UW Department of Applied Mathematics

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Hong Qian

PUBLICATIONS LIST

BOOKS
  1. Chemical Biophysics: Quantitative Analysis of Cellular Systems. (with Beard, D.A.) Cambridge Texts in Biomedical Engineering, Cambridge University Press (2008).

REVIEWS and FEATURE ARTICLES
  1. Cooperativity and specificity in enzyme kinetics: A single-molecule time-based perspective. Biophysical Journal (Mini-review), 95, 10-17 (2008).
  2. Phosphorylation energy hypothesis: Open chemical systems and their biological functions. Annual Review of Physical Chemistry, 58, 113-142 (2007).
  3. Open-system nonequilibrium steady-state: Statistical thermodynamics, fluctuations and chemical oscillations. Journal of Physical Chemistry B, 110, 15063-15074 (2006).
  4. Cycle kinetics, steady-state thermodynamics and motors -- a paradigm for living matter physics. Journal of Physics: Condensed Matter, 17, S3783-S3794 (2005).
  5. Thermodynamics of stoichiometric biochemical networks in living systems far from equilibrium. (with Beard, D.A.) Biophysical Chemistry, 114, 213-220 (2005).
  6. Fractional Brownian motion and fractional Gaussian noise. In Processes with Long-Range Correlations: Theory and Applications (Lecture Notes in Physics, Vol. 621, G. Rangarajan & M.Z. Ding, eds.), Springer, 22-33 (2003).
  7. From discrete protein kinetics to continuous Brownian dynamics: A new perspective. Protein Science, 11, 1-5 (2002).
  8. The mathematical theory of molecular motor movement and chemomechanical energy transduction. Journal of Mathematical Chemistry, 27, 219-234 (2000).
  9. Measurements of molecular transport in small systems. (with Elson, E.L.), In Cell Biology (AMS Lectures on Mathematics in the Life Science, Vol. 24, B. Goldstein & C. Wofsy eds.), American Mathematical Society, 37-49 (1994).

APPLIED MATHEMATICS
  1. On Poincaré-Hill cycle map of rotational random walk: Reversible Schnakenberg model for chemical oscillations. (with Vellela, M.)
  2. Ultrasensitive dual phosphorylation dephosphorylation cycle kinetics exhibits canonical competition behavior. (with Huang, Q.) Chaos: An Interdisciplinary Journal of Nonlinear Science,
  3. The dynamics of zeroth-order ultrasensitivity: A critical phenomenon in cell biology. (with Huang, Q.)
  4. Nonlinear oscillations and multiscale dynamics in a closed chemical reaction system. (with Li, Y. & Yi, Y.)
  5. On the degree properties of generalized random graphs. (with Shi, Y.Y.) Communications in Mathematical Sciences, 7, 175-187 (2009).
  6. Synchronized dynamics and nonequilibrium steady states in a stochastic yeast cell-cycle network. (with Ge, H. & Qian, M.) Mathematical Biosciences, 211, 132-152 (2008).
  7. Quantitative model for binary measurements of protein-protein interactions. (with Shi, Y.Y., Miller, G.A., Denisenko, O. & Bomsztyk, K.) Journal of Computational Biology, 14, 1011-1023 (2007).
  8. On detailed balance and reversibility of semi-Markov processes and single-molecule enzyme kinetics. (with Wang, H.) Journal of Mathematical Physics, 48, 013303 (2007).
  9. On the existence of potential landscape in the evolution of complex systems. (with Ao, P. & Kwon, C.) Complexity, 12, 19-27 (2007).
  10. A quasistationary analysis of a stochastic chemical reaction: Keizer's paradox. (with Vellela, M.) Bulletin of Mathematical Biology, 69, 1727-1746 (2007).
  11. A stochastic model of oscillatory blood testosterone levels. (with Heuett, W.J.) Bulletin of Mathematical Biology, 68, 1383-1399 (2006).
  12. Combining flux and energy balance analysis to model large-scale biochemical networks. (with Heuett, W.J.) Journal of Bioinformatics and Computational Biology, 4, 1227-1243 (2006).
  13. An asymptotic comparative analysis of the thermodynamics of non-covalent association. Journal of Mathematical Biology, 52, 277-289 (2006).
  14. Thermodynamic constraints for biochemical networks. (with Beard, D.A., Babson, E. & Curtis, E.) Journal of Theoretical Biology, 228, 327-333 (2004).
  15. Thermodynamics of the general diffusion process: Time-reversibility and entropy production. (with Qian, M. & Tang, X.) Journal of Statistical Physics, 107, 1129-1141 (2002). [Expanded version]
  16. Mathematical formalism for isothermal linear irreversibility. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 457, 1645-1655 (2001).
  17. A simple method of parameter space determination for diffusion-driven instability with three species. (with Murray, J.D.) Applied Mathematics Letters, 14, 405-411 (2001).
  18. A mathematical analysis of the Brownian dynamics of DNA tether. Journal of Mathematical Biology, 41, 331-340 (2000).
  19. Hysteresis in force probe measurements: A dynamic systems perspective. (with Shapiro, B.E.) Journal of Theoretical Biology, 194, 551-559 (1998).
  20. On 2-dimensional fractional Brownian motion and fractional Browian random field. (with Raymond, G.M. & Bassingthwaighte, J.B.) Journal of Physics A: Mathematical and General, 31, L527-L535 (1998).

