Hidden Intermediate State and Second Pathway Determining Folding and Unfolding Dynamics of GB1 Protein at Low Forces

Anomalous Force-Dependent Transition Rates Unveil Dual Pathways in Folding and Unfolding Dynamics of Acyl-coenzyme A Binding Protein

All-α proteins typically fold rapidly and are unable to withstand high forces. Acyl-coenzyme A binding protein (ACBP), a four-α-helix bundle protein, serves as a model protein for studying the folding dynamics of all-α proteins. In previous biochemistry and single molecule force spectroscopy experiments, a controversy exists for the folding pathway and the conformation of the transition state. In this article, we investigate the folding and unfolding dynamics of ACBP in a force range of 4-10 pN using magnetic tweezers, revealing anomalous force-dependent transition rates. The unfolding rate of ACBP remains nearly constant when force is below 6 pN, and it increases sharply when the force exceeds this threshold, while the logarithm of its folding rate is almost a linear function of force. Detailed analysis combined with molecular dynamics simulations indicates that ACBP has two transition pathways: one dominating at zero or low force and the other dominating at high force. Our results provide strong evidence that stretching force not only modulates the folding and unfolding rates but also switches the transition pathways, leading to complex force response behaviors.

Folding and Misfolding Dynamics of Irisin Protein Revealed by Single-Molecule Magnetic Tweezers

Irisin, a fibronectin III protein secreted by muscles during physical exercise, plays a significant role in the browning of white fat and cell adhesion, highlighting the importance of its conformational transitions. In this study, we investigated the folding and unfolding dynamics of a single irisin domain using a single-molecule manipulation technique known as magnetic tweezers. In addition to the native state, irisin can also fold transiently into a misfolded state. We determined the folding free energies of the native and misfolded states as well as their force-dependent folding and unfolding rates. The free energy of the misfolded state is higher than that of the unfolded state, and the misfolded state has a homogeneous force-dependent unfolding rate. The stable native state demonstrates heterogeneous unfolding rates that are within ∼1 order of magnitude. Via comparison with the well-studied 10th fibronectin III domain that has a partially folded intermediate state, our study demonstrates that proteins with similar structure can have distinct folding pathways.

Bidirectional Allostery Mechanism in Catch-Bond Formation of CD44 Mediated Cell Adhesion

Catch-bonds, whereby noncovalent ligand-receptor interactions are counterintuitively reinforced by tensile forces, play a major role in cell adhesion under mechanical stress. A basic prerequisite for catch-bond formation, as implicated in classic catch-bond models, is that force-induced remodeling of the ligand binding interface occurs prior to bond rupture. However, what strategy receptor proteins utilize to meet such specific kinetic control remains elusive. Here we report a bidirectional allostery mechanism of catch-bond formation based on theoretical and molecular dynamics simulation studies. Binding of ligand allosterically reduces the threshold force for unlocking of otherwise stably folded force-sensing element (i.e., forward allostery), so that a much smaller tensile force can trigger the conformational switching of receptor protein to high binding-strength state via backward allosteric coupling before bond rupture. Such bidirectional allostery fulfills the specific kinetic control required by catch-bond formation and is likely to be commonly utilized in cell adhesion. The essential thermodynamic and kinetic features of receptor proteins essential for catch-bond formation were identified.

Pulling Forces Differentially Affect Refolding Pathways Due to Entangled Misfolded States in SARS-CoV-1 and SARS-CoV-2 Receptor Binding Domain

