Are Protein Folding Intermediates the Evolutionary Consequence of

Subscriber access provided by ANADOLU UNIVERSITY

Article

Are Protein Folding Intermediates the Evolutionary Consequence of Functional Constraints? Athi Narayanan Naganathan, Jose M Sanchez-Ruiz, Sneha Munshi, and Swaathiratna Suresh J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp510342m • Publication Date (Web): 19 Dec 2014 Downloaded from http://pubs.acs.org on December 23, 2014

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Are Protein Folding Intermediates the Evolutionary Consequence of Functional Constraints? Athi N. Naganathan,1* Jose M. Sanchez-Ruiz,2 Sneha Munshi1 & Swaathiratna Suresh3 1

Department of Biotechnology, Bhupat & Jyoti Mehta School of Biosciences, Indian Institute of Technology Madras, Chennai 600036, India. 2

Departamento de Quimica Fisica, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain. 3

Center for Biotechnology, Anna University, Chennai 600025, India.

ACS Paragon Plus Environment

1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 51

ABSTRACT

High-resolution experiments on several apparently two-state proteins point to the existence of partially structured excited- or intermediate-states in dynamic equilibrium with native states. Are these intermediate states the byproducts of functional constraints that are by necessity evolutionarily conserved or are they merely the hidden imprints of evolutionary processes? To investigate this, we characterize the folding of Barstar that has a rich history of complex conformational behavior employing a combination of methods – statistical-mechanical model, electrostatic calculations, MD simulations and multiple-sequence alignment – that provide a detailed yet consistent view of its landscape in agreement with experiments. We find that the multi-state folding in Barstar is the direct consequence of a strong evolutionary pressure to maintain its binding affinity with Barnase through a large negative electrostatic potential on one face. A single mutation (E76K or E80K) at the binding site is shown to not only enhance the native-state stability but also alter the Barstar folding mechanism to resemble an un-frustrated two-state-like system. Our results argue that though natural proteins are expected to be minimally frustrated, functional constraints can singularly determine the folding mechanism even if it occurs at the expense of frustrated multi-state folding.

KEYWORDS Protein folding; intermediates; energetic frustration; statistical model; function; kinetics; electrostatics; equilibrium


2

Page 3 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


INTRODUCTION Early studies of single domain protein folding concluded that folding has to proceed through distinct series of events with populated intermediates that guide the organization of the polymeric chain.1,2 In many cases, however, the interpretation was complicated by the formation of non-native disulfide bridges or kinetic phases originating from cis-trans proline isomerization. Later, equilibrium and kinetic studies on CI2 revealed that proteins could indeed fold without the accumulation of detectable intermediate states3 (i.e. two-state folding4). Since then, the observation of sigmoidal unfolding curves in equilibrium and single-exponential kinetics is generally considered as evidence for a cooperative folding process that does not involve the population of intermediates, though it has been elegantly argued that two-state folding is just an approximation.5,6 It is therefore natural to expect some systems to display more complexity during folding than others. True to this, the application of hydrogen-deuterium exchange measurements,7 NMR relaxation dispersion experiments,8 multi-probe approaches,9,10 and highresolution mass spectrometry11 to several apparently two-state-like natural proteins point to the existence of partially structured excited states in equilibrium with the native state. On the other extreme, computationally designed and models of primordial proteins display a non-cooperative probe-dependent folding behavior with multi-phasic kinetics and competing non-native structural states.12,13 The corollary is that the apparently distinctive cooperative folding of natural proteins is a consequence of the mechanism of Natural Selection and that the corresponding free-energy landscapes are expected to be smooth, i.e. with minimal structural or energetic frustration.14 In fact, mutational perturbations of apomyoglobin reveal that the extant sequence has been carefully selected to destabilize intermediate states.15 In view of these observations, the relevant question to ask is why are intermediate states populated in several


3


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 51

proteins? Specifically, are the intermediate states merely the relics of evolutionary processes or the by-products of functional constraints or directly responsible for optimal functioning of protein domains? These questions assume importance, as functional requirements have been shown to act to the extent of determining the nature of fluctuations,16 timescales of protein dynamics,17-19 the folding mechanism20 and its conservation across evolutionary homologues,21,22 and the distribution of partially structured states that are binding competent.23-28 Mutational studies also strongly indicate that the folded state of single domain proteins is optimized for function and not for maximal stability29,30 or fast folding.30

Figure 1. Tertiary structure (A) and primary sequence (B) of Barstar indicating the location of helices (H; in red) and strands (S; in yellow). Tryptophan 53, a common probe employed in experiments, is shown in blue.

To investigate these questions, we focus on Barstar (PDB id: 1BTA), a monomeric intracellular inhibitor of extracellular guanyl-specific ribonuclease Barnase from Bacillus amyloliquefaciens, as a model system (Figure 1). It is an 89-residue mixed α/β protein composed of three strands and four helices. The structural arrangement is such that the beta-sheets act as a scaffold for anchoring the more flexible helical regions that are responsible for binding to


4

Page 5 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Barnase. The formation of Barnase-Barstar encounter complex is fast (kon ~106 M-1 s-1) and electrostatically driven with a remarkably tight binding (Kd ~100 pM).31 The strong binding is critical as Barstar effectively neutralizes the activity of Barnase in the intracellular milieu thus eliminating any detrimental effects on the host organism. From the folding viewpoint, different research groups have extensively studied Barstar over the last 20 years combining approaches that involve equilibrium melts,29,32 protein engineering,33,34 kinetics,35,36 time-resolved fluorescence,37 ensemble FRET,38,39 single-molecule FRET40 and force spectroscopy,41 photochemical quenching,42 and NMR.43-45 A general consensus that arises from these works is that Barstar (un)folds through multiple intermediate states, has a highly dynamic native state with mechanically labile beta-strands, shows probedependent kinetics and burst-phase amplitudes, with even the unfolded state displaying a complex behavior when probed appropriately using multi-site FRET. The most recent comprehensive multi-probe kinetic study on Barstar reveals an unfolding mechanism characterized by at least 2-3 intermediate states46 that is more complex than the three-state mechanism originally proposed.33 Despite the large body of experimental work, there is little structural information on the nature of intermediates and hence a unified picture of the folding mechanism is currently lacking. More importantly, the molecular origins of the complex folding and its relation to function are yet to be deciphered. In the current work, we employ structure-based statistical mechanical modeling, electrostatic calculations and explicit solvent molecular dynamic (MD) simulations to provide a detailed and consistent view of the folding mechanism of Barstar that highlights the unmapped subtle interplay between folding and functional constraints.


