Davydov Soliton Dynamics in Proteins: III. Applications and Calculation of Vibrational Spectra

The mechanism for energy and signal transport in proteins as suggested by Davydov is discussed. The idea is based on a coupling of amide-I oscillators to acoustic phonons in a hydrogen bonded chain. Results as obtained with the usually used ansätze are discussed. The quality of these states for an approximate solution of the time-dependent Schrödinger equation is investigated. It is found that the semiclassical ansatz is a poor approximation, while the more sophisticated |D₁> state seems to represent the exact dynamics quite well. This was shown by extensive calculations, both analytically and numerically in the two preceding papers. Calculations at a temperature of 300K for one chain, as well as for three coupled ones (as they are present in an -helix) are presented and discussed. From the calculations it is evident, that Davydov solitons are stable for reasonable parameter values at 300K for special initial excitations close to the terminal sites of the chain. Further vibrational spectra are presented and discussed. Our results suggest, that due to their strong dependence on the initial state, the Davydov |D₁> model system might be a (quantum) chaotic one.     

Davydov Soliton Dynamics in Proteins: II. The General Case

We performed long time simulations using the |D₁> approximation for the solution of the Davydov Hamiltonian. In addition we computed expectation values of the relevant operators with the state (_D/J)|D₁> and the deviation |> from the exact solution over long times, namely 10 ns. We found that in the very long time scale the |D₁> ansatz is very close to an exact solution, showing expectation values of the relevant physical observables in the state (_D/J)|D₁> being about 5-6 orders of magnitudes larger than in the deviation state |>. In the intermediate time scale of the ps range such errors, as known from our previous work, are somewhat larger, but still more or less negligibly. Thus we also report results from an investigation of the very short time (in the range 0-0.4 ps) behaviour of the |D₁> state compared with that of an expansion of the exact solution in powers of time t. This expansion is reliable for about 0.12 ps for special cases as shown in the previous paper. However, the accuracy of the exactly known value of the norm and the expectation value of the Hamiltonian finally indicates up to what time a given expansion is valid, as also shown in the preceding paper. The comparison of the expectation values of the operators representing the relevant physical observables, formed with the third order wave function and with the corresponding results of |D₁> simulations has shown, that our expansion is valid up to a time of roughly 0.10-0.15 ps. Within this time the second and third order corrections turned out to be not very important. This is due to the fact that our first order state contains already some terms of the expansion, summed up to inifinite order. Further we found good agreement of the results obtained with our expansion and those from the corresponding |D₁> simulations within the time of about 0.10 ps. At later times, the factors with explicit powers of t in second and third order become dominant, making the expansion meaningless. Possibilities for the use of such expansions for larger times are described. Alltogether we have shown (together with previous work on medium times), that the |D₁> state, although of approximative nature, is very close to an exact solution of the Davydov model on time scales from some femtoseconds up to nanoseconds. Especially the very small time region is of importance, because in this time a possible soliton formation from the initial excitation would start.     

Davydov Soliton Dynamics in Proteins: I. Initial States and Exactly Solvable Special Cases

For the Davydov Hamiltonian several special cases are known which can be solved analytically. Starting from these cases we show that the initial state for a simulation using Davydovs |D₁> approximation has to be constructed from a given set of initial lattice displacements and momenta in form of a coherent state with its amplitudes independent of the lattices site, corresponding to Davydovs |D₂> approximation. In the |D₁> ansatz the coherent state amplitudes are site dependent. The site dependences evolve from this initial state exclusively via the equations of motion. Starting the |D₁> simulation from an ansatz with site dependent coherent state amplitudes leads to an evolution which is different from the analytical solutions for the special cases. Further we show that simple construction of such initial states from the expressions for displacements and momenta as functions of the amplitudes leads to results which are inconsistent with the expressions for the lattice energy. The site-dependence of coherent state amplitudes can only evolve through the exciton-phonon interactions and cannot be introduced already in the initial state. Thus also in applications of the |D₁> ansatz to polyacetylene always |D₂> type initial states have to be used in contrast to our previous suggestion [W. Förner, J. Phys.: Condens. Matter 1994, 6, 9089-9151, on p. 9105]. Further we expand the known exact solutions in Taylor serieses in time and compare expectation values in different orders with the exact results. We find that for an approximation up to third order in time (for the wave function) norm and total energy, as well as displacements and momenta are reasonably correct for a time up to 0.12-0.14 ps, depending somewhat on the coupling strengh for the transportless case. For the oscillator system in the decoupled case the norm is correct up to 0.6-0.8 ps, while the expectation values of the number operators for different sites are reasonably correct up to roughly 0.6 ps, when calculated from the third order wave function. The most important result for the purpose to use such expansions for controlling the validity of ansatz states is, however, that the accuracy of S(t) and H(t) (constant in time, exact values known in all cases) is obviously a general indicator for the time region in which a given expansion yields reliable values also for the other, physically more interesting expectation values.     

