Fast Folding Research Articles

Internal force field in selected proteins.

The fuzzy oil drop model suggests that the tertiary conformation of a protein - particularly a globular one - can be likened to a spherical micelle. During the folding process, hydrophilic residues are exposed on the surface, while hydrophobic residues are retained inside the protein. The resulting hydrophobicity distribution can be mathematically modeled as a 3D Gaussian. The fuzzy oil drop model is strikingly effective in explaining the properties of type II antifreeze proteins and fast-folding proteins, as well as a vast majority of autonomous protein domains. This work aims to determine whether similar mechanisms apply to other types of nonbonding interactions. Our analysis indicates that electrostatic and van der Waals forces do not conform to the Gaussian pattern. The study involves a reference protein (titin) which shows a high agreement between the observed distribution of hydrophobicity and the theoretical (Gaussian) distribution, a selection of amyloid structures derived from the Protein Data Bank, as well as transthyretin - a protein known for its susceptibility to amyloid transformation.

Well-Balanced Force Field ff03CMAP for Folded and Disordered Proteins.

Molecular dynamics simulation as an important complement of experiment is widely used to study protein structures and functions. However, previous studies indicate that the current force fields cannot, simultaneously, provide accurate descriptions of folded proteins and intrinsically disordered proteins (IDPs). Therefore, a correction maps (CMAP)-optimized force field based on the Amber ff03 force field (termed ff03CMAP herein) was developed for a balanced sampling of folded proteins and IDPs. Extensive validations of short peptides, folded proteins, disordered proteins, and fast-folding proteins show that simulated chemical shifts, J-coupling constants, order parameters, and residual dipolar couplings (RDCs) with the ff03CMAP force field are in very good agreement with nuclear magnetic resonance measurements and are more accurate than other ff03-series force fields. The influence of solvent models was also investigated. It was found that the combination of ff03CMAP/TIP4P-Ew is suitable for folded proteins, and that of ff03CMAP/TIP4PD is better for disordered proteins. These findings confirm that the newly developed force field ff03CMAP can improve the balance of conformer sampling between folded proteins and IDPs.

Residue-Specific Force Field Improving the Sample of Intrinsically Disordered Proteins and Folded Proteins.

Intrinsically disordered proteins and regions (IDPs and IDRs) have attracted increasing interest with their abundance in the human proteome and critical roles in various human diseases. However, the characterization of structural dynamics of IDPs presents a challenge to general experimental methods due to their highly heterogeneous ensembles. Molecular dynamics (MD) simulation has been an alternative method with recent advances in computation power. Nevertheless, it is imperative that eligible predictions are determined by a highly precise force field, but traditional force fields sometimes give a collapsed disorder structure and overestimate the stability of IDPs. Here, we present a novel residue-specific force field, OPLSIDPSFF, to correct backbone dihedral terms for all 20 natural amino acids based on OPLS-AA/L. Extensive tests of 11 IDPs and two short peptides show that the simulated chemical shifts and J-coupling with the OPLSIDPSFF force field are in quantitative agreement with those from NMR experimental observables and are more accurate than the base generic force field. The influences of solvent models were also investigated, and it was found that TIP4P-D water had positive effects on limited observables. Furthermore, OPLSIDPSFF can still be used to model structural and dynamic properties of two tested folded proteins and fast-folding proteins. These findings confirm that the newly developed residue-specific force field OPLSIDPSFF can improve the conformer sampling of intrinsically disordered and folded proteins.

Diverse Folding Pathways of HIV-1 Protease Monomer on a Rugged Energy Landscape

The modern energy landscape theory of protein folding predicts multiple folding pathways connecting a myriad of unfolded conformations and a well-defined folded state. However, direct experimental observation of heterogeneous folding pathways is difficult. Naturally evolved proteins typically exhibit a smooth folding energy landscape for fast and efficient folding by avoiding unfavorable kinetic traps. In this case, rapid fluctuations between unfolded conformations result in apparent two-state behavior and make different pathways indistinguishable. However, the landscape roughness can be different, depending on the selection pressures during evolution. Here, we characterize the unusually rugged folding energy landscape of human immunodeficiency virus-1 protease monomer using single-molecule Förster resonance energy transfer spectroscopy. Our data show that fluctuations between unfolded conformations are slow, which enables the experimental observation of heterogeneous folding pathways as predicted by the landscape theory. Although the landscape ruggedness is sensitive to the mutations and fluorophore locations, the folding rate is similar for various protease constructs. The natural evolution of the protease to have a rugged energy landscape likely results from intrinsic pressures to maintain robust folding when human immunodeficiency virus-1 mutates frequently, which is essential for its survival.