PHYSICS and PHYSICAL CHEMISTRY
  1. Nonequilibrium phase transition in a mesoscoipic biochemical system: From stochastic to nonlinear dynamics and beyond. (with Ge, H.)
  2. Thermodynamic limit of a nonequilibrium steady-state: Maxwell-type construction for a bistable biochemical system. (with Ge, H.)
  3. Sensitivity regulation based on noise propagation in stochastic reaction networks. (with Kim, K.H. & Sauro, H.M.)
  4. Stochastic bifurcation, slow fluctuations, and bistability as an origin of biochemical complexity. (with Shi, P.-Z. & Xing, J.) Physical Chemistry Chemical Physics, 11, 4861-4870 (2009).
  5. Fluctuating enzyme and its biological functions: Positive cooperativity without multiple states. (with Shi, P.-Z.) Journal of Physical Chemistry B, 113, 2225-2230 (2009).
  6. Stochastic dynamics and nonequilibrium thermodynamics of a bistable chemical system: The Schlögl model revisited. (with Vellela, M.) Journal of the Royal Society Interface, In the press.
  7. Oscillations and multiscale dynamics in a closed chemical reaction system: Second law of thermodynamics and temporal complexity. (with Li, Y. & Yi, Y.) Journal of Chemical Physics, 129, 154505 (2008).
  8. Protein-protein interaction networks: Beyond the power-law distribution. (with Miller, G.A., Shi, Y.Y. & Bomsztyk, K.) Physical Review E, 75, 051910 (2007).
  9. Fluctuation theorems of a molecular refrigerator. (with Kim, K.H.) Physical Review E, 75, 022102 (2007).
  10. Relationship between thermodynamic driving force and one-way fluxes in reversible chemical reactions. (with Beard, D.A.) PLoS ONE, 2, e144 (2007).
  11. Continuous time random walks in closed and open single-molecule systems with microscopic reversibility. (with Wang, H.) Europhysics Letters, 76, 15-21 (2006).
  12. Generalized Haldane equation and fluctuation theorem in the steady state cycle kinetics of single enzymes. (with Xie, X.S.) Physical Review E, 74, 010902(R) (2006).
  13. Powering a burnt bridges Brownian ratchet: A model for an extracellular motor driven by proteolysis of collagen. (with Saffarian, S., Collier, I.E., Elson, E.L. & Goldberg G.) Physical Review E, 73, 041909 (2006).
  14. Grand canonical Markov model: A stochastic theory for open nonequilibrium biochemical networks. (with Heuett, W.J.) Journal of Chemical Physics, 124, 044110 (2006).
  15. Nonequilibrium steady state of a nanometric biochemical system: Determining the thermodynamic driving force from single enzyme turnover time traces. (with Min, W., Jiang, L., Yu, J., Kou, S.C. & Xie, X.S.) Nano Letters, 5, 2373-2378 (2005).
  16. Nonequilibrium potential function of chemically driven single macromolecules via Jarzynski-type log-mean-exponential heat. Journal of Physical Chemistry B, 109, 23624-23628 (2005).
  17. Nonequilibrium thermodynamics and nonlinear kinetics in a cellular signaling switch. (with Reluga, T.C.) Physical Review Letters, 94, 028101 (2005).
  18. Entropy production of Brownian macromolecules with inertia. (with Kim, K.H.) Physical Review Letters, 93, 120602 (2004).
  19. A motor protein with nonequilibrium potential: Its thermodynamics and efficiency. Physical Review E, 69, 012901 (2004).
  20. Concentration fluctuations in a mesoscopic oscillating chemical reaction system. (with Saffarian, S. & Elson, E.L.) Proceedings of the National Academy of Sciences USA, 99, 10376-10381 (2002).
  21. Equations for stochastic macromolecular mechanics of single proteins: Equilibrium fluctuations, transient kinetics and nonequilibrium steady-state. Journal of Physical Chemistry B, 106, 2065-2073 (2002).
  22. Entropy production and excess entropy in nonequilibrium steady-state of single macromolecules. Physical Review E, 65, 021111 (2002).
  23. Mesoscopic nonequilibrium thermodynamics of single macromolecules and dynamic entropy-energy compensation. Physical Review E, 65, 016102 (2002).
  24. Nonequilibrium steady-state circulation and heat dissipation functional. Physical Review E, 64, 022101 (2001).
  25. Relative entropy: Free energy associated with equilibrium fluctuations and nonequilibrium deviations. Physical Review E, 63, 042103 (2001).
  26. Transformed Poisson-Boltzmann relations and ionic distributions. (with Schellman, J.A.) Journal of Physical Chemistry B, 104, 11528-11540 (2000).
  27. Pumped biochemical reactions, nonequilibrium circulation, and stochastic resonance. (with Qian, M.) Physical Review Letters, 84, 2271-2274 (2000).
  28. Stochastic fractal behaviour in concentration fluctuation and fluorescence correlation spectroscopy. (with Raymond, G.M. & Bassingthwaighte, J.B.) Biophysical Chemistry, 80, 1-5 (1999).
  29. Entropy-enthalpy compensation: Conformational fluctuation and induced-fit. Journal of Chemical Physics, 109, 10015-10017 (1998).
  30. Vector field formalism and analysis for a class of Brownian ratchets. Physical Review Letters, 81, 3063-3066 (1998).
  31. Entropy-enthalpy compensation: Perturbation and relaxation in thermodynamic systems. (with Hopfield, J.J.) Journal of Chemical Physics, 105, 9292-9296 (1996).
  32. Helix-coil theories: A comparative studies for finite length polypeptides. (with Schellman, J.A.) Journal of Physical Chemistry, 96, 3987-3994 (1992).
  33. Analysis of confocal laser-microscope optics for three-dimensional fluorescence correlation spectroscopy. (with Elson, E.L.) Applied Optics, 30, 1185-1195 (1991).
  34. Inverse Poisson transformation and shot noise filtering. Review of Scientific Instruments, 61, 2088-2091 (1990).
  35. Characterization of the equilibrium distribution of polymer molecular weights by fluorescence distribution spectroscopy - theoretical results. (with Elson, E.L.) Applied Polymer Symposium, 43, 305-314 (1989).