Comparative effects of some hydroxylated vitamin D metabolites on parathyrin secretion by dispersed rat parathyroid cells in vitro

We have previously discussed the action of 1 α,25-(OH)₂D₃, (24R) 24,25-(OH)₂ D₃ and (25S) 25,26-(OH)₂D₃ on parathyrin secretion by isolated rat parathyroid cells. In this work, we have compared these effects with those obtained with 1 α -OH D₃, 25-OH D₃ and 1 α -OH D₂.In decreasing order, the activities were : 1 α,25-(OH)₂D₃> 1 α -OH D₃ (24R) 24,25-(OH)₂D₃ > 25-OH D₃ > (25S) 25,26(OH)₂D₃> 1 α -OH D₂. The presence of two hydroxyl groups with one hydroxyl group in α position seems to have the higher activity to inhibit the parathyroid secretion. At least, the nature of the side chain conformation also plays a part upon the effect of PTH release.     

Assessment of Minerals in Obesity-related Diseases in the Chandigarh (India) Population

Excessive Zn but normal Cu and Mg in the staple food consumed by the people of Chandigarh (Union territory and capital of Punjab and Haryana States of India) has been considered to be the major risk factor for the prevalence of obesity (33.15%) and obesity-related diseases in this region. Therefore, in the present investigations, in obesity-related diseases, the status of these minerals was estimated in their tissues, including hair, nails, and blood serum and urine, and compared with those of normal subjects. They were grouped as: normal subjects in control Group A, middle-aged diabetics in Group D_M, older diabetics in Group D_O, and diabetics with osteoarthritis in Group D+ OA, osteoarthritis in Group OA and rheumatoid arthritis in Group RA, respectively. The results evaluated in the order as: hair Zn, group D+OA>D_M>OA>A (control)>RA>D_O (p < 0.001); hair Cu, group A (control)>D_M>OA>D+OA>D_O>RA (p < 0.001); hair Mg, group A (control)>D_M>OA>D+OA>RA>D_O (p < 0.001, 0.01); hair Mn, group A (control)>RA>OA>D-OA>D_M>D_O (p < 0.001); nail Zn, group D_M>D+OA>OA>A (control)>RA>D_O (p < 0.001, 0.05); nail Cu, group A (control)>OA>D_M>D+OA>RA>D_O (p < 0.001); nail Mg, group A (control)>OA>D_M>D_O>D+OA >RA (p < 0.001); nail Mn, group A (control) >RA>OA>D+OA>D_M>D_O (p < 0.01); urine Zn, group D_O>D_M>D+OA>A (control)>RA>OA (p < 0.01); urine Cu, group RA>D+OA>D_O>OA> D_M>A (control) (p<0.001); urine Mg, group RA>OA>D+OA>D_O>D_M>A (control; p < 0.001); urine Mn, group D_O>D_M>OA>D+OA>RA>A (control; p < 0.001), respectively. The analysis of the mineral status in serum of diabetics further showed their highly significant rise from lower mean age subgroup to higher mean age subgroup than their control counter parts (p < 0.001, 0.01, and 0.05) with coincident deficiencies of Cu, Mg, and Mn in their tissues. This study would be helpful considering the status of minerals in these obesity-related diseases depending on the choice of the food consumed to improve the quality of life and prognosis for the diseases.     

