Asymmetry and free energy transduction in biology

This paper is an extension of our earlier theoretical studies on the relationship between kinetic asymmetry and free-energy transductions in biological systems induced by external fluctuations. In the first part of the paper, the asymmetry conditions necessary for external-noise-induced free-energy transductions to occur are derived for a special cyclic, four-state model in which only one reaction step is perturbed by the fluctuations. The results can be used to explain the earlier findings that asymmetry in rate constants was not required in the uphill transport of ligands induced by externally fluctuating the ligand concentrations. In the second part of the paper, the coupling between two enzyme systems through direct enzyme-enzyme inter-actions is studied. The existence of kinetic asymmetry in both the driving and the driven enzyme systems is found necessary for coupling and free-energy transductions to occur.     

An evaluation of least-squares fits to COSY spectra as a means of estimating proton—proton coupling constants II. Applications to polypeptides

Summary A new computational method for simultaneously estimating all the proton-proton coupling constants in a molecule from COSY spectra [Yang, J.-X. and Havel, T.F. (1994) J. Biomol. NMR, 4, 807–826] is applied to experimental data from two polypeptides. The first of these is a cyclic hexapeptide denoted as VDA (-d-Ala¹-Phe²-Trp³-Lys(Z)⁴-Val⁵-Phe⁶-), in deuterated DMSO, while the second is a 39-residue protein, called decorsin, in aqueous solution. The effect of different data processing strategies and different initial parameter values on the accuracy of the coupling constants was explored. In the case of VDA, most of the coupling constants did not depend strongly on the initial values chosen for the optimization or on how the data were processed. This, together with our previous experience using simulated data, implies strongly that these values are accurate estimates of the coupling constants. They also differ by an average of only 0.36 Hz from the values of the 14 coupling constants that could be measured independently by established methods. In the case of decorsin, many of the coupling constants exhibited a moderate dependence on their initial values and a strong dependence on how the data were processed. With the most successful data processing strategy, the amide- coupling constants differed by an average of 1.11 Hz from the 21 values that could be measured by established methods, while two thirds of the three-bond coupling constants fell within 1.0 Hz of the ranges obtained by applying the Karplus relation to an independently computed ensemble of distance geometry structures. The averages of the coupling constants over multiple optimizations using random initial values were computed in order to obtain the best possible estimates of the coupling constants. Most clearly incorrect averages can be identified by large standard deviations in the coupling constants or the associated line widths and chemical shifts, and can be explained by strong coupling and/or overlap with the water signal, the diagonal peaks or other cross peaks.     

Accurate measurements of coupling constants from two-dimensional nuclear magnetic resonance spectra of proteins and determination of phi-angles

A new and simple method to measure 3JHNH alpha coupling constants of proteins by adding and subtracting traces from corresponding two-dimensional nuclear Overhauser enhanced spectroscopy and two-dimensional correlated spectroscopy cross peaks after scaling is proposed. The optimal scaling for the addition and the subtraction of the two traces is obtained by minimizing an error function. The method was proven to give accurate and precise measurements of coupling constants when tested with a series of simulated spectra. The accuracy of the method was better than 0.1 Hz for all test cases including the limiting case of J = 2.0 Hz and line-width = 11.0 Hz. The accuracy of the method was better than 0.1 Hz for all test cases including The 3JHNH alpha coupling constants were measured in two-dimensional nuclear magnetic resonance spectra of the two proteins barley serine proteinase inhibitor (CI-2) and the bacterial ribonuclease (barnase) of Bacillus amyloliquefaciens. The experimentally measured coupling constants were used to calculate the constants in a Karplus equation to be: 3JHNH alpha = 6.7 cos2(phi-60) -1.3 cos(phi-60) +1.5. These constants are in good accordance with those obtained for basic pancreatic trypsin inhibitor (BPTI). In addition, special emphasis is given to the measurements of positive phi-angles, and to the contribution of molecular dynamics on the apparent coupling constants.     

