Mechanism studies of the activation of DNA methyltransferase DNMT1 triggered by histone H3 ubiquitination, revealed by multi-scale molecular dynamics simulations.

DNMT1 is a DNA methyltransferase that catalyzes and maintains methylation in CpG dinucleotides. It blocks the entrance of DNA into the catalytic pocket via the replication foci targeting sequence (RFTS) domain. Recent studies have shown that an H3-tail-conjugated two-mono-ubiquitin mark (H3Ub2) activates DNMT1 by binding to the RFTS domain. However, the activation mechanism of DNMT1 remains unclear. In this work, we combine various sampling methods of extensive simulations, including conventional molecular dynamics, Gaussian-accelerated molecular dynamics, and coarse-grained molecular dynamics, to elucidate the activation mechanism of DNMT1. Geometric and energy analyses show that binding of H3Ub2 to the RFTS domain of DNMT1 results in the bending of the α4-helix in the RFTS domain at approximately 30°-35°, and the RFTS domain rotates ∼20° anti-clockwise and moves ∼3 Å away from the target recognition domain (TRD). The hydrogen-bonding network at the RFTS-TRD interface is significantly disrupted, implying that the RFTS domain is dissociated from the catalytic core, which contributes to activating the auto-inhibited conformation of DNMT1. These results provide structural and dynamic evidence for the role of H3Ub2 in regulating the catalytic activity of DNMT1.

Efficient scheme for parametric fitting of data in arbitrary dimensions.

We propose an efficient scheme for parametric fitting expressed in terms of the Legendre polynomials. For continuous systems, our scheme is exact and the derived explicit expression is very helpful for further analytical studies. For discrete systems, our scheme is almost as accurate as the method of singular value decomposition. Through a few numerical examples, we show that our algorithm costs much less CPU time and memory space than the method of singular value decomposition. Thus, our algorithm is very suitable for a large amount of data fitting. In addition, the proposed scheme can also be used to extract the global structure of fluctuating systems. We then derive the exact relation between the correlation function and the detrended variance function of fluctuating systems in arbitrary dimensions and give a general scaling analysis.

Dynamics of growing surfaces by linear equations in 2+1 dimensions.

An extensive study on the (2+1) -dimensional super-rough growth processes, described by a special class of linear growth equations, is undertaken. This special class of growth equations is of theoretical interests since they are exactly solvable and thus provide a window for understanding the intriguing anomalous scaling behaviors of super-rough interfaces. We first work out the exact solutions of the interfacial heights and the equal-time height difference correlation functions. Through our rigorous analysis, the detailed asymptotics of the correlation function in various time regimes are derived. Our obtained analytical results not only affirm the applicability of anomalous dynamic scaling ansatz but also offer a solid example for understanding a distinct universal feature of super-rough interfaces: the local roughness exponent is always equal to 1. Furthermore, we also perform some numerical simulations for illustration. Finally, we discuss what are the essential ingredients for constructing super-rough growth equations.

Anomalous scaling of superrough growing surfaces: from correlation functions to residual local interfacial widths and scaling exponents.

A study on the (1+1) -dimensional superrough growth processes is undertaken. We first work out the exact relations among the local interfacial width w , the correlation function G , and the pth degree residual local interfacial width w(p) with p=1,2,3,... . The relations obtained are exact and thus can be applied to any (1+1) -dimensional growth processes in the continuum limit, no matter whether the interface is superrough or not. Then we investigate the influence of the macroscopic structure formation on the scaling behavior of the superrough growth processes. Moreover, we show analytically that the residual local interfacial width w(p) excludes only the influence of the macroscopic structure on the scaling behavior of the system and retains the true scaling behavior originating from the stochastic nature of the system. Finally, we analyze and simulate some superrough growth models for demonstration.

Superroughening by linear growth equations with spatiotemporally correlated noise.