BIOCHEMISTRY, BIOPHYSICS and LIFE SCIENCES
  1. Stochastic bistability and bifurcation in a mesoscopic signaling system with autocatalytic kinase. (with Bishop, L.)
  2. Positive feedback loop in Rabaptin-5 mediated Rab5 activation during endocytosis. (with Zhu, H. & Li, G.-P.)
  3. Analysis of chromatin immunoprecipitated RNA polymerase II using a simple stochastic model of inducible transcription. (with Miller, G.A., Krassovsky, K., Shi, Y.Y., Flanagin, S., Ruzzo, W.L. & Bomsztyk, K.)
  4. Open-system thermodynamic analysis of DNA polymerase fidelity. (with Cady, F.) Physical Biology, 6, 036011 (2009).
  5. A mechanism for Src kinase-dependent signaling by noncatalytic receptors. (with Cooper, J.A.) Biochemistry, 47, 5681-5688 (2008).
  6. Temporal cooperativity and sensitivity amplification in biological signal transduction. (with Cooper, J.A.) Biochemistry, 47, 2211-2220 (2008).
  7. Linear analysis near a steady-state of biochemical networks: Control analysis, correlation metrics and circuit theory. (with Heuett, W.J. & Beard, D.A.) BMC Systems Biology, 2, 44 (2008).
  8. Viscoelasticity of living materials: Mechanics and chemistry of muscle as an active macromolecular system. MCB: Molecular & Cellular Biomechanics [Special Issue in Honor of Y.C. Fung], 5, 107-117 (2008).
  9. Reducing intrinsic biochemical noise in cells and its thermodynamic limit. Journal of Molecular Biology, 362, 387-392 (2006).
  10. Metabolic futile cycles and their functions: A systems analysis of energy and control. (with Beard, D.A.) IEE Proceedings Systems Biology, 153, 192-200 (2006).
  11. Free energy distribution of binary protein-protein binding suggests cross-species interactome differences. (with Shi, Y.Y., Miller, G.A. & Bomsztyk, K.) Proceedings of the National Academy of Sciences USA, 103, 11527-11532 (2006).
  12. Chromatin looping and probability of transcription. (with Li, Q.-L. & Barkess, G.) Trends in Genetics, 22, 197-202 (2006).
  13. Ab initio prediction of thermodynamically feasible reaction directions from biochemical network stoichiometry. (with Yang, F. & Beard, D.A.) Metabolic Engineering, 7, 251-259 (2005).
  14. Thermodynamic-based computational profiling of cellular regulatory control in hepatocyte metabolism. (with Beard, D.A.) American Journal of Physiology: Endocrinology and Metabolism, 288, E633-E644 (2005).
  15. Fluorescence correlation spectroscopy with high-order and dual-color correlation to probe nonequilibrium steady-states. (with Elson, E.L.) Proceedings of the National Academy of Sciences USA, 101, 2828-2833 (2004).
  16. A stochastic analysis of a Brownian ratchet model for actin-based motility. MCB: Mechanics & Chemistry of Biosystems, 1, 267-278 (2004).
  17. Sensitivity and specificity amplification in signal transduction. (with Li, G.-P.) Cell Biochemistry and Biophysics, 39, 45-60 (2003).
  18. Thermodynamic and kinetic analysis of sensitivity amplification in biological signal transduction. Biophysical Chemistry [Special Issue in Honor of Walter Kauzmann], 105, 585-593 (2003).
  19. Amplifying signal transduction specificity without multiple phosphorylation. Biophysical Journal, 84, 1410 - 1411 (2003).
  20. Stoichiometric network theory for nonequilibrium biochemical systems. (with Beard, D.A. & Liang, S.-D.) European Journal of Biochemistry, 270, 415-421 (2003).
  21. Energy balance for analysis of complex metabolic networks. (with Beard, D.A. & Liang, S.-D.) Biophysical Journal, 83, 79-86 (2002).
  22. Single-molecule enzymology: Stochastic Michaelis-Menten kinetics. (with Elson, E.L.) Biophysical Chemistry [Special Issue in Honor of John A. Schellman], 101, 565-576 (2002).
  23. Kinetic timing: A novel mechanism for improving the accuracy of GTPase timers in endosome fusion and other biological processes. (with Li, G.-P.) Traffic, 3, 249-255 (2002).
  24. A class of flow bifurcation models with lognormal distribution and fractal dispersion. (with Bassingthwaighte, J.B.) Journal of Theoretical Biology, 205, 261-268 (2000).
  25. A simple theory of motor protein kinetics and energetics II. Biophysical Chemistry, 83, 35-43 (2000).
  26. Single-particle tracking: Brownian dynamics of viscoelastic materials. Biophysical Journal, 79, 137-143 (2000).
