M. C. Lopez Martinez

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 A DOUBLE-HELICAL MODEL FOR DNA

The translational and rotational diffusion coefficients of very short DNA fragments have been calculated using a double-helical bead model in which each nucleotide is represented by one bead. The radius of the helix is regarded as an adjustable parameter. The translational coefficient and the perpendicular rotation coefficient agree very well with experimental values for oligonuclotides with 8, 12, and 20 base pairs, for a single value of the helical radius of about 10 A. We have also calculated a nuclear magnetic resonance relaxation time in which the coefficient for rotation about the main axis is involved. As found previously with cylindrical models, the results deviate from experimental values, indicating that the internal motion of the bases has a remarkable amplitude. An attempt to quantify the extent of internal motions is presented.

Calculation of the solution properties of flexible macromolecules: methods and applications

While the prediction of hydrodynamic properties of rigid particles is nowadays feasible using simple and efficient computer programs, the calculation of such properties and, in general, the dynamic behavior of flexible macromolecules has not reached a similar situation. Although the theories are available, usually the computational work is done using solutions specific for each problem. We intend to develop computer programs that would greatly facilitate the task of predicting solution behavior of flexible macromolecules. In this paper, we first present an overview of the two approaches that are most practical: the Monte Carlo rigid-body treatment, and the Brownian dynamics simulation technique. The Monte Carlo procedure is based on the calculation of properties for instantaneous conformations of the macromolecule that are regarded as if they were instantaneously rigid. We describe how a Monte Carlo program can be interfaced to the programs in the HYDRO suite for rigid particles, and provide an example of such calculation, for a hypothetical particle: a protein with two domains connected by a flexible linker. We also describe briefly the essentials of Brownian dynamics, and propose a general mechanical model that includes several kinds of intramolecular interactions, such as bending, internal rotation, excluded volume effects, etc. We provide an example of the application of this methodology to the dynamics of a semiflexible, wormlike DNA.

Simulation of the conformation and dynamics of a double-helical model for DNA

We propose a partially flexible, double-helical model for describing the conformational and dynamic properties of DNA. In this model, each nucleotide is represented by one element (bead), and the known geometrical features of the double helix are incorporated in the equilibrium conformation. Each bead is connected to a few neighbor beads in both strands by means of stiff springs that maintain the connectivity but still allow for some extent of flexibility and internal motion. We have used Brownian dynamics simulation to sample the conformational space and monitor the overall and internal dynamics of short DNA pieces, with up to 20 basepairs. From Brownian trajectories, we calculate the dimensions of the helix and estimate its persistence length. We obtain translational diffusion coefficient and various rotational relaxation times, including both overall rotation and internal motion. Although we have not carried out a detailed parameterization of the model, the calculated properties agree rather well with experimental data available for those oligomers.

Relaxation times in transient electric birefringence and electric‐field light scattering of flexible polymer chains

We study in the present paper the response of a flexible macromolecular chain to the application or removal of an electric field. The polymer is mainly modeled as a Gaussian chain, and the case of freely jointed chains is also treated. We consider the dynamics of the chains, after the inception and subsequent cessation of an electric field. In particular, we calculate two properties. One of them is the time‐dependent chain expansion, as measured by the components of the gyration tensor, that can be determined by transient electric‐field light scattering. The other property is the transient electric birefringence, related to the reorientation of the chain segments. In this way, the dynamics of two different properties can be compared. The transient properties are analyzed in terms of a series of relaxation times. We propose the use of a mean relaxation time as a convenient representation of the rate of the dynamic process, and show that it can be deduced from simulation or experiments with more accuracy th...

Conformation and dynamics of star-branched flexible polymer chains in a flowing solution

Abstract When linear or star-branched polymer chains in dilute solution are subjected to extensional flow of adequate intensity, each chain in the sample experiences a coil-stretch transition. Using Brownian dynamics simulation, we have studied both static and dynamic aspects of this phenomenon. We have determined the power law that relates the critical extensional rate, ϵ c , to the molecular weight of the chain. In the case of linear chains we have studied the distribution of transition times. If the accumulated strain is used to characterize the flow effect a seemingly universal behavior, independent of molecular weight is found. The molecular individualism is related to the excess of the applied extensional rate over its critical value, which will determine the transition time and other features of the coil-stretch transition.

Deformation, scattering, and birefringence of flexible polymer chains under external forces or electric fields

The effect of a tensile stress or an electric field on the conformation of a flexible polymer chain has been studied by combining theory with numerical simulation. In the presence of such external agents, the macromolecule experiences the action of two opposite forces at the chain ends. Two models are considered: the Gaussian bead-and-spring chain, and the freely jointed chain with segments of fixed length. From simulated Brownian trajectories we calculate steady-state properties of the polymer under the continuing action of the external forces. Thus, we compute the chain deformation and expansion, measured by the square radius of gyration, and analyze the influence of the external force on low-angle scattering of radiation. The effect of the link orientation in the optical anisotropy or birefringence is also analyzed. From existing theories, we predict very simple relationships between expansion, low-angle scattering, and birefringence, valid for Gaussian chains of any length, and for long freely jointed chains. The simulation results confirm those relationships.

Fracture of DNA in transient extensional flow. A numerical simulation study

Using the Brownian dynamics simulation technique, we studied the fracture process of DNA chains subjected to transient extensional flow, letting the solution with DNA molecules pass through a very small orifice (radius = 0.0065 cm), thus experiencing extensional flow of the convergent (sink) type. The DNA molecules were modeled as FENE bead-spring chains with the springs obeying a modified Warner force law, as proposed by Reese and Zimm. The fracture yield was strongly dependent on flow rate and molecular weight, reaching, in our setup, a level of 100% at a flow rate of around 0.001 cm3/s for DNA with molecular weight 26 × 106 (T7 DNA). There was found to exist a critical flow rate (Qcrit) below which fracture did not occur, in accordance with what was observed in studies on polystyrene in transient extensional flow. We found that for DNA, the critical flow rate depended on the molecular weight as Qcrit ∼ M−14 when the hydrodynamic interaction effect (HI) was not included in the simulations. When HI was accounted for, the relation was found to be Qcrit ∼ M−1.1, close to the theoretical prediction for fracture of partly extended chains in transient extensional flow.