A. Introduction

Broadly speaking, macromolecular dynamics refers to the nonequilibrium behavior of large clusters of molecules or macromolecules, such as polymers, proteins, colloids, aerosols, etc. Examples of macromolecular nonequilibrium phenomena include the flow of polymeric solutions, electrophoretic motion of DNA, the folding and diffusion of proteins, and aerosol and colloid transport phenomena, to name just a few. Molecular dynamics includes the study of the transfer of material or properties at the molecular level and, hence, it is also a smaller-scale or refined view of macromolecular dynamics. In many cases, macromolecular properties can be obtained by averaging or ‘integrating-over’ the molecular level of description, as in colloidal and aerosol systems involving 'rigid' particles. In other macromolecular processes, such as protein folding, the molecular nature of the system must be retained.

This research program involves the theoretical and experimental study of nonequilibrium molecular and macromolecular phenomena that arise in contemporary science and engineering applications. This is a field rich in scientific history involving Nobel laureates such as Einstein and Chandrasekhar [1,2]. However, not only do many outstanding fundamental and applied problems still remain, but also recent advances in scientific computing and atomic-level experimentation make it possible to study such systems at levels or degrees that were once thought impossible. As elaborated below, such studies can further translate into potentially dramatic technological or engineering advances. The research program described here can be categorized in the developing area of molecular engineering, or the design and analysis of engineering systems beginning at the molecular level of description.

A great simplification in the analysis of the nonequilibrium behavior of macromolecules can be made by considering the macromolecule to be either a rigid or flexible body immersed in a molecular fluid. The individual identities of the molecules comprising the macromolecule are ‘lost’ and they simply make up a rigid or flexible body that is large compared to the size of a molecule of the surrounding fluid. The macromolecule is often modeled as a connected set of rigid bodies, or subunits, where the connectors allow for overall flexibility of the macromolecule [3-9]. The rigid bodies or subunits are called Brownian bodies or particles in that they are sufficiently small that the molecular or random nature of the surrounding fluid must be taken into account.

Our theoretical work has involved the study of internal rotational, translational and coupled translational-rotational motions in macromolecules [6,7,9]. The internal motions of macromolecules are often critical to their transport properties and, in the case of biological macromolecules, their biological activities. Notable examples include the twisting or torsional motion of DNA [3] and rotational motions of sidechains in proteins [4].

In general, it is difficult to uncouple rotational and translational motions in macromolecules due to hydrodynamic coupling, i.e., translational motions of the subunits comprising the macromolecule generate velocity fields in the surrounding solvent that lead to rotational motions of adjacent subunits, and vice-versa [5]. In macromolecules the problem is further complicated by rotational and translational Brownian motions of the subunits and the need to specify a number of intramacromolecular torques describing rotational deviations of the subunits from equilibrium positions, as in Hookean springs for translational deviations. A complete description of the general model can be found in [9].

Current work involves the application of the general model as described above to various important problems involving flexible biological macromolecules, some of which are discussed below.

Descriptions of specific applications of macromolecular modeling currently under investigation, which are critically dependent on the flexibility of the macromolecule, are given below. Many of these problems also fall under the contemporary category of artificial life processes and therefore have rather broad applications. Note that these applications include engineering where one seeks to utilize the behavior of natural processes for the production of new chemicals and products.

1. Self Replication. One of the essential functions of living cells is their ability to reproduce. Cells contain the "messenger" macromolecule RNA that has been shown to have the uncanny ability to build copies of itself. Current models of RNA self replication involve the dynamic matching of nucleotide segments to a target molecule of RNA [10]. The rate of nucleotide attachment, in the correct Watson-Crick pairing, depends to a great degree on the motion and flexibility of the target RNA and on the random or Brownian motions of the nucleotide segments.

2. Self Assembly. Dynamically similar in many ways to self replication, peptide molecules found in proteins have been shown to self assemble into large membrane structures [11]. The flexibility of the peptide chains is critical to linking with adjacent strands. Important engineering applications of self assembly include the formation of new biologically based materials.

3. Intelligent Gels. Flexible macromolecules in gels expand or contract depending on the interactions with the surrounding solvent molecules or in response to external stimuli [12]. Numerous engineering applications, including prostheses, chemical valves, drug delivery systems, among others, are among the various applications of 'intelligent' gels.

4. Motility and Biological Motors. Many cells and microorganisms utilize chemical reactions and physical changes to drive their own motion. The well-known example is bacteria that use their flagella for self propulsion. A comprehensive review of the motility of E. coli can be found in Berg [13]. Understanding, modeling, and designing macromolecular motors would appear to have a multitude of engineering applications including drug delivery systems, separation processes, among others. In general, motility adds a new and exciting dimension to the study of transport processes involving macromolecules.

In many systems of scientific and engineering interest the behavior and properties must be studied at the molecular level of description. Important examples include spatially dependent structural molecular changes in solvents, such as water, due to the presence of solutes, such as proteins [14]. Molecular dynamic computer simulations represent an exact method of analysis as opposed to the modeling approaches discussed above. In molecular dynamic simulations the trajectories of individual molecules are tracked in time as the interact with other molecules and the boundary molecules of the system. These methods are often called 'computer experiments' since the information obtained is in the form of a data set that must be treated in the same manner as a physical experiment.

One significant drawback on the use of molecular dynamics methods in macromolecular systems is the prohibitive times required to probe particle dynamics in actual systems (say on the order of 10⁰ to 10⁵ seconds). In order to circumvent this problem we are investigating the use of a hybrid molecular dynamics-Brownian dynamics algorithm for determining the long-time behavior of molecularly specified macromolecules. This technique could prove extremely useful in rigorously solving long time dynamical problems, such as protein folding, not currently possible by molecular dynamics alone.

Currently, we are using molecular dynamics to determine the mobilities of complex particles from time force autocorrelation analysis. Particles being studied include small proteins with hydrophobic and hydrophilic components in water, and porous biodegradable particles, such as those used in drug delivery systems.

An important large scale molecular dynamics simulation under development is the transport and deposition of aerosol particles and very large molecules, such as pharmaceuticals, in the human lung airways. In this system, the gas dynamics goes through a variety of regimes from continuum flow to nearly free-molecular flow. Correspondingly, the Brownian and frictional force acting on any particle contained in the flow also change dramatically. Coupled with the other physical facts that the flow is unsteady and gas exchange effects (respiration) are important, this problem is extremely difficult to tackle analytically, to say the least. Fortunately, the overall system size is still small enough that the powerful molecular dynamics simulation technique can be used to exactly study such systems. The eventual goal of this research is to use the algorithm as part of the diagnostic tools in pulmonary disease research and drug delivery system design.

In addition to the molecular dynamic studies on particle transport in the lung mentioned above, a companion experimental program has also been developed using model lung structures [18]. This program involves studies on the deposition of fluorescent polystyrene latex particles in unsteady-state flow in pores. UV optical detection methods are used for real time data analysis allowing for a direct comparison to theoretical studies. In addition, PFGSE NMR methods are being studied for use in aerocolloidal systems. The NMR technique is a non-intrusive experimental method and therefore much superior to conventional methods of particle removal and analysis. From an engineering point of view, most of the interesting properties of particles in fluids appear as a result of their environment.

1. Einstein, A., Investigations on the Theory of the Brownian Movement, Dover Publications, 1956.

2. Chandrasekhar, S., Rev. Mod. Phys., 15,1 (1943).

10. Freedman, D.H., Discover, 46, August, 1992.

11. Pennisi, E., Science News, 143, 316(1993).