2007 - Abstracts
1. Echebarria, B. and A. Karma (2007). "Amplitude equation approach to spatiotemporal dynamics of cardiac alternans." Physical Review E 76(5): 051911.
Amplitude equations are derived that describe the spatiotemporal dynamics of cardiac alternans during periodic pacing of one- [B. Echebarria and A. Karma, Phys. Rev. Lett. 88, 208101 (2002)] and two-dimensional homogeneous tissue and one-dimensional anatomical reentry in a ring of homogeneous tissue. These equations provide a simple physical understanding of arrhythmogenic patterns of period-doubling oscillations of action potential duration with a spatially varying phase and amplitude, as well as explicit quantitative predictions that can be compared to ionic model simulations or experiments. The form of the equations is expected to be valid for a large class of ionic models but the coefficients are derived analytically only for a two-variable ionic model and calculated numerically for the original Noble model of Purkinje fiber action potential. In paced tissue, this theory explains the formation of "spatially discordant alternans" by a linear instability mechanism that produces a periodic pattern of out-of-phase domains of alternans. The wavelength of this pattern, equal to twice the spacing between nodes separating out-of-phase domains, is shown to depend on three fundamental length scales that are determined by the strength of cell-to-cell coupling and conduction velocity (CV) restitution. Moreover, the patterns of alternans can be either stationary, with fixed nodes, or traveling, with moving nodes and hence quasiperiodic oscillations of action potential duration, depending on the relative strength of the destabilizing effect of CV restitution and the stabilizing effect of diffusive coupling. For the ring geometry, we recover the results of Courtemanche, Glass, and Keener [Phys. Rev. Lett. 70, 2182 (1993)] with two important modifications due to cell-to-cell diffusive coupling. First, this coupling breaks the degeneracy of an infinite-dimensional Hopf bifurcation such that the most unstable mode of alternans corresponds to the longest quantized wavelength of the ring. Second, the Hopf frequency, which determines the velocity of the node along the ring, depends both on the steepness of CV restitution and the strength of this coupling, with the net result that quasiperiodic behavior can arise with a constant conduction velocity. In both the paced geometries and the ring, the onset of alternans is different in tissue than for a paced isolated cell. The implications of these results for alternans dynamics during two-dimensional reentry are briefly discussed.
2. Gruia, F., X. Ye, D. Ionascu, M. Kubo and P. M. Champion (2007). "Low frequency spectral density of ferrous heme: Perturbations induced by axial Ligation and protein insertion." Biophysical Journal 93(12): 4404-4413.
Femtosecond coherence spectroscopy is used to probe low frequency (20-400 cm(-1)) modes of the ferrous heme group in solution, with and without 2-methyl imidazole (2MeIm) as an axial ligand. The results are compared to heme proteins (CPO, P450(cam), HRP, Mb) where insertion of the heme into the protein results in redistribution of the low frequency spectral density and in (similar to 60%) longer damping times for the coherent signals. The major effect of imidazole ligation to the ferrous heme is the "softening'' of the low frequency force constants by a factor of similar to 0.6 +/- 0.1. The functional consequences of imidazole ligation are assessed and it is found that the enthalpic CO rebinding barrier is increased significantly when imidazole is bound. The force constant softening analysis, combined with the kinetics results, indicates that the iron is displaced by only similar to 0.2 angstrom from the heme plane in the absence of the imidazole ligand, whereas it is displaced by similar to 0.4 angstrom when imidazole ( histidine) is present. This suggests that binding of imidazole ( histidine) as an axial ligand, and the concomitant softening of the force constants, leads to an anharmonic distortion of the heme group that has significant functional consequences.
3. Iwatani, Y., D. S. B. Chan, F. Wang, K. S. Maynard, W. Sugiura, A. M. Gronenborn, I. Rouzina, M. C. Williams, K. Musier-Forsyth and J. G. Levin (2007). "Deaminase-independent inhibition of HIV-1 reverse transcription by APOBEC3G." Nucleic Acids Research 35(21): 7096-7108.
APOBEC3G (A3G), a host protein that inhibits HIV-1 reverse transcription and replication in the absence of Vif, displays cytidine deaminase and single-stranded (ss) nucleic acid binding activities. HIV-1 nucleocapsid protein (NC) also binds nucleic acids and has a unique property, nucleic acid chaperone activity, which is crucial for efficient reverse transcription. Here we report the interplay between A3G, NC and reverse transcriptase (RT) and the effect of highly purified A3G on individual reactions that occur during reverse transcription. We find that A3G did not affect the kinetics of NC-mediated annealing reactions, nor did it inhibit RNase H cleavage. In sharp contrast, A3G significantly inhibited all RT-catalyzed DNA elongation reactions with or without NC. In the case of (-) strong-stop DNA synthesis, the inhibition was independent of A3Gs catalytic activity. Fluorescence anisotropy and single molecule DNA stretching analyses indicated that NC has a higher nucleic acid binding affinity than A3G, but more importantly, displays faster association/disassociation kinetics. RT binds to ssDNA with a much lower affinity than either NC or A3G. These data support a novel mechanism for deaminase-independent inhibition of reverse transcription that is determined by critical differences in the nucleic acid binding properties of A3G, NC and RT.
