Temperature-dependent downhill unfolding of ubiquitin. I. Nanosecond-to-millisecond resolved nonlinear infrared spectroscopy

Biomolecular infrared spectroscopy: making time for dynamics

Time resolved infrared spectroscopy of biological molecules has provided a wealth of information relating to structural dynamics, conformational changes, solvation and intermolecular interactions. Challenges still exist however arising from the wide range of timescales over which biological processes occur, stretching from picoseconds to minutes or hours. Experimental methods are often limited by vibrational lifetimes of probe groups, which are typically on the order of picoseconds, while measuring an evolving system continuously over some 18 orders of magnitude in time presents a raft of technological hurdles. In this Perspective, a series of recent advances which allow biological molecules and processes to be studied over an increasing range of timescales, while maintaining ultrafast time resolution, will be reviewed, showing that the potential for real-time observation of biomolecular function draws ever closer, while offering a new set of challenges to be overcome.

Temperature-Jump 2D IR Spectroscopy with Intensity-Modulated CW Optical Heating

Pulsed temperature-jump (T-jump) spectroscopy with infrared (IR) detection has been widely used to study biophysical processes occurring from nanoseconds to ∼1 ms with structural sensitivity. However, many systems exhibit structural dynamics on time scales longer than the millisecond barrier that is set by the time scale for thermal relaxation of the sample. We developed a linear and nonlinear infrared spectrometer coupled to an intensity-modulated continuous wave (CW) laser to probe T-jump-initiated chemical reactions from <1 ms to seconds. Time-dependent modulation of the CW laser leads to a <1 ms heating time as well as a constant final temperature (±3%) for the duration of the heating time. Temperature changes of up to 75 °C in D₂O are demonstrated, allowing for nonequilibrium measurements inaccessible to standard pulsed optical T-jump setups. T-jump linear absorption, pump-probe, and two-dimensional IR (2D IR) spectroscopy are applied to the unfolding and refolding of ubiquitin and a model intercalated motif (i-motif) DNA sequence, and analysis of the observed signals is used to demonstrate the limits and utility of each method. Overall, the ability to probe temperature-induced chemical processes from <1 ms to many seconds with 2D IR spectroscopy provides multiple new avenues for time-dependent spectroscopy in chemistry and biophysics.

5-Carboxylcytosine and Cytosine Protonation Distinctly Alter the Stability and Dehybridization Dynamics of the DNA Duplex

Applications associated with nucleobase protonation events are grounded in their fundamental impact on DNA thermodynamics, structure, and hybridization dynamics. Of the canonical nucleobases, N3 protonation of cytosine (C) is the most widely utilized in both biology and nanotechnology. Naturally occurring C derivatives that shift the N3 pK_a introduce an additional level of tunability. The epigenetic nucleobase 5-carboxylcytosine (caC) presents a particularly interesting example since this derivative forms Watson-Crick base pairs of similar stability and displays pH-dependent behavior over the same range as the canonical nucleobase. However, the titratable group in caC corresponds to the exocyclic carboxyl group rather than N3, and the implications of these divergent protonation events toward DNA hybridization thermodynamics, kinetics, and base pairing dynamics remain poorly understood. Here, we study the pH dependence of these physical properties using model oligonucleotides containing C and caC with FTIR and temperature-jump IR spectroscopy. We demonstrate that N3 protonation of C completely disrupts duplex stability, leading to large shifts in the duplex/single-strand equilibrium, a reduction in the cooperativity of melting, and an acceleration in the rate of duplex dissociation. In contrast, while increasing 5-carboxyl protonation in caC-containing duplexes induces an increase in base pair fluctuations, the DNA duplex can tolerate substantial protonation without significant perturbation to the duplex/single-strand equilibrium. However, 5-carboxyl protonation has a large impact on hybridization kinetics by reducing the transition state free energy. Our thermodynamic and kinetic analysis provides new insight on the impact of two divergent protonation mechanisms in naturally occurring nucleobases on the biophysical properties of DNA.

