Rapid Cooperative Two-state Folding of a Miniature α–β Protein and Design of a Thermostable Variant

Horng, Jia‐Cherng; Мороз, В. В.; Raleigh, Daniel P.

doi:10.1016/s0022-2836(03)00028-7

Cited by 43 publications

(66 citation statements)

References 36 publications

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“…Of the 12 proteins, only Villin, NTL9 and Homeodomain are not included in the 65-protein dataset and have experimental rate data at lower temperature near 298 K. By using eq. (12) we predicted the folding times for Villin, NTL9 and Homeodomain are 8.5, 1287 and 70 µs respectively, near the experimental values 0.7 [61], 827 [62] and 13 µs [63]. The differences between predicted lnW f and experimental lnk f fall in the range as shown in Figure 5.…”

Section: Comparison With Molecular Dynamics Predictionsmentioning

confidence: 52%

Statistical analyses of protein folding rates from the view of quantum transition

Luo

2014

Sci. China Life Sci.

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Understanding protein folding rate is the primary key to unlock the fundamental physics underlying protein structure and its folding mechanism. Especially, the temperature dependence of the folding rate remains unsolved in the literature. Starting from the assumption that protein folding is an event of quantum transition between molecular conformations, we calculated the folding rate for all two-state proteins in a database and studied their temperature dependencies. The non-Arrhenius temperature relation for 16 proteins, whose experimental data had previously been available, was successfully interpreted by comparing the Arrhenius plot with the first-principle calculation. A statistical formula for the prediction of two-state protein folding rate was proposed based on quantum folding theory. The statistical comparisons of the folding rates for 65 two-state proteins were carried out, and the theoretical vs. experimental correlation coefficient was 0.73. Moreover, the maximum and the minimum folding rates given by the theory were consistent with the experimental results. quantum folding, protein folding rate, temperature dependence, number of torsion mode, folding free energy Citation:Lv J, Luo LF. Statistical analyses of protein folding rates from the view of quantum transition. Sci China Life Sci, 2014Sci, , 57: 1197Sci, -1212Sci, , doi: 10.1007 It is well known that a protein chain can spontaneously fold into its unique native structure [1,2]. To paraphrase Levinthal's paradox, if a protein were to attain its correctly folded configuration by sequentially sampling all the possible conformations, it would require a period of time longer than the age of the universe to arrive at its correct native conformation [3]. Apart from theory, it is a fact that experimentally measured times for spontaneous folding of single-domain globular proteins range from microseconds [46] to tens of minutes [7]. Thus, how configurations of proteins are determined and what makes them fold so quickly are questions that constitute a longstanding puzzle in molecular biology. While two prominent models have been proposed to study the protein folding mechanism, folding nucleus [8,9] and folding tunnel [1014], the importance of topology and contact order in protein folding has been recognized over the last 15 years, and many new models to predict the protein folding rate have been published [1529]. Curiously, it is notable that the rate at which proteins fold is highly sensitive to temperature, showing non-Arrhenius behavior, i.e., the temperature dependence of the rate constant is, in fact, not exponential for these reactions. The nonlinearity of logarithm folding rate on temperature 1/T has been conventionally interpreted by the nonlinear temperature dependence of the configurational diffusion constant on rough energy landscapes [30] or by the temperature dependence of hydrophobic interaction [31,32]. Another model was proposed more recently to interpret the difference between folding and unfolding by introducing the number of dena...

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Section: Comparison With Molecular Dynamics Predictionsmentioning

confidence: 52%

Statistical analyses of protein folding rates from the view of quantum transition

Luo

2014

Sci. China Life Sci.

