Heterogeneity of Equilibrium Molten Globule State of Cytochrome c Induced by Weak Salt Denaturants under Physiological Condition

While many proteins are recognized to undergo folding via intermediate(s), the heterogeneity of equilibrium folding intermediate(s) along the folding pathway is less understood. In our present study, FTIR spectroscopy, far- and near-UV circular dichroism (CD), ANS and tryptophan fluorescence, near IR absorbance spectroscopy and dynamic light scattering (DLS) were used to study the structural and thermodynamic characteristics of the native (N), denatured (D) and intermediate state (X) of goat cytochorme c (cyt-c) induced by weak salt denaturants (LiBr, LiCl and LiClO₄) at pH 6.0 and 25°C. The LiBr-induced denaturation of cyt-c measured by Soret absorption (Δε ₄₀₀) and CD ([θ]₄₀₉), is a three-step process, N ↔ X ↔ D. It is observed that the X state obtained along the denaturation pathway of cyt-c possesses common structural and thermodynamic characteristics of the molten globule (MG) state. The MG state of cyt-c induced by LiBr is compared for its structural and thermodynamic parameters with those found in other solvent conditions such as LiCl, LiClO₄ and acidic pH. Our observations suggest: (1) that the LiBr-induced MG state of cyt-c retains the native Met80-Fe(III) axial bond and Trp59-propionate interactions; (2) that LiBr-induced MG state of cyt-c is more compact retaining the hydrophobic interactions in comparison to the MG states induced by LiCl, LiClO₄ and 0.5 M NaCl at pH 2.0; and (3) that there exists heterogeneity of equilibrium intermediates along the unfolding pathway of cyt-c as highly ordered (X1), classical (X2) and disordered (X3), i.e., D ↔ X3 ↔ X2 ↔ X1 ↔ N.     

Insight into the Unfolding Properties of Chd64, a Small,Single Domain Protein with a Globular Core and Disordered Tails

Two major lipophilic hormones, 20-hydroxyecdysone (20E) and juvenile hormone (JH), govern insect development and growth. While the mode of action of 20E is well understood, some understanding of JH-dependent signalling has been attained only in the past few years, and the crosstalk of the two hormonal pathways remains unknown. Two proteins, the calponin-like Chd64 and immunophilin FKBP39 proteins, have recently been found to play pivotal roles in the formation of dynamic, multiprotein complex that cross-links these two signalling pathways. However, the molecular mechanism of the interaction remains unexplored. The aim of this work was to determine structural elements of Chd64 to provide an understanding of molecular basis of multiple interactions. We analysed Chd64 in two unrelated insect species, Drosophila melanogaster (DmChd64) and Tribolium castaneum (TcChd64). Using hydrogen-deuterium exchange mass spectrometry (HDX-MS), we showed that both Chd64 proteins have disordered tails that outflank the globular core. The folds of the globular cores of both Chd64 resemble the calponin homology (CH) domain previously resolved by crystallography. Monitoring the unfolding of DmChd64 and TcChd64 by far-ultraviolet (UV) circular dichroism (CD) spectroscopy, fluorescence spectroscopy and size-exclusion chromatography (SEC) revealed a highly complex process. Chd64 unfolds and forms of a molten globule (MG)—like intermediate state. Furthermore, our data indicate that in some conditions, Chd64 may exists in discrete structural forms, indicating that the protein is pliable and capable of easily acquiring different conformations. The plasticity of Chd64 and the existence of terminal intrinsically disordered regions (IDRs) may be crucial for multiple interactions with many partners.     

Revisiting absorbance at 230 nm as a protein unfolding probe

Thermodynamic stability and unfolding kinetics of proteins are typically determined by monitoring protein unfolding with spectroscopic probes, such as circular dichroism (CD) and fluorescence. UV absorbance at 230 nm (A₂₃₀) is also known to be sensitive to protein conformation. However, its feasibility for quantitative analysis of protein energetics has not been assessed. Here we evaluate A₂₃₀ as a structural probe to determine thermodynamic stability and unfolding kinetics of proteins. By using Escherichia coli maltose binding protein (MBP) and E. coli ribonuclease H (RNase H) as our model proteins, we monitored their unfolding in urea and guanidinium chloride with A₂₃₀. Significant changes in A₂₃₀ were observed with both proteins on unfolding in the chemical denaturants. The global stabilities were successfully determined by measuring the change in A₂₃₀ in varying concentrations of denaturants. Also, unfolding kinetics was investigated by monitoring the change in A₂₃₀ under denaturing conditions. The results were quite consistent with those determined by CD. Unlike CD, A₂₃₀ allowed us to monitor protein unfolding in a 96-well microtiter plate with a UV plate reader. Our finding suggests that A₂₃₀ is a valid and convenient structural probe to determine thermodynamic stability and unfolding kinetics of proteins with many potential applications.     

