A mathematical model for sarcomere mechanics in cross-striated muscles taking into account the stretch and twist of actin filaments

A model of sarcomere mechanics, which takes into account the elongation of the actin and myosin filaments and twisting of the actin filaments during muscle contraction is suggested. The model accounts for the experimentally observed phenomena of the stretch and twist of actin filaments due to strong binding of myosin heads and pulling force. Some model parameters were estimated from published experimental data. The results of modelling suggest that the twist of actin filaments may play an essential role in mechanical responses of contracting muscle fibres to stepwise changes in their length.     

A mathematical model of the sarcomere mechanics of cross-striated muscle with consideration of the stretch and twist of actin filaments

A mathematical model of sarcomere mechanics, which takes into account the elongation of actin and myosin filaments and also twisting of the actin filaments in the sarcomere of striated muscle during contraction is presented. The model accounts for the experimentally observed phenomena of the stretch and twist of the actin filaments due to strong binding of myosin heads and the pulling force. Some model parameters were estimated from published experimental data. The results of modeling show that the twist of actin filaments can play a substantial role in the mechanical responses of contracting muscle fibers to step changes of their length.     

A model of the strain-induced B-Z transition

The B-to-Z transition in supercoiled circular DNA is modeled as a strain-induced nonlinear excitation process. Using a model, in which DNA is regarded as a chain of units with a bistable energy function along the twisting coordinate together with a harmonic inter-unit interaction, we show that a Z region and the accompanying two B-Z junctions of finite width appear naturally as a solution of nonlinear equations, when the strain exceeds a critical value. We examine the B-Z transition behaviour as a function of twist under various situations. We also analyse available experimental results on B-Z transition in supercoiled plasmid with G-C insertions by this mechanistic model in order to estimate the magnitude of model parameters. The energy barrier of the B-Z transition is estimated to be of the order of 1 kcal/mole per base pair. The analysis shows that if the length of the insertion is less than a certain value, the entire insertion converts to Z form at a transition point, but if the insertion is much longer, the B-Z transition exhibits a different behavior, in which part of the insertion flips to Z form and the Z region expands linearly upon changing linking number.     

A Model of the Strain-induced B-Z Transition

Abstract

The B-to-Z transition in supercoiled circular DNA is modeled as a strain-induced nonlinear excitation process. Using a model, in which DNA is regarded as a chain of units with a bistable energy function along the twisting coordinate together with a harmonic inter-unit interaction, we show that a Z region and the accompanying two B-Z junctions of finite width appear naturally as a solution of nonlinear equations, when the strain exceeds a critical value. We examine the B-Z transition behaviour as a function of twist under various situations. We also analyse available experimental results on B-Z transition in supercoiled plasmid with G-C insertions by this mechanistic model in order to estimate the magnitude of model parameters. The energy barrier of the B-Z transition is estimated to be of the order of 1 kcal/mole per base pair. The analysis shows that if the length of the insertion is less than a certain value, the entire insertion converts to Z form at a transition point, but if the insertion is much longer, the B-Z transition exhibits a different behavior, in which part of the insertion flips to Z form and the Z region expands linearly upon changing linking number.     

Structure of plectonemically supercoiled DNA

Using electron microscopy and topological methods, we have deduced an average structure for negatively supercoiled circular DNA in solution. Our data suggest that DNA has a branched plectonemic (interwound) form over the range of supercoiling tested. The length of the superhelix axis is constant at 41% of the DNA length, whereas the superhelix radius decreases essentially hyperbolically as supercoiling increases. The number of supercoils is 89% of the linking deficit. Both writhe and twist change with supercoiling, but the ratio of the change in writhe to the change in twist is fixed at 2.6:1. The extent of branching of the superhelix axis is proportional to the length of the plasmid, but is insensitive to superhelix density. The relationship between DNA flexibility constants for twisting and bending calculated using our structural data is similar to that deduced from previous studies. The extended thin form of plectonemically supercoiled DNA offers little compaction for cellular packaging, but promotes interaction between cis-acting sequence elements that may be distant in primary structure. We discuss additional biological implications of our structural data.     

Link, twist, energy, and the stability of DNA minicircles

We describe how the stability properties of DNA minicircles can be directly read from plots of various biologically intuitive quantities along families of equilibrium configurations. Our conclusions follow from extensions of the mathematical theory of distinguished bifurcation diagrams that are applied within the specific context of an elastic rod model of minicircles. Families of equilibria arise as a twisting angle alpha is varied. This angle is intimately related to the continuously varying linking number Lk for nicked DNA configurations that is defined as the sum of Twist and Writhe. We present several examples of such distinguished bifurcation diagrams involving plots of the energy E, linking number Lk, and a twist moment m3, along families of cyclized equilibria of both intrinsically straight and intrinsically curved DNA fragments.     