  27. A graphical method for force analysis: Macromolecular mechanics with atomic force microscopy. (with Shapiro, B.E.) Proteins: Structure, Function, and Genetics, 37, 576-581 (1999).
  28. Quantitative study of polymer conformation and dynamics by single-particle tracking. (with Elson, E.L.) Biophysical Journal, 76, 1598-1605 (1999).
  29. Hydrogen exchange kinetics of proteins in denaturants: A generalized two-process model. (with Chan, S.I.) Journal of Molecular Biology, 286, 607-616 (1999).
  30. Hydrogen bonds between short polar side chains and peptide backbone: Prevalence in proteins and effects on helix-forming propensities. (with Vijayakumar, M. & Zhou, H.-X.) Proteins: Structure, Function, and Genetics, 34, 497-507 (1999).
  31. Kramers' diffusion theory applied to gating kinetics of voltage-dependent ion channels. (with Sigg, D. & Bezanilla, F.) Biophysical Journal, 76, 782-803 (1999).
  32. Blood flows and metabolic components of the cardiome. (with Bassingthwaighte, J.B. & Li, Z.) Progress in Biophysics & Molecular Biology, 69, 445-461 (1998).
  33. Remarks on discrete and continuous large-scale models of DNA dynamics. (with Klapper, I.), Biophysical Journal, 74, 2504-2514 (1998).
  34. Terminal twist induced continuous writhe of a circular rod with intrinsic curvature. (with White, J.H.) Journal of Biomolecular Structure and Dynamics, 16, 663-669 (1998).
  35. Local interactions and the optimization of protein folding. (with Doyle, R., Simon, K.T. & Baker, D.) Proteins: Structure, Function, and Genetics, 29, 282-291 (1997).
  36. A simple theory of motor protein kinetics and energetics. Biophysical Chemistry, 67, 263-267 (1997).
  37. A quantitative analysis of single protein-ligand complex separation with the atomic force microscope. (with Shapiro, B.E.) Biophysical Chemistry, 67, 211-219 (1997).
  38. Thermodynamic hierarchy and local energetics of folded proteins. Journal of Molecular Biology, 267, 198-206 (1997).
  39. Interactions between a helical residue and tertiary structures: Helix propensities in small peptides and in native proteins. (with Chan, S.I.) Journal of Molecular Biology, 261, 279-288 (1996).
  40. Prediction of alpha-helices in proteins based on thermodynamic parameters from solution chemistry. Journal of Molecular Biology, 256, 663-666 (1996).
  41. Protein hydrogen exchange: Quantitative analysis by a two-process model. (with Mayo, S.L. & Morton, A.) Biochemistry, 33, 8167-8171 (1994).
  42. A thermodynamic model for helix-coil transition coupled to dimerization of short coiled-coil peptides. Biophysical Journal, 67, 349-355 (1994).
  43. The energetics of ion-pair and hydrogen-bonding interactions in a helical peptide. (with Scholtz, J.M., Robbins, V.H. & Baldwin, R.L.) Biochemistry, 32, 9668-9676 (1993).
  44. Single-residue substitution in homopolypeptides: Perturbative helix-coil theory at a single site. Biopolymers, 33, 1605-1616 (1993).
  45. Studies of the structure of actin gels using time correlation spectroscopy of fluorescence beads. (with Elson, E.L. & Frieden, C.) Biophysical Journal, 63:1000-1010 (1992).
  46. Parameters of helix-coil transition theory for alanine-based peptides of varying chain lengths in water. (with Scholtz, J.M., York, E.J., Stewart, J.M. & Baldwin, R.L.) Biopolymers [Special Issue in Honor of Bruno H. Zimm], 31, 1463-1470 (1991).
  47. Single particle tracking: Analysis of diffusion and flow in two dimensional systems. (with Sheetz, M.P. & Elson, E.L.) Biophysical Journal, 60, 910-921 (1991).
  48. On the statistics of fluorescence correlation spectroscopy. Biophysical Chemistry, 38, 49-57 (1990).
  49. Distribution of molecular aggregation by analysis of fluctuation moments. (with Elson. E.L.) Proceedings of the National Academy of Sciences USA, 87, 5479-5483 (1990).
  50. On the analysis of high order moments of fluorescence fluctuations. (with Elson, E.L.) Biophysical Journal, 57, 375-380 (1990).
  51. Nanometre-level analysis demonstrates that lipid flow does not drive membrane glycoprotein movements. (with Sheetz, M.P., Turney, S. & Elson, E.L.) Nature, 340, 284-288 (1989).
  52. Cell poking: Quantitative analysis of indentation of thick viscoelastic layers. (with Duszyk, M., Schwab, B., Zahalak, G.I. & Elson, E.L.) Biophysical Journal, 55, 683-690 (1989).