Dimerization constants of water-soluble porphyrins in aqueous alkali

Spectrophotometric analysis of changes in absorption spectra on dilution of different 2,4-disubstituted derivatives of deuteroporphyrin yielded dimerization constants (K_D) for each porphyrin in aqueous alkali. The K_D values appear to be related to the hydrophobic/hydrophilic interactions of the system such that K_D for proto- > meso- > deutero- > hemato- > coproporphyrin. The effects of alcohol, temperature, and ionic strength on the K_D were examined. A simple approach to the graphic analysis of the dilution curves is presented for use when absorbance readings at A₁₀₀ and A₀ cannot be reliably determined, and the use of soluble porphyrins as model systems for studying hydrophobic/hydrophilic interactions in aqueous media is discussed.     

Low hydration phase properties of phospholipid mixtures

An experimental investigation of the low hydration phase properties of phospholipid mixtures is described. ²H (D₂O) NMR, X-ray diffraction and differential scanning calorimetry have been used to elucidate the phase properties of mixtures of the mixed chain phospholipids palmitoyloleoylphosphatidylcholine (POPC) and palmitoyloleoylphosphatidylethanolamine (POPE). At 10% hydration pure POPE exhibited a H_II phase above 330 K, a fluid lamellar phase below 315 K, and a minimally hydrated crystalline phase below 300 K. For the 1:1 mixture, the samples exhibited only gel or fluid phases between 270 K and 360 K for hydrations in the range 15% to 30%. Below 15% hydration the mixture exhibited two fluid phases with different repeat spacings, as predicted previously.     

D2O and the sodium pump in squid nerve membrane

Summary In 10 K artificial seawater (ASW). D₂O replacement reduced the Na efflux of squid axons by about one third. In 0 K ASW, D₂O replacement had little effect. D₂O reduced the K⁺ sensitivity of the efllux but increased the affinity for K⁺. A 4° decrease in temperature mimicked the effects of D₂O. When axons were injected with arginine, to decrease the ATP/ADP ratio, they lost K⁺ sensitivity in normal ASW, as expected. Their efflux into 0 K ASW became D₂O sensitive. The results are discussed in terms of conformational changes in the Na pump molecular complex.     

Mechanisms of the multiphasic kinetics in the folding and unfolding of globular proteins

The multiphasic kinetics of the protein folding and unfolding processes are examined for a “cluster model” with only two thermodynamically stable macroscopic states, native (N) and denatured (D), which are essentially distributions of microscopic states. The simplest kinetic schemes consistent with the model are: N-(fast) → I-(slow) → D for unfolding and N ← (fast)-D₂ ← (slow)-D₁ for refolding. The fast phase during the unfolding process can be visualized as the redistribution of the native population N to I within its free energy valley. Then, this population crosses over the free energy barrier to the denatured state D in the slow phase. Therefore, the macrostate I is a kinetic intermediate which is not stable at equilibrium. For the refolding process, the initial equilibrium distribution of the denatured state D appears to be separated into D₁ and D₂ in the final condition because of the change in position of the free energy barrier. The fast refolding species D₂ is due to the “leak” from the broadly distributed D state, while the rest is the slow refolding species D₁, which must overpass the free energy barrier to reach N. At an early stage of the folding process the amino acid chain is considered to be composed of several locally ordered regions, which we call clusters, connected by random coil chain parts. Thus, the denatured state contains different sizes and distributions of clusters depending on the external condition. A later stage of the folding process is the association of smaller clusters. The native state is expressed by a maximum-size cluster with possible fluctuation sites reflecting this association. A general discussion is given of the correlation between the kinetics and thermodynamics of proteins from the overall shape of the free energy function. The cluster model provides a conceptual link between the folding kinetics and the structural patterns of globular proteins derived from the X-ray crystallographic data.     