Polymorphism and distribution of putative cell-surface adhesin-encoding ORFs among human fecal isolates of Bifidobacterium longum subsp. longum

The polymorphism of ORFs encoding putative cell-surface adhesins was investigated in Bifidobacterium longum subsp. longum. Firstly, we performed a PCR assay targeting 15 ORFs encoding putative adhesion proteins, which included 8 ORFs with a sortase targeting LPXTG motif, in 42 strains of different pulsotypes isolated from fecal samples from 12 human individuals. We found a variability in the presence of an ORF, BL0675, which encodes a putative fimbrial subunit protein. We sequenced ORFs corresponding to BL0675 in the 42 strains and adjacent ORFs corresponding to BL0674 and BL0676. The results indicated that ORFs corresponding to BL0675 were highly polymorphic with five variant types (i.e. A-, B-, C-, D-, and E-types). Meanwhile, BL0674 and BL0676, which encode an additional putative fimbrial subunit protein and a fimbrial-associated sortase-like protein, were highly conserved. Subsequent quantitative polymerase chain reaction (qPCR) assays targeting the variant types in 89 human fecal samples revealed that A-type was the most commonly distributed (74.2%), followed by B-type (59.6%), D-type (31.5%), E-type (32.6%) and C-type (5.6% prevalence). Since BL0675 is considered to be a fimbrial protein with glycoprotein-binding ability, the proteins encoded by the five variant types of BL0675 may have specific binding properties to various carbohydrate structures expressed on the human intestinal wall, thereby allowing B. longum to colonize the intestine in a host-specific manner.     

Characterization of the temperature- and pressure-induced inverse and reentrant transition of the minimum elastin-like polypeptide GVG(VPGVG) by DSC, PPC, CD, and FT-IR spectroscopy

We investigated the temperature- and pressure-dependent structure and phase behavior of a solvated oligopeptide, GVG(VPGVG), which serves as a minimalistic elastin-like model system, over a large region of the thermodynamic phase field, ranging from 2 to 120°C and from ambient pressure up to ~10 kbar, applying various spectroscopic (CD, FT-IR) and thermodynamic (DSC, PPC) measurements. We find that this octapeptide behaves as a two-state system which undergoes the well-known inverse-temperature folding transition occurring at T ≈ 36°C, and, in addition, a slow trend reversal at higher temperatures, finally leading to a reentrant unfolding close to the boiling point of water. Furthermore, the pressure-dependence of the folding/unfolding transition was studied to yield a more complete picture of the p, T-stability diagram of the system. A molecular-level picture of these processes, in particular on the role of water for the folding and unfolding events of the peptide, presented with the help of molecular-dynamics simulations, is presented in a companion article in this issue.     

Without Salt,the ‘Thermophilic’ Protein Mth10b Is Just Mesophilic

Most proteins from thermophiles or hyperthermophiles are intrinsically thermostable. However, though Methanobacterium thermoautotrophicum ΔH is a thermophilic archaeon with an optimal growth temperature of 65°C, Mth10b, an atypical member the Sac10b protein family from M. thermoautotrophicum ΔH, seems not intrinsically thermostable. In this work, to clarify the molecular mechanism of Mth10b remaining stable under its physiological conditions, the thermodynamic properties of Mth10b were studied through equilibrium unfolding experiments performed at pH 7.0 monitored by circular dichroism (CD) spectra in detail. Our work demonstrated that Mth10b is not intrinsically thermostable and that due to the masking effect upon the large numbers of destabilizing electrostatic repulsions resulting from the extremely uneven distribution of charged residues over the surface of Mth10b, salt can contribute to the thermostability of Mth10b greatly. Considering that the intracellular salt concentration is high to 0.7 M, we concluded that salt is the key extrinsic factor to Mth10b remaining stable under its physiological conditions. In other word, without salt, ‘thermophilic’ protein Mth10b is just a mesophilic one.     

