Stopped-flow Fluorescence Experiments Research Articles

The cooperative folding of annexin A2 relies on a transient nonnative intermediate

Annexins (Anxs) are a family of highly homologous proteins that bind and aggregate lipid vesicles in the presence of calcium. All members of the family contain a variable N-terminus determining specific functions, followed by a conserved core region responsible for the general calcium-dependent lipid-binding property. The core structure consists of four homologous domains (DI–DIV), each consisting of a right-handed super-helix of five α-helices. We present data from a combination of site-directed mutagenesis, NMR, and circular dichroism showing that the G25–D34 region of the N-terminus as well as the contacts between residues D38A, R63A, and Q67A of AnxA2-DI are crucial for the autonomous folding and stability of DI of AnxA2. However, we also show that the folding of the full-length protein is very robust in that mutations and truncations that disrupted the folding of AnxA2-DI did not abolish the folding of full-length AnxA2, only lowering its thermal stability. This robustness of the folding of full-length AnxA2 is likely to be mediated by the existence of at least one transient nonnative intermediate as suggested by our kinetic data using stopped-flow fluorescence experiments. We also show that hydrophobic amino acids in AnxA2-DI involved in interfacial contacts with AnxA2-DIV are important for the cooperative folding and stability of the full-length protein. Mutating all of the V57E-V98R-G101Y residues in AnxA2-DI did not affect the folding of the domain, only its stability, but prevented the cooperative folding of the full-length protein. Our collective results favor a highly cooperative and robust folding process mediated by alternative intermediate steps. Since AnxA2 is a multifunctional protein involved in several steps of the progression of cell transformation, these data on structure and folding pathways are therefore crucial to designing anticancer drugs targeting AnxA2.

Examination of the Role of Mg2+ in the Mechanism of Nucleotide Binding to the Monomeric YME1L AAA+ Domain.

The first line of defense in the mitochondrial quality control network involves the stress response from a family of ATP-dependent proteases. We have reported that a solubilized version of the mitochondrial inner membrane ATP-dependent protease YME1L displays nucleotide binding kinetics that are sensitive to the reactive oxygen species hydrogen peroxide under a limiting ATP concentration. Our observations were consistent with an altered YME1L conformational ensemble leading to increased nucleotide binding site accessibility under oxidative stress conditions. To examine this hypothesis further, we report here the results of a comprehensive study of the thermodynamic and kinetic properties underlying the binding of nucleoside di- and triphosphate to the isolated YME1L AAA+ domain (YME1L-AAA+). A combination of fluorescence titrations, molecular dynamics, and stopped-flow fluorescence experiments have demonstrated similarity between nucleotide binding behaviors for YME1L under oxidative conditions and the isolated AAA+ domain. Our data demonstrate that YME1L-AAA+ binds ATP and ADP with affinities equal to ∼30 and 5 μM, respectively, in the absence of Mg2+. We note a negative heterotropic linkage effect between Mg2+ and ATP that arises as the MgCl2 concentration is increased such that the affinity of YME1L-AAA+ for ATP decreases to ∼60 μM in the presence of 10 mM MgCl2. Molecular dynamics methods allow for structural rationalization by revealing condition-dependent conformational populations for YME1L-AAA+. Taken together, these data suggest a preliminary model in which YME1L modulates its affinity for the nucleotide to stabilize against degradation or instability inherent to such stress conditions.

Diversity of Long-Lived Intermediates along the Binding Pathway of Imatinib to Abl Kinase Revealed by MD Simulations.

Imatinib, a drug used for the treatment of chronic myeloid leukemia and other cancers, works by blocking the catalytic site of pathological constitutively active Abl kinase. While the binding pose is known from X-ray crystallography, the different steps leading to the formation of the complex are not well understood. The results from extensive molecular dynamics simulations show that imatinib can primarily exit the known crystallographic binding pose through the cleft of the binding site or by sliding under the αC helix. Once displaced from the crystallographic binding pose, imatinib becomes trapped in intermediate states. These intermediates are characterized by a high diversity of ligand orientations and conformations, and relaxation timescales within this region may exceed 3-4 ms. Analysis indicates that the metastable intermediate states should be spectroscopically indistinguishable from the crystallographic binding pose, in agreement with tryptophan stopped-flow fluorescence experiments.

