Topology in Molecular Biology
28 A. Vologodskii Fig. 3.4.Probability of linkage between two relaxed DNA molecules 7,000 and 10,000 base pairs in length as a f ...
3 Monte Carlo Simulation of DNA Topological Properties 29 agree extremely well over the whole range ofσand NaCl concentrations s ...
30 A. Vologodskii and Eb= g 2 ∑kn i=1 θ^2 i is the bending rigidity constant,kBTis the Boltzmann temperature factor. The bending ...
3 Monte Carlo Simulation of DNA Topological Properties 31 It is therefore necessary to choose a value of 〈cosθ〉= ∫π 0 cosθsinθex ...
32 A. Vologodskii and by the corresponding Debye–H ̈uckel potential gives very similar results in Monte Carlo simulations of DNA ...
3 Monte Carlo Simulation of DNA Topological Properties 33 Fig. 3.8.Effective diameter of the model chain as a function of ionic ...
34 A. Vologodskii Fig. 3.9.The simplestknotsand their Alexander polynomials, ∆(t). All four knots that can be drawn with less th ...
3 Monte Carlo Simulation of DNA Topological Properties 35 (1) Wheni=kori=k+ 1, thenak,k=−1andak,k+1= 1, independent of the type ...
36 A. Vologodskii second contour ifi>M. All elements of the Alexander matrix exceptakk, akk+1andakiare zero. The nonzero elem ...
3 Monte Carlo Simulation of DNA Topological Properties 37 Fig. 3.13.The simplest links and their Alexander polynomials, g∆(s,t). ...
38 A. Vologodskii whereφmis the angle of the projection ofrmon thex, yplane with thex axis. The perpendicular to the plane forme ...
3 Monte Carlo Simulation of DNA Topological Properties 39 3.7.2 Simulation of DNA Conformations with Low Probability of Appearan ...
40 A. Vologodskii refers to the coordinates that define the mutual geometry of the specific sites. AlthoughU(x) can greatly incr ...
3 Monte Carlo Simulation of DNA Topological Properties 41 S. Allison, R. Austin, M. Hogan, J. Chem. Phys. 90 , 3843–3854 (1989) ...
4 Dynamics of DNA Supercoiling A. Gabibov, E. Yakubovskaya, M. Lukin, P. Favorov, A. Reshetnyak, and M. Monastyrsky Summary.A ca ...
44 A. Gabibov et al. “closed ribbon”. Here by the termladderwe assume the lattice surface where the points (nucleotides) are loc ...
4 Dynamics of DNA Supercoiling 45 Topoisomerases are much smaller than the polymeric substrates in vivo and their interaction wi ...
46 A. Gabibov et al. where vectorυ⊥is in the frame (t,υgυ⊥), a right-hand system, andtis the unit tangent vector to the curveγ. ...
4 Dynamics of DNA Supercoiling 47 ∂n ∂t ={H, n}, (4.9) whereHis the Hamiltonian of the system determined as the functional of th ...
48 A. Gabibov et al. Fig. 4.2.Principle of the flow linear dichroism (FLD) method. Experimental condi- tions: DNA polymers are o ...
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