Uncovering the Early Stages of Domain Melting in Calmodulin with Ultrafast Temperature-Jump Infrared Spectroscopy

The signaling protein calmodulin (CaM) undergoes a well-known change in secondary structure upon binding Ca²⁺, but the structural plasticity of the Ca²⁺-free apo state is linked to CaM functionality. Variable temperature studies of apo-CaM indicate two structural transitions at 46 and 58 °C that are assigned to melting of the C- and N-terminal domains, respectively, but the molecular mechanism of domain unfolding is unknown. We report temperature-jump time-resolved infrared (IR) spectroscopy experiments designed to target the first steps in the C-terminal domain melting transition of human apo-CaM. A comparison of the nonequilibrium relaxation of apo-CaM with the more thermodynamically stable holo-CaM, with 4 equiv of Ca²⁺ bound, shows that domain melting of apo-CaM begins on microsecond time scales with α-helix destabilization. These observations enable the assignment of previously reported dynamics of CaM on hundreds of microsecond time scales to thermally activated melting, producing a complete mechanism for thermal unfolding of CaM.

Protein unfolding from free-energy calculations: integration of the Gaussian network model with bond binding energies

Motivated by single molecule experiments, we study thermal unfolding pathways of four proteins, chymotrypsin inhibitor, barnase, ubiquitin, and adenylate kinase, using bond network models that combine bond energies and elasticity. The protein elasticity is described by the Gaussian network model (GNM), to which we add prescribed bond binding energies that are assigned to all (nonbackbone) connecting bonds in the GNM of native state and assumed identical for simplicity. Using exact calculation of the Helmholtz free energy for this model, we consider bond rupture single events. The bond designated for rupture is chosen by minimizing the free-energy difference for the process, over all (nonbackbone) bonds in the network. Plotting the free-energy profile along this pathway at different temperatures, we observe a few major partial unfolding, metastable or stable, states, that are separated by free-energy barriers and change role as the temperature is raised. In particular, for adenylate kinase we find three major partial unfolding states, which is consistent with single molecule FRET experiments [Pirchi et al., Nat. Commun. 2, 493 (2011)] for which hidden Markov analysis reveals between three and five such states. Such states can play a major role in enzymatic activity.

Broadband two dimensional infrared spectroscopy of cyclic amide 2-Pyrrolidinone

In the past one-and-a-half decade there has been a significant methodological and technological development of two dimensional infrared (2DIR) spectroscopy, which unfolds many underlying physical and chemical processes of complex molecules, especially for biological molecules.

Intrinsically disordered proteins--relation to general model expressing the active role of the water environment

This work discusses the role of unstructured polypeptide chain fragments in shaping the protein's hydrophobic core. Based on the "fuzzy oil drop" model, which assumes an idealized distribution of hydrophobicity density described by the 3D Gaussian, we can determine which fragments make up the core and pinpoint residues whose location conflicts with theoretical predictions. We show that the structural influence of the water environment determines the positions of disordered fragments, leading to the formation of a hydrophobic core overlaid by a hydrophilic mantle. This phenomenon is further described by studying selected proteins which are known to be unstable and contain intrinsically disordered fragments. Their properties are established quantitatively, explaining the causative relation between the protein's structure and function and facilitating further comparative analyses of various structural models.

Microsecond molecular dynamics simulation of guanidinium chloride induced unfolding of ubiquitin

All atom molecular dynamics simulations have been used to explore the atomic detail mechanism of guanidinium induced unfolding of the protein ubiquitin.