5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 51

METHODS WSME Model and Parameters. The Wako-Saitô-Muñoz-Eaton model is an Ising-like statistical mechanical model that employs a binary description of folded (1) or unfolded (0) at the residuelevel, thus translating to 2N microstates for a N-residue protein.47,48 The original model and its variants have been successfully employed to characterize a number of folding-related features in a semi-quantitative fashion28,49-56 and in engineering protein stabilities.56,57 Here, we employ a detailed WSME model that incorporates three fundamental stabilization energetic terms (∆Gstab) that include van der Waals interactions (EvdW), electrostatics (Eelec) and solvation free-energy (∆Gsolv) and one destabilization term, the entropic cost of fixing a residue in native conformation (∆Sconf):

∆F = ∑ ∆G

stab m,n

n

− T ∑ ∆Sconf m

stab ∆Gm,n = EvdW + Eelec + ∆Gsolv

where (m, n) is a microstate, i.e. with a string of 1s between and including m and n. The destabilization due to the addition of co-solvents is modeled by mimicking the experimentally observed linear free-energy relation, stab m,n ∆Gm,n mcont [D] ([D]) = EvdW + Eelec + ∆Gsolv − xcont

m,n where xcont is the number of native interactions within the stretch (m, n) and mcont is the

phenomenological scaling constant. The total partition function (Z) and the residue unfolding probabilities as a function of temperature (T) are calculated employing the transfer-matrix formalism of Wako and Saitô.47 We parameterize the WSME model by semi-quantitatively reproducing the temperature- and urea-induced two-state-like thermodynamic parameters of Barstar32 by adjusting the fundamental


6

Page 7 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


parameters of the model. Native heavy-atom contacts are identified employing a vdW contact cut-off of 5 Å together with an all-to-all electrostatic treatment (i.e. without a distance cut-off) with charges assigned as per the pH 7.0 protonation state. The ionic strength value is fixed to 0.02 M in all calculations following the most recent experiments.46 The final parameters are: ∆Sconf = -16.8 J mol-1 K-1 per residue, mean-field vdW interaction energy ξ = -87.8 J mol-1 per native contact, heat capacity change per native contact ∆C pcont = -0.98 J mol-1 K-1 and mcont = 1.15 J mol-1 M-1 per native contact. The effective dielectric constant in the electrostatic term is fixed to 29 as before.56,57 Diffusive calculations were performed on the one-dimensional free-energy profiles employing the discretized version of the diffusion equation58 with a coordinate- and urea-independent diffusion coefficient value of 40,000 n2 s-1 where n is the reaction coordinate. Survival probabilities were calculated from the eigenvalues and eigenvectors obtained by the diagonalization of the 89 × 89 rate matrix.58 SSA, DSA and TSA. The WSME model exact-solution free energy profiles are calculated by accumulating the partial partition functions (Zi) of different number of structured residues (in the case of Barstar, i = 0-89). While this entirely account for the relative probabilities of partially structured states with varying degrees of order, they do not provide information on how this probability is distributed among different structural regions. To this end, we calculated the partial partition functions of single-stretch (SSA; single-sequence approximation), two-stretches (DSA; double sequence approximation) and three-stretches (TSA; triple-sequence approximation) of folded residues using identical parameters as the exact-solution calculation, i.e. ZSSA, ZDSA and ZTSA. Apart from the statistical weight we also algorithmically tabulated the regions of the protein that are predicted to be folded (strings of 1s and 0s) according to the underlying energetics thus providing in-depth structural information on the most populated partially folded states. This


7


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 51

however involved the enumeration of a total of 625,173,825 microstates according to the binomial coefficient  N + 1  where N is the protein length and m is the sequence 

2m 

approximation employed (m = 1 for SSA, m = 2 for DSA etc.).48,59 Together, they account for 97.4% of the total partition function at 283 K in the absence of denaturants, i.e. pSSA + pDSA + pTSA=0.974, with pSSA =75.27%, pDSA =16.09% and pTSA =6.04%. Estimating Signals from Two-Dimensional Structural Ensembles. To estimate the signal as a function of the one-dimensional reaction coordinate, we construct a representative twodimensional structural ensemble involving only single stretches of native-like residues. Because there is only a single stretch of native residues in each microstate, their structures can be directly obtained by editing the PDB file. The total number of contacts formed by W53 when folded was tabulated for each of microstates and then projected onto the number of structured residues as the order parameter to estimate an apparent signal. Similarly, inter-residue distances were calculated from the edited PDB files when both the residues are folded. When the region between or including the two residues is unfolded, we estimate an apparent distance (ri,j) from the freelyjointed chain (FJC) model according to

ri,2j = 2l pb i − j where lp is the persistence length (fixed to 4 Å) and b is the bond-length (fixed to 3.8 Å). These distances are then projected on to the 1D reaction coordinate as done in Ref. 54. Molecular Dynamics Simulations. The GROMACS simulation software together with the Amber-99SB*-ILDN force field was employed for the explicit solvent all-atom molecular dynamics simulations.60-62 Barstar (PDB id: 1BTA) or its mutant E80K was placed in a dodecahedral box with periodic boundary conditions and a minimum distance of 15 Å between


8

Page 9 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the structure and the box edge. Each of the proteins was solvated with TIP3P waters along with ions to maintain charge neutrality, energy-minimized and relaxed for 2 ns at 310 K with a fourfemtosecond time-step using virtual hydrogens. A single 250 ns production run was performed at 310 K for both proteins as a reference. Following this, three independent 500 ns of NVT simulation were run for each of the proteins at 430 K with randomized starting velocities. A Langevin thermostat with a damping coefficient of 1/(1 picosecond) was employed for maintaining temperatures. Long-range electrostatics was calculated using the particle mesh Ewald (PME) procedure at grid spacing of 1.2 Å and with a 10 Å cutoff for non-bonded interactions. Multiple-Sequence Alignment. 1251 sequences corresponding to the Barstar family (PF01337) were directly taken from the Pfam database63 and aligned using ClustalX64 with default parameters. Frequencies of charged and uncharged residues were calculated using the sequence numbering in Barstar (1BTA) as a reference. RESULTS Free Energy Profiles and Unfolded State Effects. The thermodynamic parameterization of the model is necessary to adjust the basic energetic and entropic terms to replicate the large heat capacity change and hence the phenomenon of cold denaturation, and the broad urea-dependent unfolding curve observed in equilibrium experiments on Barstar.32 For example, the cold denaturation temperature at 0 M urea is predicted to be ~248 K from the WSME model (Figure 2A) while the prediction from a two-state analysis of the experimental unfolding curve places this value at ~258 K. The stability at 283 K is predicted to be ~15.7 kJ mol-1 which is very similar from that of a two-state fit to the experimental data (~15.0 kJ mol-1), with a mid-point


9


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 51

urea concentration (Cm) of 3.0 M (Figure 2B).32 Multi-state folding is not evident from the thermodynamics of the model in agreement with experiments.

Figure 2. Folding Thermodynamics. (A & B) Predicted thermal and chemical unfolding curves. (C) Free-energy (FE) profiles at two different stability conditions highlighting the position of the intermediates (I) and the continuous movement of the unfolded state (U) at 283 K. (D) The global probability of finding residues to be folded as a function of sequence index under destabilizing conditions (5.5 M Urea and 283 K). The circles correspond to the residues protected from photochemical oxidation.42 The shaded regions represent the secondary structure elements.


10

Page 11 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The free energy profiles as a function of the number of structured residues as the reaction coordinate (RC) exhibits a complex multi-state scenario under both folding and unfolding conditions (Figure 2C and Supplementary Figure S1). At 283 K and in the absence of denaturant, the free-energy profile reveals four major thermodynamic states: unfolded state (U’) at an RCvalue of 34 structured residues, intermediate I1 (at an RC-value of 65), intermediate I2 (at an RCvalue of 78) and the native state (at an RC-value of 88). The number of thermodynamic states is maintained under unfolding conditions; however, the unfolded state becomes more unstructured (U’U) without any apparent macroscopic barrier suggestive of a continuous or gradual unfolding occurring with increased denaturant stress. Experimental evidence to gradual changes in Barstar unfolded state structure has been presented from ensemble multi-site38 and singlemolecule FRET,40 and kinetic quenching measurements,46 corroborating the model predictions. The changes in unfolded structure originate from at least two different regions: a major contribution from residual structure in helix H1 and minor contributions from strand S2 and helix H3 (Figure 2D). Far-UV CD, mutational studies and NMR chemical shift measurements of the unfolded state indicate the exact same helix 1 and strand 2 to be partially structured in the unfolded state.65,66 Sub-millisecond side-chain photochemical oxidation and mass spectrometry studies of Barstar reveal that residues I5, H17, L20, L24 and F74 are the most protected from oxidation (circles in Figure 2D).42 This is again in good agreement with our predictions with the exception of I5 and F74. Experiments suggest that positions 5 and 74 are protected due to nonnative interactions in the unfolded state that are not captured by the model that relies solely on native-like energetics. The presence of residual unfolded state structure in Barstar from multiple experiments and the statistical model hints that these regions facilitate folding by acting as potential nucleation sites.


