Masaki Sasai

Stochastic gene expression as a many-body problem

Gene expression has a stochastic component because of the single-molecule nature of the gene and the small number of copies of individual DNA-binding proteins in the cell. We show how the statistics of such systems can be mapped onto quantum many-body problems. The dynamics of a single gene switch resembles the spin-boson model of a two-site polaron or an electron transfer reaction. Networks of switches can be approximately described as quantum spin systems by using an appropriate variational principle. In this way, the concept of frustration for magnetic systems can be taken over into gene networks. The landscape of stable attractors depends on the degree and style of frustration, much as for neural networks. We show the number of attractors, which may represent cell types, is much smaller for appropriately designed weakly frustrated stochastic networks than for randomly connected networks.

Molecular scale precursor of the liquid–liquid phase transition of water

Spatiotemporal fluctuations of the local structure in liquid water are studied with the molecular-dynamics simulation. At temperatures around and above the melting point, each molecule alternately goes through the structured period and the destructured period. Lifetime of each period spreads from several hundred fs to 10 ps at 0 °C at 1 atm. The order parameter to describe this structural switching fluctuations is derived by carefully filtering out the fast oscillating components from the simulation data. By analyzing the neutron-weighted pair correlation function, we find that the clusters of the structured molecules and the clusters of the destructured molecules are similar to the clusters of low-density amorphous (LDA) ice and the clusters of high-density amorphous (HDA) ice, respectively. Simulated liquid water is, therefore, a composite of the LDA-like clusters and the HDA-like clusters even at temperatures well above the melting point. The large amplitude structural fluctuation of water at around an...

Growth and collapse of structural patterns in the hydrogen bond network in liquid water

Intermittent and chaotic motions of the hydrogen bond network are studied with the molecular dynamics (MD) simulation. By analyzing the fluctuation in the radial distribution function, it is shown that individual water molecule alternately goes through two different periods; the structured period during which the local structure around the molecule is developed more than the average and the destructured period during which the local structure is less developed. At room temperature the lifetime of each period is hierarchically distributed from a few hundreds fsecs to several psecs. This intermittent structural fluctuation is quantitatively analyzed by defining a new quantity, local structure index (LSI). Molecules which have the large LSI value have tendency to be close to each other to form clusters. Temporal and spatial correlations of the structural order are studied with this new method. The analyses of the structural fluctuation provide a new perspective to study the collective motion of water molecules.

Self-Consistent Proteomic Field Theory of Stochastic Gene Switches

We present a self-consistent field approximation approach to the problem of the genetic switch composed of two mutually repressing/activating genes. The protein and DNA state dynamics are treated stochastically and on an equal footing. In this approach the mean influence of the proteomic cloud created by one gene on the action of another is self-consistently computed. Within this approximation a broad range of stochastic genetic switches may be solved exactly in terms of finding the probability distribution and its moments. A much larger class of problems, such as genetic networks and cascades, also remain exactly solvable with this approximation. We discuss, in depth, certain specific types of basic switches used by biological systems and compare their behavior to the expectation for a deterministic switch.

Long time fluctuation of liquid water: 1/f spectrum of energy fluctuation in hydrogen bond network rearrangement dynamics

The power spectrum of the potential energy fluctuation of liquid water is examined and found to yield so‐called 1/f frequency dependence (f is frequency). This is in sharp contrast to spectra of simple liquids (e.g., liquid argon), which exhibit a near white spectrum. This indicates that there exists an extended multiplicity of hydrogen bond network relaxations in liquid water. A simple model of cellular dynamics is proposed to explain this frequency dependence. On the other hand, the cluster dynamics of argon also involves energy fluctuations of a 1/f type, resulting from various relaxation processes at core and surface.

Large vortex-like structure of dipole field in computer models of liquid water and dipole-bridge between biomolecules.

We propose a framework to describe the cooperative orientational motions of water molecules in liquid water and around solute molecules in water solutions. From molecular dynamics (MD) simulation a new quantity “site-dipole field” is defined as the averaged orientation of water molecules that pass through each spatial position. In the site-dipole field of bulk water we found large vortex-like structures of more than 10 Å in size. Such coherent patterns persist more than 300 ps although the orientational memory of individual molecules is quickly lost. A 1-ns MD simulation of systems consisting of two amino acids shows that the fluctuations of site-dipole field of solvent are pinned around the amino acids, resulting in a stable dipole-bridge between side-chains of amino acids. The dipole-bridge is significantly formed even for the side-chain separation of 14 Å, which corresponds to five layers of water. The way that dipole-bridge forms sensitively depends on the side-chain orientations and thereby explains the specificity in the solvent-mediated interactions between biomolecules.