The simulation of aerial movement--IV. A computer simulation model

A computer simulation model of human airborne movement is described. The body is modelled as 11 rigid linked segments with 17 degrees of freedom which are chosen with a view to modelling twisting somersaults. The accuracy of the model is evaluated by comparing the simulation values of the angles describing somersault, tilt and twist with the corresponding values obtained from film data of nine twisting somersaults. The maximum deviations between simulation and film are found to be 0.04 revolutions for somersault, seven degrees for tilt and 0.12 revolutions for twist. It is shown that anthropometric measurement errors, from which segmental inertia parameters are calculated, have a small effect on a simulation, whereas film digitization errors can account for a substantial part of the deviation between simulation and film values.     

Topological distributions and the torsional rigidity of DNA. A Monte Carlo study of DNA circles

Distributions of the linking number of circular DNA molecules, defined as the sum of twist and the writhing number, are obtained by Monte Carlo simulations of small, randomly closed DNA circles. We estimate the relative contributions of fluctuations in twist and writhe to the linking number distribution, as functions of DNA size. Published experimental data on topoisomer distributions in circular DNA molecules are interpreted to estimate the torsional rigidity of DNA in solution. We show that ignoring the writhe component of the linking number distribution, even for DNA circles as small as 250 base-pairs, leads to an underestimate for the torsional stiffness of the double helix. The value of the torsional modulus obtained from this analysis, C = 3.4 X 10(-19) erg cm, is from 10 to 40% larger than that estimated by others and more than twice as large as the values obtained from fluorescence depolarization or other time-resolved spectroscopic measurements. We also develop further the theoretical treatment of ring closure probabilities for DNA described in the previous article. It is shown that the torsional part of the ring closure probability, phi 0,1 (tau 0) is a periodic function of DNA length that contributes strongly to the ring closure probability for short chains but makes negligible contributions for chains over 1000 base-pairs in length.     

Sequence dependence of DNA conformational flexibility

By using conformational free energy calculations, we have studied the sequence dependence of flexibility and its anisotropy along various conformational variables of DNA base pairs. The results show the AT base step to be very flexible along the twist coordinate. On the other hand, homonucleotide steps, GG(CC) and AA(TT), are among the most rigid sequences. For the roll motion that would correspond to a bend, the TA step is most flexible, while the GG(CC) step is least flexible. The flexibility of roll is quite anisotropic; the ratio of fluctuations toward the major and minor grooves is the largest for the GC step and the smallest for the AA(TT) and CG steps. Propeller twisting of base pairs is quite flexible, especially of A.T base pairs; propeller twist can reach 19 degrees by thermal fluctuation. We discuss the effect of electrostatic parameters, comparison with available experimental results, and biological relevance of these results.     

The response of DNA length and twist to changes in ionic strength

We examine twist‐stretch coupling of unconstrained DNA using polyelectrolyte theory as applied to a line‐charge model along with published data on the ionic‐strength dependence of the twist angle. We conclude that twist‐stretch coupling is negative: environmental changes that stretch free DNA, unconstrained by externally applied pulling or twisting forces, are accompanied by unwinding of the double helix. We also analyze a helical model and conclude that the observed unwinding of the DNA helix when ionic strength is decreased is driven by radial swelling of the helix. © 2014 Wiley Periodicals, Inc. Biopolymers 103: 223–226, 2015.     

Analysis of conformational parameters in nucleic acid fragments. II. Co-crystal complexes of nucleic acid bases.

Studies have been made of conformational parameters in co-crystal complexes and compounds of nucleic acid bases in which there is the possibility of formation of hetero-base-pairs. Using published data extracted from the Cambridge structural database, a total of 37 base-pairs were found, of which 25 were hetero-pairs and 12 homo-pairs. These base-pairs were subject to analysis to reveal hydrogen bond parameters, propeller twist, buckle and C1'-C1' separation (or a similar parameter if C1' atoms were not present). Hetero-pairs were found to show larger twists than homo-pairs, the magnitude of twist being unrelated to hydrogen bond parameters or buckle value. The propeller twisting is less pronounced in these nucleic acid bases than in nucleosides, but still has a significant magnitude. Propeller twisting in hetero-pairs is found to be larger than in homo-pairs. Hetero-pairs appear to be formed preferentially in competitive situations.     

