J. García de la Torre

Prediction of Hydrodynamic and Other Solution Properties of Rigid Proteins from Atomic- and Residue-Level Models

Here we extend the ability to predict hydrodynamic coefficients and other solution properties of rigid macromolecular structures from atomic-level structures, implemented in the computer program HYDROPRO, to models with lower, residue-level resolution. Whereas in the former case there is one bead per nonhydrogen atom, the latter contains one bead per amino acid (or nucleotide) residue, thus allowing calculations when atomic resolution is not available or coarse-grained models are preferred. We parameterized the effective hydrodynamic radius of the elements in the atomic- and residue-level models using a very large set of experimental data for translational and rotational coefficients (intrinsic viscosity and radius of gyration) for >50 proteins. We also extended the calculations to very large proteins and macromolecular complexes, such as the whole 70S ribosome. We show that with proper parameterization, the two levels of resolution yield similar and rather good agreement with experimental data. The new version of HYDROPRO, in addition to considering various computational and modeling schemes, is far more efficient computationally and can be handled with the use of a graphical interface.

HYDRO: a computer program for the prediction of hydrodynamic properties of macromolecules

HYDRO is a program for the calculation of sedimentation and diffusion coefficients, rotational relaxation times, and intrinsic viscosities of rigid macromolecules of arbitrary shape that are represented by bead models. Actually, HYDRO contains various FORTRAN callable subroutines that can be linked to the users own programs to account for variability of shape or flexibility. Some hints are given for the use of HYDRO in various situations.

Hydrodynamic properties of rodlike and disklike particles in dilute solution

The hydrodynamic properties of cylindrical (rodlike and discoidal) particles in dilute solution have been computed using the bead-shell model treatment. Previous results [Tirado and Garcia de la Torre, J. Chem. Phys. 71, 2581 (1979); 73, 1993 (1980)] for rods with length-to-diameter ratio p>2 are now extended to short cylinders and disks down to p=0.1. The intrinsic viscosity is obtained for rods and disks, and results are presented for the three rotational relaxation times of a cylindrical particle. The hydrodynamic properties are expressed in forms that have a weak variation with p, and are therefore useful for the analysis of experimental values. We present examples of the determination of the length and diameter of the cylindrical particles, for DNA oligonucleotides and tobacco mosaic virus.

Molecular dynamics simulation of a charged biological membrane

A molecular dynamics simulation of a membrane with net charge in its liquid‐crystalline state was carried out. It was modeled by dipalmitoylphosphatidylserine lipids with net charge, sodium ions as counterions and water molecules. The behavior of this membrane differs from that was shown by other membranes without a net charge as a consequence of strong Coulomb interaction between atoms of adjacent phospholipids. The most remarkable effect produced by such interaction between neighboring lipids is a reduction of the surface area per phospholipid compared to an uncharged membrane. In addition, other properties of the membrane were also affected by this interaction between adjacent lipids such as the atom distribution across the membrane, the diffusion coefficient of the different components of the membrane and the order parameter of the phospholipid hydrocarbon region. Some comparisons of this membrane with dipalmitoylphosphatidylcholine membrane without net charge at similar conditions are presented.

A second‐order algorithm for the simulation of the Brownian dynamics of macromolecular models

Most recent works on Brownian dynamics simulation employ a first‐order algorithm developed by Ermak and McCammon [J. Chem. Phys. 69, 1352 (1978)]. In this work we propose the use of a second‐order algorithm in which the step is a combination of two first‐order steps, like in the second‐order Runge–Kutta method for differential equations. Although the computer time per step is roughly doubled, the second‐order algorithm is more efficient than the previous one because a given accuracy in the results can be achieved with less than half the number of steps. The new algorithm also allows for longer time steps without divergence. The advantage of the new procedure is illustrated in the simulation of four macromolecular systems: A quasirigid dumbbell, a semiflexible trumbbell, a semiflexible hinged rod, and a Gaussian polymer chain.

Hydration from hydrodynamics. General considerations and applications of bead modelling to globular proteins

The effect of hydration on hydrodynamic properties of globular proteins can be expressed in terms of two quantities: the δ (g/g) parameter and the thickness of the hydration layer. The two paradigms on hydration that originate these alternative measures are described and compared. For the numerical calculation of hydrodynamic properties, from which estimates of hydration can be made, we employ the bead modelling with atomic resolution implemented in programs HYDROPRO and HYDRONMR. As typical, average values, we find 0.3 g/g and a thickness of only approximately 1.2 A. However, noticeable differences in this parameter are found from one protein to another. We have made a numerical analysis, which leaves apart marginal influences of modelling imperfections by simulating properties of a spherical protein. This analysis confirms that the errors that one can attribute to the experimental quantities suffice to explain the observed fluctuations in the hydration parameters. However, for the main purpose of predicting protein solution properties, the above mentioned typical values may be safely used. Particularly for atomic bead modelling, a hydrodynamic radius of approximately 3.2 A yields predictions in very good agreement with experiments.