Calculation of the Hinge Moments of a Folding Wing Aircraft during the Flight-Folding Process

A folding wing morphing aircraft should complete the folding and unfolding process of its wings while in flight. Calculating the hinge moments during the morphing process is a critical aspect of a folding wing design. Most previous studies on this problem have adopted steady-state or quasi-steady-state methods, which do not simulate the free-flying morphing process. In this study, we construct an aeroelastic flight simulation platform based on the secondary development of ADAMS software to simulate the flight-folding process of a folding wing aircraft. A flexible multibody dynamic model of the folding wing structure is established in ADAMS using modal neutral files, and the doublet lattice method is developed to generate aerodynamic influence coefficient matrices that are suitable for the flight-folding process. The user subroutine is utilized, aerodynamic loading is realized in ADAMS, and an aeroelastic flight simulation platform of a folding wing aircraft is built. On the basis of this platform, the flight-folding process of the aircraft is simulated, the hinge moments of the folding wings are calculated, and the influences of the folding rate and the aircraft’s center of gravity (c.g.) position on the results are investigated. Results show that the steady-state method is applicable to the slow folding process. For the fast folding process, the steady-state simulation errors of the hinge moments are substantially large, and a transient method is required to simulate the flight-folding process. In addition, the c.g. position considerably affects the hinge moments during the folding process. Given that the c.g. position moves aft, the maximum hinge moments of the inner and outer wings constantly increase.

Pearl-Necklace-Like Local Ordering Drives Polypeptide Collapse.

The collapse of the polypeptide backbone is an integral part of protein folding. Using polyglycine as a probe, we explore the nonequilibrium pathways of protein collapse in water. We find that the collapse depends on the competition between hydration effects and intrapeptide interactions. Once intrapeptide van der Waal interactions dominate, the chain collapses along a nonequilibrium pathway characterized by formation of pearl-necklace-like local clusters as intermediates that eventually coagulate into a single globule. By describing this coarsening through the contact probability as a function of distance along the chain, we extract a time-dependent length scale that grows in a linear fashion. The collapse dynamics is characterized by a dynamical critical exponent z ≈ 0.5 that is much smaller than the values of z = 1–2 reported for nonbiological polymers. This difference in the exponents is explained by the instantaneous formation of intrachain hydrogen bonds and local ordering that may be correlated with the observed fast folding times of proteins.

A thermostable flavin-based fluorescent protein from Chloroflexus aggregans: a framework for ultra-high resolution structural studies.

Light-Oxygen-Voltage (LOV) domains are conserved parts of photoreceptors in plants, bacteria and fungi that bind flavins as chromophores and detect blue light. In the past, LOV domain variants have been developed as fluorescent reporter proteins (called flavin-based fluorescent proteins; FbFPs), which due to their ability to fluoresce under anaerobic conditions, fast folding kinetics and a small size of ∼12-16 kDa are a promising reporter system for quantitative real-time analysis of biological processes. Here, we present a small thermostable flavin-based fluorescent protein CagFbFP derived from a soluble LOV domain-containing histidine kinase from the thermophilic bacterium Chloroflexus aggregans. CagFbFP is composed of 107 amino acids with a molecular weight of 11.6 kDa and consists only of the conserved LOV core domain. The protein is thermostable with a melting point of about 68 °C. It crystallizes easily and its crystals diffract to 1.07 Å. Both the crystal structure and small angle scattering data show that the protein is a dimer. Unexpectedly, glutamine 148, which in LOV photoreceptor proteins is the key residue responsible for signal transduction, occupies two conformations. Molecular dynamics simulations show that the two conformations interconvert rapidly. The crystal structure of the wild-type Chloroflexus aggregans LOV domain determined at 1.22 Å resolution confirmed the presence of two alternative conformations of the glutamine 148 side chain. Overall, this protein, due to its stability and ease of crystallization, appears to be a promising model for ultra-high resolution structural studies of LOV domains and for application as a fluorescent reporter.

Targeted search for young radio pulsars in the SMC: discovery of two new pulsars

ABSTRACT We report the first rotation powered pulsars discovered in the Small Magellanic Cloud (SMC) in more than a decade. PSR J0043–73 and PSR J0052–72 were discovered during a Parkes Multi-Beam (PMB) survey of MCSNR J0127–7332, and five new, optically selected, supernova remnant (SNR) candidates identified by the XMM–Newton survey. In addition to the candidates, we adjusted the PMB rotation to include additional nine SNRs and pulsar wind nebulae. We searched for young pulsars (1–200 ms) employing a Fourier analysis with PRESTO, as well as a search for longer period pulsars (200 ms–360 s) with a fast folding algorithm. Our targeted survey had a limiting flux density of 0.039 mJy for periods greater than 50 ms. Although not the main target of this search it was also sensitive to millisecond pulsars. PSR J0043–73 has a period and dispersion measure of 937.429 37 (26) ms and 115.1 (3.4) pc cm−3, respectively, and PSR J0052–72 has a period of 191.444 328 (46) ms and a DM of 158.6 (1.6) pc cm−3.

