Molecular Biological Physics
by E.W. Prohofsky
Professor Earl Prohofsky spent the first decade of his professional career as a theoretical physicist doing analysis on second sound in super fluid helium and crystalline solids, thermal conductivity, ultrasonic attenuation and electron-vibration wave interaction. In 1973 he became interested in the question of whether vibrational waves could be important in the description and analysis of biological phenomena. At that time there were reports in the literature of experimental observations of resonant infrared absorption and low frequency Raman scattering in proteins, DNA, and RNA. The explanation for these observations required the existence of fairly long lived vibrational mode excitations, the quantized versions of which are called phonons. Phonon modes can be used as a basis set for describing all atomic motion, and such atomic motion is necessary for biological function. The phonons can form a frequency and wavelength description that can replace the position and time description of atom displacements. By this switch new insights to the energetics of processes can be gained.
Methods for the calculation of phonon frequencies in molecules in the 70's were limited to small molecules. The calculations required the diagonalization of a matrix that was 3N by 3N where N is the number of atoms in the molecule. With the computers available at the time a 50 atom molecule stretched calculational capabilities. The biological molecules of interest which showed infrared and Raman activity were DNA and RNA helices with thousands to many hundred thousand atoms. They were, however made up of repeating units called base pairs each of which was the size of some 40 atoms. The only feasible approach to large molecule calculation at the time was to use lattice methods which Prof. Prohofsky used regularly in vibrational mode analysis in crystalline solids. Lattice methods use symmetry arguments to reduce the calculation on a large to infinite size object, that has some repeating nature, to a set of calculation on an object the size of a single repeating unit. A direct comparison of theory and experiment could be made as some of the infrared and Raman observations were carried out homopolymer nucleic acid which has the exact required repeating nature.
The initial formulation of the lattice calculation on nucleic acids was carried out by James Eyster in his Ph. D. research and involved formulating the most efficient way to reduce a large macromolecule calculation to a small repeat unit calculation. The calculations also required the refinement of a set of force constants which describe the interaction between pairs of atoms that are the matrix elements in the matrix to be diagonalized. The resulting phonon frequency predictions agreed well with experimental observations. Prof. Gianni Ascarelli, also of Purdue, began a program to measure infrared absorption in several RNA polymers. The improved experimental data led to the ability to refine force constants needed to accurately describe the atom-atom interactions in nucleic acids.
In the mid 1970's Ms. K.C. Lu became a Ph. D. student working for him on a novel Green function method to improve refined force constants for use in DNA-RNA vibrational mode calculations. Prof. Lonnie VanZandt became interested in the Nucleic acid calculations and Ms. Lu in the late 70's and the two later married. Ascarelli, Prohofsky, and Van Zandt collaborated for several years forming a molecular biological physics group that worked at improved models by strong correlation of theory and experiment.
From the beginning of the program Prohofsky's intention was to develop methods that used phonon basis sets to calculate and analyze biologically significant behavior of macromolecules, rather than just develop methods to calculate vibrational frequencies. The two behaviors that were focused on were changes in shape (conformation change) of macromolecules and the separation (dissociation) of parts of macromolecules or combinations of macromolecules. Both behaviors are instrumental in biological function and enzymatic processes in general. They are however, extremely difficult to predict and analyze theoretically. The ability to predict changes in shape based on vibrational mode analysis was demonstrated very early on in the program. The third publication by Eyster and Prohofsky in 1977 reported the prediction of a "soft mode" in DNA which drove the displacive transition from A-conformation to B-conformation. When a system starts to change shape a particular displacement of the atoms takes place. Group theory analysis shows that this displacement is also an eigenvector of a vibrational mode whose eigenfrequency approaches zero. A zero frequency indicates that the system gets soft for this particular displacement, i.e. there is vanishing resistance to such displacement. Experimentally DNA changes from A-DNA to B-DNA when the water of hydration increases. The calculation showed a mode that was initially at a frequency of 12 cm-1 approached zero as the dielectric constant in the electrostatic interactions in the helix was increased, as would be expected for increased water of hydration. This mode was one in which the two backbones of the helix vibrated up and down out of phase. The resulting motion tilted the bases which is the principal difference in the two conformations.
