Growth and Replication of Living Organisms. General Law of Growth and Replication and the Unity of Biochemical and Physical Mechanisms

Introduction This carefully revised and expanded second edition of the book presents the author's continued study of growth and replication mechanisms. Previous results were published in three books and articles in “International Journal of Biomathematics” and “Biophysical Reviews and Letters”. Presently, more author's articles on this subject are reviewed in scientific journals. Some results were presented in a separate chapter on growth and replication in a collective monograph “Bioinformatics”, by Polish Academy of Sciences, Editor Dr. P. Pawlowski. However, this book is qualitatively different from the previous publications, such as the book “Physics of Growth and Replication. Physical and Geometrical Perspectives on Living Organisms' Development”. In the earlier books, as well as in the articles, the subject is considered mostly from the physical and geometrical perspectives, although all the time the author emphasizes that growth and replication are inherently multifactor phenomena that are governed by the united work of physical, biochemical and other mechanisms. In this book, we study growth and replication from a truly multidisciplinary perspective, considering the cooperative workings of both biochemical and physical growth mechanisms in their inherent and interdependent unity. In fact, we see growth as a single phenomenon that naturally includes different mechanisms, in the same way that a locomotive has working parts made of steel, plastic, glass, etc., which all work together in order to provide its motion. The most vulnerable part of the previous research was insufficient information about the biochemical factors that influence the influx of nutrients. Although, based on geometrical considerations, it was proved that the value of specific influx (amount of nutrients per unit of surface) changes during growth, we did not provide the exact functional dependence of specific influx on time or on mass of organisms. Instead, we made some reasonable assumptions about the nature of these functional dependencies and approximated them using certain functions. This time, we start from the analysis of biochemical mechanisms responsible for the synthesis of cell components, such as proteins and RNA. Then, using this knowledge, we derive the dependence of influx on the biochemical composition of cells for specific organisms and use thus found influx in the growth equation. This way, all previously loose ends are tightly tied together and we obtain a closed system of input parameters that uniquely define the growth and replication cycle. In other words, all parameters that are required for the growth equation are unambiguously derived from the biochemical characteristics of particular organisms and its physical, geometrical characteristics. An important development is that we introduced the notion of organism's “infrastructure costs”, which relate to the increasing length of signaling and transport networks during growth, and accordingly we derived equations that allow computing the amount of nutrients required to support this increasing length. This is undoubtedly a fundamental enhancement, because it allows quantitatively finding the amount of nutrients required to support transport and signaling networks. In our case, taking into account infrastructure costs significantly improved the correspondence of experimental data and results obtained through the introduced growth models on the basis of growth equation. Besides, the introduction of “infrastructure costs” has an important scientific value for many other applications. It also allows explaining many biological phenomena that are presently not fully understood. The range of experimental data sets was expanded. For instance, beside Amoeba and Schizosaccharomyces pombe fission yeast, we consider experimental data for S. cerevisiae and some other organisms, as well as cite results of other experimental studies that support our arguments. The correspondence of the modeling results and experimental data is very good, which is convincing evidence of validity of the general growth mechanism and its mathematical representation, the growth equation. One of the most important discoveries of this study is the general growth law. This general law of Nature governs the growth, replication and evolutional development of all living organisms. In biology, it has the same importance as Newton's laws in mechanics. The essence of this law is that it uniquely defines the distribution of nutritional resources between two activities that are vitally important for any organism. One is organism's maintenance, and the other is organism's growth, in other words, biomass synthesis. The fraction of nutrient influx that is directed towards the synthesis of biomass is defined by the value of the growth ratio, while the remaining nutrients support the functioning of existing biomass (maintenance influx), see figure below. When an organism grows, it has to allocate more and more nutritional resources for maintenance, and accordingly fewer nutrients are available for growth. Eventually, an organism grows to such