Bibliography

Abragam, A. (1961).
The Principles of Nuclear Magnetism.
Clarendon Press, Oxford.

Akaike, H. (1973).
Information theory and an extension of the maximum likelihood principle.
In: Petrov, B. N. and Csaki, F. (eds.): Proceedings of the Second International Symposium on Information Theory. Budapest, pages 267-281, Akademia Kiado.

Baldwin, A. J. (2014).
An exact solution for R2,eff in CPMG experiments in the case of two site chemical exchange.
J. Magn. Reson.
(10.1016/j.jmr.2014.02.023).

Barbato, G., Ikura, M., Kay, L. E., Pastor, R. W., and Bax, A. (1992).
Backbone dynamics of calmodulin studied by 15N relaxation using inverse detected two-dimensional NMR spectroscopy: the central helix is flexible.
Biochemistry, 31(23), 5269-5278.
(10.1021/bi00138a005).

Bieri, M., d'Auvergne, E., and Gooley, P. (2011).
relaxGUI: a new software for fast and simple NMR relaxation data analysis and calculation of ps-ns and $ \mu$s motion of proteins.
J. Biomol. NMR, 50, 147-155.
(10.1007/s10858-011-9509-1).

Bieri, M. and Gooley, P. R. (2011).
Automated NMR relaxation dispersion data analysis using NESSY.
BMC Bioinformatics, 12, 421.
(10.1186/1471-2105-12-421).

Bloch, F. (1946).
Nuclear induction.
Phys. Rev., 70(7-8), 460-474.
(10.1103/PhysRev.70.460).

Bloembergen, N., Purcell, E. M., and Pound, R. V. (1948).
Relaxation effects in nuclear magnetic resonance absorption.
Phys. Rev., 73(7), 679-712.
(10.1103/PhysRev.73.679).

Broyden, C. G. (1970).
The convergence of a class of double-rank minimization algorithms 1. General considerations.
J. Inst. Maths. Applics., 6(1), 76-90.
(10.1093/imamat/6.1.76).

Brüschweiler, R., Liao, X., and Wright, P. E. (1995).
Long-range motional restrictions in a multidomain zinc-finger protein from anisotropic tumbling.
Science, 268(5212), 886-889.
(10.1126/science.7754375).

Butterwick, J. A., Loria, P. J., Astrof, N. S., Kroenke, C. D., Cole, R., Rance, M., and Palmer, 3rd, A. G. (2004).
Multiple time scale backbone dynamics of homologous thermophilic and mesophilic ribonuclease HI enzymes.
J. Mol. Biol., 339(4), 855-871.
(10.1016/j.jmb.2004.03.055).

Carver, J. and Richards, R. (1972).
General 2-site solution for chemical exchange produced dependence of T2 upon Carr-Purcell pulse separation.
J. Magn. Reson., 6(1), 89-105.
(10.1016/0022-2364(72)90090-X).

Chen, J., Brooks, 3rd, C. L., and Wright, P. E. (2004).
Model-free analysis of protein dynamics: assessment of accuracy and model selection protocols based on molecular dynamics simulation.
J. Biomol. NMR, 29(3), 243-257.
(10.1023/b:jnmr.0000032504.70912.58).

Clore, G. M., Szabo, A., Bax, A., Kay, L. E., Driscoll, P. C., and Gronenborn, A. M. (1990).
Deviations from the simple 2-parameter model-free approach to the interpretation of N-15 nuclear magnetic-relaxation of proteins.
J. Am. Chem. Soc., 112(12), 4989-4991.
(10.1021/ja00168a070).

d'Auvergne, E. J. (2006).
Protein dynamics: a study of the model-free analysis of NMR relaxation data.
PhD thesis, Biochemistry and Molecular Biology, University of Melbourne. http://eprints.infodiv.unimelb.edu.au/archive/00002799/.
(10187/2281).

d'Auvergne, E. J. and Gooley, P. R. (2003).
The use of model selection in the model-free analysis of protein dynamics.
J. Biomol. NMR, 25(1), 25-39.
(10.1023/a:1021902006114).

d'Auvergne, E. J. and Gooley, P. R. (2006).
Model-free model elimination: A new step in the model-free dynamic analysis of NMR relaxation data.
J. Biomol. NMR, 35(2), 117-135.
(10.1007/s10858-006-9007-z).

d'Auvergne, E. J. and Gooley, P. R. (2007).
Set theory formulation of the model-free problem and the diffusion seeded model-free paradigm.
Mol. BioSyst., 3(7), 483-494.
(10.1039/b702202f).