E-PRINTS
  1. An analysis of the thermodynamics of hydrophobic solvation based on scaled particle theory. physics/0104085.
  2. Characterization of metastatic tumor formation by the colony size distribution. (with S.P. Lee, J.-R. Sun, W.H. McBride & H.R. Withers) q-bio.TO/0608024.

PROCEEDINGS and CHAPTERS
  1. Multiscale modeling of cardiac cellular energetics. (with Bassingthwaighte, J.B., Chizeck, H.J. & Atlas, L.E.) In The Communicative Cardiac Cell (Annual of the New York Academy of Science, Vol. 1047, S. Sideman, R. Beyar & A. Landesberg, eds.), 395-426 (2005).
  2. Constraint-based modeling of metabolomic systems. (with Beard, D.A.) In Encyclopedia of Genetics, Genomics, Proteomics, and Bioinformatics, Vol. 3: Proteomics (M. Dunn, ed.), Sec. 8: Systems Biology (R.L. Winslow, ed.), John Wiley & Sons, (2005).
  3. Stoichiometric foundation of large-scale biochemical system analysis. (with Beard, D.A. & Bassingthwaighte, J.B.), In Modelling in Molecular Biology (Natural Computing Series, G. Ciobanu & G. Rozenberg, eds.), Springer, 1-19 (2004).
  4. Strain-dependent fluorescence correlation spectroscopy: proposing a new measurement for conformational fluctuations of biological macromolecules. (with Elson, E.L.), In Fluorescence Correlation Spectroscopy: Theory and Applications (Springer Series in Chemical Physics, Vol. 65, R. Rigler & E.L. Elson eds.), Springer, 65-83 (2001).
  5. The cardiome project: An integrated view of cardiac metabolism and regional mechanical function. (with Bassingthwaighte, J.B. & Li, Z.), In Oxygen Transport to Tissue, Vol. 21, Kluwer Academic/Plenum Publishers, 541-553 (1999).
  6. Characterization of confocal laser based microscope - an optical sectioning microscopy approach. (with Elson, E.L.) In Optical Microscopy for Biology (B. Herman & K.A. Jacobson eds.), Alan R. Liss, 119-130 (1990).
  7. Interpretation of fluorescence correlation spectroscopy and photobleaching recovery in terms of molecular interactions. (with Elson, E.L.) In Quantitative Fluorescence Microscopy - Imaging and Spectroscopy (Methods in Cell Biology, Vol. 30, D.L. Taylor & Y.-L. Wang eds.), Academic Press, 307-332 (1989).
  8. Fluorescence microscopic analysis of molecular interactions in 3-dimensional samples by means of fluorescence correlation spectroscopy and photobleaching recovery. (with Elson, E.L.) Proceedings of Electron Microscopy Society of America, Vol. 46, 38-39 (1988).
  9. 3-D fluorescence correlation spectroscopy in bulk solution. (with Elson, E.L.) Proceedings of the Society of Photo-Optical Instrumentation Engineers, Vol. 909, 352-359 (1988).

