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WIREs Comput Mol Sci
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Coarse‐grained models for studying protein diffusion along DNA

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Understanding the molecular mechanism and the fast kinetics of DNA target site recognition by a protein is essential to decipher genetic activity in the cell. The speed of searching DNA may depend on the structural complexity of the proteins and the DNA molecules as well as the cellular environment. Coarse‐grained (CG) molecular dynamics simulations are powerful means to investigate the molecular details of the search performed by protein to locate the target sites. Recent studies showed how different proteins scan DNA and how the search efficiency can be enhanced and regulated by the protein properties. In this review, we discuss computational approaches to study the physical chemistry of DNA search processes using CG molecular dynamics simulations and their advantage in covering long time‐scale biomolecular processes. WIREs Comput Mol Sci 2016, 6:515–531. doi: 10.1002/wcms.1262 This article is categorized under: Structure and Mechanism > Computational Biochemistry and Biophysics
Effect of DNA curvature and supercoiling on the search dynamics of DBPs are measured by calculating proportions of sliding (S), hopping (H), and 3D diffusion (D) adopted by the searching protein as a function of (a) the change in major groove width (ΔW) for circular DNA (circumference, 50–500 bp) and (b) varying numbers of helical twists (Δlk) on 100 bp circular DNA at a 0.02 M salt concentration. The corresponding search efficiency was measured by DNA position probed and the 1D diffusion coefficient (D1) of the interacting protein. (c) The number of DNA base pairs probed by Sap‐1 using sliding dynamics varies with the change in DNA curvature (ΔW). The one‐dimensional diffusion coefficient D1 was calculated for the portions of the simulation during which Sap‐1 scanned the DNA contour via pure sliding (blue circles) and for the portions during which Sap‐1 was bound to the DNA (green circles) by either sliding or hopping dynamics. As sliding frequency decreases sharply for ΔW ≥ 1.8 Å, D1 values were not calculated beyond this point. Gray shaded region denotes DNA minicircles of circumference ≤100 bp. (d) Variation of same DNA position probed and D1 as function of change in linking number, Δlk.
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Effects of salt concentration on (a) sliding, (b) hopping, and (c) 3D diffusion for linear and circular DNA.
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(a) Structural characterization of linear (100 bp) and circular (100 bp) DNA molecules. Unlike the linear B‐DNA, whose major groove widths are constant, circular DNA shows wider major groove widths on the exterior of the circle (Wout) and narrower major groove widths inside the circle (Win). (b) Correlations between the changes in major groove width (ΔW; black) and the changes in potential energy (ΔEP; red) as functions of DNA curvature. ΔW = WoutWin and ΔEP = EPout – EPin. Curvature is defined as the inverse of the radius (r) of the DNA, which is zero for a linear DNA molecule. (c) The variations of Win (black) and corresponding electrostatic potential (EPin; red) as functions of the change in DNA linking number (Δlk).
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Sliding on a flexible DNA. The effect of DNA flexibility on the sliding and hopping propensities (a) as well as on the D1 diffusion coefficient (b).
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Traces (cyan color) of the rotation‐coupled sliding search path of Sap‐1 modeled through different coarse graining prescriptions: (a) Cα, (b) Cα–Cβ, (c) CαFHA, and (d) modified‐Cα models.
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The extent of search dynamics by sliding under the Cα, Cα–Cβ, CαFHA, and Cα‐modified models are measured by calculating (a) MSDz, which is the cumulative distance traveled during a single sliding event by the protein along the Z‐axis of the DNA and (b) the cumulative number of sliding events in terms of the total number of DNA base pairs probed. The effect of conformational space on the efficiency of DNA search is measured by (c) the number of DNA base pairs probed using sliding dynamics and (d) the 1D diffusion coefficient (D1), which is obtained from the linear behavior of the mean square displacement of Sap‐1.
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Effect of salt concentration on the interplay between (a) sliding, (b) hopping, and (c) 3D diffusion in modeling undertaken using the Cα, Cα–Cβ, CαFHA, and Cα‐modified protein–DNA models.
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Conditions required to satisfy sliding criteria by Sap‐1 in the (a) Cα, (b) Cα–Cβ, (c) CαFHA, and (d) Cα‐modified models where R denotes the distance between the center of mass of the recognition helix of Sap‐1 and the center of the closest DNA base pairs and θ represents the orientation angle between them.
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The energetics of the interface in protein–DNA complexes using different coarse‐grained models. (a) The excluded volume energy (Eev) and (b) the electrostatic energy (Eel) calculated by using the Debye–Hückel potential in molecular dynamics simulations of a 100 bp nonspecific DNA molecule with Sap‐1, modeled using the Cα, Cα–Cβ, CαFHA, Cα‐modified protein–DNA models. The mean energy is shown for different salt concentrations.
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The traces of the search path of Sap‐1 around circular DNA of (a) 200 bp, (b) 100 bp, (c) 70 bp, and (d) 60 bp at a salt concentration of 0.02 M. (e–h) The same search paths on 100 bp circular DNA twisted to various extents around the double helix. A negative value of Δlk denotes an under‐twisted DNA structure and a positive value of Δlk denotes an over‐twisted DNA structure. DNA is colored orange, while cyan and green represent the sliding and hopping modes, respectively.
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Coarse‐grained representations of the protein–DNA complex of the 93‐residue transcription factor protein Sap‐1 (PDB id: 1bc8) with DNA modeled using the (a) Cα, (b) CαFHA, (c) Cα–Cβ, and (d) Cα‐modified models. The dotted circles represent the specified distance between the protein and the DNA. The recognition region of Sap‐1 is labeled with blue and red colors, where the blue region is positively charged and red region is negatively charged. Each DNA nucleotide is presented through negatively charged phosphate beads (orange color), yellow colored sugar beads, and small pink colored bases.
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