11


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 51

Figure 3. Unfolding Kinetics. Red, green and blue in the top row represent the super-fast, fast and slow phases, respectively, at 283 K. (A) Survival probability of the folded state at a final concentration of 5.5 M urea mimicking a stopped-flow experiment. Circles are the calculated decay and the line is a tri-exponential fit. (B) FRET-monitored kinetics from the Cys-25-TNB pair (squares) and fluorescence intensity46 (circles), together with model predictions (lines). (C) Identifying the origins of the three phases from changes in survival probabilities at the indicated time-points (vertical lines in panel A). (Inset) Blow-up of the main panel between 60 and 89 structured residues. (D) One-dimensional signal dependence of W53 contacts (left axis) and specified distances (right axis). The reference free-energy profile at 3.25 M urea (~Cm) is shown in black. (E) Binned distance counts of Monte-Carlo runs at the unfolding midpoint conditions following the color code in panel D. (F) Same as panel E but for the W53 contacts that mimic time-resolved fluorescence measurements37 at 0 M urea (continuous blue) and 3.25 M urea (dashed blue). The vertical lines indicate the native (N) and unfolded (U) states, respectively.


12

Page 13 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Unfolding Kinetics and Probe-Dependence. Kinetic studies reveal multiple time-scales that vary by more than three orders of magnitude during the unfolding Barstar.46 Here, we validate the model and its predictions by comparing against the experimental kinetics and dynamics. Figure 3A plots the survival probability of the Barstar native state at 298 K and in the presence of 5.5 M urea. The model predicts three exponential phases with a slow rate of ~0.2 s-1, faster rate of ~7 s-1 and a fastest rate of ~200 s-1. Upon adjusting the one-dimensional diffusion coefficient (see Methods) to reproduce just the slow rate, we nicely capture the differences in experimental rates46 (Figure 3B). A plot of the changes in probability (p) at different time-points indicated in Figure 3A sheds light on the origin of the multi-phasic behavior (Figure 3C). The fastest rate (red in Figure 3A-3C) originates mainly from a combination of structural rearrangements within the native well and to a minor extent from between them: this is evidenced by a negative ∆p at an RC-value of ~88 (N) and a large positive ∆p at ~85 (a perturbed native state) and a minor positive ∆p at ~77 (I2). Similarly, the faster rate (green in Figure 3A-3C) arises from an exchange of population between N and intermediate states (I1, I2) while the slowest rate (blue) corresponds to the exchange between the native and unfolded wells. Time-resolved FRET (TR-FRET) measurements between the residue positions W53 and TNB-82 (thionitrobenzoic acid attached to cysteine 82) suggest that the folded and unfolded forms interconvert through a continuum of states albeit separated by a free-energy barrier.37 Specifically, at midpoint conditions, the fluorescence lifetime distributions are broader and cannot be represented as a linear sum of distributions obtained under folding (zero denaturant) or unfolding conditions (high denaturant concentrations).37 To check if the model is able to reproduce this characteristic observation, we calculated the dependence of distances and W53 contacts on the one-dimensional reaction coordinate as before (Figure 3D; see Methods). Such an


13


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 51

exercise followed by Monte-Carlo runs on free energy profiles at different stability conditions exposes a unique probe-dependence in Barstar unfolding: we find that the number of tryptophan contacts (blue; Figures 3D, 3F) and the distance between the positions 53 and 82 (green; Figures 3D, 3E) are sensitive to the population of unfolding intermediates while the same is not true for distances between 25-53 (red; Figures 3D, 3E) or 40-53 (not shown). To reproduce the experimental fluorescence lifetime distributions, we make a simple assumption that the lifetimes are inversely related to the number of W53 contacts with native and unfolded lifetimes of 0.25 and 3.75 ns, respectively. The resulting predicted distribution agrees very well with the experimental observations (see Figure 2 in reference 37) with one difference; we obtain two peaks on the folding side of the barrier corresponding to N and I2 at the midpoint while a single broad peak that possibly corresponds to I2 characterizes the experimental distribution. Folding Mechanism. We identify the specific structural regions that are expected to be the most populated during folding combining the exact-solution results with single-, double- and triple-sequence approximation (SSA, DSA and TSA) calculations (Figure 4A). This involved the algorithmic enumeration of the statistical weights and the identity of the structured regions for a total of 625,173,825 microstates that effectively account for ~97.4% of the total probability at 283 K (see Methods). An illustration of the resulting folding mechanism is provided in Figure 4B: i) the most probable region to fold first is helix 1 (Figures 2D; U), ii) H1 acquires more structure under folding conditions in a barrier-less continuous process (Figure 2C, 2D; U’), iii) this is followed by the rate-limiting step which is the condensation of the structural elements S1, H2 and S2 on H1, iv) once this rate-limiting step is surmounted the folding is slowed by the formation of the intermediate I1 which acquires structure in helix H3, v) the next step is the formation of the second intermediate I2 characterized by partial structure at the C-terminal half of


14

Page 15 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


helix H4 and nearly the entire strand S3, vi) the final step is the consolidation of structure in the above-mentioned region resulting in the fully folded Barstar. From the principle of microscopic

Figure 4. Folding Mechanism of Barstar at 283 K. (A) Free energy profiles from various sequence-approximations and from the exact-solution (ES) of the WSME model. (B) A cartoon representation of the series of folding events together with the identity of intermediate species. The numbers in red represent the weighted probability of the intermediate states and the numbers within brackets indicate the regions that are structured for single-, double- and triple-sequence approximations in that order. For example, (1,63)+(76,2) should be read as I1 having a structure that encompasses the 63 residues starting from the first residue, and 2 residues starting from the


15


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 51

76th. The illustrations on the left highlight the folded regions in green and partially structured regions in gray. W53 is shown in blue.

reversibility, the C-terminal region of the protein is predicted to unfold first, exactly as inferred from single-molecule force spectroscopy measurements and steered-MD simulations.41 Molecular Origins of Folding Complexity. We had previously shown that unfavorable chargecharge interactions on a protein surface play a dominant role in determining the nature, position (along the folding coordinate) and the relative population of intermediates.28,55,56 To check for the possible role of unfavorable electrostatics in Barstar, we calculate residue-wise charge-charge interaction energies employing both the Tanford-Kirkwood (TK) algorithm67,68 and the simplified Debye-Hückel (DH) treatment used in the WSME model (Figure 5A). This comparison serves two purposes. First, we find that surface residues D35, D39, E76 and E80 - all of which contribute favorably to the binding free energy29,31,69 - to be significantly frustrated (i.e. positive ∆Gq-q). These residues are responsible for generating a highly acidic binding surface, to complement the basic binding surface in Barnase (Figure 5B). Second, we find that the interaction energies from the two independent methods are highly correlated (r~0.94) indicating that the DH treatment in the WSME model energy function accounts for the long-range nature of electrostatic interactions quite well (Figure S2). In fact, the model performs reasonably well in reproducing the changes in stability induced by 10 of the 14 single point mutations of charged residues in Barstar (Figure 5C).29,34 Interestingly, mutations that eliminate the negative charges at the binding site make the protein more stable (circles in the first quadrant in Figure 5C) while all other experimental mutations either destabilize the folded state because of loss of favorable interactions (third quadrant in Figure 5C)


16

Page 17 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 5. Frustration from Unfavorable Charge-Charge Interactions in native Barstar. (A) Residue-wise charge-charge interaction energy (in kJ mol-1) from the TK algorithm (green) and the DH model (magenta). Shaded regions represent the secondary structure elements. (B) Electrostatic potential energy surface highlighting the large negative electrostatic potential on the Barnase-binding face of Barstar. (C) Comparison of experimental and predicted changes in stability induced by point mutations of charged residues. Dashed line is the expected 1:1 correlation.