The study of dissociation of parts of the helix also began early in the thesis work of Brian Putnam. It was found that a vibrational mode near 85 cm-1stretched the H-bonds that hold the two strands of the double helix together. It was predicted that as melting (dissociation of the two strands of the helix) began the bases would start to pull apart and this would weaken the h-bond interactions holding the two strands together. This weakening would cause increased amplitude of h-bond stretch etc. leading to further softening, dissociation and melting. The softening of this band of modes was subsequently observed by Raman scattering at the onset of helix melting. A publication by Putnam and Prohofsky in 1983 explored the nature of this H-bond breathing mode in the fork formed by an intact double helix changing into one in which the two strands were separated such as is the case in the biological processes of replication and transcription.
In the early 1980's reports of microwave irradiation of the US embassy in Moscow started many people worrying about the possibility of harmful effects of microwaves. One worry was long term gene damage that could lead to cancer or genetic defects. The molecular biological physics group at Purdue was the only group that had models of DNA vibrational modes that could be used in calculating microwave absorption by DNA. Calculations of microwave absorption and its possible effects were carried on with the simultaneous support of NIH, FDA, US Navy, and US air force. DNA has acoustic modes in the microwave region that do have a dipole moment and can absorb radiation. The problem was whether or not the interaction with water of hydration, always present in tissue, overdamped these modes and thus reduced the absorption to the point where it wasn't significant. The water interaction was found to eliminate resonant absorption in the microwave region and irradiation at levels below that causing heating were found to be harmless. After this became clear Lonnie VanZandt continued to work on detailed models of DNA-water systems in EM fields with graduate students and Virennda Saxena until VanZandt's untimely death in 1995.
Earl Prohofsky continued to work on improving the theory of macromlecular dissociations. The incorporation of weakening bonds as separations began required a cooperative nonlinear theory which was developed with his graduate student Yong-Li Gaou. Mr. Gaou not only pioneered these calculations working with Earl Prohofsky but he then switched to an entirely different area doing an experimental thesis for Ron Riffenberger. The theoretical method involved extending self consistent phonon theory, which was developed for use in quantum crystals at low temperature, to melting in DNA at high temperature. The common element that allowed it to work was the similarity between quantum fluctuations and thermal fluctuations. An effective force constant for h-bond interaction was calculated that incorporated the thermal fluctuations in interatom bond distance. Since the size of the fluctuations are determined both by the size of the force constants and the level of vibrational excitation, the entire calculation had to be done self consistently at each temperature.
The dissociation calculations were further developed and formulated as a mean field theory of melting by Prohofsky and Yu Zong Chen a post doc. The theory very accurately predicted melting temperatures for a large number of DNA helices and even predicted the salt concentration and hydrostatic pressure dependence of melting. The method could also determine the relative stability of different conformations and could predict the temperature and salt concentration dependence of the B to Z conformation change which occurs in DNA. The melting calculations were also applied to DNA triple helices and DNA-RNA triple helices where it accurately predicted both the initial separation of one of the strands and then the final melting of the remaining double helix. These triple helices are being developed as drugs which are attracted to specific genes by adding the right third element that can form a local triple helix. This triple helix can then effectively inactivate a particular part of a genome. This work led to a interaction between the Purdue group and Isis Pharmaceuticals, a drug company.
The dissociation calculations were also applied to DNA-protein complexes such as DNA-netropsin, DNA-daunomycin, and DNA-cisplatin complexes. The theory predicted with good accuracy the temperature of dissociation of the protein or drug from the helix. It also allowed determination of the premelting binding constant as a function of temperature. The theory predicted the details of the dissociation such as the sequence of bond separation. These proteins are used as antibiotics and anticancer agents and their binding to DNA is the important element in their efficacy.
Professor Prohofsky was born on 8 February 1935 in St. Paul, Minnesota. He received the B.S. at the University of Minnesota in 1957 and the Ph.D. at Cornell University in 1963. During 1962-1966 he worked as a research associate at Cornell University and as a research scientist at Sperry Road Research Center in Sudburry, Massachusetts. He came to Purdue as Assistant Professor in 1966, was promoted to Associate Professor in 1967 and to Professor in 1973. He has supervised the thesis research of over 15 students and is the author of more than 120 refereed publications and the book, Statistical Mechanics and Stability of Macromolecules, Cambridge University Press, (1995). He is a fellow of the American Physical Society and Secretary-Treasurer of the Division of Biological Physics of the APS.