Evidence of Functional Protein Dynamics from X-Ray Crystallographic Ensembles

It is widely recognized that representing a protein as a single static conformation is inadequate to describe the dynamics essential to the performance of its biological function. We contrast the amino acid displacements below and above the protein dynamical transition temperature, T_D∼215K, of hen egg white lysozyme using X-ray crystallography ensembles that are analyzed by molecular dynamics simulations as a function of temperature. We show that measuring structural variations across an ensemble of X-ray derived models captures the activation of conformational states that are of functional importance just above T_D, and they remain virtually identical to structural motions measured at 300K. Our results highlight the ability to observe functional structural variations across an ensemble of X-ray crystallographic data, and that residue fluctuations measured in MD simulations at room temperature are in quantitative agreement with the experimental observable.     

The nature of phonons and solitary waves in alpha-helical proteins.

A parametric study of the Davydov model of energy transduction in alpha-helical proteins is described. Previous investigations have shown that the Davydov model predicts that nonlinear interactions between phonons and amide-I excitations can stabilize the latter and produce a long-lived combined excitation (the so-called Davydov soliton), which propagates along the helix. The dynamics of this solitary wave are approximately those of solitons described using the nonlinear Schr?dinger equation. The present study extends these previous investigations by analyzing the effect of helix length and nonlinear coupling efficiency on the phonon spectrum in short and medium length alpha-helical segments. The phonon energy accompanying amide-I excitation shows periodic variation in time with fluctuations that follow three different time scales. The phonon spectrum is highly dependent upon chain length but a majority of the energy remains localized in normal mode vibrations even in the long chain alpha-helices. Variation of the phonon-exciton coupling coefficient changes the amplitudes but not the frequencies of the phonon spectrum. The computed spectra contain frequencies ranging from 200 GHz to 6 THz, and as the chain length is increased, the long period oscillations increase in amplitude. The most important prediction of this study, however, is that the dynamics predicted by the numerical calculations have more in common with dynamics described by using the Frohlich polaron model than by using the Davydov soliton. Accordingly, the relevance of the Davydov soliton model was applied to energy transduction in alpha-helical proteins is questionable.(ABSTRACT TRUNCATED AT 250 WORDS)     

Conformational selection mechanism governs oxygen ligation to H-NOX proteins

H-NOX proteins are at present the only structural models available for the study of the ligand binding affinity and selectivity of soluble guanylate cyclase, the physiological receptor of nitric oxide. The oxy complex and resting state structures of two bacterial H-NOX proteins of markedly different oxygen affinity, but of quite similar sequence, were studied by molecular dynamics simulations at 300 K and 400 K. Unexpectedly, the different O₂ affinity was found to be reflected in differences of the resting states structures. A conformation containing a pre-formed oxygen-binding cage is the most populated in the resting state equilibrium ensemble of the only successful O₂ binder, Tt H-NOX at 300 K, suggesting that conformational selection governs the interaction.     

Scanning force microscopy studies of X-ray-induced double-strand breaks in plasmid DNA

We present an analysis of X-ray-induced damage in ΦX174 plasmid DNA, applying doses between D = 250 and 1,500 Gy. To analyse this damage in detail, the distribution of plasmid fragments after irradiation have been determined by scanning force microscopy. The results show that even for the lowest dose of D = 250 Gy, a significant amount of double-strand breaks are observed. For increasing dose, the percentage of small fragments increases and is accompanied by a shortening of the average fragment length from < L> = 1,400 nm for a dose of D = 250 Gy to < L> = 1,080 nm after irradiation with D = 1,500 Gy. The most crucial parameter, the average number of double-strand breaks per broken plasmid (<DSB_b> ) has been determined for the first time for the applied doses. The results show that the average number of DSBs per broken plasmid <DSB_b> increases almost linearly from a value of <DSB_b> = 1.3 after irradiation with D = 250 Gy to <DSB_b> = 1.7 after exposure to D = 1,500 Gy. The presented results show that the amount of DSBs induced by X-ray radiation in plasmid DNA can be calculated with high accuracy by means of scanning force microscopy, providing relevant information regarding the interaction of X-rays with DNA molecules.