17


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 51

or stabilize the folded state through non-native effects (fourth quadrant in Figure 5C and Figure S3). Taken together, these results argue for the fact that functionally important unfavorable electrostatic interactions present in the native-state are responsible for destabilizing the folded structure in agreement with a previous protein engineering work on Barstar.29 Here, we additionally hypothesize that this subtle functional property singularly promotes the accumulation of intermediates identified in experiments and predicted by the WSME model. To verify the above hypothesis and to further eliminate any topological/packing (i.e., nonelectrostatic) origins of intermediates, we set the electrostatic interaction energy to zero in the WSME model and calculate free-energy profiles (Figure 6A). This all-attractive Gō-potential (similar to what is employed in conventional structure-based models) predicts a two-state-like system (Figure 6A) with a maximal barrier height that is higher by ~7 kJ mol-1 than that with electrostatics. The free energy profile displays a small shoulder at an RC-value of ~78 structured residues corresponding to only a minimally populated I2. This exercise therefore confirms that when the spatial distribution of amino-acid residues in Barstar is optimized for a stably folded well-packed protein, intermediates are minimally populated resulting in a near-perfect two-state system. To identify residues that contribute the most to the observed folding complexity, we follow a systematic protocol wherein we substitute every charged residue in Barstar with either the oppositely charged or neutral-residue and generate both the unfolding curves and free-energy profiles as before.57 There are 24 charged residues in Barstar resulting in a total of 48 possible mutational variants. We find a large correlation between the relative population of intermediates as predicted by the WSME model and the magnitude of net charge-charge interaction energy of the mutants in the region between residue positions 54 and 83 (Σ∆Gq-q for all residues between


18

Page 19 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 6. Molecular Origins of Folding Complexity. Relevant energy units are in kJ mol-1. (A) Comparison of WSME mode free energy profiles for wild-type (WT) Barstar with and without electrostatics near the unfolding midpoint. (B) Correlation between the intermediate-state probability from the WSME model free energy profiles (I1 in gray filled and I2 in open circles) and the TK net charge-charge interaction energy within the region 54-83 at 283 K. The red and green circles correspond to the single point mutations E76K and E80K, and E76Q and E80Q, respectively. Blue represents the WT. (C) The effect of mutations E76Q (green) and E80K (red) on the free-energy profile and the equilibrium unfolding curves as a function of urea (inset). The mutational effects of E76K and E80Q are not shown for clarity (see Figure S4).


19


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 51

54 and 83 for every mutant) as calculated from the TK algorithm (Figure 6B): more favorable is the net electrostatic interaction energy in C-terminal part of the structure the smaller is the intermediate population. The correlation is maximal at lower temperatures and persists even at respective midpoint temperatures where the intermediates are highly populated (r~0.75; Figure S4) pointing to the robustness of the calculation. This large correlation between two seemingly independent variables and methods attests to the fact that its origins are not circumstantial and report reliably on the fundamental connection between folding intermediates and destabilization energetics. The functionally optimized organization of charged-residues in Barstar falls right between the two extremes of minimal and maximal population of intermediate states I1 and I2 (blue in Figure 6B). A closer inspection reveals that the residue positions 76 and 80 effectively determine the relative population of these intermediates. The mutations E76Q and E80Q reduce the intermediate population to a small extent (i.e. increase the relative free-energies) making it approach a two-state system. However, the substitutions E76K and E80K optimize the stabilization energetics so well as to result in a near-perfect two-state system with a barrier height position and magnitude similar to that expected for a well-packed all-attractive potential (Figure 6C and Figure S5; compare the red and black free energy profiles). The stabilizing effect of these mutations is also evident in the predicted equilibrium unfolding curves that show larger Cm values compared to the wild type (inset to Figure 6C and Figure S5). To summarize, our calculations argue for the fact that residues E76 and E80 play a dominant role in not only destabilizing the native structure of Barstar (illustrated in Figure S6) but also in promoting the population of intermediates.


20

Page 21 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Agreement with Molecular Simulations. It is challenging to characterize the complete folding or unfolding mechanism of Barstar or its mutants through MD simulations as the unfolding time46 at even 6.5 M urea is ~0.4 s-1 thus placing it beyond the reach of current simulation protocols. An alternate prediction that can be tested is the fact that under identical unfolding conditions, I2 is more populated and separated by a smaller free-energy barrier from the native state in the WT than the mutant E80K, thus making the stochastic transitions to I2 more probable in simulations of the former (Figure 7A-C). Importantly, the model makes an explicit prediction on the most populated structure of I2: it is characterized by a significantly frayed C-terminus of helix H4 and only partial structure in strand S3. Since this region of the structure is highly destabilized we expect it to be the first unfold (or the last to fold) in simulations from a freeenergetic viewpoint. Explicit solvent MD simulations at 310 K reveal that both the structures are stable over the time-scale of the simulations (250 ns) and that the mutation E80K is not destabilizing. Interestingly, the C-terminal region of helix H4 and the N-terminal region of strand S3 displays marginally higher fluctuation in the WT than the mutant E80K suggesting that this region could be the first to unfold in the WT (Figure S7). To enhance the population of this partially structured state and to speed-up unfolding, we performed long MD simulations at high temperatures (430 K) for an aggregate simulation time of 3 microseconds (Figure S8). Though we do not observe complete unfolding within the time-scale of simulations (500 ns) we find several interesting observations that corroborate the WSME model predictions: i) the WT consistently displays a higher main-chain root-mean-square-deviation (RMSD) compared to the mutant E80 K in region between and including the C-terminal of helix 4 and N-terminus of


21


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 51

Figure 7. Atomic-Level Simulations. Blue and red represent the wild-type (WT) and E80K mutant of Barstar, respectively. (A-C) WSME model free energy profiles at 360 K as a function of the reaction coordinate (RC), the number of structured residues (panel A), and the expected frequency of transition between different states from short MC runs for the WT (panel B) and E80K (panel C). (D & E) The main-chain RMSD for residues 76-86 in three independent 500 ns simulations at 430 K for the WT (panel D) and E80K (panel E). (F) The average root-meansquare fluctuation (RMSF) as a function of the residue index with the shaded regions representing the secondary structure elements H4 and S3. The mean standard deviations in RMSF across the sequence are 0.15 and 0.20 Å for the WT and E80K, respectively. (G) Three snapshots (green, orange and magenta) from panel D displaying maximal RMSD with respect to the native structure (gray and surface representation). Only the C-terminal half of the structure is shown as cartoon for clarity. It can be seen that the C-terminal region of the WT is more disordered starting from the C-terminal of H4 to S3. For example, in one snapshot (magenta) the entire strand S3 is disordered apart from the C-terminal of helix H4.


