We report molecular dynamics simulations that induce, over periods of 40-500 ps, the unbinding of biotin from avidin by means of external harmonic forces with force constants close to those of AFM cantilevers. The applied forces are sufficiently large to reduce the overall binding energy enough to yield unbinding within the measurement time. Our study complements earlier work on biotin-streptavidin that employed a much larger harmonic force constant. The simulations reveal a variety of unbinding pathways, the role of key residues contributing to adhesion as well as the spatial range over which avidin binds biotin. In contrast to the previous studies, the calculated rupture forces exceed by far those observed. We demonstrate, in the framework of models expressed in terms of one-dimensional Langevin equations with a schematic binding potential, the associated Smoluchowski equations, and the theory of first passage times, that picosecond to nanosecond simulation of ligand unbinding requires such strong forces that the resulting protein-ligand motion proceeds far from the thermally activated regime of millisecond AFM experiments, and that simulated unbinding cannot be readily extrapolated to the experimentally observed rupture.

A phenomenological framework corresponding to equilibrium thermodynamics is constructed for steady states. All the key concepts including entropy are operationally defined.If a system is strictly linear, the resultant Gibbs relation justifies the postulated form in the extended irreversible thermodynamics. The resultant Maxwell's relations and stability criteria give various le Chatelier-Braun type qualitative predictions. A phenomenological fluctuation theory around steady states is also formulated.

Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary layers with technically difficult asymptotic matching, and WKB analysis. In contrast to conventional methods, the renormalization group approach requires neither ad hoc assumptions about the structure of perturbation series nor the use of asymptotic matching. Our renormalization group approach provides approximate solutions which are practically superior to those obtained conventionally, although the latter can be reproduced, if desired, by appropriate expansion of the renormalization group approximant. We show that the renormalization group equation may be interpreted as an amplitude equation, and from this point of view develop reductive perturbation theory for partial differential equations describing spatially-extended systems near bifurcation points, deriving both amplitude equations and the center manifold.

It has been suggested that principal component analysis can identify slow modes in proteins and, thereby, facilitate the study of long time dynamics. However, sampling errors due to finite simulation times preclude the identification of slow modes that can be used for this purpose. This is demonstrated numerically with the aid of simulations of the protein G-actin and analytically with the aid of a model which is exactly recoverable by principal component analysis. Although principal component analysis usually demonstrates that a set of a small number of modes captures the majority of the fluctuations, the set depends on the particular sampling time window and its width.

We present a computationally efficient scheme of modeling the phase-ordering dynamics of thermodynamically unstable phases. The scheme utilizes space-time discrete dynamical systems, viz. , cell dynamical systems (CDS). Our proposal is tantamount to proposing new Ansatze for the kinetic-level description of the dynamics. Our present exposition consists of two parts: part I (this paper) deals mainly with methodology and part II [S. Puri and Y. Oono, Phys. Rev. A (to be published)] gives detailed demonstrations.In this paper we provide a detailed exposition of model construction, structural stability of constructed models (i.e. , insensitivity to details), stability of the scheme, etc. We also consider the relationship between the CDS modeling and the conventional description in terms of partial differential equations. This leads to a new discretization scheme for semilinear parabolic equations and suggests the necessity of a branch of applied mathematics which could be called "qualitative numerical analysis. "

Computationally efficient discrete space-time models of phase-ordering dynamics of thermodynamically unstable systems (e.g., spinodal decomposition) are proposed. Two-dimensional lattice (100x100) simulations were performed to obtain scaled form factors.PACS numbers: 81.30. Hd, 02.70.+d, 64.60.Cn One of the difficult outstanding problems in phase transitions is that of the ordering dynamics of thermodynamically unstable systems, e.g., quenched binary alloys. l The process depends crucially on whether the order parameter of the system is conserved or not. In the former case the process has been called spinodal decomposition. In this Letter, to cover both cases, we use the term phase ordering for the ordering process of unstable phases in general.The purpose of the present Letter is to propose computationally efficient models of phase-ordering dynamics utilizing discretized space and time corresponding to the usual coarse-grained description of the dynamics.The theoretical study of phase ordering has a long history since the days of Cahn and Hilliard, 2 but the true revitalization of the study came from the observation of the approximate scaling law in Monte Carlo simulations by Marro et at. 3,4 They suggested that the normalized form factor S(k,t) has a scaling regime in which it behaves as S(kj)=Kt) d &(lU)kh(1)where k is the wave vector, t the time, O a master function (scaling function), lit) a time-dependent length scale which behaves as l(t) -t for some positive number , and d the spatial dimensionality. Furukawa 5 also argued for (1). Experimentally, the exponent seems to behave as follows. When the order parameter is not conserved 0-y, 6 and when it is conserved but without hydrodynamic interactions, 0-j. 7 If hydrodynamics is relevant, 0-l. 8 Analytically, Ohta, Jasnow, and Kawasaki 9 studied the nonconserved-order-parameter (NOP) case and obtained

. For the conserved-order-parameter (COP) case, Ohta 10 studied the case of the off-critical quench and obtained

We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena are RG equations. The renormalized perturbation approach may be simpler to use than other approaches, because it does not require the use of asymptotic matching, and yields practically superior approximations.

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