Fluorescence Methods Applied to the Description of Urea-Dependent YME1L Protease Unfolding.

ATP-dependent proteases are ubiquitous across all kingdoms of life and are critical to the maintenance of intracellular protein quality control. The enzymatic function of these enzymes requires structural stability under conditions that may drive instability and/or loss of function in potential protein substrates. Thus, these molecular machines must demonstrate greater stability than their substrates in order to ensure continued function in essential quality control networks. We report here a role for ATP in the stabilization of the inner membrane YME1L protease. Qualitative fluorescence data derived from protein unfolding experiments with urea reveal non-standard protein unfolding behavior that is dependent on [ATP]. Using multiple fluorophore systems, stopped-flow fluorescence experiments demonstrate a depletion of the native YME1L ensemble by urea-dependent unfolding and formation of a non-native conformation. Additional stopped-flow fluorescence experiments based on nucleotide binding and unfoldase activities predict that unfolding yields significant loss of active YME1L hexamers from the starting ensemble. Taken together, these data clearly define the stress limits of an important mitochondrial protease.

New insights into the membrane association mechanism of the glycosyltransferase WaaG from Escherichia coli

Monotopic glycosyltransferases (GTs) interact with membranes via electrostatic interactions. The N-terminal domain is permanently anchored to the membrane while the membrane interaction of the C-terminal domain is believed to be weaker so that it undergoes a functionally relevant conformational change upon donor or acceptor binding. Here, we studied the applicability of this model to the glycosyltransferase WaaG. WaaG is involved in the synthesis of lipopolysaccharides (LPS) in Gram-negative bacteria and was previously categorized as a monotopic GT. We analyzed the binding of WaaG to membranes by stopped-flow fluorescence and NMR diffusion experiments. We find that electrostatic interactions are required to bind WaaG to membranes while mere hydrophobic interactions are not sufficient. WaaG senses the membrane's surface charge density but there is no preferential binding to specific anionic lipids. However, the binding is weaker than expected for monotopic GTs but similar to peripheral GTs. Therefore, WaaG may be a peripheral GT and this could be of functional relevance in vivo since LPS synthesis occurs only when WaaG is membrane-bound. We could not observe a C-terminal domain movement under our experimental conditions.

Formation of Tertiary Interactions during rRNA GTPase Center Folding

The 60-nt GTPase center (GAC) of 23S rRNA has a phylogenetically conserved secondary structure with two hairpin loops and a 3-way junction. It folds into an intricate tertiary structure upon addition of Mg2+ ions, which is stabilized by the L11 protein in cocrystal structures. Here, we monitor the kinetics of its tertiary folding and Mg2+-dependent intermediate states by observing selected nucleobases that contribute specific interactions to the GAC tertiary structure in the cocrystals. The fluorescent nucleobase 2-aminopurine replaced three individual adenines, two of which make long-range stacking interactions and one that also forms hydrogen bonds. Each site reveals a unique response to Mg2+ addition and temperature, reflecting its environmental change from secondary to tertiary structure. Stopped-flow fluorescence experiments revealed that kinetics of tertiary structure formation upon addition of MgCl2 are also site specific, with local conformational changes occurring from 5ms to 4s and with global folding from 1 to 5s. Site-specific substitution with 15N-nucleobases allowed observation of stable hydrogen bond formation by NMR experiments. Equilibrium titration experiments indicate that a stable folding intermediate is present at stoichiometric concentrations of Mg2+ and suggest that there are two initial sites of Mg2+ ion association.