d'Auvergne, E. J. and Gooley, P. R. (2008a).
Optimisation of NMR dynamic models.
J. Biomol. NMR, 40(2), 107-133.

d'Auvergne, E. J. and Gooley, P. R. (2008b).
Optimisation of NMR dynamic models I. Minimisation algorithms and their performance within the model-free and Brownian rotational diffusion spaces.
J. Biomol. NMR, 40(2), 107-119.
(10.1007/s10858-007-9214-2).

d'Auvergne, E. J. and Gooley, P. R. (2008c).
Optimisation of NMR dynamic models II. A new methodology for the dual optimisation of the model-free parameters and the Brownian rotational diffusion tensor.
J. Biomol. NMR, 40(2), 121-133.
(10.1007/s10858-007-9213-3).

Davis, D., Perlman, M., and London, R. (1994).
Direct measurements of the dissociation-rate constant for inhibitor-enzyme complexes via the T1rho and T2 (CPMG) methods.
J. Magn. Reson., 104(3), 266-275.
(10.1006/jmrb.1994.1084).

Einstein, A. (1905).
Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen (The motion of elements suspended in static liquids as claimed in the molecular kinetic theory of heat).
Ann. Physik, 17(8), 549-560.
(10.1002/andp.19053220806).

Erdelyi, M., d'Auvergne, E., Navarro-Vazquez, A., Leonov, A., and Griesinger, C. (2011).
Dynamics of the glycosidic bond: Conformational space of lactose.
Chem. Eur. J., 17(34), 9368-9376.
(10.1002/chem.201100854).

Farrow, N. A., Zhang, O. W., Szabo, A., Torchia, D. A., and Kay, L. E. (1995).
Spectral density-function mapping using N-15 relaxation data exclusively.
J. Biomol. NMR, 6(2), 153-162.
(10.1007/bf00211779).

Favro, L. D. (1960).
Theory of the rotational brownian motion of a free rigid body.
Phys. Rev., 119(1), 53-62.
(10.1103/PhysRev.119.53).

Fletcher, R. (1970).
A new approach to variable metric algorithms.
Comp. J., 13(3), 317-322.
(10.1093/comjnl/13.3.317).

Fletcher, R. and Reeves, C. M. (1964).
Function minimization by conjugate gradients.
Comp. J., 7(2), 149-154.
(10.1093/comjnl/7.2.149).

Fushman, D., Cahill, S., and Cowburn, D. (1997).
The main-chain dynamics of the dynamin pleckstrin homology (PH) domain in solution: analysis of 15N relaxation with monomer/dimer equilibration.
J. Mol. Biol., 266(1), 173-194.
(10.1006/jmbi.1996.0771).

Fushman, D., Tjandra, N., and Cowburn, D. (1998).
Direct measurement of 15N chemical shift anisotropy in solution.
J. Am. Chem. Soc., 120(42), 10947-10952.
(10.1021/ja981686m).

Fushman, D., Tjandra, N., and Cowburn, D. (1999).
An approach to direct determination of protein dynamics from 15N NMR relaxation at multiple fields, independent of variable 15N chemical shift anisotropy and chemical exchange contributions.
J. Am. Chem. Soc., 121(37), 8577-8582.
(10.1021/ja9904991).

Gill, P. E., Murray, W., and Wright, M. H. (1981).
Practical Optimization.
Academic Press.

Goldfarb, D. (1970).
A family of variable-metric methods derived by variational means.
Math. Comp., 24(109), 23-26.
(10.1090/s0025-5718-1970-0258249-6).

Hansen, D. F., Vallurupalli, P., Lundstrom, P., Neudecker, P., and Kay, L. E. (2008).
Probing chemical shifts of invisible states of proteins with relaxation dispersion NMR spectroscopy: how well can we do?
J. Am. Chem. Soc., 130(8), 2667-2675.
(10.1021/ja078337p).

Hestenes, M. R. and Stiefel, E. (1952).
Methods of conjugate gradients for solving linear systems.
J. Res. Natn. Bur. Stand., 49(6), 409-436.
(10.6028/jres.049.044).

Horne, J., d'Auvergne, E., Coles, M., Velkov, T., Chin, Y., Charman, W., Prankerd, R., Gooley, P., and Scanlon, M. (2007).
Probing the flexibility of the DsbA oxidoreductase from Vibrio cholerae-a 15N - 1H heteronuclear NMR relaxation analysis of oxidized and reduced forms of DsbA.
J. Mol. Biol., 371(3), 703-716.
(10.1016/j.jmb.2007.05.067).

Hurvich, C. M. and Tsai, C. L. (1989).
Regression and time-series model selection in small samples.
Biometrika, 76(2), 297-307.
(10.1093/biomet/76.2.297).