Vicinal coupling constants and protein dynamics

The effects of motional averaging on the analysis of vicinal spin-spin coupling constants derived from proton NMR studies of proteins have been examined. Trajectories obtained from molecular dynamics simulations of bovine pancreatic trypsin inhibitor and of hen egg white lysozyme were used in conjunction with an expression for the dependence of the coupling constant on the intervening dihedral angle to calculate the time-dependent behavior of the coupling constants. Despite large fluctuations, the time-average values of the coupling constants are not far from those computed for the average structure in the cases where fluctuations occur about a single potential well. The calculated differences show a high correlation with the variation in the magnitude of the fluctuations of individual dihedral angles. For the cases where fluctuations involve multiple sites, large differences are found between the time-average values and the average structure values for the coupling constants. Comparison of the simulation results with the experimental trends suggests that side chains with more than one position are more common in proteins than is inferred from X-ray results. It is concluded that for the main chain, motional effects do not introduce significant errors where vicinal coupling constants are used in structure determinations; however, for side chains, the motional average can alter deductions about the structure. Accurately measured coupling constants are shown to provide information concerning the magnitude of dihedral angle fluctuations.     

Exchange interactions in a Fe5 complex: A theoretical study using density functional theory

Theoretical methods based on density functional theory have been employed to analyze the exchange interactions in an Fe₅ complex. The calculated exchange coupling constants are consistent with an S = 15/2 ground state and agree well with those reported previously for other Fe^III polynuclear complexes. The strongest antiferromagnetic interactions are those through a double oxo-benzotriazole bridging ligand, where the benzotriazole ligand seems to play a minor role and the exchange coupling constants present values typical of single oxo bridging systems.     

13 C NMR Chemical shifts and carbon-proton coupling constants of some furocoumarins and furochromones

The ¹³C NMR spectra of a variety of furocoumarins, dihydrofurocoumarins and furochromones are reported. The signals were assigned using carbon-proton coupling constants, ring annullation shifts, nuclear Overhauser effect considerations and shift effects caused by monothioester formation. Substituent effects on ¹³C chemical shifts and carbon-proton coupling constants are discussed. Methoxyl induced shifts of 5- and 8-substituted furocoumarins are additive, but their effects cannot be transferred to the furochromone system.     

The solution structure of a cyclic endothelin antagonist, BQ-123, based on 1H-1H and 13C-1H three bond coupling constants.

A cyclic pentapeptide endothelin antagonist, cyclo(dTrp-dAsp-Pro-dVal-Leu), recently reported (K. Ishikawa et al., 13th Am. Pept. Symp., Cambridge MA, 1991) has been studied by NMR spectroscopy and molecular modeling. A stable structure has been determined without the use of nuclear Overhauser effects and is based primarily on homonuclear and heteronuclear three bond coupling constants. The 13C-edited TOCSY experiment is demonstrated at natural abundance and approximately 30 mM peptide concentrations. Three bond 13C-1H coupling constants obtained by this method are shown to reduce the ambiguity in phi angle determination which exists when only interproton coupling constants are used. Three out of four phi angles were determined uniquely by this method and the fourth was reduced to two possible values. The proline phi angle was determined to be -78 degrees based on the 3JH alpha, H beta and 3JH alpha, H beta coupling constants. Comparison of amide proton temperature dependence, chemical shifts and vicinal proton coupling constants in a 20% acetonitrile/80% water solvent mixture and in (CD3)2SO indicates that the structure is similar in both solvents.     

Molecular orbital calculations of the proton-proton coupling constants in nucleosides

Molecular orbital calculations of proton-proton coupling constants are carried out for a number of nucleosides as a function of conformational characteristics of these compounds. The study of the role of the ring puckering and of the orientation of the exocyclic CH₂OH group on the vicinal coupling constants of the ribose indicates the existence, in solution, of an equilibrium between several conformations. The influence of the torsion angle around the glycosidic bond on the vicinal and long range coupling constants is also examined.     

