 
Yuri K. Shestopaloff
Growth and
Replication of Living Organisms. General Law of Growth and Replication and the
Unity of Biochemical and Physical Mechanisms
Introduction
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 Jcurve and
Scurve.
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 Jcurve and Scurve. In particular, we obtained an Scurve 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 Jcurve 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.
