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Self-consistent normal mode analysis (SCNMA) is applied to heme c type cytochrome f to study temperature-dependent protein motion. Classical normal mode analysis assumes harmonic behavior and the protein mean-square displacement has a linear dependence on temperature. This is only consistent with low-temperature experimental results. To connect the protein vibrational motions between low and physiological temperatures, we have incorporated a fitted set of anharmonic potentials into SCNMA. In addition, quantum harmonic-oscillator 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 that it may be the cause of the non-Gaussian behavior of the protein motions probed by elastic incoherent neutron scattering. The combined theory displays a dynamical transition caused by the softening of few "torsional" modes in the low-frequency regime ( <50 cm(-1) or <6 meV or >0.6 ps). 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.

The normal-mode spectrum for the four-coordinated heme compound Fe(II) octaethylporphyrin, Fe(OEP), has been determined by refining force constants to the experimental Fe vibrational density of states measured with nuclear resonance vibrational spectroscopy (NRVS). Convergence of the calculated spectrum to the data was achieved by first imposing D4 symmetry on the model structure as well as the force constants, progressively including different internal coordinates of motion, then allowing the true Ci (or S2) point group symmetry of the C(i)1 Fe(OEP) crystal structure. The NRVS-refined normal modes are in good agreement with Raman and IR spectra at high frequencies. Prior density functional theory predictions for a model porphyrin are similar to the core modes computed with the best-fit force field, but significant differences between D4 and Ci modes underline the sensitivity of porphyrin Fe normal modes to structural details. Some differences between the Ci best fit and the NRVS data can be attributed to intermolecular contacts not included in the normal-mode analysis.

The measured Fe vibrational density of states in deoxy-myoglobin, obtained from nuclear resonance vibrational spectroscopy, is compared to results from a normal-mode analysis using an all-atom empirical potential. Substantial disagreement reveals that for this one atom, the empirical potential does not accurately describe the actual forces. A Green function technique is developed to calculate the iron vibrational spectrum of deoxy-myoglobin by coupling the independently calculated heme and globin normal modes; nonbonded interactions between the heme molecule and the protein are essential for a good fit to the measurements. A projection of the eigenvectors from this potential onto the displacements induced by binding of CO demonstrates that normal modes over a broad range centered around 50-150 cm(-1) may drive the ligand-induced structural changes.

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.

Detailed Fe vibrational spectra have been obtained for the heme model complex [Fe(TPP)(CO)(1-MeIm)] using a new, highly selective and quantitative technique, Nuclear Resonance Vibrational Spectroscopy (NRVS). This spectroscopy measures the complete vibrational density of states for iron atoms, from which normal modes can be calculated via refinement of the force constants. These data and mode assignments can reveal previously undetected vibrations and are useful for validating predictions based on optical spectroscopies and density functional theory, for example. Vibrational modes of the iron porphyrin-imidazole compound [Fe(TPP)(CO)(1-MeIm)] have been determined by refining normal mode calculations to NRVS data obtained at an X-ray synchrotron source. Iron dynamics of this compound, which serves as a useful model for the active site in the six-coordinate heme protein, carbonmonoxy-myoglobin, are discussed in relation to recently determined dynamics of a five-coordinate deoxy-myoglobin model, [Fe(TPP)(2-MeHIm)]. For the first time in a six-coordinate heme system, the iron-imidazole stretch mode has been observed, at 226 cm(-)(1). The heme in-plane modes with large contributions from the nu(42), nu(49), nu(50), and nu(53) modes of the core porphyrin are identified. In general, the iron modes can be attributed to coupling with the porphyrin core, the CO ligand, the imidazole ring, and/or the phenyl rings. Other significant findings are the observation that the porphyrin ring peripheral substituents are strongly coupled to the iron doming mode and that the Fe-C-O tilting and bending modes are related by a negative interaction force constant.

Iron vibrational modes of a deoxyheme protein model (2-methylimidazole)(tetraphenylporphinato)iron(II), [Fe(TPP)(2-MeImH)], have been studied by refining normal mode calculations to nuclear resonance vibrational spectroscopy (NRVS) data. The NRVS measurements give quantitative frequencies and iron amplitudes of all modes with significant Fe vibrational motion. Modes with in-plane displacement of iron are distinguished from those involving out-of-plane motion by measurements on oriented single-crystal samples. Normal modes having large overlaps with in-plane nu(42), nu(50), and nu(53) modes of the porphyrin core are identified, as well as several modes with large iron-imidazole stretch components. An out-of-plane mode at 78 cm(-1) shows significant doming of the porphyrin core, but the largest Fe doming motion arises from the coupling of phenyls and imidazole at 25 cm(-1).