Hormone receptor-coupling factor-adenylate cyclase interaction: theoretical considerations

The steady-state response properties of two current models for receptor/nucleotide coupling protein/adenylate cyclase systems are examined by computer modeling techniques. In the model of Levitzki (Trends Pharmac. Sci., May, 1982, pp. 203-208), a ligand may give rise to full or partial agonist behavior only. In the model of Stadel, DeLean, and Lefkowitz (1982) configurations of the rate constants can be found which lead not only to full or partial agonist behavior, but also to varying degrees of inhibition at sufficiently high concentrations of ligand, as observed experimentally in a variety of adenylate cyclase systems. In the latter model, it is also possible to find configurations of the rate constants for which addition of a ligand will lead to inhibition of adenylate cyclase activity. The nature of partial agonism and reasons as to why it may be expected to occur for a wide variety of ligands are discussed.     

A proton NMR study of the glycine-mercury(II) system in aqueous solution

The proton NMR spectrum of glycine was monitored in D2O solution as a function of added Hg(II) concentration and pD. Reliable values were established for formation constants for the Hg(II):glycine 1:1 and 1:2 complexes and also for the mixed glycine/deuteroxy and glycine/chloride complexes. Ligand exchange kinetics are relatively slow, and it is possible to observe coupling to 199Hg through the coordinating nitrogen. The formation constants were used to calculate speciation over a range of ligand concentrations for the Hg(II)/glycine and Hg(II)/glycine/chloride systems.     

Determination of the phi angle in a peptide backbone by NMR spectroscopy with a combination of homonuclear and heteronuclear coupling constants.

The phi angle in a cyclic peptide is determined by the combined use of homonuclear and heteronuclear coupling constants. Two of the four coupling constants that define the phi angle in a peptide are determined exactly, two qualitatively. Via Karplus-type equations, they are transformed into dihedral angles and a good agreement is found, allowing for a determination of the phi angle with a certain range of degrees.     

Fluxes,first passage times,and the reduction of Hill diagrams

The steady-state flux resulting from the coupling of two multistate systems is considered. The dynamics of these systems are described (a) as diffusion along a continuous one-dimensional free-energy profile specified by a conformational coordinate or (b) in terms of transitions between a discrete but arbitrary number of substates. If these multistate systems are connected in a simple way, it is shown that the steady-state flux can be obtained analytically. For both the continuous and discrete cases, the exact flux is shown to be identical to that calculated from a simple kinetic scheme involving only four states, if the effective rate constants of this reduced scheme are appropriately defined in terms of the mean first passage times for moving between various points along the multistate cycles. These results clarify and quantify the manner in which the internal conformational dynamics of two multistate systems influences the steady-state flux.     

Comprehensive determination of <Superscript>3</Superscript>J<Subscript>HNHα</Subscript> for unfolded proteins using <Superscript>13</Superscript>C′-resolved spin-echo difference spectroscopy

An experiment is presented to determine ³J_HNHα coupling constants, with significant advantages for applications to unfolded proteins. The determination of coupling constants for the peptide chain using 1D ¹H, or 2D and 3D ¹H-¹⁵N correlation spectroscopy is often hampered by extensive resonance overlap when dealing with flexible, disordered proteins. In the experiment detailed here, the overlap problem is largely circumvented by recording ¹H-¹³C′ correlation spectra, which demonstrate superior resolution for unfolded proteins. J-coupling constants are extracted from the peak intensities in a pair of 2D spin-echo difference experiments, affording rapid acquisition of the coupling data. In an application to the cytoplasmic domain of human neuroligin-3 (hNlg3cyt) data were obtained for 78 residues, compared to 54 coupling constants obtained from a 3D HNHA experiment. The coupling constants suggest that hNlg3cyt is intrinsically disordered, with little propensity for structure.     

