D1.  Dependence on flexibility of the dynamics of semi-flexible rods in solution: a computer simulation approach.

      This project will:  This project will use computer simulations to study the dynamics of semi flexible polymers as a function of concentration and conformational flexibility.

Primary Faculty co-Advisors (at least 2!)

      Dr. Randall Hall, Chemistry (Simulation of Chemical Systems)

      Dr. Paul Russo, Chemistry (Experimental Macromolecular Studies)

      Dr. Browne, Physics (Simulation of Physical Processes)

Off-campus Participant:

      Mike Herman (Tulane)

   Technical Proposal:

   Computer simulation has been used extensively to explore dynamical and structural processes in every thing from chemistry and physics to social sciences such as financial planning and economics.  Computer simulations offer the ability to continuously vary system parameters and conditions making it a very attractive and predictive method.  Modern computers and cluster systems have given the computational scientist the raw power unseen in previous years. 

All-atom modeling the motion of very large molecules is still limited by processor speed.  The complexity of a macromolecular system is exhibited not just in conformational structures, but also in dynamical solution properties.  Modern computer systems and algorithms will enable simulations of both the internal conformational changes of macromolecular systems and the intermolecular dynamics of the flexible molecules.  Previous simulations have been limited by the assumptions and simplifications used to make the models computationally tractable.  Current theoretical methods and algorithms have progressed to the point where it is possible to elucidate significantly more important information.  It is hoped these new techniques, such as the Rope or tube model, and combinations of numerical techniques will greatly improve the simulation picture.

   Of considerable interest is the transition from isotropic to nematic phases in anisotropic rod-like macromolecules as concentration, i.e. number of molecules per unit volume, increase above a certain transition point seen both in natural and synthetic polymers.  It has been shown experimentally, theoretically, and in simulations that a minimum “stiffness” is needed to produce this transition.

   Rod-like polymers will exhibit two basic types of Brownian motion, translational and rotational.  The translational motion can be subdivided in two diffusive modes due to the anisotropic shape of the molecule, translational parallel (D_║) and perpendicular (D_┴) to the axis of the molecule.  Experiments cannot directly distinguish between the different diffusive modes and simulations have been limited to conformational rigid model systems with minor allowances for semi-flexible character causing discrepancies in the computational and experimental results.  It will be important to extend the current simulation work to take into account two theorized phenomenon believed possible with synthetic and natural polypeptides due to their semi-flexible nature and helical structure:  Freely Rotating end groups or “End Flopping”, and overlap or “Finger-Crossing” (see figure 1).  End flopping, thought possible in many helical polypeptides may result in retardation of the motion due to entanglements of the rods end to end.  Finger Crossing could enable a translational diffusing rod to cross over its neighbor to increase the motion in the perpendicular direction intuitively a least favorable direction of motion.  This motion has been theoretically treated as D_┴ = 0 according to Doi and Edwards (7).  The authors even question the validity of this assumption on the basis of Semi-flexible nature of some rods.

. Figure 1 “Finger-Crossing” or Overlap

 Banavar et. al suggested using a novel method to model a chain by coarse graining the picture, i.e. step back and take a simpler point of view.  Their work with protein folding using a tube model instead of the classical worm-like-chain model has shown very promising for protein simulations.  (Figure 2) It will be the goal in this work to utilize and expand the method presented by Banavar applying it to the semi-flexible rod.  Modeling the rod as a tube to “simplify” the picture and obtain greater information on the motions of the tubes as well as dynamics of tubes relative to other tubes in the unit volume.

Figure 2 from  Ref. 5

  The first step will be to model a single rod and determine the parameters needed to measure and vary keeping the axial ratio and polymer dimensions stable for the system of study.  The next step will be to move the entire tube in such a way using Brownian motion and/or Molecular Dynamics criteria.  Once the single molecule is completed it will be necessary to put more than one rod in the unit volume.  This will be computed using the number of rods per unit volume criteria established by Doi and Edwards for dilute, semi-dilute, and concentrated solutions.

   The experimental model for comparison with simulation results will be data obtained for PBLG (poly-γ-benzyl-L-glutamate) a helical polypeptide with semi-flexible character studied extensively and has been theorized to contain the characteristics specific to the proposed modeling explaining some behavior seen experimentally.  The system of study will be polypeptides in organic solvents to reduce the effects of charges as in water borne systems.  As the work progresses it is believed extensions to biological rods such as the F13 or Tobacco Mosaic Virus will be possible and beneficial to furthering the work.[PSR1] 

   Number of IGERT apprentices to be recruited and probable home departments: 

   2, Chemistry, Physics

   Consistency with the Macromolecular Education, Research & Training theme:  The project is consistent with IGERT Macromolecular Education Research and Training goals because not a single participant would be able to complete the work on their own.  It will take the unique mixture of Experimentalist, Theorist, Physicist, Simulation, etc. combined forming an interdisciplinary union of knowledge and experience to further this research endeavor. 