We give an extensive study on a class of interfacial superroughening processes with finite lateral system size in 1+1 dimensions described by linear growth equations with spatiotemporally power-law decaying correlated noise. Since some of these processes have an extremely long relaxation time, we first develop a very efficient method capable of simulating the interface morphology of these growth processes even in very late time. We numerically observe that this class of superrough growth processes indeed gradually develops macroscopic structures with the lateral size comparable to the lateral system size. Through the rigorous analytical study of the equal-time height difference correlation function, the different-time height difference correlation function, and the local width, we explicitly evaluate not only the leading anomalous dynamic scaling term but also all the subleading anomalous dynamic scaling terms which dominate over the ordinary dynamic scaling term. Moreover, the relation between the macroscopic structure formation and anomalous interfacial roughening of the superrough growth processes is analytically investigated in detail.

Extraction of backgrounds in fluctuating systems.

We undertake an extensive analytical study on the "generalized detrended fluctuation analysis" method, designed to detect the scaling behaviors of fluctuating systems but exclude out the influences of the backgrounds (or the trends). Through our extensive studies, we systematically extract out the exact backgrounds (or the trends) of the fluctuating systems to any order, expressed in terms of the Legendre polynomial. Our results are exact and can be applied to any (1+1)-dimensional continuous fluctuating systems.

Initial-stage growth phenomena and distribution of local configurations of the restricted solid-on-solid model.

We take a detailed study on the restricted solid-on-solid (RSOS) model with finite nearest-neighbor height difference S. We numerically show that, for all finite values of S, the system belongs to the random-deposition (RD) class in the early time stage and then crossovers to the Kardar-Parisi-Zhang (KPZ) class. We find that the crossover time scales as Szeta with the crossover exponent zeta=2.06. Besides, we analytically study the RSOS model by grouping consecutive sites into local configurations to obtain the Markov chain describing the time evolution of the probability distribution of these local configurations. For demonstration, we use the RSOS model with S=2 as an explicit example and calculate the correlation functions and even scaling exponents based on the obtained probability distribution of local configurations. The results are very consistent with those obtained from direct simulation of the RSOS model.

Extensive studies on linear growth processes with spatiotemporally correlated noise in arbitrary substrate dimensions.

An extensive analytical and numerical study on a class of growth processes with spatiotemporally correlated noise in arbitrary dimension is undertaken. In addition to the conventional investigation on the interface morphology and interfacial widths, we pay special attention to exploring the characteristics of the slope-slope correlation function S(r,t) and the [Q]-th degree residual local interfacial width w[Q](l,t), whose importance has been somewhat overlooked in the literature. Based on the above analysis, we give a plausible theoretical explanation about the various experimental observations of kinetically and thermodynamically unstable surface growth. Furthermore, through explicit examples, we show that the statistical methods of calculating the exponents (including the dynamic exponent z, the global roughness exponent α, and the local roughness exponent α(loc)), based on the scaling of S(r,t) and w[Q](l,t), are very reliable and rarely influenced by the finite time and/or finite-size effects. Another important issue we focus on in this paper is related to numerical calculation. For the specific class of growth processes discussed in this paper, we develop a very efficient and accurate algorithm for numerical calculation of the dynamics of interface configuration, the structure factor, the various correlation functions, the interfacial width and its variants in arbitrary dimensions, even with very large system size and very late time. The proposed systematical algorithm can be easily generalized to other linear processes and some special nonlinear processes.

On the long-term fitness of cells in periodically switching environments.

Because all the cell populations are capable of making switches between different genetic expression states in response to the environmental change, Thattai and van Oudenaarden (Genetics 167, 523-530, 2004) have raised a very interesting question: In a constantly fluctuating environment, which type of cell population (heterogeneous or homogeneous) is fitter in the long term? This problem is very important to development and evolution biology. We thus take an extensive analysis about how the cell population evolves in a periodically switching environment either with symmetrical time-span or asymmetrical time-span. A complete picture of the phase diagrams for both cases is obtained. Furthermore, we find that the systems with time-dependent cellular transitions all collapse to the same set of dynamical equations with the modified parameters. Furthermore, we also explain in detail how the fitness problem bears much resemblance to the phenomenon, stochastic resonance, in physical sciences. Our results could be helpful for the biologists to design artificial evolution experiments and unveil the mystery of development and evolution.