4. Karma, A. and R. F. Gilmour (2007). "Nonlinear dynamics of heart rhythm disorders." Physics Today 60(3): 51-57.
5. Leu, B. M., N. J. Silvernail, M. Z. Zgierski, G. R. A. Wyllie, M. K. Ellison, W. R. Scheidt, J. Y. Zhao, W. Sturhahn, E. E. Alp and J. T. Sage (2007). "Quantitative vibrational dynamics of iron in carbonyl porphyrins." Biophysical Journal 92(11): 3764-3783.
We use nuclear resonance vibrational spectroscopy and computational predictions based on density functional theory ( DFT) to explore the vibrational dynamics of Fe-57 in porphyrins that mimic the active sites of histidine-ligated heme proteins complexed with carbon monoxide. Nuclear resonance vibrational spectroscopy yields the complete vibrational spectrum of a Mossbauer isotope, and provides a valuable probe that is not only selective for protein active sites but quantifies the mean-squared amplitude and direction of the motion of the probe nucleus, in addition to vibrational frequencies. Quantitative comparison of the experimental results with DFT calculations provides a detailed, rigorous test of the vibrational predictions, which in turn provide a reliable description of the observed vibrational features. In addition to the well-studied stretching vibration of the Fe-CO bond, vibrations involving the Fe-imidazole bond, and the Fe-Npyr bonds to the pyrrole nitrogens of the porphyrin contribute prominently to the observed experimental signal. All of these frequencies show structural sensitivity to the corresponding bond lengths, but previous studies have failed to identify the latter vibrations, presumably because the coupling to the electronic excitation is too small in resonance Raman measurements. We also observe the FeCO bending vibrations, which are not Raman active for these unhindered model compounds. The observed Fe amplitude is strongly inconsistent with three-body oscillator descriptions of the FeCO fragment, but agrees quantitatively with DFT predictions. Over the past decade, quantum chemical calculations have suggested revised estimates of the importance of steric distortion of the bound CO in preventing poisoning of heme proteins by carbon monoxide. Quantitative agreement with the predicted frequency, amplitude, and direction of Fe motion for the FeCO bending vibrations provides direct experimental support for the quantum chemical description of the energetics of the FeCO unit.
6. McCauley, M. J. and M. C. Williams (2007). "Mechanisms of DNA binding determined in optical tweezers experiments." Biopolymers 85(2): 154-168.
The last decade has seen rapid development in single molecule manipulation of RNA and DNA: Measuring the response force for a particular manipulation has allowed the free energies of various nucleic acid structures and configurations to be determined. Optical tweezers represent a class of single molecule experiments that allows the energies and structural dynamics of DNA to be probed up to and beyond the transition from the double helix to its melted single strands. These experiments are capable of high force resolution over a wide dynamic range. Additionally, these investigations may be compared with results obtained when the nucleic acids are in the presence of proteins or other binding ligands. These ligands may bind into the major or minor groove of the double helix, intercalate between bases or associate with an already melted single strand of DNA. By varying solution conditions and the pulling dynamics, energetic and dynamic information may be deduced about the mechanisms of binding to nucleic acids, providing insight into the function of proteins and the utility of drug treatments. (c) 2006 Wiley Periodicals, Inc.
7. McCauley, M. J., J. Zimmerman, L. J. Maher and M. C. Williams (2007). "HMGB binding to DNA: Single and double box motifs." Journal of Molecular Biology 374(4): 993-1004.
High mobility group (HMG) proteins are nuclear proteins believed to significantly affect DNA interactions by altering nucleic acid flexibility. Group B (HMGB) proteins contain HMG box domains known to bind to the DNA minor groove without sequence specificity, slightly intercalating base pairs and inducing a strong bend in the DNA helical axis. A dual-beam optical tweezers system is used to extend double-stranded DNA (dsDNA) in the absence as well as presence of a single box derivative of human HMGB2 [HMGB2(boxA)] and a double box derivative of rat HMGB1 [HMGB1(boxA +box B)]. The single box domain is observed to reduce the persistence length of the double helix, generating sharp DNA bends with an average bending angle of 99+/-9 degrees and, at very high concentrations, stabilizing dsDNA against denaturation. The double box protein contains two consecutive HMG box domains joined by a flexible tether. This protein also reduces the DNA persistence length, induces an average bending angle of 77+/-7 degrees, and stabilizes dsDNA at significantly lower concentrations. These results suggest that single and double box proteins increase DNA flexibility and stability, albeit both effects are achieved at much lower protein concentrations for the double box. In addition, at low concentrations, the single box protein can alter DNA flexibility without stabilizing dsDNA, whereas stabilization at higher concentrations is likely achieved through a cooperative binding mode. (C) 2007 Elsevier Ltd. All rights reserved.