Phenanthroline bridged bis(β-cyclodextrin)s/adamantane-carboxylic acid supramolecular complex as an efficient fluorescence sensor to Zn2+

A water-soluble fluorescent Zn2+ sensor, 1,10-phenanthroline bridged bis(β-cyclodextrin) (1), was synthesized by “click chemistry”, and its fluorescence sensing behavior toward Zn2+ against various metal ions was investigated under physiological conditions. Significantly, 1 showed high selectivity and sensitivity toward Zn2+ with a limit of detection (LOD) down to 10−7 M. Moreover, the spectrophotometric studies demonstrated that after complexation with 1-admantanecarboxylic acid sodium salt (AdCA), the 1/AdCA complex gave much stronger binding affinity and lower LOD value toward Zn2+ through a cyclodextrin/substrate/Zn2+ triple recognition mode. The fluorescence stopped-flow experiments also indicated that the association rate of complex 1/AdCA to Zn2+ was much faster than compound 1 to the same ion. Furthermore, the fluorescence intensity of 1 and 1/AdCA was greatly enhanced after binding Zn2+ in living cells, and thus 1 and complex 1/AdCA could be considered as a biosensor for Zn2+ at the cellular level.

Dynamic Association and Dissociation of the Tumor Supressor PTEN to Model Membranes

The tumor suppressor gene, Phosphatase and tensin homolog deleted on chromosome 10 (PTEN) encodes a 403-amino acid protein that is mutated or deleted in a variety of human cancers. It binds to the plasma membrane to dephosphorylate the 3-position of phosphatidylinositol-3,4,5-trisphosphate producing phosphatidylinositol-4,5-bisphosphate (PI[4,5]P2). PTEN is an agonist to PI 3-Kinase, thereby inhibiting the PI3K/Akt signaling pathway and controlling cell proliferation and survival. PTEN membrane association depends strongly on the composition and lateral distribution of the lipids in the membrane. Using kinetic methods, we aim to examine this multi-step process. Stopped-flow and steady state fluorescence experiments support our hypothesis that the association ofPTEN to the plasma membrane is synergistic; depending on both electrostatic interactions between the protein and anionic lipids like phosphatidylserine (PS) as well as specific binding to PI(4,5)P2 to form a stable protein-membrane complex. In addition, our results suggest that other lipids found in the inner leaflet of the plasma membrane might participate in PTEN binding.Furthermore, we use single molecule TIRF microscopy to determine the membrane binding and lateral diffusion constant of wtPTEN on supported lipid bilayers with differing lipid compositions. The information gained from these two techniques describes the dynamic and equilibrium behavior of wtPTEN binding to various binary and tertiary lipid compositions.

Generation of a stable, aminotyrosyl radical-induced α2β2 complex of Escherichia coli class Ia ribonucleotide reductase

Ribonucleotide reductase (RNR) catalyzes the conversion of nucleoside diphosphates to deoxynucleoside diphosphates (dNDPs). The Escherichia coli class Ia RNR uses a mechanism of radical propagation by which a cysteine in the active site of the RNR large (α2) subunit is transiently oxidized by a stable tyrosyl radical (Y•) in the RNR small (β2) subunit over a 35-Å pathway of redox-active amino acids: Y122• ↔ [W48?] ↔ Y356 in β2 to Y731 ↔ Y730 ↔ C439 in α2. When 3-aminotyrosine (NH2Y) is incorporated in place of Y730, a long-lived NH2Y730• is generated in α2 in the presence of wild-type (wt)-β2, substrate, and effector. This radical intermediate is chemically and kinetically competent to generate dNDPs. Herein, evidence is presented that NH2Y730• induces formation of a kinetically stable α2β2 complex. Under conditions that generate NH2Y730•, binding between Y730NH2Y-α2 and wt-β2 is 25-fold tighter (Kd = 7 nM) than for wt-α2

Kinetics of α-Globin Binding to α-Hemoglobin Stabilizing Protein (AHSP) Indicate Preferential Stabilization of Hemichrome Folding Intermediate