Extension of torsionally stressed DNA by external force.

Metropolis Monte Carlo simulation was used to study the elasticity of torsionally stressed double-helical DNA. Equilibrium distributions of DNA conformations for different values of linking deficit, external force, and ionic conditions were simulated using the discrete wormlike chain model. Ionic conditions were specified in terms of DNA effective diameter, i.e., hard-core radius of the model chain. The simulations show that entropic elasticity of the double helix depends on how much it is twisted. For low amounts of twisting (less than about one turn per twist persistence length) the force versus extension is nearly the same as in the completely torsionally relaxed case. For more twisting than this, the molecule starts to supercoil, and there is an increase in the force needed to realize a given extension. For sufficiently large amounts of twist, the entire chain is plectonemically supercoiled at low extensions; a finite force must be applied to obtain any extension at all in this regime. The simulation results agree well with the results of recent micromanipulation experiments.     

Twist propagation in dinucleosome arrays

We present a Monte Carlo simulation study of the distribution and propagation of twist from one DNA linker to another for a two-nucleosome array subjected to externally applied twist. A mesoscopic model of the array that incorporates nucleosome geometry along with the bending and twisting mechanics of the linkers is employed and external twist is applied in stepwise increments to mimic quasistatic twisting of chromatin fibers. Simulation results reveal that the magnitude and sign of the imposed and induced twist on contiguous linkers depend strongly on their relative orientation. Remarkably, the relative direction of the induced and applied twist can become inverted for a subset of linker orientations—a phenomenon we refer to as “twist inversion”. We characterize the twist inversion, as a function of relative linker orientation, in a phase diagram and explain its key features using a simple model based on the geometry of the nucleosome/linker complex. In addition to twist inversion, our simulations reveal “nucleosome flipping”, whereby nucleosomes may undergo sudden flipping in response to applied twist, causing a rapid bending of the linker and a significant change in the overall twist and writhe of the array. Our findings shed light on the underlying mechanisms by which torsional stresses impact chromatin organization.     

Conformation and rigidity of DNA microcircles containing waf1 response element for p53 regulatory protein

The tumor-suppressor activity of p53 is closely related to its DNA-binding properties. It binds a number of DNA response-elements and it is likely that these share a common structural feature. Here, we present a new, general method to determine the absolute twist of flexible DNA promoter sequences based on direct imaging of the topology of microcircles containing the sequences. We have used magnetically driven dynamic force microscopy ("MacMode" AFM) to observe, in solution, the conformation of 168 base-pair DNA microcircles, each containing four equally spaced copies of the waf1/cip1/p21 p53 response-element. Analysis of the images showed that the microcircles are markedly puckered with a small excess of negatively writhed molecules. The average measured values of writhe are 0.109+/-0.013 (for 60 positively writhed molecules) and -0.098+/-0.011 (for 65 negatively writhed molecules). These values lead directly to a difference in linking number for the positively and negatively writhed molecules prior to ligation, from which we derive a twist mismatch of 178 degrees (overtwist). This is 44.5 degrees for each 42-mer precursor containing a single waf1/cip1/p21 p53 response-element, in good agreement with the range of values deduced by indirect biochemical techniques. The two values of writhe may also be used to determine the ratio of the bending (B) to twisting (C) rigidity, yielding B/C=0.23. This is about one-third of the value for long, random-sequence DNA, suggesting that the waf1/cip1/p21 p53 response-element is extremely flexible, a result that is also consistent with indirect biochemical experiments. These results support the idea, proposed by us earlier, that torsional stress may play a role in the regulation of p53 binding through modulation of twist at the binding site.     

Twist limits for late twisting double somersaults on trampoline

An angle-driven computer simulation model of aerial movement was used to determine the maximum amount of twist that could be produced in the second somersault of a double somersault on trampoline using asymmetrical movements of the arms and hips. Lower bounds were placed on the durations of arm and hip angle changes based on performances of a world trampoline champion whose inertia parameters were used in the simulations. The limiting movements were identified as the largest possible odd number of half twists for forward somersaulting takeoffs and even number of half twists for backward takeoffs. Simulations of these two limiting movements were found using simulated annealing optimisation to produce the required amounts of somersault, tilt and twist at landing after a flight time of 2.0 s. Additional optimisations were then run to seek solutions with the arms less adducted during the twisting phase. It was found that 3½ twists could be produced in the second somersault of a forward piked double somersault with arms abducted 8° from full adduction during the twisting phase and that three twists could be produced in the second somersault of a backward straight double somersault with arms fully adducted to the body. These two movements are at the limits of performance for elite trampolinists.     