22

Page 23 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


strand 3 (Figure 7D and 7E) in agreement with that expected for the intermediate I2, ii) the partial unfolding process is reversible indicating an equilibrium between the native sate and I2, iii) the mutant E80K is more stable with minimal RMSD fluctuations over the entire time-scale of simulations with very few stochastic transitions to the excited state I2 exactly as expected from the WSME model free-energy profiles, iv) a plot of residue-wise fluctuations reveals that most regions (including loops) exhibit near-identical dynamics between the WT and E80K mutant (Figure 7F and Figure S9) – the only exceptions are the region corresponding to I2 (Figure 7G) and helix H3 that displays larger dynamics in the mutant than the WT. Despite the obvious limitations of the water model, the associated force-field parameters (especially in the high temperature regime) and limited sampling, the agreement between the WSME model and molecular simulations argues for the reliability of our predictions. DISCUSSION The folding mechanism of Barstar has been under intense scrutiny over the past two decades with multiple lines of experimental evidence pointing to a probe-dependent multi-state folding behavior. However, the connection between experimental observation and structural features is unclear. For example, there are no modeling or simulation studies on the possible structure of intermediates that populated en route to folding that is simultaneously consistent with different experimental observables. Therefore, we first take a minimalist approach wherein we employ the Ising-like WSME model with electrostatics to characterize the folding behavior of Barstar. We predict multiple features - the presence of two intermediate states apart from the endstates, continuous movement of the unfolded state in response to changing solvent conditions, residual structure in helix H1, tri-phasic unfolding behavior – in good agreement with experiments. The ability to capture kinetic features upon constraining the model employing


23


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 51

thermodynamic data attests to the robustness of the method. Importantly, we present for the first time a structural view of at least two of the intermediate states that are populated during the folding of Barstar. A well-folded region from residues 1-63 characterizes the first intermediate I1 that also encompasses some flickering structure in central region of H4. The region from residues 1-76 defines the second intermediate I2 with only a partial structure in C-terminal region of H4 and strand S3. Atomistic simulations indicate that C-terminal region of H4 and strand S3 are thermodynamically less stable exhibiting larger fluctuations than the mean behavior, in good agreement with the WSME model predictions. The one-dimensional free energy profile together with approximations of the FRET-monitored distances and contacts calculated from structural ensembles is able to identify the origins of the unique experimental observation that Barstar unfolds through a continuum of states before and after the main unfolding barrier.37 However, the model points to a maximal barrier of ~6.5 kJ mol-1 between N and I2 and ~7.5 kJ mol-1 between I2 and I1, thus hinting that these numbers might an over-estimation of the real barrier height. Taken together, the model in conjunction with experiments suggests that Barstar folds through a reasonably well-defined pathway that is aided by residual structure in helix H1 and with the rate-determining step being the condensation of the entire N-terminal half of the structure up to W53. The C-terminal half of the structure subsequently folds in a step-wise fashion that is in semi-quantitative agreement with TR-FRET measurements. A more fundamental question that has received little attention is: what structural-energetic reasons determine this probe-dependent multi-state (un)folding behavior in Barstar? The minimum frustration theory14 postulates that functional requirements can roughen up the landscape even from purely native interactions thus complicating the folding behavior. A number


24

Page 25 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


of examples of topological and energetic frustration have also been presented primarily employing native-centric all-attractive potentials.70-73 On the other hand, short- and long-range electrostatic interactions that can be either attractive or repulsive are increasingly being identified as playing a major role in determining the disordered nature of proteins74 and their dimensions,75,76 the stability of partially structured states,28,55,56 and the specificity/affinity of protein-protein77,78 and protein-nucleic acid interactions.26,79 This distinct role of charged residues has been evolutionarily tuned to an extreme in the case of Barstar wherein acidic residues responsible for binding Barnase line an entire face of the structure. This in turn results in a highly frustrated native state thus complicating the (un)folding behavior. The residues that contribute the most to favorable binding are D35, D39, E76 and E80. Intriguingly, experiments29 point to a counter-intuitive behavior: i) the substitutions D35A and D39A increase the stability by only a minimal extent (∆∆G ~1.3 kJ mol-1) but decrease the binding affinity by as much as four orders of magnitude, and ii) the substitutions E76A and E80A increase the stability by ~9 kJ mol-1, minimally affect the association rate but increase the dissociation rates by a factor of four and two, respectively. The structure of Barstar therefore presents a fascinating case wherein four charged residues on the same protein face and on two adjacent helices (D35 and D39 on H2, E76 and E80 on H4) contribute to the stability and binding affinity to different degrees. If the structure of Barstar had been evolutionarily optimized for high native-state stability, then position 76 or 80 should either be neutral (as demonstrated in experiments and discussed above) or preferably positively charged as it enhances the stability to a larger extent. We present strong evidence to this stabilizing contribution of positively charged residues at positions 76 and 80 from three independent methods – WSME model with DH electrostatics, TK calculation and all-


25


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 51

atom MD simulations – that are mutually consistent with each other. From the folding viewpoint, a positively charged residue at position 76 or 80 is also the most preferred residue type as it alters the folding mechanism of Barstar to resemble a highly cooperative un-frustrated two-state system. From a functional perspective, the presence of a positive charge at position 76 or 80 is expected to further slow down the association rate and simultaneously increase the dissociation rate of the Barnase-Barstar complex thus effectively reducing the binding affinity. Multiple sequence alignment (see Methods) provides a picture that is consistent with this expectation: there is a strong evolutionary pressure against positively charged residues in both the binding helices H2 and H4, though neutral residues can also be found to a relatively larger extent at positions 76 and 80 in helix H4 (Figure 8A). Sequence composition analysis across multiple organisms cannot account for possible structural-energetic offshoots of small differences in amino-acid identity (for example, non-local electrostatics) or co-evolutionary mutations in Barstar or Barnase. As an alternate and direct procedure we predict the folding characteristics of the only available structural-functional homolog of Barstar in the Protein Data Bank, YHCO from E. coli (PDB id: 2C6X, Figure 8B), using the statistical model. We identify a similar multistate behavior in this domain that is primarily determined by the binding site residue E79, the structural equivalent of E80 in Barstar (Figure 8C). These results confirm that functional constraints, i.e. the necessity to bind Barnase to eliminate potentially lethal nuclease activity within the host cell, disallow the presence of a positive charge at these positions; this is despite the fact that positively charged residues (and neutral residues to a minor extent) at positions 76 or 80 simplify the folding behavior to the extent of completely eliminating partially structured states in equilibrium. However, it is not clear from published works if the presence of partially


26

Page 27 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


structured states promotes efficient binding or if they facilitate proteolytic degradation required for functional control. These are open questions that can be addressed experimentally by merely destabilizing the intermediate through the single point mutations we propose.

Figure 8. Sequence and Structural Comparison. (A) The probability of finding acidic (red) or basic (blue) residues as a function of residue index from a multiple–sequence alignment of 1251 similar sequences (see Methods). The structural elements contributing to the binding interface H2 and H4 are shaded in blue with the vertical dashed lines representing positions 35, 39, 76 and 80, respectively. (B) Structural alignment of Barstar (green) and YHCO (magenta). (C) The predicted midpoint free energy profiles (in kJ mol-1) for WT (continuous black) and E79K YHCO (dashed black), respectively.