Using VIPT-jump to distinguish between different folding mechanisms: application to BBL and a Trpzip

Protein folding involves a large number of sequential molecular steps or conformational substates. Thus, experimental characterization of the underlying folding energy landscape for any given protein is difficult. Herein, we present a new method that can be used to determine the major characteristics of the folding energy landscape in question, e.g., to distinguish between activated and barrierless downhill folding scenarios. This method is based on the idea that the conformational relaxation kinetics of different folding mechanisms at a given final condition will show different dependences on the initial condition. We show, using both simulation and experiment, that it is possible to differentiate between disparate kinetic folding models by comparing temperature jump (T-jump) relaxation traces obtained with a fixed final temperature and varied initial temperatures, which effectively varies the initial potential (VIP) of the system of interest. We apply this method (hereafter refer to as VIPT-jump) to two model systems, tryptophan zipper (Trpzip)-2c and BBL, and our results show that BBL exhibits characteristics of barrierless downhill folding, whereas Trpzip-2c folding encounters a free energy barrier. In addition, using the T-jump data of BBL we are able to provide, via Langevin dynamics simulations, a realistic estimate of its conformational diffusion coefficient.

Atomic-level description of ubiquitin folding

Equilibrium molecular dynamics simulations, in which proteins spontaneously and repeatedly fold and unfold, have recently been used to help elucidate the mechanistic principles that underlie the folding of fast-folding proteins. The extent to which the conclusions drawn from the analysis of such proteins, which fold on the microsecond timescale, apply to the millisecond or slower folding of naturally occurring proteins is, however, unclear. As a first attempt to address this outstanding issue, we examine here the folding of ubiquitin, a 76-residue-long protein found in all eukaryotes that is known experimentally to fold on a millisecond timescale. Ubiquitin folding has been the subject of many experimental studies, but its slow folding rate has made it difficult to observe and characterize the folding process through all-atom molecular dynamics simulations. Here we determine the mechanism, thermodynamics, and kinetics of ubiquitin folding through equilibrium atomistic simulations. The picture emerging from the simulations is in agreement with a view of ubiquitin folding suggested from previous experiments. Our findings related to the folding of ubiquitin are also consistent, for the most part, with the folding principles derived from the simulation of fast-folding proteins, suggesting that these principles may be applicable to a wider range of proteins.

Direct quantification of the attempt frequency determining the mechanical unfolding of ubiquitin protein

Understanding protein dynamics requires a comprehensive knowledge of the underlying potential energy surface that governs the motion of each individual protein molecule. Single molecule mechanical studies have provided the unprecedented opportunity to study the individual unfolding pathways along a well defined coordinate, the end-to-end length of the protein. In these experiments, unfolding requires surmounting an energy barrier that separates the native from the extended state. The calculation of the absolute value of the barrier height has traditionally relied on the assumption of an attempt frequency, υ(‡). Here we used single molecule force-clamp spectroscopy to directly determine the value of υ(‡) for mechanical unfolding by measuring the unfolding rate of the small protein ubiquitin at varying temperatures. Our experiments demonstrate a significant effect of the temperature on the mechanical rate of unfolding. By extrapolating the unfolding rate in the absence of force for different temperatures, varying within the range spanning from 5 to 45 °C, we measured a value for the activation barrier of ΔG(‡) = 71 ± 5 kJ/mol and an exponential prefactor υ(‡) ∼4 × 10(9) s(-1). Although the measured prefactor value is 3 orders of magnitude smaller than the value predicted by the transition state theory (∼6 × 10(12) s(-1)), it is 400-fold higher than that encountered in analogous experiments studying the effect of temperature on the reactivity of a protein-embedded disulfide bond (∼10(7) M(-1) s(-1)). This approach will allow quantitative characterization of the complete energy landscape of a folding polypeptide from highly extended states, of capital importance for proteins with elastic function.