   How does the project form a vector cross-product of existing research themes by the participants? 

Existing research directions.  Dr. Russo’s major research area is the study of Rod-like polymers in complex fluids.  Dr. Browne’s major research area concerns the behavior of systems of many degrees of freedom whose steady state is far from equilibrium, such as fluid motion, chemical reactions, and biological systems.  Dr. Hall’s expertise resides in quantum mechanical simulation of various systems, primarily using ab initio and modeling calculations on clusters, glasses, and the effect of mutation and crossover on evolution and protein folding.

New research direction.  Dr. Russo’s knowledge of the physical properties of macromolecular systems and his bredth of experimental work will serve as a guide for confirming computational work.  This work will take his research into a new direction of simulation validating results of years of experimental data.  Dr. Hall’s work with modeling simulation programs and methodology and Dr. Browne’s knowledge of the physical aspects of interactions between atoms in macromolecules to ultimately create simplified models and algorithms that can be used to investigate long range orientational order as well as short range entropical effects.

How do students benefit from the team-oriented research, beyond what would be available to them from either advisor separately?  Student is prepared for better diversity by working in the areas of Computational Simulation, Macromolecular Theory, as well as Physics in general. 

Briefly describe the support level available to each individual faculty or off-campus

participant (i.e., without IGERT) 

  Dr. Hall will be providing the computer access for the introductory simulations with the 24 Node Beowulf cluster that is owned by his group.  Dr. Russo has an individual NSF award from the division of materials research.  It is up for renewal in one year.  Dr. Browne’s time and experience with complex systems and the physics associated with this will be invaluable to the team effort.

   Interdisciplinary strengths of the team project:  The team of Drs. Russo, Hall, and Browne combine to form a complimentary mixture of experimental, theory, and simulation for this project.  Dr. Russo’s work in rigid and semi-flexible macromolecules will be the guide for the computational results.  Dr.  Hall's main interest in research is in computer simulations involving numerous types of systems.  He brings years of knowledge of computer simulation and technique to the group.  Dr. Brown is a physicist specializing in the statistical mechanics of systems with multiple degrees of freedom, such as chemical reactions and fluid motions. He brings expertise of building simplified models for complicated many body systems and will be extremely useful in developing models for the flexibility of the systems of study.

   Commitment of faculty & off-campus participants to work side-by-side with apprentices: 

Hall, a full professor within the Department of Chemistry, actively pursues research using computer simulations and many different simulation programs.  Dr. Hall, as primary advisor, will meet with the students to discuss the development of programs which will be used to run the molecular dynamics simulations.  He and off-campus Professor Heran may assist with discussions regarding the programs used as necessary.  Dr. Russo, a named full professor within the macromolecular studies group in the department of chemistry, will provide direction and advice on theoretical aspects of semi-flexible rod polymers as well as experimental results derived in his research group in the past.  Dr. Browne is presently a full professor within the Department of Physics.  His major involvement will include collaboration in the algorithms and mathematical models of rod “cross-over” and end-group “flapping”

References: 

(1)  Russo, Paul S; Baylis, Michael; Bu Aimei; Stryjewski, Wieslaw; Doucet, Garrett; Temyanko, Elena; Tipton, Debbie. “Self-diffusion of a semiflexible polymer measured across the lyotropic liquid-crystallline-phase boundary” Journal of Chemical Physics 1999, Volume 111, No. 4, 1748.

(2)  Bu, Zemei; Russo, Paul S.; Tipton, Debbie; Negulescu, Ioan I. “Self-Diffusion of Rodlike Polymers in Isotropic Solutions”  Macromolecules, 1994, 27, 6871

(3)  Yethiraj, Arun; Fynewever, Herb. “Isotropic to nematic transition in semiflexible polymer melts” Molecular Physics 1998, Volume 93, No. 5, 693

(4)  Banavar, Jayanth R.; Maritan, Amos. “Colloquium:  Geometrical approach to protein folding:  A tube picture” Reviews of Modern Physics 2003, 75, 23

(5)  Banavar, Jayanth R.; Flammini, Alessandro; Marendzzo, Davide; Martin, Amos; Trovato, Antonio “Geometry of Compact Tubes and Protein Structures” ComPlexUs 2003, 1, 4 - 13

(6)  Fournier, J.B. “Wormlike chain or tense string? A question of resolution” Continuum Mechanical Thermodynamics 2002, 14, 241

(7)  Doi, M.; Edwards, S.F. “The theory of polymer dynamics”

(8)  Allen, M.P.; Tildesley, D.J. “Computer simulation of liquids”