Single-molecule force spectroscopy (SMFS) experiments can monitor protein refolding by applying a small force of a few piconewtons (pN) and slowing down the folding process. Bell theory predicts that in the narrow force regime where refolding can occur, the folding time should increase exponentially with increased external force. In this work, using coarse-grained molecular dynamics simulations, we compared the refolding pathways of SARS-CoV-1 RBD and SARS-CoV-2 RBD (RBD refers to the receptor binding domain) starting from unfolded conformations with and without a force applied to the protein termini. For SARS-CoV-2 RBD, the number of trajectories that fold is significantly reduced with the application of a 5 pN force, indicating that, qualitatively consistent with Bell theory, refolding is slowed down when a pulling force is applied to the termini. In contrast, the refolding times of SARS-CoV-1 RBD do not change meaningfully when a force of 5 pN is applied. How this lack of a Bell response could arise at the molecular level is unknown. Analysis of the entanglement changes of the folded conformations revealed that in the case of SARS-CoV-1 RBD, an external force minimizes misfolding into kinetically trapped states, thereby promoting efficient folding and offsetting any potential slowdown due to the external force. These misfolded states contain non-native entanglements that do not exist in the native state of either SARS-CoV-1-RBD or SARS-CoV-2-RBD. These results indicate that non-Bell behavior can arise from this class of misfolding and, hence, may be a means of experimentally detecting these elusive, theoretically predicted states.

An accurate probabilistic step finder for time-series analysis

Noisy time-series data-from various experiments, including Förster resonance energy transfer, patch clamp, and force spectroscopy, among others-are commonly analyzed with either hidden Markov models or step-finding algorithms, both of which detect discrete transitions. Hidden Markov models, including their extensions to infinite state spaces, inherently assume exponential-or technically geometric-holding time distributions, biasing step locations toward steps with geometric holding times, especially in sparse and/or noisy data. In contrast, existing step-finding algorithms, while free of this restraint, often rely on ad hoc metrics to penalize steps recovered in time traces (by using various information criteria) and otherwise rely on approximate greedy algorithms to identify putative global optima. Here, instead, we devise a robust and general probabilistic (Bayesian) step-finding tool that neither relies on ad hoc metrics to penalize step numbers nor assumes geometric holding times in each state. As the number of steps themselves in a time-series are a priori unknown, we treat these within a Bayesian nonparametric (BNP) paradigm. We find that the method developed, BNP Step (BNP-Step), accurately determines the number and location of transitions between discrete states without any assumed kinetic model and learns the emission distribution characteristic of each state. In doing so, we verify that BNP-Step can analyze sparser data sets containing higher noise and more closely spaced states than otherwise resolved by current state-of-the-art methods. What is more, BNP-Step rigorously propagates measurement uncertainty into uncertainty over state transition locations, numbers, and emission levels as characterized by the posterior. We demonstrate the performance of BNP-Step on both synthetic data as well as data drawn from force spectroscopy experiments.

Ligand-dependent folding and unfolding dynamics and free energy landscapes of acylphosphatase

Acylphosphatase (AcP) is an enzyme which catalyses the hydrolysis of acylphosphate. The binding with the phosphate ion (Pi) assumes significance in preserving both the stability and enzymatic activity of AcP. While previous studies using single molecule force spectroscopy explored the mechanical properties of AcP, the influence of Pi on its folding and unfolding dynamic behaviors remains unexplored. In this work, using stable magnetic tweezers, we measured and compared the force-dependent folding and unfolding rates of AcP in the Tris buffer and phosphate buffer within a force range from 2 pN to 40 pN. We found that Pi exerts no discernible effect on the folding dynamics but consistently decreases the force-dependent unfolding rate of AcP by a constant ratio across the entire force spectrum. The free energy landscapes of AcP in the absence and presence of Pi are constructed. Our results reveal that Pi selectively binds to the native state of AcP, stabilizing it and suggesting the general properties of specific ligand-receptor interactions.

Exploring the free energy landscape of proteins using magnetic tweezers

Proteins fold to their native states by searching through the free energy landscapes. As single-domain proteins are the basic building block of multiple-domain proteins or protein complexes composed of subunits, the free energy landscapes of single-domain proteins are of critical importance to understand the folding and unfolding processes of proteins. To explore the free energy landscapes of proteins over large conformational space, the stability of native structure is perturbed by biochemical or mechanical means, and the conformational transition process is measured. In single molecular manipulation experiments, stretching force is applied to proteins, and the folding and unfolding transitions are recorded by the extension time course. Due to the broad force range and long-time stability of magnetic tweezers, the free energy landscape over large conformational space can be obtained. In this article, we describe the magnetic tweezers instrument design, protein construct design and preparation, fluid chamber preparation, common-used measuring protocols including force-ramp and force-jump measurements, and data analysis methods to construct the free energy landscape. Single-domain cold shock protein is introduced as an example to build its free energy landscape by magnetic tweezers measurements.