Receptor tyrosine kinases regulate α1D-adrenoceptor signaling properties: Phosphorylation and desensitization

Human α_1D-adrenoceptors (truncated at the amino terminus (Δ1–79) to increase their membrane expression) were stably expressed in Rat-1 fibroblasts (1–1.5 pmol/mg protein). The receptors were functional as evidenced by a robust increase in intracellular calcium in response to noradrenaline. Using this cell line, the possibility that activation of receptor tyrosine kinases could modulate this adrenoceptor subtype was studied. It was observed that cell preincubation with insulin, IGF-I, EGF or PDGF markedly reduced the intracellular calcium increase observed in response to noradrenaline. Inhibitors of PI3K and PKC essentially blocked insulin-, IGF-I- and EGF-induced desensitizations. Interestingly, PDGF-induced α_1D-adrenergic desensitization was only partially ameliorated by PI3K inhibitors and was not affected by those of PKC. Insulin, IGF-I, EGF and PDGF induced concentration-dependent increases in the phosphorylation state of α_1D-adrenoceptors; phosphorylation took place on serine residues. Inhibitors of PI3K and PKC markedly reduced the effects of insulin, IGF-I and EGF on this parameter. These inhibitors only marginally reduced PDGF-induced α_1D-adrenoceptors phosphorylation. The ability of IGF-I to induce α_1D-adrenergic desensitization and phosphorylation was confirmed in cells expressing non-truncated rat α_1D-adrenenoceptors. Our data indicate that the function and phosphorylation state of α_1D-adrenoceptors is modulated by activation of receptor tyrosine kinases. Insulin, IGF-I and EGF actions take place through the action of PI3K and PKC; additional pathway(s) seem to participate in PDGF-induced α_1D-adrenoceptor desensitization and phosphorylation.     

Loop energy in DNA

The loop function ?(N), representing the statistical weight of N complementary residues in a closed ring, has been determined by analysis of high-resolution melting curves of a series of recombinant homopoly(A · T)_N inserts in pBR322 DNA, where 150 > N > 50 base pairs (bp). Loops are found more stable and therefore presumably less elastic than expected for an ideal, freely jointed chain. A value of 97 ± 2 bp is obtained for the empirical orientation-stiffness parameter D in the expression for nonideal chains, ?(N) = (N + D)^?1.7. The 10% increase in apparent stiffness over that of an ideal chain closely coincides with the extent of residual stacking in the loop. It is thus concluded that the more favorable loop energy, such as expected of smaller loops, is due to the incipient helical orientation of some residues, predisposing the loop to reclosure. A quantitative loop function is essential for the prediction and assignment of domains in DNA.     

1,25-Dihydroxyvitamin D3 receptor in bovine thymus gland

1,25-Dihydroxyvitamin D₃ [1,25-(OH)₂D₃] receptor was characterized after partial purification of thymus cytosol by ammonium sulfate fractionation. The 1,25-(OH)₂D₃ receptor sediments at 3.7S in 5–20% sucrose gradients. The binding of 1,25-(OH)₂D₃ in thymic cytosol was a saturable process with high affinity (Kd = 0.12?0.48 nM) at 4°C. Competition for 1,25-(OH)₂[³H]D₃ receptor by nonradioactive analogs demonstrated the affinities of these analogs to be in order; 1,25-(OH)₂D₃ = 1,24R,25-(OH)₃D₃ = 1,25S,26-(OH)₃D₃ = 1,25R,26-(OH)₃D₃ > 1,25-(OH)₂D₃-26,23 lactone > 25-OHD₃ > 23R,25-(OH)₂D₃ > 24R,25-(OH)₂D₃ > 23S,25-(OH)₂D₃ ? 25-OHD₃-26,23 lactone. The receptor bound to DNA cellulose columns in low salt buffer and eluted as a single peak at 0.21 M KCl. These findings provide evidence that the thymus possesses a 1,25-(OH)₂D₃ receptor with properties indistinguishable from 1,25-(OH)₂D₃ receptors in other tissues.     