Structure of a B-DNA decamer with a central T-A step: C-G-A-T-T-A-A-T-C-G.

The X-ray crystal structure analysis of the decamer C-G-A-T-T-A-A-T-C-G has been carried out to a resolution of 1.5 A. The crystals are space group P2(1)2(1)2(1), cell dimensions a = 38.60 A, b = 39.10 A, c = 33.07 A. The structure was solved by molecular replacement and refined with X-PLOR and NUCLSQ. The final R factor for a model with 404 DNA atoms, 108 water molecules and one magnesium hexahydrate cation is 15.7%. The double helix is essentially isostructural with C-G-A-T-C-G-A-T-C-G, with closely similar local helix parameters. The structure of the T-T-A-A center differs from that found in C-G-C-G-T-T-A-A-C-G-C-G in that the minor groove in our decamer is wide at the central T-A step rather than narrow, and the twist angle of the T-A step is small (31.1 degrees) rather than large. Whereas the tetrad model provides a convenient framework for discussing local DNA helix structure, it cannot be the entire story. The articulated helix model of DNA structure proposes that certain sequence regions of DNA show preferential twisting or bending properties, whereas other regions are less capable of deformation, in a manner that may be useful in sequence recognition by drugs and protein. Further crystal structure analyses should help to delineate the precise nature of sequence-dependent articulation in the DNA double helix.     

Energetics of DNA twisting. II. Topoisomer analysis

A gel electrophoresis method has been developed for resolving small (approximately equal to 250 bp DNA topoisomers. In this size range only one major topoisomer band is observed, except for ligase closure conditions in which the probabilities are nearly equal for circularization by untwisting and overtwisting the corresponding linear DNA. The two probabilities are nearly equal when delta Tw is close to 0.5, if the mean helical twist of the linear DNA is n + delta Tw, where n is an integer and delta Tw is the fractional twist. We determine delta Tw of the linear DNA in standard conditions (20 degrees C, no ethidium) by titration experiments in which delta Tw is varied at the time of ligase closure, either by changing temperature or ethidium concentration. The endpoint (delta Tw = 0.5) is found when the two topoisomers formed by untwisting and overtwisting are present at equal concentrations. This analysis assumes that the net writhe is zero and the DNA helix is isotropically bendable. The results confirm the analysis of cyclization probabilities given in the preceding paper: delta Tw = 0 at the two maxima in the curve of j-factor versus DNA length and delta Tw = 0.5 at the minimum. Consequently, we can determine the DNA lengths at which Tw takes on integral values and use them to measure precisely the average helix repeat. From the difference between the delta Tw values of DNAs with 237 and 247 bp, we obtain an approximate value for the helix repeat of h = 10.4 +/- 0.1 bp/turn, in good agreement with earlier values found by the band-shift and nuclease-cutting methods. The twist is integral at 250.8 +/- 0.4 bp and from h = 10.4 +/- 0.1 we find n = 24; then 250.8/24 gives h = 10.45 +/- 0.02 bp/turn. The mean linking number (Lk) changes in a stepwise manner as delta Tw is varied for 250 bp DNAs. This result is expected when the free energy of twisting half a turn becomes large compared to thermal fluctuations. In these experiments, it is possible to obtain the mean Tw value from the mean Lk value only when delta Tw = 0.5, and consequently the mean Lk value is not simply related to DNA length for 250 bp DNAs except when delta Tw = 0.5.(ABSTRACT TRUNCATED AT 400 WORDS)     

ISWI induces nucleosome sliding on nicked DNA.

The ATPase ISWI is the molecular motor of several remodeling factors that trigger nucleosome sliding in vitro. In search for the underlying mechanism, we found that unilateral binding of ISWI to a model nucleosome correlated with directional movement of the nucleosome toward the enzyme. It has been proposed that ISWI might loosen histone-DNA interactions through twisting DNA. However, nucleosome sliding assays on nicked DNA substrates suggest that propagation of altered twist is not involved. Surprisingly, nicks in the linker DNA in front of the nucleosome facilitate sliding. These data suggest that the rate of nucleosome sliding is limited by a conformational change other than twisting, such as the formation of a short loop, of DNA at the entry into the nucleosome.