Progress of molecular biology resulted in the accumulation of information on biomolecular interactions, which are complex enough to be termed as networks. Dynamical behavior generated by complex ...network systems is considered to be the origin of the biological functions. One of the largest missions in modern life science is to obtain logical understanding for the dynamics of complex systems based on experimentally identified networks. However, a network does not provide sufficient information to specify dynamics explicitly, i.e. it lacks information of mathematical formulae of functions or parameter values. One has to develop mathematical models under assumptions of functions and parameter values to know the detail of dynamics of network systems. In this review, on the other hand, we introduce our own mathematical theory to understand the behavior of biological systems from the information of regulatory networks alone. Using the theory, important aspects of dynamical properties can be extracted from networks. Namely, key factors for observing/controlling the whole dynamical system are determined from network structure alone. We also show an application of the theory to a real biological system, a gene regulatory network for cell-fate specification in ascidian. We demonstrate that the system was completely controllable by experimental manipulations of the key factors identified by the theory from the information of network alone. This review article is an extended version of the Japanese article, Controlling Cell-Fate Specification System Based on a Mathematical Theory of Network Dynamics, published in SEIBUTSU BUTSURI Vol. 60, p. 349–351 (2020).
Modern biology provides many networks describing regulations between many species of molecules. It is widely believed that the dynamics of molecular activities based on such regulatory networks are ...the origin of biological functions. However, we currently have a limited understanding of the relationship between the structure of a regulatory network and its dynamics. In this study we develop a new theory to provide an important aspect of dynamics from information of regulatory linkages alone. We show that the “feedback vertex set” (FVS) of a regulatory network is a set of “determining nodes” of the dynamics. The theory is powerful to study real biological systems in practice. It assures that (i) any long-term dynamical behavior of the whole system, such as steady states, periodic oscillations or quasi-periodic oscillations, can be identified by measurements of a subset of molecules in the network, and that (ii) the subset is determined from the regulatory linkage alone. For example, dynamical attractors possibly generated by a signal transduction network with 113 molecules can be identified by measurement of the activity of only 5 molecules, if the information on the network structure is correct. Our theory therefore provides a rational criterion to select key molecules to control a system. We also demonstrate that controlling the dynamics of the FVS is sufficient to switch the dynamics of the whole system from one attractor to others, distinct from the original.
•A new theory to connect structure of a regulatory network and its dynamics.•Dynamics of whole system can be identified by a subset of variables in the system.•The subset is determined as a “feedback vertex set” of the network graph.•The theory combines two mathematical concepts from different fields•We analyze complex regulatory networks in biology as applications of our theory.
In living cells, chemical reactions are connected by sharing their products and substrates, and form complex networks, e.g., metabolic pathways. Here we developed a theory to predict the sensitivity, ...i.e., the responses of concentrations and fluxes to perturbations of enzymes, from network structure alone. Nonzero response patterns turn out to exhibit two characteristic features, localization and hierarchy. We present a general theorem connecting sensitivity with network topology that explains these characteristic patterns. Our results imply that network topology is an origin of biological robustness. Finally, we suggest a strategy to determine real networks from experimental measurements.
In biological cells, chemical reaction pathways lead to complex network systems like metabolic networks. One experimental approach to the dynamics of such systems examines their "sensitivity": each ...enzyme mediating a reaction in the system is increased/decreased or knocked out separately, and the responses in the concentrations of chemicals or their fluxes are observed. In this study, we present a mathematical method, named structural sensitivity analysis, to determine the sensitivity of reaction systems from information on the network alone. We investigate how the sensitivity responses of chemicals in a reaction network depend on the structure of the network, and on the position of the perturbed reaction in the network. We establish and prove some general rules which relate the sensitivity response to the structure of the underlying network. We describe a hierarchical pattern in the flux response which is governed by branchings in the network. We apply our method to several hypothetical and real life chemical reaction networks, including the metabolic network of the Escherichia coli TCA cycle.
Modern biology has provided many examples of large networks describing the interactions between multiple species of bio-molecules. It is believed that the dynamics of molecular activities based on ...such networks are the origin of biological functions. On the other hand, we have a limited understanding for dynamics of molecular activity based on networks. To overcome this problem, we have developed two structural theories, by which the important aspects of the dynamical properties of the system are determined only from information on the network structure, without assuming other quantitative details. The first theory, named Linkage Logic, determines a subset of molecules in regulatory networks, by which any long-term dynamical behavior of the whole system can be identified/controlled. The second theory, named Structural Sensitivity Analysis, determines the sensitivity responses of the steady state of chemical reaction networks to perturbations of the reaction rate. The first and second theories investigate the dynamical properties of regulatory and reaction networks, respectively. The first theory targets the attractors of the regulatory network systems, whereas the second theory applies only to the steady states of the reaction network systems, but predicts their detailed behavior. To demonstrate the utility of our methods several biological network systems, and show they are practically useful to analyze behaviors of biological systems.