EPR spectroscopic study of a dinuclear copper(II) complex of tolfenamic acid

The copper(II) complex with tolfenamic acid [Cu(tolf)₂(H₂O)]₂ was studied by X-band and K-band EPR spectroscopies in the temperature range from 90 to 300 K. The Cu²⁺ ions in dinuclear complex show a strong antiferromagnetic exchange interaction with |J| = 292 cm⁻¹. The EPR spectra, which were observed for [Cu(tolf)₂(H₂O)]₂, are typical powder spectra of the copper pairs. The spectra exhibit the hyperfine structure in low temperature range. The values of the spin-Hamiltonian parameters were determined on the basis of the best fit for the simulated spectra at both K-band (0.75 cm⁻¹) at T = 298 K and X-band (0.3 cm⁻¹) at T = 93 K as compared with the experimentally observed spectra. These values show that the local environment around the copper species is distorted tetragonal pyramid. This EPR evidence is consistent with the crystallographic data.     

Metal ion-biomolecule interactions. Part 13. NMR evidence for the formation of the mixed ligand thymidine-mercury-guanosine complex. A model for a putative Hg(Il) interstrand cross-linking structure of DNA

¹H and ¹³C NMR evidence is presented for the formation of the mixed ligand complex, [ThyHg Guo] (E). This was obtained through equilibration, in dimethyl sulfoxide solution, of 1 equivalent of the symmetrical complex [ThyHgThy] (C) with 2 equivalents of free guanosine, or similarly 1 equivalent of [GuoHgGuo] (D) with 2 equivalents of free thymidine. The relative stabilities of the nucleoside-mercury-nucleoside complexes involved in the equilibration process is C > D > E. The mixed ligand complex E appears to contain a ThyN₃HgGuoN₁ bond and thus supports an interstrand structure previously proposed for Hg(II) binding to DNA. The relative stability C > D > E is consistent with the postulate that the [ThyHgThy] interstrand complex represents the thermodynamically most stable mode of Hg(Il)- DNA interaction under physiological conditions.     

Sedimentation coefficients of DNA topoisomers: the helical wormlike chain

The sedimentation coefficient s_N of the DNA topoisomer with the linking number N is evaluated as a function of N and chain length on the basis of a (circular) twisted wormlike chain, i.e., a special case of the helical wormlike chain. Evaluation is carried out by an application of the Oseen–Burgers procedure of hydrodynamics to the cylinder model with the preaveraged Oseen tensor. The necessary mean reciprocal distance between two contour points is obtained by a Monte Carlo method. It is shown that s_N increases as |ΔN| is increased from 0 in the range of small |ΔN|, where ΔN = N ? N , with N the number of helix turns in the linear DNA chain in the undeformed state. It is found that there is semiquantitative agreement between the Monte Carlo values and the experimental data obtained by Wang for s_N.     

Photodynamic induction of DNA–protein cross-linking in solution by several sensitizers and visible light

The combined effect of several sensitizers and light on H ₂O or D₂O solutions of DNA-histone complexes, as well as the significance of singlet oxygen (¹O₂), in this photosensitizing reaction has been studied. On H₂O solutions, the production of ¹O₂, as well as the formation of DNA-protein cross-links (DPCs), were found to be dependent on light dose for all the sensitizers. Mesotetra (4N-methylpyridyl) porphine (T₄ MPyP), methylene blue (MB), and toluidine blue (TB) were the best photosensitizers with regard to tryptophan photolysis, followed by hematoporphyrin (HP), thioflavine T (TT), and pyronin G (PG). The formation of DPCs showed high initial rates, reaching a plateau at dose over 90 J/cm ². Under these irradiation conditions, the percentage of DPCs induced by the sensitizers decreases in the order T₄ MPyP > MB > TB ? HP ≈ TT ? PG (≈0). These DPCs were totally destroyed with proteinase K (15μg/ml). The irradiation of the DNA-histone-sensitizer solutions in the presence of L -carnosine (5 × 10^-4 M) produced approximately a 50% of DPCs inhibition for T₄ MPyP, MB, and TB, and a total inhibition for HP, TT, and PG. The substitution of H₂O by D₂O as solvent significantly increased the photodegradation of tryptophan, as well as the photoinduction of DPCs by the sensitizers. The results obtained indicate that singlet oxygen is the main agent responsible in the DNA–protein cross-linking formation. © 1993 John Wiley & Sons, Inc.