Simulating the T-jump-triggered unfolding dynamics of trpzip2 peptide and its time-resolved IR and two-dimensional IR signals using the Markov state model approach

We proposed a computational protocol of simulating the T-jump peptide unfolding experiments and the related transient IR and two-dimensional IR (2DIR) spectra based on the Markov state model (MSM) and nonlinear exciton propagation (NEP) methods. MSMs partition the conformation space into a set of nonoverlapping metastable states, and we can calculate spectra signal for each of these states using the NEP method. Thus the overall spectroscopic observable for a given system is simply the sum of spectra of different metastable states weighted by their populations. We show that results from MSMs constructed from a large number of simulations have a much better agreement with the equilibrium experimental 2DIR spectra compared to that generated from straightforward MD simulations starting from the folded state. This indicates that a sufficient sampling of important relevant conformational states is critical for calculating the accurate spectroscopic observables. MSMs are also capable of simulating the unfolding relaxation dynamics upon the temperature jump. The agreement of the simulation using MSMs and NEP with the experiment not only provides a justification for our protocol, but also provides the physical insight of the underlying spectroscopic observables. The protocol we developed has the potential to be extended to simulate a wide range of fast triggering plus optical detection experiments for biomolecules.

Power-law dependence of the melting temperature of ubiquitin on the volume fraction of macromolecular crowders

The dependence of the melting temperature increase (ΔT(m)) of the protein ubiquitin on the volume fraction (ϕ) of several commonly used macromolecular crowding agents (dextran 6, 40, and 70 and ficoll 70) was quantitatively examined and compared to a recently developed theoretical crowding model, i.e., ΔT(m) ∼ (R(g)∕R(c))(α)φ(α∕3). We found that in the current case this model correctly predicts the power-law dependence of ΔT(m) on φ but significantly overestimates the role of the size (i.e., R(c)) of the crowding agent. In addition, we found that for ubiquitin the exponent α is in the range of 4.1-6.5, suggesting that the relation of α=3∕(3ν-1) is a better choice for estimating α based on the Flory coefficient (ν) of the polypeptide chain. Taken together these findings highlight the importance of improving our knowledge and theoretical treatment of the microcompartmentalization of the commonly used model crowding agents.

The folding of single domain proteins--have we reached a consensus?

Rather than stressing the most recent advances in the field, this review highlights the fundamental topics where disagreement remains and where adequate experimental data are lacking. These topics include properties of the denatured state and the role of residual structure, the nature of the fundamental steps and barriers, the extent of pathway heterogeneity and non-native interactions, recent comparisons between theory and experiment, and finally, dynamical properties of the folding reaction.

Folding dynamics of a small protein at room temperature via simulated coherent two-dimensional infrared spectroscopy

Understanding protein folding is of fundamental and practical importance in chemistry and biology. Despite the great success that has been made in tackling this problem, a detailed knowledge of how the elementary processes such as hydrogen-bond formation occur during protein folding has remained largely elusive. Using the combined power of molecular dynamics simulation with electrostatic polarization and coherent two-dimensional infrared spectroscopy, we are able to delineate the order of the hydrogen-bond formation event of a 17-residue peptide during its folding from an extended state to the native α-helix state. The folding is carried out by a single trajectory room-temperature molecular dynamics simulation that includes the polarization effect of hydrogen bonding, which is critical to the successful folding of the peptide. The onset and evolution of the isotope-labeled amide I vibration diagonal and cross peaks on the simulated 2DIR spectra allow us to build a structure-spectrum connection, and thus provide a microscopic picture of the helix folding process.

A one-dimensional free energy surface does not account for two-probe folding kinetics of protein alpha(3)D

We present fluorescence-detected measurements of the temperature-jump relaxation kinetics of the designed three-helix bundle protein alpha(3)D taken under solvent conditions identical to previous infrared-detected kinetics. The fluorescence-detected rate is similar to the IR-detected rate only at the lowest temperature where we could measure it (326 K). The fluorescence-detected rate decreases by a factor of 3 over the 326-344 K temperature range, whereas the IR-detected rate remains nearly constant over the same range. To investigate this probe dependence, we tested an extensive set of physically reasonable one-dimensional (1D) free energy surfaces by Langevin dynamics simulation. The simulations included coordinate- and temperature-dependent roughness, diffusion coefficients, and IR/fluorescence spectroscopic signatures. None of these can reproduce the IR and fluorescence data simultaneously, forcing us to the conclusion that a 1D free energy surface cannot accurately describe the folding of alpha(3)D. This supports the hypothesis that alpha(3)D has a multidimensional free energy surface conducive to downhill folding at 326 K, and that it is already an incipient downhill folder with probe-dependent kinetics near its melting point.