Linkage logic theory provides a mathematical criterion to control network dynamics by manipulating activities of a subset of network nodes, which are collectively called a feedback vertex set (FVS). ...Because many biological functions emerge from dynamics of biological networks, this theory provides a promising tool for controlling biological functions. By manipulating the activity of FVS molecules identified in a gene regulatory network (GRN) for fate specification of seven tissues in ascidian embryos, we previously succeeded in reproducing six of the seven cell types. Simultaneously, we discovered that the experimentally reconstituted GRN lacked information sufficient to reproduce muscle cells. Here, we utilized linkage logic theory as a tool to find missing edges in the GRN. Then, we identified a FVS from an updated version of the GRN and confirmed that manipulating the activity of this FVS was sufficient to induce all seven cell types, even in a multi-cellular environment. Thus, linkage logic theory provides tools to find missing edges in experimentally reconstituted networks, to determine whether reconstituted networks contain sufficient information to fulfil expected functions, and to reprogram cell fate.
•We measured the three-dimensional morphology of growing snow crystal.•Side branch formed by step bunching on not only prism face but also basal face.•Side branching interrupts the supply of ...diffusing molecules on basal plane.
The nature of sidebranching in the facetted regions of snow crystals is investigated. It is shown that during the growth of a snow crystal, an initial sidebranch-pair forms after step bunching occurs on the leading prism planes, followed by step bunching on the adjacent flat basal face, producing a macrostep between the main branch and sidebranch feature. A Michelson interferometer–reflecting microscope setup was used to in-situ observe the three-dimensional morphology of a growing snow-crystal branch in a diffusion chamber. The macrostep on the basal plane was found to occur in the cases of simple facet growth, repetitive facet growth, and rounded tip growth, with the rounded tips forming at higher supersaturations. Thus, snow-crystal sidebranching involves a separation of the supply route of diffusing molecules on basal plane from the tip of the main-branch. Moreover, the sidebranches would fully sprout when the supersaturation increased, at which time the facetted branch tip abruptly narrowed and became rounded. These results indicate important roles of both the surface diffusion of water molecules and step migration for dendritic morphological instability on snow crystals.
We consider systems of differential equations which model complex regulatory networks by a graph structure of dependencies. We show that the concepts of informative nodes (Mochizuki and Saito, J ...Theor Biol 266:323–335,
2010
) and determining nodes (Foias and Temam, Math Comput 43:117–133,
1984
) coincide with the notion of feedback vertex sets from graph theory. As a result we can determine the long-time dynamics of the entire network from observations on only a feedback vertex set. We also indicate how open loop control at a feedback vertex set, only, forces the remaining network to stably follow prescribed stable or unstable trajectories. We present three examples of biological networks which motivated this work: a specific gene regulatory network of ascidian cell differentiation (Imai et al., Science 312:1183–1187,
2006
), a signal transduction network involving the epidermal growth factor in mammalian cells (Oda et al., Mol Syst Biol 1:1–17,
2005
), and a mammalian gene regulatory network of circadian rhythms (Mirsky et al., Proc Natl Acad Sci USA 106:11107–11112,
2009
). In each example the required observation set is much smaller than the entire network. For further details on biological aspects see the companion paper (Mochizuki et al., J Theor Biol,
2013
, in press). The mathematical scope of our approach is not limited to biology. Therefore we also include many further examples to illustrate and discuss the broader mathematical aspects.
Insect pests cause serious damage in crop production, and various attempts have been made to produce insect-resistant crops, including the expression of genes for proteins with anti-herbivory ...activity, such as Bt (Bacillus thuringiensis) toxins. However, the number of available genes with sufficient anti-herbivory activity is limited. MLX56 is an anti-herbivory protein isolated from the latex of mulberry plants, and has been shown to have strong growth-suppressing activity against the larvae of a variety of lepidopteran species. As a model of herbivore-resistant plants, we produced transgenic tomato lines expressing the gene for MLX56. The transgenic tomato lines showed strong anti-herbivory activities against the larvae of the common cutworm, Spodoptera litura. Surprisingly, the transgenic tomato lines also exhibited strong activity against the attack of western flower thrips, Frankliniera occidentalis. Further, growth of the hadda beetle, Henosepilachna vigintioctopunctata, fed on leaves of transgenic tomato was significantly retarded. The levels of damage caused by both western flower thrips and hadda beetles were negligible in the high-MLX56-expressing tomato line. These results indicate that introduction of the gene for MLX56 into crops can enhance crop resistance against a wide range of pest insects, and that MLX56 can be utilized in developing genetically modified (GM) pest-resistant crops.
The mechanistic details underlying the assembly of rod-shaped chromosomes during mitosis and how they segregate from each other to act as individually mobile units remain largely unknown. Here, we ...construct a coarse-grained physical model of chromosomal DNA and condensins, a class of large protein complexes that plays key roles in these processes. We assume that condensins have two molecular activities: consecutive loop formation in DNA and inter-condensin attractions. Our simulation demonstrates that both of these activities and their balancing acts are essential for the efficient shaping and segregation of mitotic chromosomes. Our results also demonstrate that the shaping and segregation processes are strongly correlated, implying their mechanistic coupling during mitotic chromosome assembly. Our results highlight the functional importance of inter-condensin attractions in chromosome shaping and segregation.
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