We present significantly advanced studies of the previously introduced physical growth mechanism and unite it with biochemical growth factors. Obtained results allowed formulation of the general growth law which governs growth and evolutional development of all living organisms, their organs and systems. It was discovered that the growth cycle is predefined by the distribution of nutritional resources between maintenance needs and biomass production. This distribution is quantitatively defined by the growth ratio parameter, which depends on the geometry of an organism, phase of growth and, indirectly, the organism's biochemical machinery. The amount of produced biomass, in turn, defines the composition of biochemical reactions. Changing amount of nutrients diverted to biomass production is what forces organisms to proceed through the whole growth and replication cycle. The growth law can be formulated as follows: the rate of growth is proportional to influx of nutrients and growth ratio. Considering specific biochemical components of different organisms, we find influxes of required nutrients and substitute them into the growth equation; then, we compute growth curves for amoeba, wild type fission yeast, and fission yeast's mutant. In all cases, predicted growth curves correspond very well to experimental data. Obtained results prove validity and fundamental scientific value of the discovery.

Living organisms need energy to be 'alive'. Energy is produced by the biochemical processing of nutrients, and the rate of energy production is called the metabolic rate. Metabolism is very important from evolutionary and ecological perspectives, and for organismal development and functioning. It depends on different parameters, of which organism mass is considered to be one of the most important. Simple relationships between the mass of organisms and their metabolic rates were empirically discovered by M. Kleiber in 1932. Such dependence is described by a power function, whose exponent is referred to as the allometric scaling coefficient. With the increase of mass, the metabolic rate usually increases more slowly; if mass increases by two times, the metabolic rate increases less than two times. This fact has far-reaching implications for the organization of life. The fundamental biological and biophysical mechanisms underlying this phenomenon are still not well understood. The present study shows that one such primary mechanism relates to transportation of substances, such as nutrients and waste, at a cellular level. Variations in cell size and associated cellular transportation costs explain the known variance of the allometric exponent. The introduced model also includes heat dissipation constraints. The model agrees with experimental observations and reconciles experimental results across different taxa. It ties metabolic scaling to organismal and environmental characteristics, helps to define perspective directions of future research and allows the prediction of allometric exponents based on characteristics of organisms and the environments they live in.

First, we briefly describe the general growth mechanism, which governs the growth of living organisms, and its mathematical representation, the growth equation. Using the growth equation, we compute the growth curve for S. cerevisiae and show that it corresponds to available experimental data. Then, we propose a new method for finding the amount of synthesized biomass without complicated stoichiometric computations and apply this method to evaluation of biomass production by S. cerevisiae. We find that obtained results are very close to values obtained by methods of metabolic flux analysis. Since methods of metabolic flux analysis require finding produced biomass, which is one of the most important parameters affecting stoichiometric models, a priori knowledge of produced biomass can significantly improve methods of metabolic flux analysis in many aspects, which we also discuss. Besides, based on the general growth mechanism, we considered evolutionary development of S. cerevisiae and find that it is a more ancient organism than S. pombe and is apparently its direct predecessor.

The relationship between the organism's growth and its geometrical form was suggested by many ancient and modern thinkers. Many other factors influence growth and replication. All these numerous factors, such as biochemical, physical, work in cooperation. In this paper, we consider the impact of geometrical and physical characteristics of organisms, such as surface, volume and geometrical form, on organisms' growth and replication. The mathematical basis of our study is the growth equation, which describes growth from the physical perspective. First, we model the growth of cells by different shapes, and compare theoretical results to experimental data. We discover that the growth dependencies produced by the growth equation fit experimental data very accurately if we take into account two considerations. First, the cell, or a multicellular growing object, can switch into a replication phase before its physical growth potential is exhausted. Second, the inflow of substance through a unit of the membrane's surface increases during growth, because the cell's growing volume allows it to process more nutrients. Then, we consider overgrowth from the physical perspective, introduce the notion of a growth ratio as an important geometrical characteristic of the growth and overgrowth processes, and generalize our findings.

Understanding biological phenomena requires a systemic approach that incorporates different mechanisms acting on different spatial and temporal scales, since in organisms the workings of all components, such as organelles, cells, and organs interrelate. This inherent interdependency between diverse biological mechanisms, both on the same and on different scales, provides the functioning of an organism capable of maintaining homeostasis and physiological stability through numerous feedback loops. Thus, developing models of organisms and their constituents should be done within the overall systemic context of the studied phenomena. We introduce such a method for modeling growth and regeneration of livers at the organ scale, considering it a part of the overall multi-scale biochemical and biophysical processes of an organism. Our method is based on the earlier discovered general growth law, postulating that any biological growth process comprises a uniquely defined distribution of nutritional resources between maintenance needs and biomass production. Based on this law, we introduce a liver growth model that allows to accurately predicting the growth of liver transplants in dogs and liver grafts in humans. Using this model, we find quantitative growth characteristics, such as the time point when the transition period after surgery is over and the liver resumes normal growth, rates at which hepatocytes are involved in proliferation, etc. We then use the model to determine and quantify otherwise unobservable metabolic properties of livers.