Free Energy Landscape of Type III Fibronectin Domain with Identified Intermediate State and Hierarchical Symmetry

The tenth domain of type III fibronectin (FNIII_{10}) mediates cell adhesion to the extracellular matrix. Despite its structural similarity to immunoglobulin domains, FNIII_{10} exhibits unique unfolding behaviors. We employed magnetic tweezers to investigate the unfolding and folding dynamics of FNIII_{10} under physiological forces (4-50 pN). Our results showed that FNIII_{10} follows a consistent transition pathway with an intermediate state characterized by detached A and G β strands. We determined the folding free energies and all force-dependent transition rates of FNIII_{10} and found that both unfolding rates from the native state to the intermediate state and from the intermediate state to the unfolded state deviate from Bell's model. We constructed a quantitative free energy landscape with well-defined traps and barriers that exhibits a hierarchical symmetrical pattern. Our findings provide a comprehensive understanding of FNIII_{10} conformational dynamics and demonstrate how free energy landscape of multistate biomolecules can be precisely mapped, illuminating the relationship between thermal stability, intermediate states, and folding rates in protein folding.

An accurate probabilistic step finder for time-series analysis

Noisy time-series data is commonly collected from sources including Förster Resonance Energy Transfer experiments, patch clamp and force spectroscopy setups, among many others. Two of the most common paradigms for the detection of discrete transitions in such time-series data include: hidden Markov models (HMMs) and step-finding algorithms. HMMs, including their extensions to infinite state-spaces, inherently assume in analysis that holding times in discrete states visited are geometrically-or, loosely speaking in common language, exponentially-distributed. Thus the determination of step locations, especially in sparse and noisy data, is biased by HMMs toward identifying steps resulting in geometric holding times. In contrast, existing step-finding algorithms, while free of this restraint, often rely on ad hoc metrics to penalize steps recovered in time traces (by using various information criteria) and otherwise rely on approximate greedy algorithms to identify putative global optima. Here, instead, we devise a robust and general probabilistic (Bayesian) step-finding tool that neither relies on ad hoc metrics to penalize step numbers nor assumes geometric holding times in each state. As the number of steps themselves in a time-series are, a priori unknown, we treat these within a Bayesian nonparametric (BNP) paradigm. We find that the method developed, Bayesian Nonparametric Step (BNP-Step), accurately determines the number and location of transitions between discrete states without any assumed kinetic model and learns the emission distribution characteristic of each state. In doing so, we verify that BNP-Step can analyze sparser data sets containing higher noise and more closely-spaced states than otherwise resolved by current state-of-the-art methods. What is more, BNP-Step rigorously propagates measurement uncertainty into uncertainty over state transition locations, numbers, and emission levels as characterized by the posterior. We demonstrate the performance of BNP-Step on both synthetic data as well as data drawn from force spectroscopy experiments.

Single-Molecule Study of DNAzyme Reveals Its Intrinsic Conformational Dynamics

DNAzyme is a class of DNA molecules that can perform catalytic functions with high selectivity towards specific metal ions. Due to its potential applications for biosensors and medical therapeutics, DNAzyme has been extensively studied to characterize the relationships between its biochemical properties and functions. Similar to protein enzymes and ribozymes, DNAzymes have been found to undergo conformational changes in a metal-ion-dependent manner for catalysis. Despite the important role the conformation plays in the catalysis process, such structural and dynamic information might not be revealed by conventional approaches. Here, by using the single-molecule fluorescence resonance energy transfer (smFRET) technique, we were able to investigate the detailed conformational dynamics of a uranyl-specific DNAzyme 39E. We observed conformation switches of 39E to a folded state with the addition of Mg²⁺ and to an extended state with the addition of UO₂²⁺. Furthermore, 39E can switch to a more compact configuration with or without divalent metal ions. Our findings reveal that 39E can undergo conformational changes spontaneously between different configurations.