Probing the folding transition state of ubiquitin mutants by temperature-jump-induced downhill unfolding

Crucial to revealing mechanistic details of protein folding is a characterization of the transition state ensemble and its structural dynamics. To probe the transition state of ubiquitin thermal unfolding, we examine unfolding dynamics and kinetics of wild-type and mutant ubiquitin using time-resolved nonlinear infrared spectroscopy after a nanosecond temperature jump. We observe spectral changes on two different time scales. A fast nonexponential microsecond phase is attributed to downhill unfolding from the transition state region, which is induced by a shift of the barrier due to the rapid temperature change. Slow millisecond changes arise from thermally activated folding and unfolding kinetics. Mutants that stabilize or destabilize beta strands III-V lead to a decreased or increased amplitude of the microsecond phase, indicating that the disruption or weakening of these strands occurs in the transition state. Unfolding features from microseconds to milliseconds can be explained by temperature-dependent changes of a two-dimensional free energy surface constructed by the native contacts between beta strands of the protein. In addition, the results support the possibility of an intermediate state in thermal unfolding.

Exploiting the downhill folding regime via experiment

Traditionally, folding experiments have been directed at determining equilibrium and relaxation rate constants of proteins that fold with two-state-like kinetics. More recently, the combination of free energy surface approaches inspired by theory with the discovery of proteins that fold in the downhill regime has greatly widened the battlefield for experimentalists. Downhill folding proteins cross very small or no free energy barrier at all so that all relevant partially folded conformations become experimentally accessible. From these combined efforts we now have tools to estimate the height of thermodynamic and kinetic folding barriers. Procedures to measure with atomic resolution the structural heterogeneity of conformational ensembles at varying unfolding degrees are also available. Moreover, determining the dynamic modes driving folding and how they change as folding proceeds is finally at our fingertips. These developments allow us to address via experiment fundamental questions such as the origin of folding cooperativity, the relationship between structure and stability, or how to engineer folding barriers. Moreover, the level of detail attained in this new breed of experiments should provide powerful benchmarks for computer simulations of folding and force-field refinement.

Temperature-dependent downhill unfolding of ubiquitin. II. Modeling the free energy surface

To provide evidence for the interpretation of temperature-dependent unfolding kinetics and the downhill unfolding scenario presented in the accompanying experimental article (Part I), the free energy surface of ubiquitin unfolding is calculated using statistical mechanical models of the Muñoz-Eaton (ME) form. The models allow only two states for each amino acid residue, folded or unfolded, and permutations of these states generate an ensemble of microstates. One-dimensional free energy curves are calculated using the number of folded residues as a reaction coordinate. The proposed sequential unfolding of ubiquitin's beta-sheet is tested by mapping the free energy onto two reaction coordinates inspired by the experiment as follows: the number of folded residues in ubiquitin's stable beta-strands I and II and those of the less stable strands III-V. Although the original ME model successfully captures folding features of zipper-like one-dimensional folders, it misses important tertiary interactions between residues that are far from each other in primary sequence. To take tertiary contacts into account, partially folded microstates based on a spherical growth model are included in the calculation and compared with the original model. By calculating the folding probability of each residue for a given point on the free energy surface, the unfolding pathway of ubiquitin is visualized. At low temperature, thermal unfolding occurs along a sequential unfolding pathway as follows: disruption of the beta-strands III-V followed by unfolding of the strands I and II. At high temperature, multiple unfolding routes are formed. The heterogeneity of the transition state explains the global nonexponential unfolding observed in the T-jump experiment at high temperature. The calculation also reports a high stability for the alpha-helix of ubiquitin.