92C05 Biophysics
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Markov State Modelling as a concept for a coarse grained description of the essential kinetics of a molecular system in equilibrium has gained a lot of atten- tion recently. The last 10 years have seen an ever increasing publication activity on how to construct Markov State Models (MSMs) for very different molecular systems ranging from peptides to proteins, from RNA to DNA, and via molecu- lar sensors to molecular aggregation. Simultaneously the accompanying theory behind MSM building and approximation quality has been developed well be- yond the concepts and ideas used in practical applications. This article reviews the main theoretical results, provides links to crucial new developments, outlines the full power of MSM building today, and discusses the essential limitations still to overcome.
Density functional study of guanine and uracil quartets and of guanine quartet metal/ion complexes
(2000)
The structures and interaction energies of guanine and uracil quartets have been determined by B3LYP hybrid density functional calculations. The total interaction energy $\Delta$E$^{T}$ of the $\it{C}$$_{4h}$-symmetric guanine quartet consisting of Hoogsteen type base pairs with two hydrogen bonds between two neighbour bases is -66.07 kcal/mol at the highest level. The uracil quartet with C6-H6...O4 interactions between the individual bases has only a small interaction energy of -20.92 kcal/mol and the interaction energy of -24.63 kcal/mol for the alternative structure with N3-H3...O4 hydrogen bonds is only slightly more negative. Cooperative effects contribute between 10 and 25 \% to all interaction energies. Complexes of metal ions with G-quartets can be classified into different structure types. The one with Ca$^{2+}$ in the central cavity adopts a $\it{C}$$_{4h}$-symmetric structure with coplanar bases, whereas the energies of the planar and non-planar Na$^{+}$ complexes are almost identical. The small ions Li$^{+}$, Be$^{2+}$, Cu$^{+}$ and Zn$^{2+}$ prefer a non-planar $\it{S}$$_{4}$-symmetric structure. The lack of co-planarity prevents probably a stacking of these base quartets. The central cavity is too small for K$^{+}$ ions and therefore this ion favours in contrast to all other investigated ions a $\it{C}$$_{4}$-symmetric complex, which is 4.73 kcal/mol more stable than the $\it{C}$$_{4h}$-symmetric one. The distance 1.665 {\AA} between K$^{+}$ and the root mean squares plane of the guanine bases is approximately half of the distance between two stacked G-quartets. The total interaction energy of alkaline earth ion complexes exceeds the ones with alkali ions. Within both groups of ions the interaction energy decreases with an increasing row position in the periodic table. The B3LYP and BLYP methods lead to similar structures and energies. Both methods are suitable for hydrogen-bonded biological systems. Compared with the before mentioned methods the HCTH functional leads to longer hydrogen bonds and different relative energies for two U-quartets. Finally we calculated also structures and relative energies with the MMFF94 forcefield. Contrary to all DFT methods, MMFF94 predicts bifurcated C-H...O contacts in the uracil quartet. In the G-quartet the MMFF94 hydrogen bond distances N2-H22...N7 are shorter than the DFT distances, whereas the N1-H1...O6 distances are longer.