Variational selection of features for molecular kinetics

The modeling of atomistic biomolecular simulations using kinetic models such as Markov state models (MSMs) has had many notable algorithmic advances in recent years. The variational principle has opened the door for a nearly fully automated toolkit for selecting models that predict the long time-scale kinetics from molecular dynamics simulations. However, one yet-unoptimized step of the pipeline involves choosing the features, or collective variables, from which the model should be constructed. In order to build intuitive models, these collective variables are often sought to be interpretable and familiar features, such as torsional angles or contact distances in a protein structure. However, previous approaches for evaluating the chosen features rely on constructing a full MSM, which in turn requires additional hyperparameters to be chosen, and hence leads to a computationally expensive framework. Here, we present a method to optimize the feature choice directly, without requiring the construction of the final kinetic model. We demonstrate our rigorous preprocessing algorithm on a canonical set of 12 fast-folding protein simulations and show that our procedure leads to more efficient model selection.

Ultrafast folding kinetics of WW domains reveal how the amino acid sequence determines the speed limit to protein folding

Protein (un)folding rates depend on the free-energy barrier separating the native and unfolded states and a prefactor term, which sets the timescale for crossing such barrier or folding speed limit. Because extricating these two factors is usually unfeasible, it has been common to assume a constant prefactor and assign all rate variability to the barrier. However, theory and simulations postulate a protein-specific prefactor that contains key mechanistic information. Here, we exploit the special properties of fast-folding proteins to experimentally resolve the folding rate prefactor and investigate how much it varies among structural homologs. We measure the ultrafast (un)folding kinetics of five natural WW domains using nanosecond laser-induced temperature jumps. All five WW domains fold in microseconds, but with a 10-fold difference between fastest and slowest. Interestingly, they all produce biphasic kinetics in which the slower phase corresponds to reequilibration over the small barrier (<3 RT) and the faster phase to the downhill relaxation of the minor population residing at the barrier top [transition state ensemble (TSE)]. The fast rate recapitulates the 10-fold range, demonstrating that the folding speed limit of even the simplest all-β fold strongly depends on the amino acid sequence. Given this fold's simplicity, the most plausible source for such prefactor differences is the presence of nonnative interactions that stabilize the TSE but need to break up before folding resumes. Our results confirm long-standing theoretical predictions and bring into focus the rate prefactor as an essential element for understanding the mechanisms of folding.

Probing (UN)Folding Transition Paths of Fast-Folding Proteins by Single-Molecule Fluorescence: Exploring the Role of Secondary Structure, Fold Topology and Sequence

Protein folding involves formation of secondary structural elements and their collapse into well-defined 3-dimensional structure. Attempts to study how these processes cooperate to form the native structure and determine folding mechanisms has been focus of research for decades. Addressing these questions require looking at the distributions of behaviors of individual molecules, which has been successfully attained by theory and computer simulations. Experimentally, the problem must be approached by single-molecule spectroscopic methods, which have not had the required time-resolution. We are investigating protein folding at the single-molecule level combining advanced custom-built fluorescence-based SM-FRET techniques optimized for high-count rates and a maximum likelihood analysis (MLA) of photon arrival times that we developed for the detection of (un)folding transition paths of microsecond folding proteins. To investigate the roles of secondary structure, fold topology, and amino acid sequence we are performing these experiments on three fast-folding protein models, all consisting of three secondary structure elements in an antiparallel arrangement: En-HD (three α-helices), and Nedd4-WW3 and FBP11WW2, which fold onto homologous 3-stranded β-sheets but with different amino acid sequence. We are investigating their folding transition paths by 2-color SM-FRET using variants labeled with FRET pairs at the two ends in free diffusion experiments. Because these proteins fold-unfold in microseconds, free diffusion offers the opportunity to catch folding transitions during the diffusive trajectories without immobilization and thus without significantly perturbing folding landscape. Our analysis of these data using MLA of photon trajectories (rather than binning) provides the free energy landscape as a function of the experimental order parameter (FRET-pair distance) and the intramolecular diffusion coefficient. Subsequent reconstruction of the molecular trajectories from the photon trajectories using stochastic methods provide a direct glimpse of barrier crossing events.