Mapping Transient Partial Unfolding by Protein Engineering and Native-State Proteolysis

Transient partial unfolding of proteins under native conditions may have significant consequences in the biochemical and biophysical properties of proteins. Native-state proteolysis offers a facile way to investigate the thermodynamic and kinetic accessibilities of partially unfolded forms (cleavable forms) under native conditions. However, determination of the structure of the cleavable form, which is populated only transiently, remains challenging. Although in some cases partially cleaved products from proteolysis provide information on the structure of this elusive form, proteolysis of many proteins does not accumulate detectable intermediates. Here, we describe a systematic approach to determining structures of cleavable forms by protein engineering and native-state proteolysis. By devising φ_c analysis, which is analogous to conventional φ analysis, we have determined the structure of the cleavable form of Escherichia coli maltose-binding protein (MBP), which does not accumulate any partially cleaved products. We mutated 10 buried residues in MBP to alanine and determined φ_c values from the effects of the mutations on global stability and proteolytic susceptibility. The result of this analysis suggests that two C-terminal helices in MBP are unfolded in their cleavable form. The effect of ligand binding on proteolytic susceptibility and C-terminal deletion mutations also confirms the proposed structure. Our approach and methodology are generally applicable not only in elucidating the mechanism of proteolysis but also in investigating other important processes involving partial unfolding under native conditions such as protein misfolding and aggregation.     

Can non-mechanical proteins withstand force? Stretching barnase by atomic force microscopy and molecular dynamics simulation

Atomic force microscopy (AFM) experiments have provided intriguing insights into the mechanical unfolding of proteins such as titin I27 from muscle, but will the same be possible for proteins that are not physiologically required to resist force? We report the results of AFM experiments on the forced unfolding of barnase in a chimeric construct with I27. Both modules are independently folded and stable in this construct and have the same thermodynamic and kinetic properties as the isolated proteins. I27 can be identified in the AFM traces based on its previous characterization, and distinct, irregular low-force peaks are observed for barnase. Molecular dynamics simulations of barnase unfolding also show that it unfolds at lower forces than proteins with mechanical function. The unfolding pathway involves the unraveling of the protein from the termini, with much more native-like secondary and tertiary structure being retained in the transition state than is observed in simulations of thermal unfolding or experimentally, using chemical denaturant. Our results suggest that proteins that are not selected for tensile strength may not resist force in the same way as those that are, and that proteins with similar unfolding rates in solution need not have comparable unfolding properties under force.     

Direct observation of the temperature-induced melting process of the Salmonella fourU RNA thermometer at base-pair resolution

In prokaryotes, RNA thermometers regulate a number of heat shock and virulence genes. These temperature sensitive RNA elements are usually located in the 5′-untranslated regions of the regulated genes. They repress translation initiation by base pairing to the Shine–Dalgarno sequence at low temperatures. We investigated the thermodynamic stability of the temperature labile hairpin 2 of the Salmonella fourU RNA thermometer over a broad temperature range and determined free energy, enthalpy and entropy values for the base-pair opening of individual nucleobases by measuring the temperature dependence of the imino proton exchange rates via NMR spectroscopy. Exchange rates were analyzed for the wild-type (wt) RNA and the A8C mutant. The wt RNA was found to be stabilized by the extraordinarily stable G14–C25 base pair. The mismatch base pair in the wt RNA thermometer (A8–G31) is responsible for the smaller cooperativity of the unfolding transition in the wt RNA. Enthalpy and entropy values for the base-pair opening events exhibit linear correlation for both RNAs. The slopes of these correlations coincide with the melting points of the RNAs determined by CD spectroscopy. RNA unfolding occurs at a temperature where all nucleobases have equal thermodynamic stabilities. Our results are in agreement with a consecutive zipper-type unfolding mechanism in which the stacking interaction is responsible for the observed cooperativity. Furthermore, remote effects of the A8C mutation affecting the stability of nucleobase G14 could be identified. According to our analysis we deduce that this effect is most probably transduced via the hydration shell of the RNA.     