Molecular dynamics simulations of creatine kinase and adenine nucleotide translocase in mitochondrial membrane patch

Interaction between mitochondrial creatine kinase (MtCK) and adenine nucleotide translocase (ANT) can play an important role in determining energy transfer pathways in the cell. Although the functional coupling between MtCK and ANT has been demonstrated, the precise mechanism of the coupling is not clear. To study the details of the coupling, we turned to molecular dynamics simulations. We introduce a new coarse-grained molecular dynamics model of a patch of the mitochondrial inner membrane containing a transmembrane ANT and an MtCK above the membrane. The membrane model consists of three major types of lipids (phosphatidylcholine, phosphatidylethanolamine, and cardiolipin) in a roughly 2:1:1 molar ratio. A thermodynamics-based coarse-grained force field, termed MARTINI, has been used together with the GROMACS molecular dynamics package for all simulated systems in this work. Several physical properties of the system are reproduced by the model and are in agreement with known data. This includes membrane thickness, dimension of the proteins, and diffusion constants. We have studied the binding of MtCK to the membrane and demonstrated the effect of cardiolipin on the stabilization of the binding. In addition, our simulations predict which part of the MtCK protein sequence interacts with the membrane. Taken together, the model has been verified by dynamical and structural data and can be used as the basis for further studies.     

NMR investigations of proline and its derivatives. 4-Proton magnetic resonance parameters and structure of acetyl-proline amide.

The proton magnetic resonance (PMR) spectrum of acetyl-proline amide in D2O solution has been analysed by computer simulation. The spectra of the cis and the trans isomers have been separated and their PMR parameters (chemical shift and coupling constants) are given. Vicinal coupling constants of the pyrrolidine ring are interpreted by means of a Karplus zone relation. The chemical shift effect of the anisotropy of both peptide planes is considered. It follows that both isomers are puckered with Cgamma in an endo position, but the cis isomer is more rigid than the trans isomer, which moreover undergoes a small interconversion of the Cgamma and Cdelta atoms between two extreme spatial positions. The dihedral angle phi has different values in both isomers. Thus, the dihedral angle between the two peptide planes is smaller in the trans isomer than in the cis isomer.     

Two-dimensional 1H and 31P NMR spectra and restrained molecular dynamics structure of a mismatched GA decamer oligodeoxyribonucleotide duplex

Assignment of the 1H and 31P NMR spectra of a tandem G.A mismatched base pair decamer oligodeoxyribonucleotide duplex, d(CCAAGATTGG)2, has been made by two-dimensional 1H-1H and heteronuclear 31P-1H correlated spectroscopy. Unusual downfield 31P resonances have been assigned by a pure absorption phase constant-time heteronuclear 31P-1H correlated spectrum to be associated with the phosphates on the 5'- and 3'-sides of the mismatched guanosine residue. JH3'-P coupling constants for each of the phosphates of the decamer were obtained from the 1H-31P J-resolved selective proton-flip 2D spectrum. The two most downfield-shifted 31P resonances each appear to consist of two overlapping signals that can be resolved into two distinct doublets with different coupling constants in the J-resolved spectrum. This as well as the temperature dependence of the 31P spectra demonstrates that two distinct conformations exist at lower temperatures. By use of a modified Karplus relationship, the C4'-C3'-O3'-P torsional angles (epsilon) were obtained. A linear correlation between 31P chemical shifts and the measured coupling constants is quite good (only when the larger set of coupling constants of the two most downfield 31P signals is included). The 31P chemical shifts as well as the measured coupling constants tend to follow the positional variation seen in other duplexes of interior phosphates resonating more upfield than terminal residues and of interior phosphates exhibiting smaller coupling constants; however, this pattern is disrupted at the site of the mismatch. Modeling and initial NOESY distance restrained molecular mechanics energy minimization and restrained molecular dynamics support previous observations that the mismatched guanine and adenine bases are both in anti conformations. Most significantly, the epsilon backbone torsional angle variaions calculated from the NOESY distance restrained structures are in agreement with both the crystal structure values and the measured JH3'-P coupling constants.     

Electron paramagnetic resonance of the excited triplet state of metal-free and metal-substituted cytochrome c.

