Quantitative Biology

A theoretical construction of the genetic material establishes the unique and ideal character of DNA. A similar conclusion is reached for amino acids and proteins.

Living systems transmit heritable information using the replicating gene sequences and the cycling regulators assembled around gene sequences. Here I develop a framework for heredity and development that includes the cycling regulators parsed in terms of what an organism can sense about itself and its environment by defining entities, their sensors, and the sensed properties. Entities include small molecules (ATP, ions, metabolites, etc.), macromolecules (individual proteins, RNAs, polysaccharides, etc.), and assemblies of molecules. While concentration may be the only relevant property measured by sensors for small molecules, multiple properties that include concentration, sequence, conformation, and modification may all be measured for macromolecules and assemblies. Each configuration of these entities and sensors that is recreated in successive generations in a given environment thus specifies a potentially vast amount of information driving complex development in each generation. This Entity-Sensor-Property framework explains how sensors limit the number of distinguishable states, how distinct molecular configurations can be functionally equivalent, and how regulation of sensors prevents detection of some perturbations. Overall, this framework is a useful guide for understanding how life evolves and how the storage of information has itself evolved with complexity since before the origin of life.

Advances in biology have mostly relied on theories that were subsequently revised, expanded or eventually refuted using experimental and other means. Theoretical biology used to primarily provide a basis to rationally examine the frameworks within which biological experiments were carried out and to shed light on overlooked gaps in understanding. Today, however, theoretical biology has generally become synonymous with computational and mathematical biology. This could in part be explained by a relatively recent tendency in which a "data first", rather than a "theory first", approach is preferred. Moreover, generating hypotheses has at times become procedural rather than theoretical. This situation leaves our understanding enmeshed in data, which should be disentangled from much noise. Given the many unresolved questions in biology and medicine, it seems apt to revive the role of pure theory in the biological sciences. This paper makes the case for a "philosophical biology" (philbiology), distinct from but quite complementary to philosophy of biology (philobiology), which would entail biological investigation through philosophical approaches. Philbiology would thus be a reincarnation of theoretical biology, adopting the true sense of the word "theory" and making use of a rich tradition of serious philosophical approaches in the natural sciences. A philbiological investigation, after clearly defining a given biological problem, would aim to propose a set of empirical questions, along with a class of possible solutions, about that problem. Importantly, whether or not the questions can be tested using current experimental paradigms would be secondary to whether the questions are inherently empirical or not. The final goal of a philbiological investigation would be to develop a theoretical framework that can lead observational and/or interventional experimental studies of the defined problem.

The controversy concerning both the definition of the species and methods for inferring the boundaries and numbers of species has occupied biologists for centuries, and the debate itself has become known as the species problem. The modern theory of evolution depends on a fundamental redefinition of "species". Here we show that based on the model of evolutionary continuum combined with fuzzy theory that the evolution system is a uncountable infinite set and species is a fuzzy set, the contradiction between discrete biological entities and continuous evolution system is solved, i.e. when a species evolved, the individuals scattered in space but continuously distributed on time sequences. Moreover, the calculation methods for species are suggested both in theory and practice.

Using the classical tools of nonlinear dynamics, we study the process of self-organization and the appearance of the chaos in the metabolic process in a cell with the help of a mathematical model of the transformation of steroids by a cell Arthrobacter globiformis. We constructed the phase-parametric diagrams obtained under a variation of the dissipation of the kinetic membrane potential. The oscillatory modes obtained are classified as regular and strange attractors. We calculated the bifurcations, by which the self-organization and the chaos occur in the system, and the transitions "chaos-order", "order-chaos", "order-order", and "chaos-chaos" arise. Feigenbaum's scenarios and the intermittences are found. For some selected modes, the projections of the phase portraits of attractors, Poincaré sections, and Poincaré maps are constructed. The total spectra of Lyapunov indices for the modes under study are calculated. The structural stability of the attractors is demonstrated. A general scenario of the formation of regular and strange attractors in the given metabolic process in a cell is found. The physical nature of their appearance in the metabolic process is studied.

Degeneracy is a salient feature of genetic codes, because there are more codons than amino acids. The conventional table for genetic codes suffers from an inability of illustrating a symmetrical nature among genetic base codes. In fact, because the conventional wisdom avoids the question, there is little agreement as to whether the symmetrical nature actually even exists. A better understanding of symmetry and an appreciation for its essential role in the genetic code formation can improve our understanding of nature coding processes. Thus, it is worth formulating a new integrated symmetrical table for genetic codes, which is presented in this paper. It could be very useful to understand the Nobel laureate Crick wobble hypothesis: how one transfer ribonucleic acid can recognize two or more synonymous codons, which is an unsolved fundamental question in biological science.

The existing life table method needs to calculate the age-specific mortality first, not only has too many and complicated calculation steps, but also introduces the multiple approximation to bring error. This paper redefines the probability of death for the life table as the average probability of death of a group of people born in a certain period at a later time. Based on this definition, a new method for the life table is proposed to obtain the life expectancy, which has the same meaning to that from the traditional life table. Using the Japanese population data to verify the method, the results show that it is consistent with the life expectancy of the birth of the baby, the maximum relative difference is no more than 0.1%, and average relative difference is less than 0.03%. The theory and method of life table described in this paper are simple and easy to understand. The needed data are easy to obtained from statistics, and the calculation is easy, the results obtained are accurate and reliable. It should be a very valuable demographic method for application.

Homicide investigations often depend on the determination of a minimum post-mortem interval (PMI min ) by forensic entomologists. The age of the most developed insect larvae (mostly blow fly larvae) gives reasonably reliable information about the minimum time a person has been dead. Methods such as isomegalen diagrams or ADH calculations can have problems in their reliability, so we established in this study a new growth model to calculate the larval age of \textit{Lucilia sericata} (Meigen 1826). This is based on the actual non-linear development of the blow fly and is designed to include uncertainties, e.g. for temperature values from the crime scene. We used published data for the development of \textit{L. sericata} to estimate non-linear functions describing the temperature dependent behavior of each developmental state. For the new model it is most important to determine the progress within one developmental state as correctly as possible since this affects the accuracy of the PMI estimation by up to 75%. We found that PMI calculations based on one mean temperature value differ by up to 65% from PMIs based on an 12-hourly time temperature profile. Differences of 2\degree C in the estimation of the crime scene temperature result in a deviation in PMI calculation of 15 - 30%.

Biochemical pathways emerge from a series of Brownian collisions between various types of biological macromolecules within separate cellular compartments and in highly viscous cytosol. Functioning of biochemical networks suggests that such serendipitous collisions, as a whole, result into a perfect synchronous order. Nonetheless, owing to the very nature of Brownian collisions, a small yet non-trivial probability can always be associated with the events when such synchronizations fail to emerge consistently; which account for a damage of a biochemical pathway. The repair mechanism of the system then attempts to minimize the damage, in the pursuit to bring restore the appropriate level of synchronization between reactant concentrations. Present work presents a predictive probabilistic model that describes the various facets of this complicated and coupled process(damaging and repairing). By describing the cytosolic reality of Brownian collisions with Chapman-Kolmogorov equations, the model presents analytical answers to the questions, with what probability a fragment of any pathway may suffer damage within an arbitrary interval of time? and with what probability the damage to a pathway can be repaired within any arbitrary interval of time?

We present a model of single species fishery which alternates closed seasons with pulse captures. The novelty is that the length of a closed season is determined by the stock size of the last capture. The process is described by a new type of impulsive differential equations recently introduced. The main result is a fishing effort threshold which determines either the sustainability of the fishery or the extinction of the resource.