8. Pons, A. J., A. Karma, S. Akamatsu, M. Newey, A. Pomerance, H. Singer and W. Losert (2007). "Feedback control of unstable cellular solidification fronts." Physical Review E 75(2): 021602
We present a feedback control scheme to stabilize unstable cellular patterns during the directional solidification of a binary alloy. The scheme is based on local heating of cell tips which protrude ahead of the mean position of all tips in the array. The feasibility of this scheme is demonstrated using phase-field simulations and, experimentally, using a real-time image processing algorithm, to track cell tips, coupled with a movable laser spot array device to heat the tips locally. We demonstrate, both numerically and experimentally, that spacings well below the threshold for a period-doubling instability can be stabilized. As predicted by the numerical calculations, cellular arrays become stable with uniform spacing through the feedback control which is maintained with minimal heating.
9. Sato, D., Y. Shiferaw, Z. L. Qu, A. Garfinkel, J. N. Weiss and A. Karma (2007). "Inferring the cellular origin of voltage and calcium alternans from the spatial scales of phase reversal during discordant alternans." Biophysical Journal 92(4): L33-L35.
Beat-to-beat alternation of the action potential duration (APD) in paced cardiac cells has been linked to the onset of lethal arrhythmias. Both experimental and theoretical studies have shown that alternans at the single cell level can be caused by unstable membrane voltage (V-m) dynamics linked to steep APD-restitution, or unstable intracellular calcium (Ca) cycling linked to high sensitivity of Ca release from the sarcoplasmic reticulum on sarcoplasmic reticulum Ca load. Identifying which of these two mechanisms is the primary cause of cellular alternans, however, has remained difficult since Ca and Vm are bidirectionally coupled. Here, we use numerical simulations of a physiologically detailed ionic model to show that the origin of alternans can be inferred by measuring the length scales over which APD and Cai alternans reverse phase during spatially discordant alternans. The main conclusion is that these scales are comparable to a few millimeters and equal when alternans is driven by APD restitution, but differ markedly when alternans is driven predominantly by unstable Ca cycling. In the latter case, APD alternans still reverses phase on a millimeter tissue scale due to electrotonic coupling, while Ca alternans reverses phase on a submillimeter cellular scale. These results show that experimentally accessible measurements of Cai and Vm in cardiac tissue can be used to shed light on the cellular origin of alternans.
10. Silvernail, N. J., A. Barabanschikov, J. W. Pavlik, B. C. Noll, J. Y. Zhao, E. E. Alp, W. Sturhahn, J. T. Sage and W. R. Scheidt (2007). "Interplay of structure and vibrational dynamics in six-coordinate heme nitrosyls." Journal of the American Chemical Society 129(8): 2200
The isolation of two polymorphic forms of nitrosyl(1-methylimidazole)(tetra-p-fluorophenylporphinato)iron(II) provides a unique opportunity to explore the interplay of structure and vibrational dynamics in six-coordinate {FeNO}(7) nitrosyliron porphyrinates. The two species display differing vibrational spectroscopic properties both in nu(NO) (IR) and the iron vibrational modes obtained through the use of nuclear resonance vibrational spectroscopy. Structural characterization of the two complexes has yielded extremely high-quality structures that further confirm that coordination of NO leads to ligand tilting and asymmetry in the equatorial Fe-N-p bond distances. The two polymorphic structures (monoclinic and triclinic crystal systems) differ in the relative orientations of the two axial ligands and small but significant differences in coordination group bond distances. Although DFT calculations suggest that the NO/imidazole orientations should be indistinguishable, real experimental (structural and vibrational) differences between the two are found. The observed variation in the axial and equatorial Fe-N bonds is strongly correlated to the dynamics of the Fe-NO unit and other motions of iron. Other structural differences appear to have little effect on the vibrational properties of the two forms. The in-plane motions of iron in CO versus NO heme complexes illustrate distinct dynamic differences.