Sequential Unfolding of Beta Helical Protein by Single-Molecule Atomic Force Microscopy

The parallel βhelix is a common fold among extracellular proteins, however its mechanical properties remain unexplored. In Gram-negative bacteria, extracellular proteins of diverse functions of the large ‘TpsA’ family all fold into long βhelices. Here, single-molecule atomic force microscopy and steered molecular dynamics simulations were combined to investigate the mechanical properties of a prototypic TpsA protein, FHA, the major adhesin of Bordetella pertussis. Strong extension forces were required to fully unfold this highly repetitive protein, and unfolding occurred along a stepwise, hierarchical process. Our analyses showed that the extremities of the βhelix unfold early, while central regions of the helix are more resistant to mechanical unfolding. In particular, a mechanically resistant subdomain conserved among TpsA proteins and critical for secretion was identified. This nucleus harbors structural elements packed against the βhelix that might contribute to stabilizing the N-terminal region of FHA. Hierarchical unfolding of the βhelix in response to a mechanical stress may maintain β-helical portions that can serve as templates for regaining the native structure after stress. The mechanical properties uncovered here might apply to many proteins with β-helical or related folds, both in prokaryotes and in eukaryotes, and play key roles in their structural integrity and functions.     

Decoding Structural Properties of a Partially Unfolded Protein Substrate: En Route to Chaperone Binding

Many proteins comprising of complex topologies require molecular chaperones to achieve their unique three-dimensional folded structure. The E.coli chaperone, GroEL binds with a large number of unfolded and partially folded proteins, to facilitate proper folding and prevent misfolding and aggregation. Although the major structural components of GroEL are well defined, scaffolds of the non-native substrates that determine chaperone-mediated folding have been difficult to recognize. Here we performed all-atomistic and replica-exchange molecular dynamics simulations to dissect non-native ensemble of an obligate GroEL folder, DapA. Thermodynamics analyses of unfolding simulations revealed populated intermediates with distinct structural characteristics. We found that surface exposed hydrophobic patches are significantly increased, primarily contributed from native and non-native β-sheet elements. We validate the structural properties of these conformers using experimental data, including circular dichroism (CD), 1-anilinonaphthalene-8-sulfonic acid (ANS) binding measurements and previously reported hydrogen-deutrium exchange coupled to mass spectrometry (HDX-MS). Further, we constructed network graphs to elucidate long-range intra-protein connectivity of native and intermediate topologies, demonstrating regions that serve as central “hubs”. Overall, our results implicate that genomic variations (or mutations) in the distinct regions of protein structures might disrupt these topological signatures disabling chaperone-mediated folding, leading to formation of aggregates.     

Effects of Ligand Binding on the Mechanical Properties of Ankyrin Repeat Protein Gankyrin

Ankyrin repeat proteins are elastic materials that unfold and refold sequentially, repeat by repeat, under force. Herein we use atomistic molecular dynamics to compare the mechanical properties of the 7-ankyrin-repeat oncoprotein Gankyrin in isolation and in complex with its binding partner S6-C. We show that the bound S6-C greatly increases the resistance of Gankyrin to mechanical stress. The effect is specific to those repeats of Gankyrin directly in contact with S6-C, and the mechanical ‘hot spots’ of the interaction map to the same repeats as the thermodynamic hot spots. A consequence of stepwise nature of unfolding and the localized nature of ligand binding is that it impacts on all aspects of the protein''s mechanical behavior, including the order of repeat unfolding, the diversity of unfolding pathways accessed, the nature of partially unfolded intermediates, the forces required and the work transferred to the system to unfold the whole protein and its parts. Stepwise unfolding thus provides the means to buffer repeat proteins and their binding partners from mechanical stress in the cell. Our results illustrate how ligand binding can control the mechanical response of proteins. The data also point to a cellular mechano-switching mechanism whereby binding between two partner macromolecules is regulated by mechanical stress.     

Differential chemical and thermal unfolding pattern of Rv3588c and Rv1284 of Mycobacterium tuberculosis — A comparison by fluorescence and circular dichroism spectroscopy

The thermal and chemical unfolding pathways of two β carbonic anhydrases, Rv3588c and Rv1284 of Mycobacterium tuberculosis have been compared by fluorescence and circular dichroism. Chemical and thermal denaturation of the tertiary and secondary structures of these two ubiquitous enzymes of the pathogen reveals that the unfolding of Rv3588c is mediated through the formation of a molten globule intermediate with depleted tertiary structure. However, Rv1284 directly unfolds from the native to the unfolded state. Calculation of the thermodynamic parameters suggest that overall Rv3588c is more stable than Rv1284. Stern–Volmer analysis together with the fluorescence spectra of the proteins suggest that Trp115 in Rv1284 is more buried than Trp10 in Rv3588c. The tryptophan residues in both the proteins are surrounded by positively charged amino acid residues.     