Three-Color Single-Molecule FRET and Fluorescence Lifetime Analysis of Fast Protein Folding

We describe the theory, experiment, and analysis of three-color Förster resonance energy transfer spectroscopy for probing conformational dynamics of a fast-folding protein, α3D. To site-specifically label fluorophores, a cysteine residue and an unnatural amino acid were labeled first, and then we appended a cysteine residue to the C-terminus of the protein by the sortase-mediated ligation for the third dye. All three FRET efficiencies were determined using alternating excitation of the donor and acceptor 1. Due to fast folding on a millisecond time scale, we used a maximum likelihood method that analyzes photon trajectories without binning the data. The extracted kinetic parameters agree well with the previously measured parameters with two-color FRET, suggesting the third fluorophore does not affect the folding dynamics of the protein. The FRET efficiencies for all three dye pairs were calculated after various corrections. They were compared with the FRET efficiencies obtained from the two-color segments collected in the same experiment. The FRET efficiencies of the folded state agree with those from the two-color segments, whereas the unfolded state FRET efficiencies are different. This happens because fluctuations of all three inter-dye distances contribute to the three-color FRET efficiency. This difference can be accounted for by using the Gaussian chain model with the parameters obtained from the two-color segments. Therefore, three-color FRET provides additional information on the flexibility of molecules that cannot be obtained from a combination of two-color FRET experiments. Using the delay times of photons from the laser pulse, fluorescence lifetimes were determined using the maximum likelihood analysis. The correlation between FRET efficiencies and lifetimes of the donor, acceptor 1, and acceptor 2 was visualized in two-dimensional FRET efficiency-lifetime histograms, which can be used to demonstrate the presence of conformational dynamics in a protein.

Three Color Single-Molecule FRET of Fast IDP Binding and Folding

Molecular interactions of intrinsically disordered proteins (IDPs) are different from those between folded molecules because IDP binding involves large convormational changes. To understand the mechanism of IDP binding, three-color Förster resonance energy transfer (FRET) will be very useful because both the interaction between two molecules and conformational changes can be probed simultaneously. In this work, we investigated binding of a disordered protein, the transactivation domain (TAD) of p53 and one of its binding partners, nuclear coactivator binding domain (NCBD) of CBP. TAD labeled with Alexa488 (donor) and Alexa594 (acceptor 1, A1) site-specifically was immobilized on a glass surface and incubated with CF680R (acceptor 2, A2)-labeled NCBD in solution. To determine all three FRET efficiencies, alternating excitation of the donor and A1 is typically used. However, in binding experiments, direct excitation of A2 attached to NCBD in solution by A1 excitation laser produces a high background signal. Therefore, we devised a method using a single donor excitation that determines all three FRET efficiencies by utilizing incomplete labeling of A2. When TAD binds to unlabled NCBD, the FRET efficiency between the donor and A1 (E1) can be determined. Using this information, it is possible to determine the other two FRET efficiencies in principle. However, due to the fast binding and dissociation kinetics, the bound and unbound states are not well separated in binned FRET efficiency trajectories (1 ms bin time), which prevents pre-determination of E1. We employed the maximum likelihood method developed by Gopich and Szabo that analyzes photon trajectories directly without binning the data. By globally analyzing the data using a kinetic model that includes binding to both labeled and unlabled NCBD, rate coefficients of the sub-millisecond kinetics and all three FRET efficiencies were determined accurately.

Superfunneled Energy Landscape of Protein Evolution Unifies the Principles of Protein Evolution, Folding, and Design.

Evolution is essential for shaping the biological functions. Darwin proposed the selection as the driving force for evolution upon mutations. While mutations are clear, the quantification of the selection force is still challenging. In this study, we identified and quantified both thermodynamic stability and kinetic accessibility as the selection forces for protein evolution. The protein evolution can be viewed and quantified as a trajectory moving along a superfunneled energy landscape with a line attractor at the bottom. The resulting evolved sequences and structures show strong protein characteristics including the hydrophobic core, high designability, and fast folding. The evolution principle uncovered here is validated on real proteins and sheds light on the protein design.

Extensive tests and evaluation of the CHARMM36IDPSFF force field for intrinsically disordered proteins and folded proteins.

