Peter S. Stern

Protein normal-mode dynamics: trypsin inhibitor, crambin, ribonuclease and lysozyme

We have developed a new method for modelling protein dynamics using normal-mode analysis in internal co-ordinates. This method, normal-mode dynamics, is particularly well suited for modelling collective motion, makes possible direct visualization of biologically interesting modes, and is complementary to the more time-consuming simulation of molecular dynamics trajectories. The essential assumption and limitation of normal-mode analysis is that the molecular potential energy varies quadratically. Our study starts with energy minimization of the X-ray co-ordinates with respect to the single-bond torsion angles. The main technical task is the calculation of second derivative matrices of kinetic and potential energy with respect to the torsion angle co-ordinates. These enter into a generalized eigenvalue problem, and the final eigenvalues and eigenvectors provide a complete description of the motion in the basic 0.1 to 10 picosecond range. Thermodynamic averages of amplitudes, fluctuations and correlations can be calculated efficiently using analytical formulae. The general method presented here is applied to four proteins, trypsin inhibitor, crambin, ribonuclease and lysozyme. When the resulting atomic motion is visualized by computer graphics, it is clear that the motion of each protein is collective with all atoms participating in each mode. The slow modes, with frequencies of below 10 cm-1 (a period of 3 ps), are the most interesting in that the motion in these modes is segmental. The root-mean-square atomic fluctuations, which are dominated by a few slow modes, agree well with experimental temperature factors (B values). The normal-mode dynamics of these four proteins have many features in common, although in the larger molecules, lysozyme and ribonuclease, there is low frequency domain motion about the active site.

Born–Oppenheimer energy surfaces of similar molecules: Interrelations between bond lengths, bond angles, and frequencies of normal vibrations in alkanes

CH bond lengths, HCH and HCC bond angles, and CH symmetric and asymmetric stretching frequencies in alkane molecules are placed into four groups according to their occurrence in CH4, –CH3, CH2, and –CH, and are seen to vary in a regular fashion. The physical rationale offered for these variations relates them to balanced interactions between adjacent orbitals of CH and CC bonds, which are assumed to be common to all energy surfaces of alkane molecules. The regular variations are quantitatively reproduced by a consistent force field of alkanes, which in place of the usual harmonic stretching potentials uses only two Morse potentials, one for the CH bond, common to all four groups, and one for the CC bond. The correlated variation in bond lengths and bond angles, due to orbital interactions, is represented mainly by stretch–bend, stretch–stretch, and bend–bend cross terms. The resulting stretching frequencies, being dependent upon the second derivative of the Morse function, decrease with increasing bond le...

Predicting antigenic sites on proteins

The ability to predict antigenic sites on proteins is of major importance for the production of synthetic peptide vaccines and synthetic peptide probes of antibody structure. Many predictive methods, based on various assumptions about the nature of the antigenic response have been proposed and tested. This review will discuss the principles underlying the various approaches to predicting antigenic sites and will attempt to answer the question of how well they work.

Locust diuretic hormone-stimulated synthesis and excretion of cyclic-AMP: A novel Malpighian tubule bioassay

Endogenous cyclic-AMP concentrations in Malpighian tubules of locusts increase as a result of diuretic hormone stimulation, and the level of increase is shown to be dependent on basal intracellular levels of cyclic-AMP. Furthermore, the increase in endogenous cyclic-AMP is in such excess as to cause excretion of high levels of cyclic-AMP in the urine.

Semiclassical calculation of electronic spectra of supercooled anharmonic molecules

The electronic absorption spectrum of supercooled methyl benzene is calculated using a semiclassical procedure which avoids the calculation of the vibronic eigenstates. Classical trajectories are used to generate the time dependent potential energy gap [U(τ)] for the electronic transition. This energy gap is utilized to calculate the spectrum. This procedure may be easily applied to large anharmonic polyatomic molecules. (AIP)

Reactivity induced by complex formation: The reaction of O(3P) with HCl dimers

The reaction of O(3P) with HCl⋅M (M=HCl, Ar) complexes has been studied. While the monomer HCl, in its ground vibrational state, reacts extremely slow with O(3P), it is shown here that the van der Waals complexes react with an efficiency of about 3 orders of magnitude larger than that of the monomer. The reactivity of DCl, on the other hand, is not enhanced by the complex formation. Molecular dynamics simulation indicates that the collision complex lifetime increases by several orders of magnitude due to the existence of the “third body” in the cluster. A model for explaining the complex induced enhancement of reactivity is presented and is supported by ab initio calculations.

Jaws. A film of enzyme dynamics

Offprint requests to. C. Sander dominate atomic displacements and that surprisingly few of these suffice to describe experimentally determined fluctuations of atomic position. We have now calculated the normal mode dynamics of the enzymes lysozyme and ribonuclease [2]. A film of their lowest frequency normal modes shows opening and closing of the active site cleft. This jawlike behaviour is due to the collective motion of entire protein domains and is likely to facilitate catalysis. We are led to the suggestion that optimization of enzyme function in natural evolution or genetic engineering must affect not only the nature and positioning of active site residues but also the nature and positioning of key residues modulating domain dynamics.

Do molecular properties affect atmospheric dispersion of vapors

Abstract Turbulent diffusion is anomalously large and considered as universal, i.e. independent of molecular properties. A recent report in Science raised doubts on this, based on measurements of pesticide mixture dispersion in air. This touches the very basis of current understanding of turbulence. We offer an explanation why and how molecular properties affect dispersion despite universal eddy transport.

Stochastic Fluctuations Induced Extra Resonances

The theory of nonlinear optics has been developed mostly for monochromatic laser light, and in most situations this approximation is adequate. Several authors1 however, have dealt with the influence of laser phase fluctuations on various, processes such as resonance fluorescence2 or multiphoton transitions3. More recently, a new family of Pressure Induced Extra Resonances in Four Wave Mixing (PIER4) has been observed4. These resonances are a manifestation of the crucial role played by collisions (and other dephasing processes) in nonlinear (NL) interactions. In these experiments, four wave mixing (FWM) signals were observed from Na vapor in the presence of high buffer gas pressure. Several different resonances were observed, but in general, the dephasing process (collision) removes the destructive interference between two (or more) terms in the explicit expression for the NL susceptibility, enabling the observation of these resonances. The “conventional” theory of nonlinear susceptibilities accounts for the observed phenomena, subject to the condition that time ordering is treated properly (i.e. by double sided diagrams).

The Morse Potential as a Bridge Between Molecular Structure and Dynamics

CH bond lengths, HCH and HCC bond angles and CH symmetric and asymmetric stretching frequencies in alkane molecules are placed into four groups according to their occurrence in CH4,—CH3, 〉CH2 and–〉CH, and are seen to vary in a regular fashion. The physical rationale offered for these variations relates them to balanced interactions between adjacent orbitals of CH and CC bonds, which are assumed to be common to all energy surfaces of alkane molecules. Structural and dynamic observables are correlated by two Morse potentials, one for the CH bond and one for the CC bond. The stretching “force constants” thus become decreasing functions of bond length. The new force field reproduces the observed trend in bond lengths, bond angles and vibrational frequencies, mostly to within experimental accuracy.