11. Sokoloff, J. B. (2007). "Theory of friction between neutral polymer brushes." Macromolecules 40(11): 4053-4058.
A type of static friction between two polymer brush coated surfaces resulting from fluctuations from mean-field theory is found, but with creeplike motion for forces below the force of static friction, which is much more rapid than the usual creep between solid surfaces in contact. At sufficiently light loads, it is shown that polymer brush coated surfaces can slide, with the load supported entirely by osmotic pressure, and thus exhibit no static friction and only extremely weak viscous kinetic friction.
12. Vladescu, I. D., M. J. McCauley, M. E. Nunez, I. Rouzina and M. C. Williams (2007). "Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching." Nature Methods 4(6): 517-522.
We used single DNA molecule stretching to investigate DNA intercalation by ethidium and three ruthenium complexes. By measuring ligand-induced DNA elongation at different ligand concentrations, we determined the binding constant and site size as a function of force. Both quantities depend strongly on force and, in the limit of zero force, converge to the known bulk solution values, when available. This approach allowed us to distinguish the intercalative mode of ligand binding from other binding modes and allowed characterization of intercalation with binding constants ranging over almost six orders of magnitude, including ligands that do not intercalate under experimentally accessible solution conditions. As ligand concentration increased, the DNA stretching curves saturated at the maximum amount of ligand intercalation. The results showed that the applied force partially relieves normal intercalation constraints. We also characterized the flexibility of intercalator-saturated dsDNA for the first time.
13. Williams, M. C. (2007). "Stuffing a virus with DNA: Dissecting viral genome packaging." Proceedings of the National Academy of Sciences of the United States of America 104(27): 11125-11126.
14. Wu, K. A. and A. Karma (2007). "Phase-field crystal modeling of equilibrium bcc-liquid interfaces." Physical Review B 76(18): 184107.
We investigate the equilibrium properties of bcc-liquid interfaces modeled with a continuum phase-field crystal (PFC) approach [K. R. Elder and M. Grant, Phys. Rev. E 70, 051605 (2004)]. A multiscale analysis of the PFC model is carried out which exploits the fact that the amplitudes of crystal density waves decay slowly into the liquid in the physically relevant limit where the freezing transition is weakly first order. This analysis yields a set of coupled equations for these amplitudes that is similar to the set of equations derived from Ginzburg-Landau (GL) theory [K.-A. Wu , Phys. Rev. B 73, 094101 (2006)]. The two sets only differ in the details of higher order nonlinear couplings between different density waves, which is determined by the form of the nonlinearity assumed in the PFC model and by the ansatz that all polygons with the same number of sides have equal weight in GL theory. Despite these differences, for parameters (liquid structure factor and solid density wave amplitude) of Fe determined from molecular dynamics (MD) simulations, the PFC and GL amplitude equations yield very similar predictions for the overall magnitude and anisotropy of the interfacial free-energy and density wave profiles. These predictions are compared with MD simulations as well as numerical solutions of the PFC model.
15. Ye, X., D. Ionascu, F. Gruia, A. Yu, A. Benabbas and P. M. Champion (2007). "Temperature-dependent heme kinetics with nonexponential binding and barrier relaxation in the absence of protein conformational substates." Proceedings of the National Academy of Sciences of the United States of America 104(37): 14682-14687.
We present temperature-dependent kinetic measurements of ultrafast diatomic ligand binding to the "bare" protoheme (L-1-FePPIX-L-2, where L-1 = H2O or 2-methyl imidazole and L-2 = CO or NO). We found that the binding of CO is temperature-dependent and nonexponential over many decades in time, whereas the binding of NO is exponential and temperature-independent. The nonexponential nature of CO binding to protoheme, as well as its relaxation above the solvent glass transition, mimics the kinetics of CO binding to myoglobin (Mb) but on faster time scales. This demonstrates that the nonexponential kinetic response observed for Mb is not necessarily due to the presence of protein conformational substates but rather is an inherent property of the solvated heme. The nonexponential kinetic data were analyzed by using a linear coupling model with a distribution of enthalpic barriers that fluctuate on slower time scales than the heme-CO recombination time. Below the solvent glass transition (T-g approximate to 180 K), the average enthalpic rebinding barrier for H2O-PPIX-CO was found to be approximate to 1 kJ/mol. Above T, the barrier relaxes and is approximate to 6 kJ/mol at 290 K. Values for the first two moments of the heme doming coordinate distribution extracted from the kinetic data suggest significant anharmonicity above T-g. In contrast to Mb, the protoheme shows no indication of the presence of "distal" enthalpic barriers. Moreover, the wide range of Arrhenius prefactors (10(9) to 10(11) s(-1)) observed for CO binding to heme under differing conditions suggests that entropic barriers may be an important source of control in this class of biochemical reactions.