BOOK REVIEWS
  1. Molecular Modeling and Simulation: An Interdisciplinary Guide by Tamar Schlick, SIAM Review, 47, 843-845 (2005).
  2. Mathematical Physiology by James Keener and James Sneyd, SIAM Review, 46, 587-590 (2004).
  3. Computational Molecular Biology: An Algorithmic Approach by Pavel A. Pevzner, SIAM Review, 43, 733-735(2001).
  4. An Introduction to Chaos in Nonequilibrium Statistical Mechanics by J. R. Dorfman, Bulletin of Mathematical Biology, 63, 597-601 (2001).
  5. Stochastic Processes in Quantum Physics by Masao Nagasawa, SIAM Review, 43, 218-220 (2001).

OTHER MISCELLANEA
  1. A Polymer Sensibility: On the Occasion of My Grandfather's 100th Birthday. Dong Hua Da Xue Bao, 200, October, 17 (2007).
  2. Bruno H. Zimm (1920-2005) (with E.L. Elson and J.M. Schurr) Biophysical Chemistry, 121, 155-156 (2006).
  3. Mark Greener: Enzymology's New Frontiers. The Scientist, 18, 16-20 (2004).
  4. John Schellman and Biophysical Chemistry. University of Oregon, Chemistry Department News Letters,12-13 (2004).
  5. Biophysical Chemistry of Proteins and Nucleic Acids: A Festschrift For John A. Schellman. (with J. Hofrichter and R.L. Baldwin) Biophysical Chemistry, 101, 7-8 (2002).

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