Energy landscape phases

In another approach, the micellizatiOTi can be seen as a journey on a multidimensional energy landscape (phase space, i.e., a space spanned by all parameters) towards an equilibrium state that represents a global minimum on the landscape. One can imagine that the most probable path corresponds to the path of minimal energy, which naturally introduces a constraint. Such an approach was recently used by Diamant and coworkers for surfactant micelles [67]. Here, we will briefly review a generic model for block copolymers. 

C.-B. Li, Y. Matsunaga, M. Toda, and T. Komatsuzaki, Phase-space reaction network on a multisaddle energy landscape HCN isomerization, J. Chem. Phys. 123, 184301 (2005). 

In what follows, we use simple mean-field theories to predict polymer phase diagrams and then use numerical simulations to study the kinetics of polymer crystallization behaviors and the morphologies of the resulting polymer crystals. More specifically, in the molecular driving forces for the crystallization of statistical copolymers, the distinction of comonomer sequences from monomer sequences can be represented by the absence (presence) of parallel attractions. We also devote considerable attention to the study of the free-energy landscape of single-chain homopolymer crystallites. For readers interested in the computational techniques that we used, we provide a detailed description in the Appendix. ... 

Development of time-dependent DFS studies have to await further technological challenges in AFM where the lag phase of a mechanical contraption like a tip of AFM probe riding on a cantilever hovering over the rugged surface of a protein anchored on a platform by its very nature is slow compared to time-scales involved in the conformational dynamics from one peak to another in the energy landscape of a protein. As we encountered similar problems in molecular dynamics (MD), density functional studies (DFT), and 3D multi-nuclear NMR studies, analysis of voluminous data is very tedious. 

The energy landscape approach can elucidate such general properties of molecular recognition as the nature of the thermodynamic phases and barriers on the ligand-protein association pathway [127,128]. This method evaluates equilibrium thermodynamic properties of the system from Monte Carlo simulations of the system at a broad temperature range with the aid of the optimized data analysis and the weighted histogram analysis technique [148-153],... 

The Allan variance analyses of energy fluctuations can tell us about the nature of the configurational energy landscapes and the existence of (multidimensional) cooperativity among individual DOFs, enhanced for an intermediate time scale at the transition temperature. However, what can we learn or deduce from an (observed) scalar time series about the geometrical aspects of the underlying multidimensional state (or phase) space buried in the observations The so-called embedding theorems attributed to Whitney [75] and Takens [76] provide us with a clue to the answer of such a question (see also Section VI.A and Refs. 77-80). 

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