Methionine Mutations of Outer Membrane Protein X Influence Structural Stability and Beta-Barrel Unfolding

We report the biochemical and biophysical characterization of outer membrane protein X (OmpX), an eight-stranded transmembrane β-barrel from E. coli, and compare the barrel behavior with a mutant devoid of methionine residues. Transmembrane outer membrane proteins of bacterial origin are known to display high tolerance to sequence rearrangements and mutations. Our studies with the triple mutant of OmpX that is devoid of all internal methionine residues (M18L; M21L; M118L) indicate that Met replacement has no influence on the refolding efficiency and structural characteristics of the protein. Surprisingly, the conserved substitution of Met→Leu leads to barrel destabilization and causes a lowering of the unfolding free energy by a factor of ∼8.5 kJ/mol, despite the mutations occurring at the loop regions. We report that the barrel destabilization is accompanied by a loss in cooperativity of unfolding in the presence of chemical denaturants. Furthermore, we are able to detect an unfolding intermediate in the Met-less barrel, whereas the parent protein exhibits a classic two-state unfolding. Thermal denaturation measurements also suggest a greater susceptibility of the OmpX barrel to heat, in the Met-less construct. Our studies reveal that even subtle variations in the extra-membrane region of rigid barrel structures such as OmpX, may bear severe implications on barrel stability. We propose that methionines contribute to efficient barrel structuring and protein-lipid interactions, and are therefore important elements of OmpX stability.     

Kinetic Control in Protein Folding for Light Chain Amyloidosis and the Differential Effects of Somatic Mutations

Light chain amyloidosis is a devastating disease where immunoglobulin light chains form amyloid fibrils, resulting in organ dysfunction and death. Previous studies have shown a direct correlation between the protein thermodynamic stability and the propensity for amyloid formation for some proteins involved in light chain amyloidosis. Here we investigate the effect of somatic mutations on protein stability and in vitro fibril formation of single and double restorative mutants of the protein AL-103 compared to the wild-type germline control protein. A scan rate dependence and hysteresis in the thermal unfolding and refolding was observed for all proteins. This indicates that the unfolding/refolding reaction is kinetically determined with different kinetic constants for unfolding and refolding even though the process remains experimentally reversible. Our structural analysis of AL-103 and AL-103 delP95aIns suggests a kinetic coupling of the unfolding/refolding process with cis–trans prolyl isomerization. Our data reveal that the deletion of proline 95a (AL-103 delP95aIns), which removes the trans–cis di-proline motif present in the patient protein AL-103, results in a dramatic increment in the thermodynamic stability and a significant delay in fibril formation kinetics with respect to AL-103. Fibril formation is pH dependent; all proteins form fibrils at pH 2; reactions become slower and more stochastic as the pH increases up to pH 7. Based on these results, we propose that, in addition to thermodynamic stability, kinetic stability (possibly influenced by the presence of cis proline 95a) plays a major role in the AL-103 amyloid fibril formation process.     

Dynameomics: A Consensus View of the Protein Unfolding/Folding Transition State Ensemble across a Diverse Set of Protein Folds

The Dynameomics project aims to simulate a representative sample of all globular protein metafolds under both native and unfolding conditions. We have identified protein unfolding transition state (TS) ensembles from multiple molecular dynamics simulations of high-temperature unfolding in 183 structurally distinct proteins. These data can be used to study individual proteins and individual protein metafolds and to mine for TS structural features common across all proteins. Separating the TS structures into four different fold classes (all proteins, all-α, all-β, and mixed α/β and α + β) resulted in no significant difference in the overall protein properties. The residues with the most contacts in the native state lost the most contacts in the TS ensemble. On average, residues beginning in an α-helix maintained more structure in the TS ensemble than did residues starting in β-strands or any other conformation. The metafolds studied here represent 67% of all known protein structures, and this is, to our knowledge, the largest, most comprehensive study of the protein folding/unfolding TS ensemble to date. One might have expected broad distributions in the average global properties of the TS relative to the native state, indicating variability in the amount of structure present in the TS. Instead, the average global properties converged with low standard deviations across metafolds, suggesting that there are general rules governing the structure and properties of the TS.     

