The dynamical transition in proteins and non-Gaussian behavior of low frequency modes in Self Consistent Normal Mode Analysis

Self Consistent Normal Mode Analysis (SCNMA) is applied to heme c type cytochrome f to study temperature dependent protein motion. Classical Normal Mode Analysis (NMA) assumes harmonic behavior and the protein Mean Square Displacement (MSD) has a linear dependence on temperature. This is only consistent with low temperature experimental results. To connect the protein vibrational motions between low temperature and physiological temperature, we have incorporated a fitted set of anharmonic potentials into SCNMA. In addition, Quantum Harmonic Oscillator (QHO) theory has been used to calculate the displacement distribution for individual vibrational modes. We find that the modes involving soft bonds exhibit significant non-Gaussian dynamics at physiological temperature, which suggests it may be the cause of the non-Gaussian behavior of the protein motions probed by Elastic Incoherent Neutron Scattering (EINS). The combined theory displays a dynamical transition caused by the softening of few "torsional" modes in the low frequency regime (< 50cm-1or 0.6ps). These modes change from Gaussian to a classical distribution upon heating. Our theory provides an alternative way to understand the microscopic origin of the protein dynamical transition.Comment: 17 pages, 6 figures, 1 tabl

Dynamical versus statistical mesoscopic models for DNA denaturation

We recently proposed a dynamical mesoscopic model for DNA, which is based, like statistical ones, on site-dependent finite stacking and pairing enthalpies. In the present article, we first describe how the parameters of this model are varied to get predictions in better agreement with experimental results that were not addressed up to now, like mechanical unzipping, the evolution of the critical temperature with sequence length, and temperature resolution. We show that the model with the new parameters provides results that are in quantitative agreement with those obtained from statistical models. Investigation of the critical properties of the dynamical model suggests that DNA denaturation looks like a first-order phase transition in a broad temperature interval, but that there necessarily exists, very close to the critical temperature, a crossover to another regime. The exact nature of the melting dynamics in this second regime still has to be elucidated. We finally point out that the descriptions of the physics of the melting transition inferred from statistical and dynamical models are not completely identical and discuss the relevance of our model from the biological point of view

Statistical Mechanics of Torque Induced Denaturation of DNA

A unifying theory of the denaturation transition of DNA, driven by temperature T or induced by an external mechanical torque Gamma is presented. Our model couples the hydrogen-bond opening and the untwisting of the helicoidal molecular structure. We show that denaturation corresponds to a first-order phase transition from B-DNA to d-DNA phases and that the coexistence region is naturally parametrized by the degree of supercoiling sigma. The denaturation free energy, the temperature dependence of the twist angle, the phase diagram in the T,Gamma plane and isotherms in the sigma, Gamma plane are calculated and show a good agreement with experimental data.Comment: 5 pages, 3 figures, model improve

Stacking Interactions in Denaturation of DNA Fragments

A mesoscopic model for heterogeneous DNA denaturation is developed in the framework of the path integral formalism. The base pair stretchings are treated as one-dimensional, time dependent paths contributing to the partition function. The size of the paths ensemble, which measures the degree of cooperativity of the system, is computed versus temperature consistently with the model potential physical requirements. It is shown that the ensemble size strongly varies with the molecule backbone stiffness providing a quantitative relation between stacking and features of the melting transition. The latter is an overall smooth crossover which begins from the \emph{adenine-thymine} rich portions of the fragment. The harmonic stacking coupling shifts, along the $T$-axis, the occurrence of the multistep denaturation but it does not change the character of the crossover. The methods to compute the fractions of open base pairs versus temperature are discussed: by averaging the base pair displacements over the path ensemble we find that such fractions signal the multisteps of the transition in good agreement with the indications provided by the specific heat plots.Comment: European Physical Journal E (2011) in pres

RFabsorption involving biological macromolecules

The fundamental intramolecular frequency of a globular protein can be obtained from the measurements of acoustic velocities of bulk protein matter. This lowest frequency for common size molecules is shown to be above several hundred GHz. All modes below this frequency would then be intermolecular modes or bulk modes of the molecule and surrounding matter or tissue. The lowest frequency modes of an extended DNA double helix are also shown to be bulk modes because of interaction with water. Only DNA modes, whose frequency is well above 4 GHz, can be intrahelical modes, that is, confined to the helix rather than in the helix plus surroundings. Near 4 GHz, they are heavily damped and, therefore, not able to resonantly absorb. Modes that absorb radio frequency (RF) below this frequency are bulk modes of the supporting matter. Bulk modes rapidly thermalize all absorbed energy. The implication of these findings for the possibility of athermal RF effects is considered. The applicability of these findings for other biological molecules is discussed. (C) 2004 Wiley-Liss, Inc

Calculated enhancement of open base pair probability downstream of a (TATA)2 box.

The modified self-consistent phonon approximation is generalized to calculate the open base pair probability of a (TATA)2 insert between two semi-infinite poly(dA-dC) . poly(dG-dT) helices. An iterative method based entirely on the Green's function method is developed to compute the open interbase hydrogen bond probability of the insert and near bases versus temperature. The open interbase hydrogen bond probability is calculated for two temperatures and compared with perfect homopolymer open base pair probabilities at room temperature. The probability of opening is enhanced by a factor of two for the major groove bond of the AT pair at the transcriptional downstream end of the (TATA)2 insert. The total base pair opening probability of that pair is enhanced by 54%. The probability of the next inline GC base pair to be open is increased by a factor of ten

Synergistic effects in the melting of DNA hydration shell: melting of the minor groove hydration spine in poly(dA).poly(dT) and its effect on base pair stability.

We propose that water of hydration in contact with the double helix can exist in several states. One state, found in the narrow groove of poly(dA).poly(dT), should be considered as frozen to the helix, i.e., an integral part of the double helix. We find that this enhanced helix greatly effects the stability of that helix against base separation melting. Most water surrounding the helix is, however, melted or disassociated with respect to being an integral part of helix and plays a much less significant role in stabilizing the helix dynamically, although these water molecules play an important role in stabilizing the helix conformation statically. We study the temperature dependence of the melting of the hydration spine and find that narrow groove nonbonded interactions are necessary to stabilize the spine above room temperature and to show the broad transition observed experimentally. This calculation requires that synergistic effects of nonbonded interactions between DNA and its hydration shell affect the state of water-base atom hydrogen bonds. The attraction of waters into narrow groove tends to retain waters in the groove and compress or strain these hydrogen bonds

Vibrational fluctuations of hydrogen bonds in a DNA double helix with nonuniform base pairs.

The Green's function technique is applied to a study of breathing modes in a DNA double helix which contains a region of different base pairs from the rest of the double helix. The calculation is performed on a G-C helix in the B conformation with four consecutive base pairs replaced by A-T. The average stretch in hydrogen bonds is found amplified around the A-T base pair region compared with that of poly(dG)-poly(dC). This is likely related to the A-T regions lower stability against hydrogen bond melting. The A-T region may be considered to be the initiation site for melting in such a helix

Salt dependent premelting base pair opening probabilities of B and Z DNA Poly [d(G-C)] and significance for the B-Z transition

We calculate room temperature thermal fluctuational base pair opening probabilities of B and Z DNA Poly[d(G-C)] at various salt concentrations and discuss the significance of thermal fluctuation in facilitating base pair disruption during B to Z transition. Our calculated base pair opening probability of the B DNA at lower salt concentrations and the probability of the Z DNA at high salt concentrations are in agreement with observations. The salt dependence of the probabilities indicates a B to Z transition at a salt concentration close to the observed concentration