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“…The relaxation spectra of the beta-containing protein G (NuG2) (38), NTL9 (39), and GTT (40) (a WW domain) each show a high-flux relaxation (Fig. 1, blue) that occurs on timescales 3-10 times faster than the slowest relaxation.…”

Section: Resultsmentioning

confidence: 99%

Simple few-state models reveal hidden complexity in protein folding

Beauchamp

McGibbon

Lin

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

164

212

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Markov state models constructed from molecular dynamics simulations have recently shown success at modeling protein folding kinetics. Here we introduce two methods, flux PCCA+ (FPCCA+) and sliding constraint rate estimation (SCRE), that allow accurate rate models from protein folding simulations. We apply these techniques to fourteen massive simulation datasets generated by Anton and Folding@home. Our protocol quantitatively identifies the suitability of describing each system using two-state kinetics and predicts experimentally detectable deviations from two-state behavior. An analysis of the villin headpiece and FiP35 WW domain detects multiple native substates that are consistent with experimental data. Applying the same protocol to GTT, NTL9, and protein G suggests that some beta containing proteins can form long-lived native-like states with small register shifts. Even the simplest protein systems show folding and functional dynamics involving three or more states. M ore than fifty years ago, Anfinsen (1) found that primary sequence encodes functional ribonuclease. Today, the process by which proteins self-assemble into their biologically-relevant states remains a key question in biophysics. A modern theory of protein folding must explain a variety of disparate experimental results. First, proteins can fold via a number of mechanisms, ranging from the simplest two-state model (2) to models with more complexity (3). Some proteins may not fold at all-recent work has shown that many eukaryotic proteins are either intrinsically disordered or fold only upon binding to their target (4). The misfolding and aggregation of other proteins have been associated with neurodegenerative disorders such as Alzheimer's disease (5). A "solution" to the protein folding problem must capture not only the folded and unfolded states but intermediate, disordered, and misfolded states as well.Kinetic models with two (2) or more (3, 6) states have been the dominant paradigm for understanding protein folding dynamics. This picture generalizes to an arbitrary number of states; the resulting dynamical model is known as the master equation (7). Recently, several labs (8-13) have used molecular dynamics simulations to parameterize discrete time master equations (also known as Markov state models) that describe the folding dynamics of proteins. Such procedures typically involve clustering the observed conformations to determine microstates, then counting transitions between microstates to estimate rates.Markov state model approaches have typically been limited by two issues. First, the models so constructed have involved hundreds or thousands of states, leading to difficulty making direct connections to experimentally-derived models of folding kinetics. To address this problem, we have developed flux PCCA+ (FPCCA+). Like its precursors PCCA and PCCA+ (14-16), FPCCA+ allows one to construct macrostate models that optimally capture the slow dynamics observed in a microstate model; the advantage of FPCCA+ is in its ability to ignore slow but ...

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“…To further flesh out this potential theory of molecular kinetics, we have delved into the nature of the free energy landscapes of the villin headpiece (HP-35 NleNle) (14) and a 39 residue fragment of NTL9 (15). Furthermore, because complex networks for real systems are difficult to comprehend, we construct simple, generic models that capture qualitative phenomena like apparent two-state folding and provide an intuition for molecular kinetics.…”

mentioning

confidence: 99%

Protein folded states are kinetic hubs

Bowman

Pande

2010

Proc. Natl. Acad. Sci. U.S.A.

211

268

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Understanding molecular kinetics, and particularly protein folding, is a classic grand challenge in molecular biophysics. Network models, such as Markov state models (MSMs), are one potential solution to this problem. MSMs have recently yielded quantitative agreement with experimentally derived structures and folding rates for specific systems, leaving them positioned to potentially provide a deeper understanding of molecular kinetics that can lead to experimentally testable hypotheses. Here we use existing MSMs for the villin headpiece and NTL9, which were constructed from atomistic simulations, to accomplish this goal. In addition, we provide simpler, humanly comprehensible networks that capture the essence of molecular kinetics and reproduce qualitative phenomena like the apparent two-state folding often seen in experiments. Together, these models show that protein dynamics are dominated by stochastic jumps between numerous metastable states and that proteins have heterogeneous unfolded states (many unfolded basins that interconvert more rapidly with the native state than with one another) yet often still appear two-state. Most importantly, we find that protein native states are hubs that can be reached quickly from any other state. However, metastability and a web of nonnative states slow the average folding rate. Experimental tests for these findings and their implications for other fields, like protein design, are also discussed.

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Rapid Cooperative Two-state Folding of a Miniature α–β Protein and Design of a Thermostable Variant

Cited by 43 publications

References 36 publications

Statistical analyses of protein folding rates from the view of quantum transition

Statistical analyses of protein folding rates from the view of quantum transition

Simple few-state models reveal hidden complexity in protein folding

Protein folded states are kinetic hubs

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