Evolution of Biological Systems in Random Media: Limit Theorems and Stability

Snake venomics: From the inventory of toxins to biology

Optimality models used in behavioral ecology, and especially on insect parasitoids, have taken a variety of approaches, from classical analytical tools to individualbased simulations. The increasing awareness that much of the observable behavior in parasitoids depends on the state of the insect (be it the physiological or informational state) has led to the increasing use of stochastic dynamic programming models. However, optimal behaviors of one individual often depend upon the behavior of conspecifics, further complicating the issue. While classical game theory may be applied when behavior is not state dependent, genetic algorithms (GA) provide a powerful way in finding optimal behaviors for situations where such optimal behavior depends upon an animal’s state and on the frequency of alternative behaviors of conspecifics. More generally, GAs can be used when there is a need to find the optimal strategy among a number of different alternative behaviors whose number is far too great to be exhaustively checked. GAs are search algorithms that proceed in a fashion analogous to natural selection. They are individual-based simulations that identify optimal solutions by searching the enormous space of potential solutions mimicking the process of evolution in biological systems. In this chapter, we discuss research questions in parasitoid behavioral ecology that might benefit from applying GA as a research tool for optimality models. Examples will be developed and explained. Among others, using the foraging problem of estimating habitat quality, we show how fast GAs find optimal solutions for parameter spaces that are impossible to solve numerically otherwise.

Recent studies in the green alga Chlamydomonas and other flagellated cells have revealed new insights into the relationships between the structure and function of the eukaryotic flagellum. These advances provide a basis from which a unified view can be constructed of how a flagellum operates. In addition, investigations of flagellar assembly offer new perspectives revealing the mechanisms used by cells to create these nanoscale structures. New developments in the molecular biology of Chlamydomonas provide powerful tools for the continued exploration of flagellar biology in this cell. These studies are of interest not only within the field of biology, but also in physics and materials science; the problems of fabrication, assembly, function and regulation of nanoscale machines have been elegantly solved during the evolution of biological systems, providing models from which much remains to be learned.

The laws of classical mechanics and quantum theory do not distinguish between the past and the future. But a lot of phenomena tell us that the "arrow of time" points only in one direction. For example, in biology we discover evolutionary processes leading to diversification and increasing complexity; it is a typical feature of such evolutionary processes that "forward" in time is possible but "backward" in time is impossible. At what level can phenomena like these be described? There is another problem in connection with time: within usual quantum theory, space-coordinates and time are not symmetrical to each other, which is in contrast to the basic results of special theory of relativity. In usual quantum theory coordinates are operators and play the role of statistical quantities; time however does not behave statistically and remains a simple parameter when we go from classical to quantum mechanics. For this reason there is no uncertainty relation for the time and energy within usual quantum theory which would agree in its physical content with that for the coordinates and momenta. The purpose of this paper is to show, on the basis of new aspects, that both one-sidedness of time and its uncertainty are charateristics at the fundamental level of quantum theory. We have extended usual quantum theory on the basis of space-time arguments. In this connection a time-operator appeared and there is in general temporal asymmetry at the microscopic level. The picture might be important in the description of phenomena with an "arrow of time", i.e., processes which belong to the physics of becoming. Furthermore, we have derived an uncertainty relation for the energy and time which agrees in its physical content with the uncertainty relation for the momentum and the coordinate; this relation is different from that of usual quantum theory. Within the frame of this physical picture all the concepts (diversity, natural selection, mutation), which are presently used in connection with the evolution of biological systems, are already established at the quantum mechanical level and, therefore, our theoretical picture might also be the foundation for the explanation of the phenomena at the biological (macro-molecular) level.

The presence of heavy metals in the environment can lead to ecological and health problems. The evolution of biological systems, such as activated sludge, exposed to heavy metals is still underexplored. Therefore, this study sought to develop a model of microorganism activity and growth in activated sludge and used it to investigate the toxicity of five metals: Cu, Cd, Ni, Zn, and Ag. Patterns in the evolution of the toxic effects caused by these metals were similar at the beginning of exposure. Differences in toxicity between metal ions were noted for longer exposure times. Changes in model parameters indicate the influence of metal ions on the mass and energy balance of living cells. Decreases in new enzyme units and biomass production yields in contaminated activated sludge indicate a shift from anabolic reactions to metal homeostasis and resistance.

