The interactions between proteins, DNA, and RNA in living cells constitute molecular networks that govern various cellular functions. To investigate the global dynamical properties and stabilities of such networks, we studied the cell-cycle regulatory network of the budding yeast. With the use of a simple dynamical model, it was demonstrated that the cell-cycle network is extremely stable and robust for its function. The biological stationary state, the G₁state, is a global attractor of the dynamics. The biological pathway, the cell-cycle sequence of protein states, is a globally attracting trajectory of the dynamics. These properties are largely preserved with respect to small perturbations to the network. These results suggest that cellular regulatory networks are robustly designed for their functions.

Oscillations within the cell regulate the timing of many important life cycles. However, in this noisy environment, oscillations can be highly inaccurate owing to phase fluctuations. It remains poorly understood how biochemical circuits suppress these phase fluctuations and what is the incurred thermodynamic cost. Here, we study three different types of biochemical oscillation, representing three basic oscillation motifs shared by all known oscillatory systems. In all the systems studied, we find that the phase diffusion constant depends on the free-energy dissipation per period, following the same inverse relation parameterized by system-specific constants. This relationship and its range of validity are shown analytically in a model of noisy oscillation. Microscopically, we find that the oscillation is driven by multiple irreversible cycles that hydrolyse fuel molecules such as ATP; the number of phase coherent periods is proportional to the free energy consumed per period. Experimental evidence in support of this general relationship and testable predictions are also presented.

The global demand for data storage is currently outpacing the world's storage capabilities. DNA, the carrier of natural genetic information, offers a stable, resource- and energy-efficient and sustainable data storage solution. In this review, we summarize the fundamental theory, research history, and technical challenges of DNA storage. From a quantitative perspective, we evaluate the prospect of DNA, and organic polymers in general, as a novel class of data storage medium.

Biomolecular networks have to perform their functions robustly. A robust function may have preferences in the topological structures of the underlying network. We carried out an exhaustive computational analysis on network topologies in relation to a patterning function in Drosophila embryogenesis. We found that whereas the vast majority of topologies can either not perform the required function or only do so very fragilely, a small fraction of topologies emerges as particularly robust for the function. The topology adopted by Drosophila , that of the segment polarity network, is a top ranking one among all topologies with no direct autoregulation. Furthermore, we found that all robust topologies are modular—each being a combination of three kinds of modules. These modules can be traced back to three subfunctions of the patterning function, and their combinations provide a combinatorial variability for the robust topologies. Our results suggest that the requirement of functional robustness drastically reduces the choices of viable topology to a limited set of modular combinations among which nature optimizes its choice under evolutionary and other biological constraints. ### Synopsis Biological systems have to function robustly and at the same time to be evolvable and adaptive to diverse and changing environments. Functional robustness as a system's property of the underlying network may have consequences on the network's topological structure ([Waddington, 1957][1]; [Barkai and Leibler, 1997][2]; [Li et al , 2004][3]; [El‐Samad et al , 2005][4]; [Wagner, 2005][5]). For a given function, how many distinct network topologies can perform the function and how many can do so robustly ([Wagner, 2005][5])? What are the key features among these robust topologies—what are common and what are variable? How would nature pick among them? Is it possible to construct a ‘periodic table’ for robust topologies corresponding to a given function? To address these questions, we carried out an exhaustive computational analysis on the network topologies that perform a specific function. The function was chosen to be a well‐defined patterning function in Drosophila embryogenesis, which is highly conserved among all insets, that of setting up a stable periodic pattern of gene expression that defines the sharp boundaries between parasegments ([Figure 1F][6]). The biomolecular network responsible for this patterning function in Drosophila is the segmentation polarity gene network ([Martizez Arias, 1993][7]; [DiNardo et al , 1994][8]; [Perrimon, 1994][9]) ([Figure 1C][6]). This network has both intra‐ and intercellular interactions and its core topology consists of three interacting nodes ([Figure 1D][6]). We constructed a mathematical model to evaluate the ability of performing the patterning function for each and (almost) all topologies consisting of three nodes with intra‐ and intercellular interaction. In the model, the functional behavior of a topology is modeled by differential equations with parameters characterizing the nodes and the interacting links in the topology. The ability of the topology to perform the function is assessed by randomly sampling the parameters and observing the fraction ( Q ) of the sampling that enabled the system to achieve the required patterning ([von Dassow et al , 2000][10]; [Ingolia, 2004][11]). We found that the vast majority of the topologies cannot perform the patterning function ( Q ≈0), implying a severe functional constraint on topology ([Wagner, 2005][5]). On the other hand, many more than a few distinct topologies are robust in performing this patterning function. Interestingly, a common feature emerges when comparing all the robust topologies—each of them can be understood as a particular combination of three submodules (not to be confused with the three nodes) from three groups ([Figure 3B][12]). Each group of submodule corresponds to a subfunction of the patterning function studied. The organization of robust topologies as modular combinations provides nature with multiple choices to solve the patterning problem. Furthermore, each robust core topology can be ‘dressed’ up with additional neutral and/or nearly neutral links, which enhances the variability and flexibility of robust topologies, making them more evolvable and adaptable ([Schuster et al , 1994][13]; [Kirschner and Gerhart, 2005][14]). This ‘periodic table’ of robust topologies also provides us with a framework to suggest and comprehend the topology nature picked. [Figure 1A][6] is the segmentation polarity network constructed in previous studies ([Ingolia, 2004][11]), which corresponds to the topology of [Figure 1B][6]. In this model, the direct autoregulation on wg (W) has no support from the experimental literature but is needed for the model to function robustly. If we disallow this presumed link, the ‘periodic table’ would suggest an alternative of [Figure 1D][6]. The corresponding network of [Figure 1C][6] has experimental support on every node and link in it. To further discriminate the two models, [Figure 1A and C][6], we subject both to mutant tests, requiring them not only to generate the wild‐type pattern but also to produce the observed mutant patterns when the knockout effect is simulated. [Figure 1C][6] and its topology [Figure 1D][6] win out in the tests and stand out as a better working model for the Drosophila segmentation polarity network. The topology [Figure 1D][6] is not the most robust among the topologies that can robustly perform the required patterning function. However, it is the top one among all topologies that do not have any direct autoregulation. Direct positive autoregulation may result in a less flexible system, which may impair the other functional abilities of the Hh and Wg pathways. Thus, the topological variety that resulted from the modular combination can be a...