Shneior Lifson

Consistent Force Field for Calculations of Conformations, Vibrational Spectra, and Enthalpies of Cycloalkane and n‐Alkane Molecules

An inductive method for a systematic selection of energy functions of interatomic interactions in large families of molecules is suggested and is applied to the family of cycloalkane and n‐alkane molecules. Equilibrium conformations, vibrational frequencies, and excess enthalpies, including strain energies and vibrational enthalpies, are all derived from the same set of energy functions. The energy‐function parameters are optimized by a least‐squares algorithm to give the best possible agreement with a large amount and variety of observed data. Analytical derivatives of the various calculated quantities with respect to the energy parameters help to facilitate the computational procedures. The resulting agreement with experiment is used as a measure of success of the energy functions with optimized parameters, referred to as “consistent force field” (CFF). Different CFFs are compared and selected according to their relative success. Energy functions commonly used in conformational analysis are examined in...

A Helical Polymer with a Cooperative Response to Chiral Information

Polyisocyanates, long studied as theoretical models for wormlike chains in dilute solution and liquid crystals, differ from their biological helical analogs in the absence of a pre-determined helical sense. These polymers have an unusual sensitivity to chiral effects that arises from a structure in which alternating right- and left-handed long helical blocks are separated by infrequent and mobile helical reversals. Statistical thermodynamic methods yield an exact description of the polymer and the cooperative nature of its chiral properties. Minute energies that favor one of the helical senses drive easily measurable conformational changes, even though such energies may be extremely difficult to calculate from structural theory. In addition, the chiral nature of the polymer can be used to test theoretical ideas concerned with cholesteric liquid crystals, one of which solves the problem of assigning the helical sense.

The Macromolecular Route to Chiral Amplification

Cooperative phenomena, described by one-dimensional statistical physical methods, are observed between the enantiomeric characteristics of monomeric materials and the polymers they produce. The effect of minute energies associated with this amplified chirality, although currently not interpretable, can be easily measured. Nonlinear relationships between enantiomeric excess or enantiomeric content and polymer properties may offer the possibility of developing chiral catalysts and chiral chromatographic materials in which the burden of large enantiomeric excess or content may be considerably alleviated. New approaches to information and sensor technology may become possible.

Refinement of protein conformations using a macromolecular energy minimization procedure

Abstract This paper presents a rapid refinement procedure capable of deriving the stable conformation of a macromolecule from experimental model co-ordinates. All the degrees of freedom of the molecule are allowed to vary and all parts of the structure are refined simultaneously in a general force-field. The procedure has been applied to myoglobin and lysozyme. The deviations of peptide bonds from planar conformation and of various bond angles from their respective average values are found to contribute significantly to the refined protein conformation. Hydrogen atoms are not included in the present refinement. A set of non-bonded potential functions, applicable to the equilibrium of a folded protein in an aqueous medium, is described and tested on myoglobin.

Consistent Force Field Calculations. II. Crystal Structures, Sublimation Energies, Molecular and Lattice Vibrations, Molecular Conformations, and Enthalpies of Alkanes

A set of energy functions of internal coordinates and interatomic distances is used for calculating simultaneously and consistently many properties of alkanes. Comparison between calculated and experimental data is used as a means for systematically selecting energy functions and determining their parameters. Properties calculated are: unit‐cell parameters; heat of sublimation; molecular and lattice vibrations; thermal expansion of the unit cell—all these for n‐hexane and n‐octane crystals. Enthalpy differences—for gauche–trans butane and for axial–equatorial methyl‐cyclohexane. Excess enthalpies for the series cyclopentane through cyclodedcane and molecular conformations and vibrations for a selected number of cyclo‐ and n‐alkanes molecules. Some of the results and conclusions from these calculations are: molecular vibrations in the crystal are in part higher than in the gas, and the corresponding enthalpy difference contributes to the heat of sublimation equally as much as the lattice vibrations. Anharm...

Partition Functions of Linear‐Chain Molecules

A new method is proposed for the derivation of partition functions of linear‐chain molecules. It consists of defining sequences, sequence partition functions, and sequence‐generating functions and using them to derive an equation for the contribution of each chain element to the partition function of the whole chain. The method has a more general applicability than the combinatorial and matrix methods. Several applications are discussed.

On the Self‐Diffusion of Ions in a Polyelectrolyte Solution

The self‐diffusion of ions in a polyelectrolyte solution is investigated both with respect to the average time an ion is associated with a particular polyelectrolyte molecule and with respect to the effect of the electrostatic field of the macro‐ions on the macroscopic self‐diffusion constant. The results on the macroscopic self‐diffusion constant are shown to be generally compatible with experiments on self‐diffusion of counterions in polyelectrolyte solutions. On the other hand, the study of the time of association of a counterion with a particular macro‐ion yields results which cannot be reconciled with the common interpretation of transference experiments on the same solutions.

Consistent force field for calculation of vibrational spectra and conformations of some amides and lactam rings

Abstract The vibrations and equilibrium conformations of the linear amides N -methylformamide, acetamide, and N -methylacetamide, and the ring amides 2-pyrrolidone, 2-piperidone, and ϵ-caprolactam are calculated simultaneously from intramolecular energy functions. The parameters of the energy functions related to the amide group and its vicinity are optimized by least squares to give a best fit to the vibrational spectra and conformations of the linear amides, including many deuterated analogues. The resulting “consistent force field” (CFF) is transferred to the lactams, together with the force field of cycloalkanes obtained previously. Spectral assignments for the lactams, as well as for both the in-plane and out-of-plane frequencies of the trans amides, are suggested. The δ(NH) mode (amide II) in lactams is found to be shared by two frequencies in the region of 1400 cm −1 , whose character changes, moreover, by deuteration. The δ(C′O) frequency in lactams is assigned to observed frequencies in the 500 cm −1 region. The transferability of CFF from trans amides to lactams seems acceptable, but further improvement of the force field may be obtained by a more detailed study of the spectra of lactams.

Specific recognition in the tertiary structure of β-sheets of proteins

The frequency of occurrence of nearest neighbour residue pairs on adjacent antiparallel (βA) and parallel (βP) strands is obtained from 30 known protein structures. The specificity of interstrand recognition due to such pairing as a factor in the folding of β-sheets is studied by statistical methods. Residues of sufficiently high count for statistical analysis are treated individually while the rest are combined into small groups of similar size, polarity, and/or genetic exchangeability. The hypothesis of specific recognition between individuals and small groups is contrasted with the alternative hypothesis of non-specific recognition between broad classes (hydrophobia, neutral, polar) of residues. A χ2 test of pair correlations favours specific recognition against non-specific recognition with a high level of confidence. The largest and most significant correlations are: Ser/Thr (1.9 ± 0.3), Ile/Val (1.7 ± 0.3) and Lys-Arg/Asp-Gln (1.8 ± 0.3) in βA, and Ile/Leu (1.9 ± 0.4) in βP. The pair Gly/Gly never occurs in any β-sheet. The specific residue-pair correlations derived here may be useful in statistical prediction methods of protein tertiary structure.

Neighbor Interactions and Internal Rotations in Polymer Molecules. III. Statistics of Interdependent Rotations and Their Application to the Polyethylene Molecule

The internal rotations around the skeletal bonds of polyethylene are hindered due to interaction between the neighboring hydrogens. Since second and higher orders of neighborhood are not negligible, the internal rotations are interdependent. The statistics of such interdependent rotations is developed and applied to obtain the configurational partition function and the mean‐square end‐to‐end distance of the macromolecule.