The complete iron atom vibrational spectrum has been obtained by refinement of normal mode calculations to nuclear inelastic x-ray absorption data from (nitrosyl)iron(II)tetraphenylporphyrin, FeTPP(NO), a useful model for heme dynamics in myoglobin and other heme proteins. Nuclear resonance vibrational spectroscopy (NRVS) provides a direct measurement of the frequency and iron amplitude for all normal modes involving significant displacement of (57)Fe. The NRVS measurements on isotopically enriched single crystals permit determination of heme in-plane and out-of-plane modes. Excellent agreement between the calculated and experimental values of frequency and iron amplitude for each mode is achieved by a force-field refinement. Significantly, we find that the presence of the phenyl groups and the NO ligand leads to substantial mixing of the porphyrin core modes. This first picture of the entire iron vibrational density of states for a porphyrin compound provides an improved model for the role of iron atom dynamics in the biological functioning of heme proteins.

A normal-mode and statistical mechanical calculation was carried out to determine the vibrational normal modes, contribution of internal fluctuations to the free energy, and hydrogen bond disruption of DNA triplex poly(dA).2poly(dT). The calculation was performed on both the x-ray fiber diffraction model with a N-type sugar conformation, and a newly proposed model with a S-type sugar conformation. Our calculated normal modes for the S-type structure are in better agreement with observed IR spectra for samples in D2O solution. We also find that the contribution of internal fluctuations to free energy, premelting hydrogen bond disruption probability, and hydrogen bond melting temperatures for the Hoogsteen and Watson-Crick hydrogen bonds all show that the S-type structure is dynamically more stable than the N-type structure in a nominal solution environment. Therefore our calculation supports experimental findings that the triplex d(T)n.d(A)nd(T)n most likely adopts a S-type sugar conformation in solution or at high humidity. Our calculations, however, do not preclude the possibility of an N-type conformation at lower humidities.

We use the modified self-consistent phonon approximation theory to calculate temperature dependent interbase hydrogen bond disruption profiles for a number of six base pair repeating sequence infinite B-DNA polymers with various guanine-cytosine/adenine-thymine ratios. For comparison we also include results we have obtained in our earlier work on several B-DNA homopolymers, copolymers and a four-base-pair repeating sequence polymer. Our theory gives a statistical estimate of thermal fluctuational disruption probability of individual hydrogen bonds in individual base pairs in DNA as a function of temperature. The calculated probabilities show no sequence dependence at premelting temperatures, in agreement with proton exchange measurements. These probabilities however become very sensitive to base sequence at temperatures close to the observed melting temperatures. Multiphasic critical transitions are found in which a portion of base pairs are disrupted at temperature below the final disruption temperature. These transitions include localized as well as non-localized base pair opening. The localized transitions involve disruption of a few base-pairs at every other location without large scale base unstacking, and they may not appear in the observed UV curves with current resolution. On the other hand the overall disruption behavior is consistent with observations. The midpoint transition temperatures are close to the observed melting temperatures and these temperatures show the observed linear dependence on guanine-cytosine content. Our calculations indicate that our theory can be used effectively to calculate H-bond disruption behavior of different DNA sequences.

We calculate thermal fluctuational base pair opening probability and the drug binding constant of a daunomycin-bound Poly d(CGTA).Poly d(TACG) at temperatures from room temperature to its melting temperature. For comparison we also carry out a calculation on a drug-free DNA with the same sequence. Our calculations are carried out by means of a statistical approach using microscopic structures and established force fields and with cooperative effects incorporated into the algorithm. Both hydrogen bond disruption probabilities and drug unstacking probability are determined self-consistently. These probabilities are then used to determine temperature dependent base pair opening probabilities and the drug binding constant. The calculated base pair opening probabilities and drug binding constant are found to be in fair agreement with experiments carried out at room temperature. Our calculation shows cooperative base pair disruption and drug dissociation at certain critical temperatures close to the observed melting temperatures for similar helices. We find that the temperature dependence of the drug binding constant fits well to the van't Hoff relation, in agreement with observations. Our calculation indicates the occurrence of a premelting transition in the drug-bound DNA helix. Some comments are made about this premelting transition.