The photoactivated metastable triplate states of the porphyrin (free-base, i.e., metal-free) zinc and tin derivatives of horse cytochrome c were investigated using electron paramagnetic resonance. Zero-field splitting parameters, line shape, and Jahn-Teller distortion in the temperature range 3.8-150 K are discussed in terms of porphyrin-protein interactions. The zero-field splitting parameters D for the free-base, Zn and Sn derivatives are 465 x 10(-4), 342 x 10(-4) and 353 x 10(-4) cm-1, respectively, and are temperature invariant over the temperature ranges studied. AN E value at 4 K of 73 x 10(-4) cm-1 was obtained for Zn cytochrome c, larger than any previously found for Zn porphyrins derivatives of hemeproteins, showing that the heme site of cytochrome c imposes an asymmetric field. Though the E value for Zn cytochrome c is large, the geometry of the site appears quite constrained, as indicated by a spectral line shape showing a single species. Intersystem crossing occurred predominantly to the T2 > zero-field spin sublevel. EPR line shape changes with respect to temperature of Zn cyt c are interpreted in terms of vibronic coupling, and a maximum Jahn-Teller crystal-field splitting of approximately 180 cm-1 is obtained. Sn cytochrome c in comparison with the Zn protein exhibits a photoactivated triplet line shape that is less well resolved in the X-Y region. The magnitude of E value is approximately 60 x 10(-4) cm-1 at 4 K; its value rapidly tends toward zero with increasing temperature, from which a value for the Jahn-Teller crystal-field splitting of > or = 40 cm-1 is estimated. In contrast to those for the metal cytochromes, the magnitude of E value for the free-base derivative was essentially zero at all temperatures studied. This finding is discussed as a consequence of an excited-state tautomerization process that occurs even at 4 K.     

Quantification of H/D Isotope Effects on Protein Hydrogen-bonds by h3JNC′ and 1JNC′ Couplings and Peptide Group 15N and 13C′ Chemical Shifts

The effect of hydrogen/deuterium exchange on protein hydrogen bond coupling constants (h3)J(NC') has been investigated in the small globular protein ubiquitin. The couplings across deuterated or protonated hydrogen bonds were measured by a long-range quantitative HA(CACO)NCO experiment. The analysis is combined with a determination of the H(N)/D(N) isotope effect on the amide group (1)J(NC') couplings and the (15)N and (13)C' chemical shifts. On average, H-bond deuteration exchange weakens (h3)J(NC') and strengthens (1)J(NC') couplings. A correlation is found between the size of the (15)N isotope shift, the (15)N chemical shift, and the (h3)J(NC') coupling constants. The data are consistent with a reduction of donor-acceptor overlap as expected from the classical Ubbelohde effect and the common understanding that H(N)/D(N) exchange leads to a shortening of the N-hydron bond length.     

Measurement of long-range2 13C-1H coupling constants of 95% uniformly 13C-labeled polysaccharide from streptococcus mitis J22

The coaggregation of Streptococcus mitis strain J22 in the early stages of dental plaque formation has been shown to result from interaction of cell wall polysaccharides with lectins on the surface of other oral bacterial species. This bacterium was grown in a medium containing ¹³C as the sole carbon source. We have isolated the lectin receptor polysaccharide from this strain with full enrichment in ¹³C and have determined a number of two-bond and three-bond ¹³C-¹H coupling constants from measurements of the offsets in two-dimensional homonuclear nmr spectra [exclusive correlated spectroscopy (E-COSY) method]. A scheme for reliable extraction of these coupling constants from homonuclear Hartmann-Hahn and nuclear Overhauser effect spectroscopy spectra is tested in model compounds. We interpret the three-bond coupling across the glycosidic linkage in terms of dihedral angles in order to provide conformational information to supplement molecular modeling and nuclear Overhauser effect data. We show that the E-COSY method works well even for coupling constants smaller than the nmr line width and that a number of the ³J_CH across the glycosidic linkage are in the range of 1–2 Hz, which is much smaller than many previously reported values. © 1994 John Wiley & Sons, Inc.