Fast and Forceful Refolding of Stretched α-Helical Solenoid Proteins

Anfinsen's thermodynamic hypothesis implies that proteins can encode for stretching through reversible loss of structure. However, large in vitro extensions of proteins that occur through a progressive unfolding of their domains typically dissipate a significant amount of energy, and therefore are not thermodynamically reversible. Some coiled-coil proteins have been found to stretch nearly reversibly, although their extension is typically limited to 2.5 times their folded length. Here, we report investigations on the mechanical properties of individual molecules of ankyrin-R, β-catenin, and clathrin, which are representative examples of over 800 predicted human proteins composed of tightly packed α-helical repeats (termed ANK, ARM, or HEAT repeats, respectively) that form spiral-shaped protein domains. Using atomic force spectroscopy, we find that these polypeptides possess unprecedented stretch ratios on the order of 10-15, exceeding that of other proteins studied so far, and their extension and relaxation occurs with minimal energy dissipation. Their sequence-encoded elasticity is governed by stepwise unfolding of small repeats, which upon relaxation of the stretching force rapidly and forcefully refold, minimizing the hysteresis between the stretching and relaxing parts of the cycle. Thus, we identify a new class of proteins that behave as highly reversible nanosprings that have the potential to function as mechanosensors in cells and as building blocks in springy nanostructures. Our physical view of the protein component of cells as being comprised of predominantly inextensible structural elements under tension may need revision to incorporate springs.     

Using an amino acid fluorescence resonance energy transfer pair to probe protein unfolding: application to the villin headpiece subdomain and the LysM domain

Previously, we have shown that p-cyanophenylalanine (Phe CN) and tryptophan (Trp) constitute an efficient fluorescence resonance energy transfer (FRET) pair that has several advantages over commonly used dye pairs. Here, we aim to examine the general applicability of this FRET pair in protein folding-unfolding studies by applying it to the urea-induced unfolding transitions of two small proteins, the villin headpiece subdomain (HP35) and the lysin motif (LysM) domain. Depending on whether Phe CN is exposed to solvent, we are able to extract either qualitative information about the folding pathway, as demonstrated by HP35, which has been suggested to unfold in a stepwise manner, or quantitative thermodynamic and structural information, as demonstrated by LysM, which has been shown to be an ideal two-state folder. Our results show that the unfolding transition of HP35 reported by FRET occurs at a denaturant concentration lower than that measured by circular dichroism (CD) and that the loop linking helix 2 and helix 3 remains compact in the denatured state, which are consistent with the notion that HP35 unfolds in discrete steps and that its unfolded state contains residual structures. On the other hand, our FRET results on the LysM domain allow us to develop a model for extracting structural and thermodynamic parameters about its unfolding, and we find that our results are in agreement with those obtained by other methods. Given the fact that Phe CN is a non-natural amino acid and, thus, amenable to incorporation into peptides and proteins via existing peptide synthesis and protein expression methods, we believe that the FRET method demonstrated here is widely applicable to protein conformational studies, especially to the study of relatively small proteins.     

Ligand-Induced Changes of the Apparent Transition-State Position in?Mechanical Protein Unfolding

Force-spectroscopic measurements of ligand-receptor systems and the unfolding/folding of nucleic acids or proteins reveal information on the underlying energy landscape along the pulling coordinate. The slope Δx^‡ of the force-dependent unfolding/unbinding rates is interpreted as the distance from the folded/bound state to the transition state for unfolding/unbinding and, hence, often related to the mechanical compliance of the sample molecule. Here we show that in ligand-binding proteins, the experimentally inferred Δx^‡ can depend on the ligand concentration, unrelated to changes in mechanical compliance. We describe the effect in single-molecule, force-spectroscopy experiments of the calcium-binding protein calmodulin and explain it in a simple model where mechanical unfolding and ligand binding occur on orthogonal reaction coordinates. This model predicts changes in the experimentally inferred Δx^‡, depending on ligand concentration and the associated shift of the dominant barrier between the two reaction coordinates. We demonstrate quantitative agreement between experiments and simulations using a realistic six-state kinetic scheme using literature values for calcium-binding kinetics and affinities. Our results have important consequences for the interpretation of force-spectroscopic data of ligand-binding proteins.