SOLPRO: theory and computer program for the prediction of SOLution PROperties of rigid macromolecules and bioparticles

Abstract Single-valued hydrodynamic coefficients of a rigid particle can be calculated from existing theories and computer programs for either bead models or ellipsoids. Starting from these coefficients, we review the procedures for the calculation of complex solution properties depending on rotational diffusion, such as the decays of electric birefringence and fluorescence anisotropy. We also describe the calculation of the scattering form factor of bead models. The hydrodynamic coefficients and solution properties can be combined to give universal, shape-dependent functions, which were initially intended for ellipsoidal particles, and are extended here for the most general case. We have implemented all these developments in a new computer program, SOLPRO, for calculation of SOLution PROperties, which can be linked to existing software for bead models or ellipsoids.

Joint determination by Brownian dynamics and fluorescence quenching of the in-depth location profile of biomolecules in membranes

The in-depth molar distribution function of fluorophores is revealed by a new methodology for fluorescence quenching data analysis in membranes. Brownian dynamics simulation was used to study the in-depth location profile of quenchers. A Lorentzian profile was reached. Since the Stern-Volmer equation is valid at every depth in the membrane for low quencher concentrations, the molar distribution of the fluorophore (also regarded as a Lorentzian) can be achieved. The average location and the broadness of the fluorophore distribution can be calculated. The importance of the knowledge of the location width is demonstrated and discussed, since this parameter reveals important conclusions on structural features of the interaction of membranes with probes and biomolecules (e.g., conformational freedom in proteins), as well as photophysical properties (e.g., differential fluorophore quantum yields). Subsequent use of this methodology by the reader does not, necessarily, involve the performance of simulations and is not limited to the use of Lorentzian function distributions.

Steady-state behavior of dilute polymers in elongational flow. Dependence of the critical elongational rate on chain length, hydrodynamic interaction, and excluded volume

The steady-state properties of flexible polymer chains in solutions undergoing elongational flow have been studied using Brownian dynamics simulation. The coil–stretch transition is observed when the elongational rate, e exceeds a certain critical value ec. In this work, we describe in detail the simulation procedure and how to extract polymer dimensions, solution viscosity, and birefringence from the trajectories. Preliminary simulations involving no hydrodynamic interaction (HI) are used to check the simulation procedures by comparing their results with theoretical predictions for such an (unphysical) case. Afterwards, simulations with fluctuating nonaveraged HI are carried out to provide results comparable with experiments. After simulations with and without intramolecular potential, we arrive at a most important conclusion: the chain length dependence of ec is the same in theta conditions as in good solvent conditions. Combining ec with other solution properties such as the longest relaxation time, the intrinsic viscosity, and the radius of gyration, dimensionless compound quantities can be formulated. From our simulation results, we obtain numerical values for such quantities, which include the HI effect, and which are therefore useful for analyzing experimental data.The steady-state properties of flexible polymer chains in solutions undergoing elongational flow have been studied using Brownian dynamics simulation. The coil–stretch transition is observed when the elongational rate, e exceeds a certain critical value ec. In this work, we describe in detail the simulation procedure and how to extract polymer dimensions, solution viscosity, and birefringence from the trajectories. Preliminary simulations involving no hydrodynamic interaction (HI) are used to check the simulation procedures by comparing their results with theoretical predictions for such an (unphysical) case. Afterwards, simulations with fluctuating nonaveraged HI are carried out to provide results comparable with experiments. After simulations with and without intramolecular potential, we arrive at a most important conclusion: the chain length dependence of ec is the same in theta conditions as in good solvent conditions. Combining ec with other solution properties such as the longest relaxation time...

HYDROMIC: prediction of hydrodynamic properties of rigid macromolecular structures obtained from electron microscopy images.

Abstract. We have developed a procedure for the prediction of hydrodynamic coefficients and other solution properties of macromolecules and macromolecular complexes whose volumes have been generated from electron microscopy images. Starting from the structural files generated in the three-dimensional reconstructions of such molecules, it is possible to construct a hydrodynamic model for which the solution properties can be calculated. We have written a computer program, HYDROMIC, that implements all the stages of the calculation. The use of this procedure is illustrated with a calculation of the solution properties of the volume of the cytosolic chaperonin CCT, obtained from cryoelectron microscopy images.