1. 1 Thermodynamic principles of system biology
At the beginning, we first review the basic and thermodynamic principles of system biology obtained in past times, and which act theoretical foundation for the discussion of patterns of flower pigmentation (Zhao, 2016; 2017; 2018).
The color of a cell is associated with a special signaling network or a thermodynamic system (Zhao, 2016; 2017; 2018). In view of this theory, a signal, such as enzyme or receptor activity, corresponds to a type of protein conformational state (or thermodynamic system), and any protein complex (or protein DNA complex, condensed matter in view of physics) represent a type of signaling network (physiological system), in which many types of signals can be inputted and integrated, finally many types of signaling activities can be outputted. The color substances are the product of this physiological system (signaling activity) (Li et al. 2014; Zhang et al. 2021). This makes us analyze patterns of flower color by applying principles of thermodynamics (Crapse et al. 2021).
The formation of color cells from its original ancestor cell is an irreversible process in view of thermodynamics (Lurié & Wagensberg, 1979; Zhao 2016). When a color cell is produced in the irreversible process of development, it will remain its trait forever. It means that color cells show epigenetics (Goldberg et al., 2007). This principle gives a satisfied explanation to the stability of flower color patterns.
The distribution of different color cells can be described by partition function of complex thermal system (or condensed mater) (Zhao, 2012, 2017). As development is an irreversible process and the principles of equilibrium thermodynamics can be only validated in a limited range of time and space in which the thermal equilibrium can be reached, the first task of us is to ascertain that in which range the equilibrium principles can be applied. Fortunately, the principle of equilibrium thermodynamics is at least validated in the formation of color cell in its development. At present, the thermal parameters of color cell cannot be measured directly and experimentally. but we can judge it by external trait of flower, such as quantity of color cells and position of color cells (color spot).
The production of a color cell in the development results from complex thermodynamic integration of diversified factors. The bioinformation of gene, environmental factors (temperature and concentration of oxygen), the nutrition state, and products of other cells can be interacted or integrated at diversified levels of hierarchical structure of signaling network.
Three basic patterns of flower pigmentation are striped, speckled, circled flower. All other complex figure can be considered as complex combination and variers of these patterns.
1.2 Thermodynamics
Although the concept of thermodynamic stability of a color cell related system is very clear, we cannot measure it experimentally by applying experimental methods of traditional thermodynamics. Thus, we adopt different method to do so.
Firstly, we deduce some predictions (patterns of flower pigmentation) by applying basic principles of thermodynamics. If we can find it in nature, the principles will be approved. Secondly, when the principles are tested, we can use biological trait or observable features to judge or deduce the general profile of stability of color cell related system.
The stability of color cell related system of physiology is changed with time and space, in order to analyze its trait, we should firstly simplify it. In a simple model, we only study the role of distance (or radius) from Flower Pistil to desired position. We can further conclude that: In the circle line round the flower Pistil, if there is no color alteration in this line, the thermodynamic stability of color related thermal system for all cells is same.
If an individual shows two colors at different parts and at any parts it shows one color, it belongs two states distribution. The principle of it can be expressed in figure 1.
ΔG is the stability of color related system of physiology, Ɩ is the distance between reference point and site in flower, the yellow and red lines represent hypothesized stability line of color cell related system. p is the probability of color cell.
In figure 1, the stability lines of color cell related systems are the hypothesized profile and actual they are not straight, but curve, but this does not affect our understanding of it. The P can be calculated from stabilities of red and yellow color related system by principle of partition function of condensed matter (Zhao, 2012, 2017). If the stability of a color system of the cell is more stable, it dominates the color of individual cell. If the stability of two types of color systems of cells is almost same, the population of two types of color cell can be distributed according to its thermodynamic stability, the motley area may appear.
1.3 Theoretical Prediction
If the flower color is related to a thermal system and production of flower pigmentation is controlled thermodynamically, we should predict following phenomena:
- There is no standard figure for flower pigmentation, the flower pigmentation will vary from flower to flower because thermal distribution of color cell shows randomness. Or in other words, there is no position within flowers which show fixed color. The size and position of flower pigmentation vary.
- The figure of flower pigmentation is sensitive to temperature, genes, drug, environmental factors which influence the thermal state of color cells. The size and position of speckle, color line in flower will also vary.
- The color line and population of color speckle will change with the environmental change.
1.4 Materials
The flower of Mirabilis Jalapa L is selected for it is common over the world and it show different color at different parts in same flower. It is the hybrid of yellow and red of Mirabilis Jalapa L. Normally, most of its flower is yellow and little are red.