Ishima, R. and Torchia, D. (1999).
Estimating the time scale of chemical exchange of proteins from measurements of transverse relaxation rates in solution.
J. Biomol. NMR, 14(4), 369-372.
(10.1023/A:1008324025406).

Ishima, R. and Torchia, D. A. (2005).
Error estimation and global fitting in transverse-relaxation dispersion experiments to determine chemical-exchange parameters.
J. Biomol. NMR, 32(1), 41-54.
(10.1007/s10858-005-3593-z).

Kay, L. E., Torchia, D. A., and Bax, A. (1989).
Backbone dynamics of proteins as studied by 15N inverse detected heteronuclear NMR spectroscopy: application to staphylococcal nuclease.
Biochemistry, 28(23), 8972-8979.
(10.1021/bi00449a003).

Kleckner, I. R. and Foster, M. P. (2012).
GUARDD: user-friendly MATLAB software for rigorous analysis of CPMG RD NMR data.
J. Biomol. NMR, 52(1), 11-22.
(10.1007/s10858-011-9589-y).

Korzhnev, D. M., Billeter, M., Arseniev, A. S., and Orekhov, V. Y. (2001).
NMR studies of Brownian tumbling and internal motions in proteins.
Prog. NMR Spectrosc., 38(3), 197-266.
(10.1016/s0079-6565(00)00028-5).

Korzhnev, D. M., Kloiber, K., Kanelis, V., Tugarinov, V., and Kay, L. E. (2004a).
Probing slow dynamics in high molecular weight proteins by methyl-TROSY NMR spectroscopy: application to a 723-residue enzyme.
J. Am. Chem. Soc., 126(12), 3964-3973.
(10.1021/ja039587i).

Korzhnev, D. M., Kloiber, K., and Kay, L. E. (2004b).
Multiple-quantum relaxation dispersion NMR spectroscopy probing millisecond time-scale dynamics in proteins: theory and application.
J. Am. Chem. Soc., 126(23), 7320-7329.
(10.1021/ja049968b).

Korzhnev, D. M., Neudecker, P., Mittermaier, A., Orekhov, V. Y., and Kay, L. E. (2005a).
Multiple-site exchange in proteins studied with a suite of six NMR relaxation dispersion experiments: an application to the folding of a Fyn SH3 domain mutant.
J. Am. Chem. Soc., 127(44), 15602-15611.
(10.1021/ja054550e).

Korzhnev, D. M., Orekhov, V. Y., and Kay, L. E. (2005b).
Off-resonance R(1rho) NMR studies of exchange dynamics in proteins with low spin-lock fields: an application to a Fyn SH3 domain.
J. Am. Chem. Soc., 127(2), 713-721.
(10.1021/ja0446855).

Kullback, S. and Leibler, R. A. (1951).
On information and sufficiency.
Ann. Math. Stat., 22(1), 79-86.
(10.1214/aoms/1177729694).

Lee, L. K., Rance, M., Chazin, W. J., and Palmer, A. G. (1997).
Rotational diffusion anisotropy of proteins from simultaneous analysis of N-15 and C-13(alpha) nuclear spin relaxation.
J. Biomol. NMR, 9(3), 287-298.
(10.1023/a:1018631009583).

Lefevre, J., Dayie, K., Peng, J., and Wagner, G. (1996).
Internal mobility in the partially folded DNA binding and dimerization domains of GAL4: NMR analysis of the N-H spectral density functions.
Biochemistry, 35(8), 2674-2686.
(10.1021/bi9526802).

Levenberg, K. (1944).
A method for the solution of certain non-linear problems in least squares.
Quarterly of Applied Mathematics, 2, 164-168.

Linhart, H. and Zucchini, W. (1986).
Model Selection.
Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York, NY, USA.

Lipari, G. and Szabo, A. (1982a).
Model-free approach to the interpretation of nuclear magnetic-resonance relaxation in macromolecules I. Theory and range of validity.
J. Am. Chem. Soc., 104(17), 4546-4559.
(10.1021/ja00381a009).

Lipari, G. and Szabo, A. (1982b).
Model-free approach to the interpretation of nuclear magnetic-resonance relaxation in macromolecules II. Analysis of experimental results.
J. Am. Chem. Soc., 104(17), 4559-4570.
(10.1021/ja00381a010).

Luz, Z. and Meiboom, S. (1963).
Nuclear magnetic resonance study of protolysis of trimethylammonium ion in aqueous solution - order of reaction with respect to solvent.
J. Chem. Phys., 39(2), 366-370.
(10.1063/1.1734254).