The evolution of biological systems is strongly influenced by physical factors, such as applied forces, geometry or the stiffness of the micro-environment. Mechanical changes are particularly important in solid tumour development, as altered stromal-epithelial interactions can provoke a persistent increase in cytoskeletal tension, driving the gene expression of a malignant phenotype. In this work, we propose a novel multi-scale treatment of mechano-transduction in cancer growth. The avascular tumour is modelled as an expanding elastic spheroid, whilst growth may occur both as a volume increase and as a mass production within a cell rim. Considering the physical constraints of an outer healthy tissue, we derive the thermo-dynamical requirements for coupling growth rate, solid stress and diffusing biomolecules inside a heterogeneous tumour. The theoretical predictions successfully reproduce the stress-dependent growth curves observed by in vitro experiments on multicellular spheroids.

Inspired by the evolution of biological systems, genetic algorithms have been applied to generate solutions for optimization problems in a variety of scientific and engineering disciplines. For a given problem, a suitable genome representation must be defined along with a mutation operator to generate subsequent generations. Unlike natural systems, which display a variety of complex rearrangements (e.g., mobile genetic elements), mutation for genetic algorithms commonly utilizes only random pointwise changes. Furthermore, generalizing beyond pointwise mutations poses a key difficulty as useful genome rearrangements depend on the representation and problem domain. To move beyond the limitations of manually defined pointwise changes, here we propose the use of techniques from masked language models to automatically generate mutations. As a first step, common subsequences within a given population are used to generate a vocabulary. The vocabulary is then used to tokenize each genome. A masked language model is trained on the tokenized data in order to generate possible rearrangements (i.e., mutations). In order to illustrate the proposed strategy, we use string representations of molecules and use a genetic algorithm to optimize for drug-likeness and synthesizability. Our results show that moving beyond random pointwise mutations accelerates genetic algorithm optimization.

Most biologists agree that evolution is contingent on inherited information shaped by natural selection. This apparent consensus could be taken to indicate agreement on the forces shaping evolution, but vivid discussions reveal divergences on how evolution is perceived. The predominant Modern Synthesis (MS) paradigm holds the position that evolution occurs through random changes acting on genomic inheritance. However, studies from recent decades have revealed that evolutionary inheritance also includes DNA-methylation, RNA, symbionts, and culture, among other factors. This has fueled a demand of a broader evolutionary perspective, for example from the proponents of the Extended Evolutionary Synthesis (EES). Despite fundamental disagreements the different views agree that natural selection happens through dissimilar perpetuation of inheritable information. Yet, neither the MS, nor the ESS dwell extensively on the nature of hereditary information. We do - and conclude that information in and of itself is immaterial. We then argue that the quality upon which natural selection acts henceforth is also immaterial. Based on these notions, we arrive at the information-centric Information Continuum Model (ICM) of evolution. The ICM asserts that hereditary information is embedded in diverse physical forms (DNA, RNA, symbionts etc.) representing a continuum of evolutionary qualities, and that information may migrate between these physical forms. The ICM leaves theoretical exploration of evolution unrestricted by the limitations imposed by the individual physical forms wherein the hereditary information is embedded (e.g. genomes). ICM bestows us with a simple heuristic model that adds explanatory dimensions to be considered in the evolution of biological systems.

Variation coupled to selection is the hallmark of natural evolution. Although there is no full agreement concerning the best way to create variation, mutation or recombination (1), computational simulation studies have demonstrated the importance of homologous recombination in the evolution of biological systems (2,3). As compared to random mutagenesis, recombination may be advantageous in combining beneficial mutations that have arisen independently and may be synergistic, while simultaneously removing deleterious mutations.KeywordsRandom MutagenesisExonuclease ActivityKlenow FragmentElongation TimeDirected Evolution MethodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Interactions among proteins mediate regulatory, mechanical, structural and transport functions and are fundamental in the modulation of all cellular activities. About 15 years ago, it was first noted that physical interactions link most if not all proteins to each other in complex networks. The analysis of maps representing current knowledge about these molecular networks can provide insights that range from specific hypotheses on the function of a given protein to system‐level properties on the organisation or evolution of biological systems. Here, we provide an updated introduction to the numerous ways and available tools by which protein–protein interaction maps can be analysed, and caveats that need to be kept in mind. Key Concepts Protein–protein interaction maps are important tools to develop functional hypothesis, contextualise ‘omic’ gene lists, analyse system properties and systems evolution and provide an important basis for analysing system dynamics. Networks can be assembled from small‐scale literature data, bioinformatic prediction and experimental high‐throughput technologies of which affinity‐purification followed by mass spectrometry or binary yeast‐based assays are most common. Global and local properties of protein–protein interaction maps can be influenced by sociological, technological and experimental biases that need to be taken into account. High‐throughput technologies can provide data that are in quality at least comparable to the high‐quality fraction from small‐scale studies in public databases. Carefully benchmarked and appropriate quality controls must be implemented for all approaches. Binary and co‐complex methodologies give rise to differential and complementary sets of protein interactions. Bioinformatic tools are available that enable nonspecialists to analyse and use protein–protein interaction networks.