Entropic mechanism of large fluctuation in allosteric transition

A statistical mechanical model of allosteric transitions in proteins is developed by extending the structure-based model of protein folding to cases of multiple native conformations. The partition function is calculated exactly within the model and the free-energy surface reflecting allostery is derived. This approach is applied to an example protein, the receiver domain of the bacterial enhancer-binding protein NtrC. The model predicts the large entropy associated with a combinatorial number of preexisting transition routes. This large entropy lowers the free-energy barrier of the allosteric transition, which explains the large structural fluctuation observed in the NMR data of NtrC. The global allosteric transformation of NtrC is explained by the shift of preexisting distribution of conformations upon phosphorylation, but the local structural adjustment around the phosphorylation site is explained by the complementary induced-fit mechanism. Structural disordering accompanied by fluctuating interactions specific to two allosteric conformations underlies a large number of routes of allosteric transition.

Roles of noise in single and coupled multiple genetic oscillators

The noisy fluctuation of chemical reactions should profoundly affect the oscillatory dynamics of gene circuit. In this paper a prototypical genetic oscillator, repressilator, is numerically simulated to analyze effects of noise on oscillatory dynamics. The oscillation is coherent when the protein number and the rate of the DNA state alteration are within appropriate ranges, showing the phenomenon of coherence resonance. Stochastic fluctuation not only disturbs the coherent oscillation in a chaotic way but also destabilizes the stationary state to make the oscillation relatively stable. Bursting in translation, which is a source of intense stochastic fluctuation in protein numbers, suppresses the destructive effects of the finite leakage rate of protein production and thus plays a constructive role for the persistent oscillation. When multiple repressilators are coupled to each other, the cooperative interactions among repressilators enhance the coherence in oscillation but the dephasing fluctuation among multiple repressilators induces the amplitude fluctuation in the collective oscillation.

Monomer-Shuffling and Allosteric Transition in KaiC Circadian Oscillation

Circadian rhythms in living organisms have long been attributed solely to a transcription-translation loop comprising a negative or positive feedback. The rhythms in cyanobacteria are known to be modulated by kaiC, kaiA and kaiB genes. It was recently shown, however, that their product proteins KaiC, KaiA and KaiB are sufficient to reconstitute the circadian rhythm in the phosphorylation level of KaiC in vitro. It has since been unclear why such an oscillatory behavior can occur in the absence of the apparent transcription-translation feedback. In the meantime, it has been reported that the monomer exchange between KaiC hexamers occurs in a phosphorylation-dependent manner, which suggests that the monomer shuffling is also involved in the circadian rhythm (H. Kageyama et al., Mol. Cell, 23, 161 (2006)). To further clarify the role of the monomer shuffling, we have performed a computational modeling of interactions among Kai proteins assuming the allosteric transition of KaiC hexamer as well as the monomer shuffling. The results show that the existence of both monomer shuffling and allosteric transition can synchronize the phosphorylation level of the KaiC hexamers, and stabilizes its oscillation.

Unidirectional Brownian motion observed in an in silico single molecule experiment of an actomyosin motor

The actomyosin molecular motor, the motor composed of myosin II and actin filament, is responsible for muscle contraction, converting chemical energy into mechanical work. Although recent single molecule and structural studies have shed new light on the energy-converting mechanism, the physical basis of the molecular-level mechanism remains unclear because of the experimental limitations. To provide a clue to resolve the controversy between the lever-arm mechanism and the Brownian ratchet-like mechanism, we here report an in silico single molecule experiment of an actomyosin motor. When we placed myosin on an actin filament and allowed myosin to move along the filament, we found that myosin exhibits a unidirectional Brownian motion along the filament. This unidirectionality was found to arise from the combination of a nonequilibrium condition realized by coupling to the ATP hydrolysis and a ratchet-like energy landscape inherent in the actin-myosin interaction along the filament, indicating that a Brownian ratchet-like mechanism contributes substantially to the energy conversion of this molecular motor.