27


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 51

Work on designed proteins present indirect evidence that Natural Selection is responsible for smoothening the folding landscape of natural proteins;12,13 here, we show evidence for the other extreme that Barstar is a clear example of a protein whose multi-phasic folding and conformational heterogeneity is an unambiguous result of Natural Selection that has optimized the structure for high-affinity binding and not for smooth un-frustrated folding or stability. Though it is too early to generalize this observation, a few examples are already available in the literature that point to this possibility. The more recent example is that of the structuralthermodynamic comparison of the homologous proteins HEWL/apo-BLA.80 Though the native folded structures are near identical they exhibit a vastly different stability profiles,80 barriers,56,80 and conformational landscapes56 that has been linked to possible functional origins. DNAbinding proteins are another class of proteins that frequently display complex unfolding behavior in equilibrium81 even to the extent of large-scale tuning of the stability of homologs;82 this could in fact be a direct manifestation of the structural proximity of positively charged residues required for binding DNA. Moreover, these domains search for their cognate binding site among millions of similar sites along the DNA thus requiring some degree of structural flexibility83,84 that could in turn manifest in the form of intermediates at equilibrium. In summary, there could potentially be an exciting functional role or origins for the now frequently observed partially structured excited- or intermediate-states in the protein native ensembles that have so far been unexplored.


28

Page 29 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ASSOCIATED CONTENT Supporting Information. Figures supporting the subtle effects of charge-charge interactions on the stability and free energy profile of Barstar and its mutants. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *[email protected] Funding Sources We thank Jayant B. Udgaonkar and G. Krishnamoorthy for discussions on Barstar folding. ANN acknowledges the Innovative Young Biotechnologist Award (2012) from the Department of Biotechnology, New Delhi, India. ABBREVIATIONS WSME, Wako-Saitô-Muñoz-Eaton; TK, Tanford-Kirkwood; DH, Debye-Hückel; RC, reaction coordinate; MD, molecular dynamics; FRET, Förster Resonance Energy Transfer; NMR, Nuclear Magnetic Resonance; CD, Circular Dichroism.


29


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 51

REFERENCES (1)

Baldwin, R. L. Specific Intermediates in the Folding Reactions of Small Proteins

and the Mechanism of Protein Folding. Ann. Rev. Biochem. 1982, 51, 459-489. (2)

Ptitsyn, O. B. In Protein Folding; Creighton, T. E., Ed.; W. H. Freeman & Co.,

New York.: 1992, p 243-300. (3)

Jackson, S. E.; Fersht, A. R. Folding of Chymotrypsin Inhibitor-2 .1. Evidence for

a 2-State Transition. Biochemistry 1991, 30, 10428-10435. (4)

Tanford, C. Protein Denaturation. Adv. Prot. Chem. 1968, 23, 121-282.

(5)

Lumry, R.; Biltonen, R. L.; Brandts, J. F. Validity of the “Two-State” Hypothesis

for Conformational Transitions of Proteins. Biopolymers 1966, 4, 917-944. (6)

Jackson, W. M.; Brandts, J. F. Thermodynamics of Protein Denaturation - a

Calorimetric Study of Reversible Denaturation of Chymotrypsinogen and Conclusions Regarding Accuracy of 2-State Approximation. Biochemistry 1970, 9, 2294-2301. (7)

Englander, S. W. Protein Folding Intermediates and Pathways Studied by

Hydrogen Exchange. Ann. Rev. Biophys. Biomol. Struct. 2000, 29, 213-238. (8)

Sekhar, A.; Kay, L. E. NMR Paves the Way for Atomic Level Descriptions of

Sparsely Populated, Transiently Formed Biomolecular Conformers. Proc. Natl. Acad. Sci. U.S.A. 2013, 110, 12867-12874.


30

Page 31 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(9)

Larios, E.; Li, J. S.; Schulten, K.; Kihara, H.; Gruebele, M. Multiple Probes

Reveal a Native-Like Intermediate During Low-Temperature Refolding of Ubiquitin. J. Mol. Biol. 2004, 340, 115-125. (10)

Vu, D. M.; Brewer, S. H.; Dyer, R. B. Early Turn Formation and Chain Collapse

Drive Fast Folding of the Major Cold Shock Protein CspA of Escherichia Coli. Biochemistry 2012, 51, 9104-9111. (11)

Hu, W. B.; Walters, B. T.; Kan, Z. Y.; Mayne, L.; Rosen, L. E.; Marqusee, S.;

Englander, S. W. Stepwise Protein Folding at near Amino Acid Resolution by Hydrogen Exchange and Mass Spectrometry. Proc. Natl. Acad. Sci. U.S.A. 2013, 110, 7684-7689. (12)

Walters, A. L.; Deka, P.; Corrent, C.; Callender, D.; Varani, G.; Sosnick, T.;

Baker, D. The Highly Cooperative Folding of Small Naturally Occurring Proteins Is Likely the Result of Natural Selection. Cell 2007, 128, 613-624. (13)

Sadqi, M.; de Alba, E.; Perez-Jimenez, R.; Sanchez-Ruiz, J. M.; Muñoz, V. A

Designed Protein as Experimental Model of Primordial Folding. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 4127-4132. (14)

Bryngelson, J. D.; Onuchic, J. N.; Socci, N. D.; Wolynes, P. G. Funnels,

Pathways, and the Energy Landscape of Protein-Folding - a Synthesis. Proteins 1995, 21, 167195. (15)

Isogai, Y. Native Protein Sequences Are Designed to Destabilize Folding

Intermediates. Biochemistry 2006, 45, 2488-2492.


31


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(16)

Page 32 of 51

Ramanathan, A.; Agarwal, P. K. Evolutionarily Conserved Linkage between

Enzyme Fold, Flexibility, and Catalysis. PLoS Biol. 2011, 9, e1001193. (17)

Mandel, A. M.; Akke, M.; Palmer, A. G. I. Backbone Dynamics of Escherichia

Coli Ribonuclease HI: Correlations with Structure and Function in an Active Enzyme. J. Mol. Biol. 1995, 246, 144-163. (18)

Henzler-Wildman, K. A.; Lei, M.; Thai, V.; Kerns, S. J.; Karplus, M.; Kern, D. A

Hierarchy of Timescales in Protein Dynamics Is Linked to Enzyme Catalysis. Nature 2007, 450, 913-916. (19)

Doshi, U.; McGowan, L. C.; Ladani, S. T.; Hamelberg, D. Resolving the Complex

Role of Enzyme Conformational Dynamics in Catalytic Function. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 5699-5704. (20)

Naganathan, A. N.; Orozco, M. The Native Ensemble and Folding of a Protein

Molten-Globule: Functional Consequence of Downhill Folding. J. Am. Chem. Soc. 2011, 133, 12154-12161. (21)

Naganathan, A. N.; Li, P.; Perez-Jimenez, R.; Sanchez-Ruiz, J. M.; Muñoz, V.

Navigating the Downhill Protein Folding Regime Via Structural Homologues. J. Am. Chem. Soc. 2010, 132, 11183-11190. (22)

Carstensen, L.; Sperl, J. M.; Bocola, M.; List, F.; Schmid, F. X.; Sterner, R.

Conservation of the Folding Mechanism between Designed Primordial (βα)8-Barrel Proteins and Their Modern Descendant. J. Am. Chem. Soc. 2012, 134, 12786-12791.


32

Page 33 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(23)

Swain, J. F.; Gierasch, L. M. The Changing Landscape of Protein Allostery. Curr.