We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme value statistics of correlated variables. The distribution is Gaussian for all periodic systems, while in the case of random manifolds there exists a family of universal functions ranging from the Gaussian to the Gumbel distribution. Both of these scenarios are a priori experimentally accessible in finite, macroscopic, disordered elastic systems.

Article Limit theorems for difference equations in random media with applications to biological systems was published on March 1, 2003 in the journal Random Operators and Stochastic Equations (volume 11, issue 1).

We consider random walks on $\Z$ in a stationary random medium, defined by an ergodic dynamical system, in case when possible jumps are $\{-L,\ldots,-1,0,+1\}$ for some fixed integer L. We provide a recurrence criterion expressed in terms of sign of maximal Liapounov exponent of a certain random matrix and give an algorithm of calculation of that exponent. Next, we characterize existence of absolutely continuous invariant measure for Markov chain of the environments viewed from particle and also characterize, in transient cases, existence of a nonzero drift. To study validity of central limit theorem, we consider notion of harmonic coordinates introduced by Kozlov. We characterize existence of both invariant measure and harmonic coordinates and show in recurrent case that existence of those two objects is equivalent to validity of an invariance principle. We give sufficient conditions for validity of central limit theorem in transient cases. Finally, we consider previous results in context of a random medium defined by an irrational rotation on circle and study their realization in terms of regularity and Diophantine approximation.

The asymptotic behavior of the solutions of linear equations with random coefficients, random external forces and with affine boundary conditions is studied, motivated by a transmission-reflection problem for a one-dimensional wave equation in a random slab. The fluctuations of the coefficients are on a small scale in such a way that our problem is a diffusion-approximation problem except that we impose boundary conditions which force the solution to be anticipating. In the limit we obtain linear stochastic differential equations with affine boundary conditions, studied by Ocone and Pardoux. Our main tools are diffusion approximation results (Papanicolaou, Stroock and Varadhan or Ethier and Kurtz) and the properties of the limiting equations involving generalized Stratonovich integrals (Ocone and Pardoux). As an application, the transmission-reflection problem is discussed. We prove that the solution has a density with respect to the Lebesgue measure and satisfies the Markov field property.

Large deviation rates for supercritical and critical branching processes.- How fast does a general branching random walk spread?.- Boltzmann-Gibbs weights in the branching random walk.- Stochastic monotonicity and branching processes.- Multilevel multitype branching models of an information system.- On the shape of the wavefront of branching random walk.- Limiting distributions in branching processes with two types of particles.- Depth-first search of random trees, and Poisson point processes.- Towards dependence in general branching processes.- A criterion of boundedness of discrete branching random walk.- Quasistationarity in a branching model of division-within-division.- Population and density dependent branching processes.- Directed polymers in random media and spin glass models on trees..- A conceptual proof of the Kesten-Stigum theorem for multi-type branching processes.- On two measures defined on the boundary of a branching tree.- Which critically branching populations persist?.- A simple path to Biggins' martingale convergence for branching random walk.- Unsolved problems concerning random walks on trees.- Branching processes with local dependencies.- Sharpness of second moment criteria for branching and tree-indexed processes.- On the recognition and structure of probability generating functions.- Record values of a family of branching processes.- Limit skeleton for critical crump-mode-Jagers branching processes.- Markov cascades.- Limit theorems for branching processes with random migration stopped at zero.