Calculations of the normal mode spectrum of a netropsin-DNA complex, an isolated DNA helix of the same sequence, and a free netropsin molecule were carried out and compared with observations. We find that the frequency of modes of the complex that are primarily vibrations localized to the helix are relatively unchanged from the frequencies found for similar modes of the isolated helix. On the other hand, the frequencies of thosemodes of the complex that are found to be primarily in the netropsin are found to change significantly in the complex from that of the free netropsin. Further analysis indicates that the changes in the "netropsin modes" are primarily due to the conformational deformation induced in the netropsin by formation of the complex. All the frequencies and shifts in frequency are in good agreement with recent Raman measurements.

We carry out temperature-dependent lattice dynamics calculations to determine the vibrational normal modes associated with the interbase H-bond breathing motion in several B-DNA copolymers at temperatures from room temperature to the melting temperatures. We take into consideration Raman selection rules and incorporate a simple empirical model of Raman susceptibility in the interbase H bonds in our calculation and compare them to Raman measurements. Our calculations are carried out using empirical force constants that are not further refined to low-frequency spectra. Our calculations show the existence of strong interbase H-bond breathing modes at frequencies and with relative oscillator strengths close to the observed Raman peaks in the range of 60-140 cm-1 for the DNA sequences considered except for one helix. The correlation between the calculated and observed frequencies and oscillator strengths indicates that the observed Raman peaks in the frequency range are likely interbase H-bond breathing modes. We find that these modes exhibit sizable temperature as well as sequence dependence. We show the softening of these modes on approaching thermal denaturation that is also in agreement with the observed behavior in Raman and melting measurements. The sensitivity of the calculation on the empirical model of Raman susceptibility and the possible reasons for the discrepancy between a few calculated values and observations are discussed.

We calculate room temperature thermal fluctuational base pair opening probability of a daunomycin-poly d(GCAT).poly d(ATGC) complex. This system is constructed at an atomic level of detail based on x-ray analysis of a crystal structure. The base pair opening probabilities are calculated from a modified self-consistent phonon approach of anharmonic lattice dynamics theory. We find that daunomycin binding substantially enhances the thermal stability of one of the base pairs adjacent the drug because of strong hydrogen bonding between the drug and the base. The possible effect of this enhanced stability on the drug inhibition of DNA transcription and replication is discussed. We also calculate the probability of drug dissociation from the helix based on the selfconsistent calculation of the probability of the disruption of drug-base H-bonds and the unstacking probability of the drug. The calculations can be used to determine the equilibrium drug binding constant which is found to be in good agreement with observations on similar daunomycin-DNA systems.

Both theoretical analysis and observation of the continuity of the melted fraction of base pairs indicate that the melting transition in DNA is second order. Analysis of the salt dependence of the transition by polyelectrolyte limiting laws, however, has first-order dynamics imbedded in the analysis. This paper proposes that the observation taken to be a latent heat of melting in the limiting law analysis could instead be a specific heat anomaly associated with a second-order transition. The limiting laws can be reconstructed based on a second-order transition with a specific heat anomaly. The T2M dependence of this excess heat is also consistent with its being a specific heat anomaly of a system displaying classical critical behavior. Classical critical behavior indicates that theoretical mean field approaches such as MSPA should be particularly appropriate to helix melting studies.

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.

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.

The effect of an open loop of various sizes on the thermal stability of the adjoining intact base pairs in a duplex DNA chain is studied in a lattice model of Poly(dG).Poly(dC). We find that for a Y-shaped fork configuration the thermal fluctuation at the fork is so enhanced that the life time of the adjoining base pair is much smaller than the 1 millisecond time scale associated with helicase separation of a base pair in some systems. Our analysis indicates that thermal fluctuational base pair opening may be of importance in facilitating the enzyme unwinding process during chain elongation of a replicating DNA. It is most likely that the thermal fluctuational opening of the base pair at the junction of a replicating fork is fast enough so that a DNA unwinding enzyme can encounter an unstacked base pair with reasonable probability. This conclusion can explain several experimental observations regarding the temporal relationship between ATP hydrolysis by accessory proteins and primer elongation by a holoenzyme complex in ssDNA. We also discuss a mechanism by which the energy associated with ATP hydrolysis may enhance the thermal driven base opening mechanism.

