z The central role of the biochemical networks in cellular function provides a strong motivation to search for the underlying principles of the adaptive evolution of
biochemical networks. As seen in Fig. 1, the favored physiological systems will lead to a selection force on biochemical networks in the evolutionary process.
Because the biochemical networks are the backbone of the physiological systems, they should have enough robustness to tolerate parameter variations and less sensitivity to attenuate the influence of external
disturbance so that the favored physiological functions could be preserved in the evolutionary process.
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z In order to test whether a physiological function would prevail under a new environment or not, the
robustness and sensitivity criteria have been
developed to measure the tolerance of the metabolite variations in metabolite concentration of a biochemical network in face of environmental changes (Chen et al.
2005). The design mechanisms for the biochemical networks by selection force in the evolutionary
process will be described as follows.
Fig. 1
The natural
selection process of hierarchical
biological networks.
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z The dynamic system of a biochemical network can be
represented in the following S-system (Savageau, 1976; Voit, 2000).
(12)
where are metabolites, such as substrates,
enzymes, factors or products of a biochemical network, in
which denote the n-dependent variables (intermediate metabolites and products) and denote the
independent variables (initial reactants and enzymes), and denote the rate constants, and and represent the kinetic parameters of the biochemical network. These parameters could be estimated by experimental data or microarray data.
1 1
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z The evolutionary time is much longer than the
transient time of the nonlinear biochemical network in (12) and the phenotype of a biochemical network is close to the steady state. Therefore, for simplicity, we shall focus on the relationship between the robustness and evolution design principles of a biochemical
network at the steady-state case.
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z Consider the steady state of biochemical network in (12), we get
(13) Taking the logarithm on both sides of (13), introducing new variable and after some rearrangements, we get
(14)
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z The above equations could be represented by the following steady-state equation (Voit, 2000)
(15) where
in which denotes the system matrix of the
catalytic interactions among the dependent variables and indicates the catalytic interactions between the dependent variables and the independent
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z If the inverse of exists, the steady state (or phenotype) of the biochemical network is solved by (Voit, 2000)
(16) The steady state in (16) is one of the equilibrium points of the nonlinear biochemical network in (12).
Actually, there are many equilibrium points for (12), which represent different phenotypes. Only the
equilibrium point (or phenotype) in (16) is favored by natural selection in the evolution via specification of parameters and environmental enzymes
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z Biochemical networks perform their physiological
functions within some local regions of the equilibrium point. In the evolutionary process, suppose that there exist some parameter variations, and in (12), which could be considered as design parameters in the evolutionary process owing to
genetic mutations or environmental changes. Then the corresponding perturbative steady state of the
biochemical network is given by (Chen et al. 2005)
(17)
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z Because the biochemical networks are the backbone of physiological systems of organisms, a biochemical network should be sufficiently robust to tolerate the
variations due to genetic mutations and environmental changes to maintain its function properly in the
evolutionary process. It is found that if the following robustness condition holds (Chen et al. 2005)
(18) then the phenotype of the perturbed genetic network exists as follows
(19)
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z If the robustness condition is violated, the steady state of the perturbed biochemical network in (19) may
cease to exist or move to another equilibrium point with a change of the phenotype. The changes and will influence the phenotype variation in (19). Their effects on the phenotype have been
discussed by the following sensitivity analysis of
biochemical network (Voit, 2000; Chen et al. 2005).
(20)
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z In order to tolerate the variations and to
preserve the favored phenotype of a biochemical network in the evolutionary process, the sensitivities in (20) should be below some values as follows
(21) or equivalently
(22) where , and are some small sensitivity values so that the phenotypes of perturbed biochemical networks would not change too much in (19) in comparison with the
nominal values in (16) and can be favored by natural selection.
,
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z Remark:
(i) According to the above analyses, the perturbed biochemical networks with parameter variations that
violate the robustness criterion in (18) will be eliminated by natural selection. Therefore, the perturbed biochemical
network should satisfy the robustness criterion in order to guarantee not to be perturbed too much from its
equilibrium (for the normal physiological function) in the evolutionary process. Because the violation of (18) means a lethal perturbation, the robustness criterion in (18) is the necessary condition for survival under natural selection.
From the robustness criterion in (18), natural selection favors the perturbed biochemical networks with small
perturbations so that the robustness criterion is
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z A biochemical network with redundancy and
self-regulation can attenuate perturbation Further, a biochemical network with adequate negative
feedbacks can increase to tolerate large parameter variations in the evolutionary process. These robust adaptive designs with
feedbacks are also favored by natural selection in the evolutionary process of biochemical networks. This is why there is so much redundancy due to duplicated genes, modularity, self-regulation and feedback
pathways in the biochemical networks in organisms.
D
.
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z (ii) The sensitivity criteria in (21) or (22) determine the ranges of the sensitivities of phenotype change to parameter variations and environmental changes by natural selection in the evolutionary process. For a functional biochemical network, it should satisfy the sensitivity criteria to prevent the metabolite
concentration from being changed too much by environmental changes. Hence, the steady state (phenotype) of a biochemical network can be
preserved while exposing the parameter variation and environmental changes to natural selection in
evolutionary process.
YD
Δ
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z The assumption that the three sensitivity criteria in (21) all hold for natural selection is derived from the fact
that biochemical networks are the backbone of
physiological systems and cannot be too sensitive to environmental changes especially for some core
(conserved) biochemical networks.
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z If some sensitivity criteria in (21) are relaxed, i.e. some of the inequalities in (21) are violated or some are specified much larger, the phenotypes with changes to some environmental variations will also be favored by natural selection. In this situation, the phenotype of biochemical networks are much influenced by
environmental variations to move toward another equilibrium so that they may be more adaptive to
environmental changes in the evolutionary process. In this case, new phenotypes are more easily generated in order to be more adaptive to the new environment.
si
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z (iii) The robustness criterion in (18) and sensitivity criteria in (21) are called the adaptive design rules of natural selection on biochemical networks in the
evolutionary process. There are many perturbed biochemical networks that can satisfy the adaptive design rules of natural selection in the evolutionary process (Chen et al. 2007). If they are selected by natural selection, there are some differences in
phenotype among these selected biochemical
networks. After several generations in the evolutionary process, due to co-option of existing biochemical
networks, diversities of the biochemical networks with conserved physiological function but with different
structures will be developed.
Adaptive Design Principles of the Biochemical Networks in
Evolutionary Process
z This is the origin of the diversities of biochemical networks within organisms in evolution. However, if the requirements on the robustness in (18) and
sensitivities in (21) are stricter (or more conservative), only a few solutions (or structures) can be selected by natural selection to meet these requirements. This is the reason why a conserved core biochemical network has less diversity (Chen et al. 2007).