One-step asparaginyl endopeptidase (OaAEP1)-based protein immobilization for single-molecule force spectroscopy

Enzymatic protein ligation has become the most powerful and widely used method for high-precision atomic force microscopy single-molecule force spectroscopy (AFM-SMFS) study of protein mechanics. However, this methodology typically requires the functionalization of the glass surface with a corresponding peptide sequence/tag for enzymatic recognition and multiple steps are needed. Thus, it is time-consuming and a high level of experience is needed for reliable results. To solve this problem, we simplified the procedure using two strategies both based on asparaginyl endopeptidase (AEP). First, we designed a heterobifunctional peptide-based crosslinker, GL-peptide-propargylglycine, which links to an N 3-functionalized surface via the click reaction. Then, the target protein with a C-terminal NGL sequence can be immobilized via the AEP-mediated ligation. Furthermore, we took advantage of the direct ligation between primary amino in a small molecule and protein with C-terminal NGL by AEP. Thus, the target protein can be immobilized on an amino-functionalized surface via AEP in one step. Both approaches were successfully applied to the AFM-SMFS study of eGFP, showing consistent single-molecule results.

Free-energy landscape of two-state protein acylphosphatase with large contact order revealed by force-dependent folding and unfolding dynamics

Acylphosphatase (AcP) is a small protein with 98 amino acid residues that catalyzes the hydrolysis of carboxyl-phosphate bonds. AcP is a typical two-state protein with slow folding rate due to its relatively large contact order in the native structure. The mechanical properties and unfolding behavior of AcP has been studied by atomic force microscope. Here using stable magnetic tweezers, we measured the force-dependent folding rates within a force range 1-3 pN, and unfolding rates 15-40 pN. The obtained unfolding rates show different force sensitivities at forces below and above ∼27 pN, which determines a free-energy landscape with two energy barriers. Our results indicate that the free-energy landscape of small globule proteins have general Bactrian camel shape, and large contact order of the native state produces a high barrier dominate at low forces.

Molecular homogeneity of GB1 revealed by single molecule force spectroscopy

In single molecule studies, the ergodic hypothesis is inherently assumed, which states that the time average of a physical quantity of a single member of an ensemble is the same as the average of the same quantity on the whole ensemble at a given time. This hypothesis implies the homogeneity of a molecular ensemble of a system of interest. However, it is difficult to test the validity of the ergodic hypothesis experimentally. Recent theoretical work suggested that heterogeneity may be widely present in single molecule force spectroscopy studies. Here we used atomic force microscope based single molecule force spectroscopy to examine the molecular homogeneity/heterogeneity of a small globular protein GB1 in its mechanical unfolding reaction. Using a polyprotein (GB1)₄, we directly measured the ensemble average and time average for a single molecule of the mechanical unfolding force and kinetic parameters that characterize the mechanical unfolding free energy profile of GB1. Our results showed that the ensemble averages of these physical quantities are indeed the same as the time averages for single molecules, and individual molecules did not show any differences amongst them in these physical quantities. These results are consistent with the expectation of the ergodic hypothesis and indicate that GB1 is a homogeneous molecular ensemble in its mechanical unfolding reaction on the time scale of our force spectroscopy experiments.

A loosened gating mechanism of RIG-I leads to autoimmune disorders

DDX58 encodes RIG-I, a cytosolic RNA sensor that ensures immune surveillance of nonself RNAs. Individuals with RIG-I_E510V and RIG-I_Q517H mutations have increased susceptibility to Singleton-Merten syndrome (SMS) defects, resulting in tissue-specific (mild) and classic (severe) phenotypes. The coupling between RNA recognition and conformational changes is central to RIG-I RNA proofreading, but the molecular determinants leading to dissociated disease phenotypes remain unknown. Herein, we employed hydrogen/deuterium exchange mass spectrometry (HDX-MS) and single molecule magnetic tweezers (MT) to precisely examine how subtle conformational changes in the helicase insertion domain (HEL2i) promote impaired ATPase and erroneous RNA proofreading activities. We showed that the mutations cause a loosened latch-gate engagement in apo RIG-I, which in turn gradually dampens its self RNA (Cap2 moiety:m7G cap and N_1-2-2′-O-methylation RNA) proofreading ability, leading to increased immunopathy. These results reveal HEL2i as a unique checkpoint directing two specialized functions, i.e. stabilizing the CARD2-HEL2i interface and gating the helicase from incoming self RNAs; thus, these findings add new insights into the role of HEL2i in the control of antiviral innate immunity and autoimmunity diseases.