a size that the amount of available nutrients is sufficient only for maintenance purposes, and no nutrients are left for growth. At this point, the organism stops growing and either replicates or switches to a quiescent state. Fig. G1. Growth cycle regulation and progression.Quantitatively, the amount of nutrients that an organism can afford to use for biomass synthesis is defined by the value of the growth ratio parameter. This parameter is derived from a quantitative relationship of organism's surface and volume, which are inherently interconnected geometrical characteristics of a growing organism. In order to understand this arrangement, think about the following. Whatever way nutrients may come to an organism, such as through a fruit stem, or lungs' or blood vessels' surface, they provide functioning of mass (associated with volume that has certain geometry). However, nutrients have to be delivered to every unit of this volume, which cannot be done other than by delivering influx of nutrients through a certain surface associated with every unit of volume. Besides, each unit of volume of a living organism produces waste, which also has to be removed as a flux of waste through certain surface associated with every unit of volume. This is how the inherent unity of mass (associated with volume) and surface work together, providing functioning of organisms, their organs and systems. The distribution of nutrients depends on the particular geometry of volume. If the organism's geometrical form is flattened, such as a disk, then the amount of surface per unit of volume is larger compared to an organism that has a spherical shape, which is the most economical geometrical form with regard to the amount of surface per unit of volume. Let us assume that specific influx (amount of nutrients per unit of surface) is the same for both organisms and equal to k = 1 . Then, for a spherical organism, the amount of nutrients per unit of volume will be less. For instance, suppose a disk has radius and height equal to one, and a sphere has radius one as well. Then, the surfaces of disk and sphere are the same: , . Their volumes are equal to accordingly , . Then, amounts of nutrients per unit of volume are , . If we assume that at some point in time, a unit of volume in both cases requires the same amount of nutrients for maintenance, let us say 3, then, in the case of a spherical organism, no nutrients will be available for biomass synthesis and, consequently, a spherical organism stops growing, while a unit of volume of a disk like organism still can spend 3 units of nutrients for maintenance and one unit for growth. In fact, if we assume that the disk's height remains fixed at one, it can continue growing until it reaches a volume of , when , and growth stops. So, the final volume of such a disk like cell will be three times that of a spherical one. We may conclude that in general, spherical should be smaller. Indeed, this is true. Among the smallest organisms many have spherical shape [Jorgensen, 2004]. Evolutionarily, through variability, adaptation and selection, Nature adjusted the distribution of nutritional resources to an optimum level that provides the best possible regime both from the perspective of the fastest synthesis of new biomass and at the same time maintaining functioning of existing organisms at the highest level. Change of the growth ratio, which monotonically decreases during growth, accordingly changes the amount of synthesized biomass. In fact, the amount of synthesized biomass defines the composition of biochemical reactions. This is how and why an organism sequentially progresses through the growth cycle, switching between different growth and replication phases by changing the composition of biochemical reactions due to the changing value of the synthesized biomass, whose increase at any given moment is defined as a fraction (quantitatively equal to the growth ratio) of a total nutrient influx. We would like to emphasize that the growth ratio and a chain of events that is triggered by the change of growth ratio during growth, is not something that a certain mathematical model introduces for convenience, but the mathematical formulation and the actual working of the real fundamental mechanism that governs the growth of all living species in Nature. In the same way as laws of classical mechanics are not mathematical abstractions but the mathematical formulation of fundamental physical laws, the general growth mechanism and its mathematical formulation, the growth equation, present a correct formulation of a general law of Nature, the general growth law. This book will present many convincing proofs that this general growth law today can be considered as a well founded and credible scientific theory. Certainly, many more things need to be don9781612890982\\How do youth organizations use new Media? How do they address Internet savvy youth who are also apathetic citizens? How has this evolved with new demands for interactivity in social media? These ae contemporary challenges facing any orgainzation active online. Spanning seven years of research, this book edamines these issues and considers three separate pooltical contexts with a variety of analytical tools