Opin. Struct. Biol. 2006, 16, 102-108. (24)

Kalbitzer, H. R.; Spoerner, M.; Ganser, P.; Hozsa, C.; Kremer, W. Fundamental

Link between Folding States and Functional States of Proteins. J. Am. Chem. Soc. 2009, 131, 16714-16719. (25)

Schrank, T. P.; Bolen, D. W.; Hilser, V. J. Rational Modulation of

Conformational Fluctuations in Adenylate Kinase Reveals a Local Unfolding Mechanism for Allostery and Functional Adaptation in Proteins. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 1698416989. (26)

Marcovitz, A.; Levy, Y. Frustration in Protein-DNA Binding Influences

Conformational Switching and Target Search Kinetics. Proc. Natl. Acad. Sci. U.S.A. 2011, 108, 17957-17962. (27)

Knott, M.; Best, R. B. A Preformed Binding Interface in the Unbound Ensemble

of an Intrinsically Disordered Protein: Evidence from Molecular Simulations. PLOS Comp. Biol. 2012, 8. (28)

Naganathan, A. N.; Orozco, M. The Conformational Landscape of an Intrinsically

Disordered DNA-Binding Domain of a Transcription Regulator. J. Phys. Chem. B 2013, 117, 13842-13850. (29)

Schreiber, G.; Buckle, A. M.; Fersht, A. R. Stability and Function: Two

Constraints in the Evolution of Barstar and Other Proteins. Structure 1994, 15, 945-951.


33


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(30)

Page 34 of 51

Jager, M.; Zhang, Y.; Bieschke, J.; Nguyen, H.; Dendle, M.; Bowman, M. E.;

Noel, J. P.; Gruebele, M.; Kelly, J. W. Structure-Function-Folding Relationship in a WW Domain. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 10648-10653. (31)

Ikura, T.; Urakubo, Y.; Ito, N. Water-Mediated Interaction at a Protein–Protein

Interface. Chem. Phys. 2004, 307, 111-119. (32)

Agashe, V. R.; Udgaonkar, J. B. Thermodynamics of Denaturation of Barstar:

Evidence for Cold Denaturation and Evaluation of the Interaction with Guanidine Hydrochloride. Biochemistry 1995, 34, 3286-3299. (33)

Nolting, B.; Golbik, R.; Neira, J. L.; SolerGonzalez, A. S.; Schreiber, G.; Fersht,

A. R. The Folding Pathway of a Protein at High Resolution from Microseconds to Seconds. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 826-830. (34)

Pradeep, L.; Udgaonkar, J. B. Effect of Salt on the Urea-Unfolded Form of

Barstar Probed by m-Value Measurements. Biochemistry 2004, 43, 11393-11402. (35)

Zaidi, F. N.; Nath, U.; Udgaonkar, J. B. Multiple Intermediates and Transition

States During Protein Unfolding. Nat. Struct. Biol. 1997, 4, 1016-1024. (36)

Bhuyan, A. K.; Udgaonkar, J. B. Observation of Multistate Kinetics During the

Slow Folding and Unfolding of Barstar. Biochemistry 1999, 38, 9158-9168. (37)

Lakshmikanth, G. S.; Sridevi, K.; Krishnamoorthy, G.; Udgaonkar, J. B. Structure

Is Lost Incrementally During the Unfolding of Barstar. Nat. Struct. Biol. 2001, 8, 799-804.


34

Page 35 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(38)

Sinha, K. K.; Udgaonkar, J. B. Dependence of the Size of the Initially Collapsed

Form During the Refolding of Barstar on Denaturant Concentration: Evidence for a Continuous Transition. J. Mol. Biol. 2005, 353, 704-718. (39)

Sinha, K. K.; Udgaonkar, J. B. Barrierless Evolution of Structure During the

Submillisecond Refolding Reaction of a Small Protein. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 7998-8003. (40)

Hofmann, H.; Golbik, R. P.; Ott, M.; Hubner, C. G.; Ulbrich-Hofmann, R.

Coulomb Forces Control the Density of the Collapsed Unfolded State of Barstar. J. Mol. Biol. 2008, 376, 597-605. (41)

Sharma, D.; Feng, G.; Khor, D.; Genchev, G. Z.; Lu, H.; Li, H. Stabilization

Provided by Neighboring Strands Is Critical for the Mechanical Stability of Proteins. Biophys. J. 2008, 95, 3935-3942. (42)

Chen, J.; Rempel, D. L.; Gau, B. C.; Gross, M. L. Fast Photochemical Oxidation

of Proteins and Mass Spectrometry Follow Submillisecond Protein Folding at the Amino-Acid Level. J. Am. Chem. Soc. 2012, 134, 18724−18731. (43)

Sahu, S. C.; Bhuyan, A. K.; Majumdar, A.; Udgaonkar, J. B. Backbone Dynamics

of Barstar: A 15N NMR Relaxation Study. Proteins: Struct. Funct. Genet. 2000, 41, 460–474. (44)

Li, H.; Frieden, C. Comparison of C40/82A and P27A C40/82A Barstar Mutants

Using 19F NMR. Biochemistry 2007, 46, 4337-4347.


35


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(45)

Page 36 of 51

Hofmann, H.; Weininger, U.; Low, C.; Golbik, R. P.; Balbach, J.; Ulbrich-

Hofmann, R. Fast Amide Proton Exchange Reveals Close Relation between Native-State Dynamics and Unfolding Kinetics. J. Am. Chem. Soc. 2009, 131, 140–146. (46)

Sarkar, S. S.; Udgaonkar, J. B.; Krishnamoorthy, G. Unfolding of a Small Protein

Proceeds Via Dry and Wet Globules and a Solvated Transition State. Biophys. J. 2013, 105, 2392-2402. (47)

Wako, H.; Saito, N. Statistical Mechanical Theory of Protein Conformation .2.

Folding Pathway for Protein. J. Phys. Soc. Japan 1978, 44, 1939-1945. (48)

Muñoz, V.; Eaton, W. A. A Simple Model for Calculating the Kinetics of Protein

Folding from Three-Dimensional Structures. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 1131111316. (49)

Garcia-Mira, M. M.; Sadqi, M.; Fischer, N.; Sanchez-Ruiz, J. M.; Muñoz, V.

Experimental Identification of Downhill Protein Folding. Science 2002, 298, 2191-2195. (50)

Kubelka, J.; Henry, E. R.; Cellmer, T.; Hofrichter, J.; Eaton, W. A. Chemical,

Physical, and Theoretical Kinetics of an Ultrafast Folding Protein. Proc. Natl. Acad. Sci. USA 2008, 105, 18655-18662. (51)

Faccin, M.; Bruscolini, P.; Pelizzola, A. Analysis of the Equilibrium and Kinetics

of the Ankyrin Repeat Protein Myotrophin. J. Chem. Phys. 2011, 134, 075102. (52)

Bruscolini, P.; Naganathan, A. N. Quantitative Prediction of Protein Folding

Behaviors from a Simple Statistical Model. J. Am. Chem. Soc. 2011, 133, 5372-5379.


36

Page 37 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(53)

Caraglio, M.; Pelizzola, A. Effects of Confinement on Thermal Stability and

Folding Kinetics in a Simple Ising-Like Model. Phys. Biol. 2012, 9, 016006. (54)

Sivanandan, S.; Naganathan, A. N. A Disorder-Induced Domino-Like

Destabilization Mechanism Governs the Folding and Functional Dynamics of the Repeat Protein IκBα. PLOS Comp. Biol. 2013, 9, e1003403. (55)

Narayan, A.; Naganathan, A. N. Evidence for the Sequential Folding Mechanism

in RNase H from an Ensemble-Based Model. J. Phys. Chem. B 2014, 118. (56)

Naganathan, A. N. Predictions from an Ising-Like Statistical Mechanical Model

on the Dynamic and Thermodynamic Effects of Protein Surface Electrostatics. J. Chem. Theory Comput. 2012, 8, 4646-4656. (57)

Naganathan, A. N. A Rapid, Ensemble and Free Energy Based Method for

Engineering Protein Stabilities. J. Phys. Chem. B 2013, 117, 4956-4964. (58)

Lapidus, L. J.; Steinbach, P. J.; Eaton, W. A.; Szabo, A.; Hofrichter, J. Effects of

Chain Stiffness on the Dynamics of Loop Formation in Polypeptides. Appendix: Testing a 1Dimensional Diffusion Model for Peptide Dynamics. J. Phys. Chem. B 2002, 106, 11628-11640. (59)

Henry, E. R.; Eaton, W. A. Combinatorial Modeling of Protein Folding Kinetics:

Free Energy Profiles and Rates. Chem. Phys. 2004, 307, 163-185. (60)

Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. Gromacs 4: Algorithms for

Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 435-447.


