Yuri K. Shestopaloff

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


The work presents the author’s continued study of growth and replication mechanisms. Previous results were published in two books and articles in “International Journal of Biomathematics” and “Biophysical Reviews and Letters”. 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 perspective, although all the time we emphasized 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 the 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 the motion of the locomotive.
     The most vulnerable part of the previous research was insufficient information about the biochemical factors that influence the influx of nutrients. Although we proved that the value of specific influx changes during growth, based on geometrical considerations, 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 this influx in the growth equation. This way, all previously loose ends are tied together. 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.
     We introduced the notion of organism’s “infrastructure costs”, which relate to the increasing length of signaling and transport networks during growth, and derived appropriate equations that allow computing the amount of nutrients required to support this expansion. This is an important enhancement, because it significantly improves 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 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 many other experimental studies that support our arguments. The correspondence of the modeling results and experimental data is very good, which is the evidence of validity of the physical growth mechanism and its mathematical representation, the growth equation. One of the important discoveries of this study is that the fraction of influx of nutrients 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.

     The value of the growth ratio, which represents a quantitative relationship of organism’s surface and volume, considered as inherently interconnected characteristics of the growing organism, defines the distribution of nutrients. Evolutionarily, through selection, Nature adjusted the distribution of nutritional resources to optimum level that provides the best possible regime; both from the perspective of fast synthesis of new biomass and the perspective of maintaining the high functionality of existing organisms. Change of the growth ratio during growth accordingly changes the amount of synthesized biomass, which in turn leads to changes in 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 change of the growth ratio; sometimes, with addition of other biochemical mechanisms. We would like to emphasize that the growth ratio and a chain of events it triggers 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 physical growth mechanism and its mathematical formulation, the growth equation, present a correct formulation of a general law of Nature. This book will present many convincing proofs that this strong statement is a well founded and very credible hypothesis. Certainly, many more things need to be done until the scientific community will accept this hypothesis as a scientific theory, but the foundation is already very solid.
We present many direct and indirect proofs of the validity of the growth equation, so that the hypothesis that the general growth law is that “upper manager” that together with biochemical mechanisms governs the growth and replication of living species can be thoroughly examined by anybody willing to take an unobstructed view to the presented material.
     This time, we introduce systems of equations and constraints that are required to model the growth and replication of multicellular organisms. This is an interesting subject that requires further study. However, the theoretical foundations are laid, and the road to modeling multicellular organisms, including complex organisms such as humans, is open for those willing to explore this terra incognita with new conceptual approaches and new tools that we introduce and describe in this book.
     We significantly enhance the results of previous studies that discovered two types of growth of individual organisms. One is when organisms such as amoeba use almost the whole range of the growth curve defined by the physical growth mechanism. The other type of growth is when fast growing organisms use only the fastest part of the growth curve in order to secure the fastest possible growth and replication. These growth scenarios of individual organisms strikingly remind two typical population growth scenarios, the so called J-curve and S-curve.
     We also introduce the equation for population growth. Based on specific features of two types of individual growth, we arrived at similar population growth dependencies such as J-curve and S-curve. In particular, we obtained an S-curve for the population growth that is very similar to the classic growth curve produced by the logistic equation. This is the case when an individual organism proceeds through the whole growth cycle defined by the growth equation, such as amoeba. When starving, such organisms increase their growth period without significant decrease in size. Another growth scenario is when each individual organism, in a nutritionally poor environment, strives to survive by significantly reducing its size but preserving approximately the same growth period. For populations of such organisms, we obtained the J-curve of population growth.
     Overall, the study convincingly proves that biochemical and physical growth mechanisms work in close cooperation, directing growth and replication, with the leading role given to the physical growth mechanism. This could be expected if one thinks for a moment about the problem, taking into account the inherently spatial nature of our world.


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Last modified: 01/10/21