Tug-of-War between Internal and External Frictions and Viscosity Dependence of Rate in Biological Reactions

The role of water in biological processes is studied in three reactions, namely, the Fe-CO bond rupture in myoglobin, GB1 unfolding, and insulin dimer dissociation. We compute both internal and external components of friction on relevant reaction coordinates. In all of the three cases, the cross-correlation between forces from protein and water is found to be large and negative that serves to reduce the total friction significantly, increase the calculated reaction rate, and weaken solvent viscosity dependence. The computed force spectrum reveals bimodal 1/f noise, suggesting the use of a non-Markovian rate theory.

Recent Advances and Emerging Challenges in the Molecular Modeling of Mechanobiological Processes

Many biological processes result from the effect of mechanical forces on macromolecular structures and on their interactions. In particular, the cell shape, motion, and differentiation directly depend on mechanical stimuli from the extracellular matrix or from neighboring cells. The development of experimental techniques that can measure and characterize the tiny forces acting at the cellular scale and down to the single-molecule, biomolecular level has enabled access to unprecedented details about the involved mechanisms. However, because the experimental observables often do not provide a direct atomistic picture of the corresponding phenomena, particle-based simulations performed at various scales are instrumental in complementing these experiments and in providing a molecular interpretation. Here, we will review the recent key achievements in the field, and we will highlight and discuss the many technical challenges these simulations are facing, as well as suggest future directions for improvement.

Structural features and electrostatic energy storage of electric double layers in confined polyelectrolyte solutions under low-salt conditions

Self-consistent field theory is used to systematically study the characteristics and electrostatic energy storage of electric double layers in confined polyelectrolyte solutions for salt-free and low salt concentration systems.

Two energy barriers and a transient intermediate state determine the unfolding and folding dynamics of cold shock protein

Cold shock protein (Csp) is a typical two-state folding model protein which has been widely studied by biochemistry and single molecule techniques. Recently two-state property of Csp was confirmed by atomic force microscopy (AFM) through direct pulling measurement, while several long-lifetime intermediate states were found by force-clamp AFM. We systematically studied force-dependent folding and unfolding dynamics of Csp using magnetic tweezers with intrinsic constant force capability. Here we report that Csp mostly folds and unfolds with a single step over force range from 5 pN to 50 pN, and the unfolding rates show different force sensitivities at forces below and above ~8 pN, which determines a free energy landscape with two barriers and a transient intermediate state between them along one transition pathway. Our results provide a new insight on protein folding mechanism of two-state proteins.

Molecular Fluctuations as a Ruler of Force-Induced Protein Conformations

Molecular fluctuations directly reflect the underlying energy landscape. Variance analysis examines protein dynamics in several biochemistry-driven approaches, yet measurement of probe-independent fluctuations in proteins exposed to mechanical forces remains only accessible through steered molecular dynamics simulations. Using single molecule magnetic tweezers, here we conduct variance analysis to show that individual unfolding and refolding transitions occurring in dynamic equilibrium in a single protein under force are hallmarked by a change in the protein's end-to-end fluctuations, revealing a change in protein stiffness. By unfolding and refolding three structurally distinct proteins under a wide range of constant forces, we demonstrate that the associated change in protein compliance to reach force-induced thermodynamically stable states scales with the protein's contour length increment, in agreement with the sequence-independent freely jointed chain model of polymer physics. Our findings will help elucidate the conformational dynamics of proteins exposed to mechanical force at high resolution which are of central importance in mechanosensing and mechanotransduction.