Intrinsically disordered proteins (IDPs) have received increasing attention in recent studies due to their structural heterogeneity and critical biological functions. To fully understand the structural properties and determine accurate ensembles of IDPs, molecular dynamics (MD) simulation was widely used to sample diverse conformations and reveal the structural dynamics. However, the classical state-of-the-art force fields perform well for folded proteins while being unsatisfactory for the simulations of disordered proteins reported in many previous studies. Thus, improved force fields were developed to precisely describe both folded proteins and disordered proteins. Preliminary tests show that our newly developed CHARMM36IDPSFF (C36IDPSFF) force field can well reproduce the experimental observables of several disordered proteins, but more tests on different types of proteins are needed to further evaluate the performance of C36IDPSFF. Here, we extensively simulate short peptides, disordered proteins, and fast-folding proteins as well as folded proteins, and compare the simulated results with the experimental observables. The simulation results show that C36IDPSFF could substantially reproduce the experimental observables for most of the tested proteins but some limitations are also found in the radius of gyration of large disordered proteins and the stability of fast-folding proteins. This force field will facilitate large scale studies of protein structural dynamics and functions using MD simulations.

Direct observation of the fast and robust folding of a slipknotted protein by optical tweezers.

Understanding the folding mechanism of knotted and slipknotted proteins has attracted considerable interest. Due to their topological complexity, knotted and slipknotted proteins are predicted to fold slowly and involve large topological barriers. Molecular dynamics simulation studies suggest that a slipknotted conformation can serve as an important intermediate to help greatly reduce the topological difficulty during the folding of some knotted proteins. Here we use a single molecule optical tweezers technique to directly probe the folding of a small slipknotted protein AFV3-109. We found that stretching AFV3-109 can lead to the untying of the slipknot and complete unfolding of AFV3-109. Upon relaxation, AFV3-109 can readily refold back to its native slipknot conformation with high fidelity when the stretching force is lower than 6 pN. The refolding of AFV3-109 occurs in a sharp two-state like transition. Our results indicate that, different from knotted proteins, the folding of a slipknotted protein like AFV3-109 can be fast, and may not necessarily involve a high topological barrier.

Quantitative comparison of adaptive sampling methods for protein dynamics.

Adaptive sampling methods, often used in combination with Markov state models, are becoming increasingly popular for speeding up rare events in simulation such as molecular dynamics (MD) without biasing the system dynamics. Several adaptive sampling strategies have been proposed, but it is not clear which methods perform better for different physical systems. In this work, we present a systematic evaluation of selected adaptive sampling strategies on a wide selection of fast folding proteins. The adaptive sampling strategies were emulated using models constructed on already existing MD trajectories. We provide theoretical limits for the sampling speed-up and compare the performance of different strategies with and without using some a priori knowledge of the system. The results show that for different goals, different adaptive sampling strategies are optimal. In order to sample slow dynamical processes such as protein folding without a priori knowledge of the system, a strategy based on the identification of a set of metastable regions is consistently the most efficient, while a strategy based on the identification of microstates performs better if the goal is to explore newer regions of the conformational space. Interestingly, the maximum speed-up achievable for the adaptive sampling of slow processes increases for proteins with longer folding times, encouraging the application of these methods for the characterization of slower processes, beyond the fast-folding proteins considered here.

Subsystem decomposition of process networks for simultaneous distributed state estimation and control

An appropriate subsystem configuration is a prerequisite for a successful distributed control/state estimation design. Existing subsystem decomposition methods are not designed to handle simultaneous distributed estimation and control. In this article, we address the problem of subsystem decomposition of general nonlinear process networks for simultaneous distributed state estimation and distributed control based on community structure detection. A systematic procedure based on modularity is proposed. A fast folding algorithm that approximately maximizes the modularity is used in the proposed procedure to find candidate subsystem configurations. Two chemical process examples of different complexities are used to illustrate the effectiveness and applicability of the proposed approach. © 2018 American Institute of Chemical Engineers AIChE J, 65: 904–914, 2019

The Formation of Hydrophobic Core Regulates the Protein Folding of Villin Elucidated with Parallel Cascade Selection Molecular Dynamics

Villin is a fast-folding protein and has a unique hydrophobic core at the center in its folded form. In the present study, the folding process of Villin was investigated with parallel cascade selec...

The Effect of Electrostatic Interactions on the Folding Kinetics of a 3-α-Helical Bundle Protein Family.

The trio of protein segment repeats called spectrins diverges by more than 2 orders of magnitude in their folding and unfolding rates, despite having very similar stabilities and almost coincidental topologies. Experimental studies revealed that the mutation of five particular residues dramatically alters the kinetic rates in the slow folders, making them similar to the rates of the fast folder. This is considered to be an exceptional behavior which seems in principle to challenge the current understanding of the protein folding process. In this work, we analyze this scenario, using a simplified computational model, combined with state-of-the-art kinetic analysis techniques. Our model faithfully separates the kinetics of the fast and slow folders and captures the effect of the five mutations. We show that the inclusion of electrostatics in the model is necessary to explain the experimental findings.