Mandel, A. M., Akke, M., and Palmer, 3rd, A. G. (1995).
Backbone dynamics of escherichia coli ribonuclease HI: correlations with structure and function in an active enzyme.
J. Mol. Biol., 246(1), 144-163.
(10.1006/jmbi.1994.0073).

Marquardt, D. W. (1963).
An algorithm for least squares estimation of non-linear parameters.
SIAM J., 11, 431-441.
(10.1137/0111030).

Mazur, A., Hammesfahr, B., Griesinger, C., Lee, D., and Kollmar, M. (2013).
ShereKhan-calculating exchange parameters in relaxation dispersion data from CPMG experiments.
Bioinformatics, 29(14), 1819-1820.
(10.1093/bioinformatics/btt286).

McConnell, H. (1958).
Reaction rates by nuclear magnetic resonance.
J. Chem. Phys., 28(3), 430-431.
(10.1063/1.1744152).

Meiboom, S. (1961).
Nuclear magnetic resonance study of proton transfer in water.
J. Chem. Phys., 34(2), 375-388.
(10.1063/1.1700960).

Miloushev, V. Z. and Palmer, 3rd, A. G. (2005).
R(1rho) relaxation for two-site chemical exchange: general approximations and some exact solutions.
J. Magn. Reson., 177(2), 221-227.
(10.1016/j.jmr.2005.07.023).

Moré, J. J. and Thuente, D. J. (1994).
Line search algorithms with guaranteed sufficient decrease.
ACM Trans. Maths. Softw., 20(3), 286-307.
(10.1145/192115.192132).

Morin, S. (2011).
A practical guide to protein dynamics from 15N spin relaxation in solution.
Prog. NMR Spectrosc., 59(3), 245-262.
(10.1016/j.pnmrs.2010.12.003).

Morin, S. and Gagné, S. (2009a).
Simple tests for the validation of multiple field spin relaxation data.
J. Biomol. NMR, 45, 361-372.
(10.1007/s10858-009-9381-4).

Morin, S. and Gagné, S. M. (2009b).
NMR dynamics of PSE-4 $ \beta$-lactamase: An interplay of ps-ns order and $ \mu$s-ms motions in the active site.
Biophys. J., 96(11), 4681-4691.
(10.1016/j.bpj.2009.02.068).

Morin, S., Linnet, T. E., Lescanne, M., Schanda, P., Thompson, G. S., Tollinger, M., Teilum, K., Gagné, S., Marion, D., Griesinger, C., Blackledge, M., and d'Auvergne, E. J. (2014).
relax: the analysis of biomolecular kinetics and thermodynamics using NMR relaxation dispersion data.
Bioinformatics.
(10.1093/bioinformatics/btu166).

Nocedal, J. and Wright, S. J. (1999).
Numerical Optimization.
Springer Series in Operations Research. Springer-Verlag, New York.

O'Connell, N. E., Grey, M. J., Tang, Y., Kosuri, P., Miloushev, V. Z., Raleigh, D. P., and Palmer, 3rd, A. G. (2009).
Partially folded equilibrium intermediate of the villin headpiece HP67 defined by 13C relaxation dispersion.
J. Biomol. NMR, 45(1-2), 85-98.
(10.1007/s10858-009-9340-0).

Orekhov, V. Y., Korzhnev, D. M., Diercks, T., Kessler, H., and Arseniev, A. S. (1999a).
H-1-N-15 NMR dynamic study of an isolated alpha-helical peptide (1-36)bacteriorhodopsin reveals the equilibrium helix-coil transitions.
J. Biomol. NMR, 14(4), 345-356.
(10.1023/a:1008356809071).

Orekhov, V. Y., Korzhnev, D. M., Pervushin, K. V., Hoffmann, E., and Arseniev, A. S. (1999b).
Sampling of protein dynamics in nanosecond time scale by 15N NMR relaxation and self-diffusion measurements.
J. Biomol. Struct. Dyn., 17(1), 157-174.
(10.1080/07391102.1999.10508348).

Orekhov, V. Y., Pervushin, K. V., Korzhnev, D. M., and Arseniev, A. S. (1995).
Backbone dynamics of (1-71)bacterioopsin and (1-36)bacterioopsin studied by 2-dimensional H-1-N-15 NMR-spectroscopy.
J. Biomol. NMR, 6(2), 113-122.
(10.1007/BF00211774).

Palmer, 3rd, A. G. and Massi, F. (2006).
Characterization of the dynamics of biomacromolecules using rotating-frame spin relaxation NMR spectroscopy.
Chem. Rev., 106(5), 1700-1719.
(10.1021/cr0404287).