37


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(61)

Page 38 of 51

Best, R. B.; Hummer, G. Optimized Molecular Dynamics Force Fields Applied to

the Helix-Coil Transition of Polypeptides. J. Phys. Chem. B 2009, 113, 9004-9015. (62)

Lindorff-Larsen, K.; Piana, S.; Palmo, K.; Maragakis, P.; Klepeis, J. L.; Dror, R.

O.; Shaw, D. E. Improved Side-Chain Torsion Potentials for the Amber ff99sb Protein Force Field. Proteins: Struct. Funct. Bioinf. 2010, 78, 1950-1958. (63)

Finn, R. D.; Bateman, A.; Clements, J.; Coggill, P.; Eberhardt, R. Y.; Eddy, S. R.;

Heger, A.; Hetherington, K.; Holm, L.; Mistry, J.; Sonnhammer, E. L. L.; Tate, J.; Punta, M. Pfam: The Protein Families Database. Nuc. Acids Res. 2014, 42, D222-D230. (64)

Larkin, M. A.; Blackshields, G.; Brown, N. P.; Chenna, R.; McGettigan, P. A.;

McWilliam, H.; Valentin, F.; Wallace, I. M.; Wilm, A.; Lopez, R.; Thompson, J. D.; Gibson, T. J.; Higgins, D. G. Clustal W and Clustal X Version 2.0. Bioinformatics 2007, 23, 2947-2948. (65)

Wong, K.; Freund, S. M.; Fersht, A. R. Cold Denaturation of Barstar: 1H, 15N and

13

C Nmr Assignment and Characterisation of Residual Structure. J. Mol. Biol. 1996, 1996, 805–

818. (66)

Nolting, B.; Golbik, R.; Soler-Gonzalez, A. S.; Fersht, A. R. Circular Dichroism

of Denatured Barstar Suggests Residual Structure. Biochemistry 1997, 36, 9899-9905. (67)

Tanford, C.; Kirkwood, J. G. Theory of Protein Titration Curves. I. General

Equations for Impenetrable Spheres. J. Am. Chem. Soc. 1957, 79, 5333-5339. (68)

Ibarra-Molero, B.; Loladze, V. V.; Makhatadze, G. I.; Sanchez-Ruiz, J. M.

Thermal Versus Guanidine-Induced Unfolding of Ubiquitin. An Analysis in Terms of the


38

Page 39 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Contributions from Charge-Charge Interactions to Protein Stability. Biochemistry 1999, 38, 8138-8149. (69)

Lee,

L.;

Tidor,

B.

Optimization

of

Binding

Electrostatics:

Charge

Complementarity in the Barnase-Barstar Protein Complex. Prot. Sci. 2001, 10, 362-377. (70)

Ferreiro, D. U.; Hegler, J. A.; Komives, E. A.; Wolynes, P. G. Localizing

Frustration in Native Proteins and Protein Assemblies. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 19819-19824. (71)

Li, W.; Wolynes, P. G.; Takada, S. Frustration, Specific Sequence Dependence,

and Nonlinearity in Large-Amplitude Fluctuations of Allosteric Proteins. Proc. Natl. Acad. Sci. U.S.A. 2011, 108, 3504-3509. (72)

Capraro, D. T.; Roy, M.; Gosavi, S.; Onuchic, J. N.; Jennings, P. A. β-Bulge

Triggers Route-Switching on the Functional Landscape of Interleukin-1β. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 1490-1493. (73)

Gosavi, S. Understanding the Folding-Function Tradeoff in Proteins. PLoS One

2013, 8, e61222. (74)

Uversky, V. N.; Gillespie, J. R.; Fink, A. L. Why Are "Natively Unfolded"

Proteins Unstructured under Physiologic Conditions? Proteins: Struct. Funct. Genet. 2000, 41, 415-427. (75)

Mao, A. H.; Crick, S. L.; Vitalis, A.; Chicoine, C. L.; Pappu, R. V. Net Charge

Per Residue Modulates Conformational Ensembles of Intrinsically Disordered Proteins. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 8183-8188.


39


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(76)

Page 40 of 51

Müller-Späth, S.; Soranno, A.; Hirschfeld, V.; Hofmann, H.; Ruegger, S.;

Reymond, L.; Nettels, D.; Schuler, B. Charge Interactions Can Dominate the Dimensions of Intrinsically Disordered Proteins. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 14609-14614. (77)

Xu, D.; Lin, S. L.; Nussinov, R. Protein Binding Versus Protein Folding: The

Role of Hydrophilic Bridges in Protein Associations. J. Mol. Biol. 1997, 265, 68-84. (78)

Ganguly, D.; Zhang, W.; Chen, J. Electrostatically Accelerated Encounter and

Folding for Facile Recognition of Intrinsically Disordered Proteins. PLOS Comp. Biol. 2013, 9, e1003363. (79)

Vuzman, D.; Levy, Y. DNA Search Efficiency Is Modulated by Charge

Composition and Distribution in the Intrinsically Disordered Tail. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 21004-21009. (80)

Halskau, O.; Perez-Jimenez, R.; Ibarra-Molero, B.; Underhaug, J.; Muñoz, V.;

Martinez, A.; Sanchez-Ruiz, J. M. Large-Scale Modulation of Thermodynamic Protein Folding Barriers Linked to Electrostatics. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 8625-8630. (81)

Privalov, P. L.; Dragan, A. I. Microcalorimetry of Biological Macromolecules.

Biophys. Chem. 2007, 126, 16-24. (82)

Moody, C. L.; Tretyachenko-Ladokhina, V.; Laue, T. M.; Senear, D. F.; Cocco,

M. J. Multiple Conformations of the Cytidine Repressor DNA-Binding Domain Coalesce to One Upon Recognition of a Specific DNA Surface. Biochemistry 2011, 50, 6622-6632. (83)

Slutsky, M.; Mirny, L. A. Kinetics of Protein-DNA Interaction: Facilitated Target

Location in Sequence-Dependent Potential. Biophys. J. 2004, 87, 4021-4035.


40

Page 41 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(84)

Murugan, R. Theory of Site-Specific DNA-Protein Interactions in the Presence of

Conformational Fluctuations of DNA Binding Domains. Biophys. J. 2010, 99, 353-359.


41


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 51

TOC Graphic


42

Page 43 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


66x62mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

116x177mm (300 x 300 DPI)


Page 44 of 51

Page 45 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


83x42mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

143x268mm (300 x 300 DPI)


Page 46 of 51

Page 47 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


61x49mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

139x255mm (300 x 300 DPI)


Page 48 of 51

Page 49 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


110x74mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

64x50mm (300 x 300 DPI)


Page 50 of 51

Page 51 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


27x9mm (300 x 300 DPI)


Are Protein Folding Intermediates the Evolutionary Consequence of

Recommend Documents