We study the contribution of various vibrational modes to the melting of poly(dG).poly(dC). We find that the principal contribution comes from the H-bond breathing modes that have been observed in Raman scattering and that we have associated with helix melting. We show the softening of these modes on approach to melting in agreement with the observed behavior. We also describe the contribution to melting from base rotation modes that others have suggested are important in melting.

Experimental estimates of the premelting Adenine-Thymine base pair opening probability for some B-DNA sequences are two orders of magnitude smaller than those of other B-DNA sequences. The AT pairs in the sequence with smaller open probability seem to be those that have a well defined spine of hydration in the minor groove. We show that this spine of hydration can significantly enhance the thermal stability of the base pairs to which they are attached. The effect of this spine of hydration coupled with the possible stabilization effect contributed from neighboring GC pairs can explain the differences in the observed AT pair opening probability for different AT containing B-DNA sequences.

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.

The Green function technique is used to study the open hydrogen bond probability of poly(dT-dA).poly(dT-dA) when an effective enzyme is attached to the helix. The DNA interstrand hydrogen bond mean motion and probability of fluctuating to an open state depends on the internal vibrational frequency of the enzyme. An enzyme with internal frequency of 80 cm-1 reduces hydrogen bond motion and the resulting probability of hydrogen bond fluctuational opening. An enzyme with internal frequency of 72 cm-1 increases hydrogen bond motion and the probability of hydrogen bond breaking.

Modified self-consistent phonon theory when applied to the DNA double helix indicates the existence of fairly long-lived states in which single interbase H bonds are disrupted. One can then postulate a number of situations in which particular disrupted H bonds can enhance particular proton exchange. In this paper we postulate a number of such partially open states for a B-conformation GC base pair and calculate the probability of each of these states for a B-conformation poly(dG).poly(dC). We compare these probabilities to those probabilities needed to explain various observed proton exchange rates. We propose that, for a GC base pair in B conformation, there are two amino proton exchangeable states--a cytosine amino proton exchangeable state and a guanine amino proton exchangeable state; both require the disruption of only the corresponding interbase H bond. The imino proton exchange, however, requires the disruption of all three interbase H bonds and this defines a third open state. Our calculated probabilities for a GC base pair in these three states are in fair agreement with available experimental estimates from measurements of amino and imino proton exchange.

We employ a mean field, modified, self-consistent phonon theory to evaluate the single base-pair opening rate and the probability of a base pair in the amino proton exchangeable state for the homopolymer poly(dA).poly(dT) at temperatures below the helix-coil transition region. Our calculated premelting single base-pair opening probabilities are in general agreement with several available experimental estimates from imino proton exchange and formaldehyde-induced DNA melting measurements. These calculated opening probabilities, however, are in disagreement with the prediction of the helix-coil transition theory. Possible reasons for the differences are discussed, especially the possible different definition of a meaningful open state in the premelting region. The premelting open state of the modified self-consistent phonon approximation theory seems to be appropriate to describe a solvent-accessible open configuration that is sufficient to facilitate important chemical reactions such as imino proton exchange and formaldehyde reaction with the bases. This can be compared with the completely unstacked open state of the helix-coil transition theory originally defined in the helix-coil transition region. We propose that the amino proton exchangeable state is different from the open state associated with melting and only involves the breaking of the amino interbase H bond. The agreement between the calculated and experimentally estimated probability of a base pair in the amino proton exchangeable state seems to support this hypothesis.

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 an alternating poly(dC-dG).poly(dC-dG) helix in the B conformation with four consecutive base pairs replaced by a model of a biological promoter region with four alternating T-A,A-T base pairs, henceforth referred to as (TATA)2. The average stretch of interbase hydrogen bonds is found to be amplified around the insert. This is likely related to the (TATA)2 insert having a lower stability against hydrogen bond melting than the two semi-infinite poly(dC-dG).poly(dC-dG) helices. The insert region may be considered to be a site of enhanced tendency to melt in such a helix. The results show that an alternating AT insert of four base pairs has a larger average hydrogen bond stretch inside and outside the insert region than the average hydrogen bond stretch inside and outside an insert of four consecutive A-T base pairs, henceforth referred to as (AAAA).(TTTT). Calculations are performed which show that the enhancement of the average hydrogen bond stretch around an alternating TA type insert is greatly dependent upon the local modes and not the inband modes. The amount of local mode enhanced average stretch is explored as a function of insert size.

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.