Perrin, F. (1934).
Mouvement Brownien d'un ellipsoïde (I). Dispersion diéletrique pour des molécules ellipsoïdales.
J. Phys. Radium, 5, 497-511.
(10.1051/jphysrad:01934005010049700).

Perrin, F. (1936).
Mouvement Brownien d'un ellipsoïde (II). Rotation libre et dépolarisation des fluorescences. Translation et diffusion de molécules ellipsoïdales.
J. Phys. Radium, 7, 1-11.
(10.1051/jphysrad:01936007010100).

Polak, E. and Ribière, G. (1969).
Note sur la convergence de méthodes de directions conjuguées.
Revue Française d'Informatique et de Recherche Opérationnelle, 16, 35-43.

Schurr, J. M., Babcock, H. P., and Fujimoto, B. S. (1994).
A test of the model-free formulas. Effects of anisotropic rotational diffusion and dimerization.
J. Magn. Reson. B, 105(3), 211-224.
(10.1006/jmrb.1994.1127).

Schwarz, G. (1978).
Estimating dimension of a model.
Ann. Stat., 6(2), 461-464.
(10.1214/aos/1176344136).

Shanno, D. F. (1970).
Conditioning of quasi-Newton methods for function minimization.
Math. Comp., 24(111), 647-656.
(10.1090/s0025-5718-1970-0274029-x).

Steihaug, T. (1983).
The conjugate gradient method and trust regions in large scale optimization.
SIAM J. Numer. Anal., 20(3), 626-637.
(10.1137/0720042).

Sugase, K., Konuma, T., Lansing, J. C., and Wright, P. E. (2013).
Fast and accurate fitting of relaxation dispersion data using the flexible software package GLOVE.
J. Biomol. NMR, 56(3), 275-283.
(10.1007/s10858-013-9747-5).

Sun, H., d'Auvergne, E. J., Reinscheid, U. M., Dias, L. C., Andrade, C. K. Z., Rocha, R. O., and Griesinger, C. (2011).
Bijvoet in solution reveals unexpected stereoselectivity in a michael addition.
Chem. Eur. J., 17(6), 1811-1817.
(10.1002/chem.201002520).

Tjandra, N., Wingfield, P., Stahl, S., and Bax, A. (1996).
Anisotropic rotational diffusion of perdeuterated HIV protease from N-15 NMR relaxation measurements at two magnetic.
J. Biomol. NMR, 8(3), 273-284.
(10.1007/bf00410326).

Tollinger, M., Skrynnikov, N. R., Mulder, F. A. A., Forman-Kay, J. D., and Kay, L. E. (2001).
Slow dynamics in folded and unfolded states of an sh3 domain.
J. Am. Chem. Soc., 123(46), 11341-11352.
(10.1021/ja011300z).

Trott, O., Abergel, D., and Palmer, A. (2003).
An average-magnetization analysis of R-1 rho relaxation outside of the fast exchange.
Mol. Phys., 101(6), 753-763.
(10.1080/0026897021000054826).

Trott, O. and Palmer, 3rd, A. G. (2002).
R1rho relaxation outside of the fast-exchange limit.
J. Magn. Reson., 154(1), 157-160.
(10.1006/jmre.2001.2466).

Trott, O. and Palmer, 3rd, A. G. (2004).
Theoretical study of R(1rho) rotating-frame and R2 free-precession relaxation in the presence of n-site chemical exchange.
J. Magn. Reson., 170(1), 104-112.
(10.1016/j.jmr.2004.06.005).

Viles, J., Duggan, B., Zaborowski, E., Schwarzinger, S., Huntley, J., Kroon, G., Dyson, H., and Wright, P. (2001).
Potential bias in NMR relaxation data introduced by peak intensity analysis and curve fitting methods.
J. Biomol. NMR, 21, 1-9.
(10.1023/A:1011966718826).

Woessner, D. E. (1962).
Nuclear spin relaxation in ellipsoids undergoing rotational brownian motion.
J. Chem. Phys., 37(3), 647-654.
(10.1063/1.1701390).

Zhuravleva, A. V., Korzhnev, D. M., Kupce, E., Arseniev, A. S., Billeter, M., and Orekhov, V. Y. (2004).
Gated electron transfers and electron pathways in azurin: a NMR dynamic study at multiple fields and temperatures.
J. Mol. Biol., 342(5), 1599-1611.
(10.1016/j.jmb.2004.08.001).

Zucchini, W. (2000).
An introduction to model selection.
J. Math. Psychol., 44(1), 41-61.
(10.1006/jmps.1999.1276).

The relax user manual (PDF), created 2014-07-03.