by representing phylogenetic trees into a 3D projection of the sequence space. With the case of the aminodeoxychorismate synthase, an enzyme involved in folate synthesis, we show that this representation raises interesting questions about the complexity of the evolution of a given biological function, in particular concerning its capacity to explore the sequence space.

New Schemes of Dynamic Preservation of Diversity: Remarks on Stability and Topology Abstract We address the biological dynamics problem of the persistence of several species in conditions of non-existence of an equilibrium, including an example of stabilization by predation and the very controversial “competitive exclusion” (which depends on the precise definition of persistence). We give normal forms for various examples of such (essentially dynamical) persistence and comments on the involved topology, which implies the presence of exceptional heteroclinic connections binding equilibria on the boundary.

Genotype Components as Predictors of Phenotype in Model Gene Regulatory Networks Abstract Models of gene regulatory networks (GRN) have proven useful for understanding many aspects of the highly complex behavior of biological control networks. Randomly generated non-Boolean networks were used in experimental simulations to generate data on dynamic phenotypes as a function of several genotypic parameters. We found that predictive relationships between some phenotypes and quantitative genotypic parameters such as number of network genes, interaction density, and initial condition could be derived depending on the strength of the topological (positional) genotype on specific phenotypes. We quantitated the strength of the topological genotype effect (TGE) on a number of phenotypes in multi-gene networks. For phenotypes with a low influence of topological genotype, derived and empirical relationships using quantitative genotype parameters were accurate in phenotypic outcomes. We found a number of dynamic network properties, including oscillation behaviors, that were largely dependent on genotype topology, and for which no such general quantitative relationships were determinable. It remains to be determined if these results are applicable to biological gene regulatory networks.