Human α-hemoglobin stabilizing protein (AHSP) is a conserved mammalian erythroid protein that facilitates the production of Hemoglobin A by stabilizing free α-globin. AHSP rapidly binds to ferrous α with association (k'(AHSP)) and dissociation (k(AHSP)) rate constants of ≈10 μm(-1) s(-1) and 0.2 s(-1), respectively, at pH 7.4 at 22 °C. A small slow phase was observed when AHSP binds to excess ferrous αCO. This slow phase appears to be due to cis to trans prolyl isomerization of the Asp(29)-Pro(30) peptide bond in wild-type AHSP because it was absent when αCO was mixed with P30A and P30W AHSP, which are fixed in the trans conformation. This slow phase was also absent when met(Fe(3+))-α reacted with wild-type AHSP, suggesting that met-α is capable of rapidly binding to either Pro(30) conformer. Both wild-type and Pro(30)-substituted AHSPs drive the formation of a met-α hemichrome conformation following binding to either met- or oxy(Fe(2+))-α. The dissociation rate of the met-α·AHSP complex (k(AHSP) ≈ 0.002 s(-1)) is ∼100-fold slower than that for ferrous α·AHSP complexes, resulting in a much higher affinity of AHSP for met-α. Thus, in vivo, AHSP acts as a molecular chaperone by rapidly binding and stabilizing met-α hemichrome folding intermediates. The low rate of met-α dissociation also allows AHSP to have a quality control function by kinetically trapping ferric α and preventing its incorporation into less stable mixed valence Hemoglobin A tetramers. Reduction of AHSP-bound met-α allows more rapid release to β subunits to form stable fully, reduced hemoglobin dimers and tetramers.

Structural and Dynamical Insights into the Molten-Globule Form of Ovalbumin

Ovalbumin is a 45 kDa egg-white glycoprotein which belongs to the class of serpin superfamily. We have studied the structural properties of both native and partially unfolded molten-globule forms of ovalbumin using a diverse array of spectroscopic tools. Time-resolved fluorescence measurements provided important structural and dynamical insights into the native and molten-globule states. Fluorescence anisotropy decay analysis indicated that there is a conformational swelling from the native to the molten-globule form of ovalbumin. We have also carried out red-edge excitation shift measurements to probe the dipolar relaxation dynamics around the intrinsic tryptophan residues. Additionally, stopped-flow fluorescence experiments revealed that the conformational transition from the native to the molten-globule form proceeds in a stepwise manner involving a burst-phase with a submillisecond conformational change followed by biphasic slower conformational reorganizations on the millisecond time scale leading to the final molten-globule state.

Guest Binding Dynamics with Cucurbit[7]uril in the Presence of Cations

The binding dynamics of R-(+)-2-naphthyl-1-ethylammonium cation (NpH(+)) with cucurbit[7]uril (CB[7]) was investigated. Competitive binding with Na(+) or H(3)O(+) cations enabled the reaction to be slowed down sufficiently for the kinetics to be studied by fluorescence stopped-flow experiments. The binding of two Na(+) cations to CB[7], i.e., CB[7]·Na(+) (K(01) = 130 ± 10 M(-1)) and Na(+)·CB[7]·Na(+) (K(02) = 21 ± 2 M(-1)), was derived from the analysis of binding isotherms and the kinetic studies. NpH(+) binds only to free CB[7] ((1.06 ± 0.05) × 10(7) M(-1)), and the association rate constant of (6.3 ± 0.3) × 10(8) M(-1) s(-1) is 1 order of magnitude lower than that for a diffusion-controlled process and much higher than the association rate constant previously determined for other CB[n] systems. The high equilibrium constant for the NpH(+)@CB[7] complex is a consequence of the slow dissociation rate constant of 55 s(-1). The kinetics results showed that formation of a complex between a positively charged guest with CB[n] can occur at a rate close to the diffusion-controlled limit with no detection of a stable exclusion complex.

Probing the Functional Mechanism of Escherichia coli GroEL Using Circular Permutation

BackgroundThe Escherichia coli chaperonin GroEL subunit consists of three domains linked via two hinge regions, and each domain is responsible for a specific role in the functional mechanism. Here, we have used circular permutation to study the structural and functional characteristics of the GroEL subunit.Methodology/Principal FindingsThree soluble, partially active mutants with polypeptide ends relocated into various positions of the apical domain of GroEL were isolated and studied. The basic functional hallmarks of GroEL (ATPase and chaperoning activities) were retained in all three mutants. Certain functional characteristics, such as basal ATPase activity and ATPase inhibition by the cochaperonin GroES, differed in the mutants while at the same time, the ability to facilitate the refolding of rhodanese was roughly equal. Stopped-flow fluorescence experiments using a fluorescent variant of the circularly permuted GroEL CP376 revealed that a specific kinetic transition that reflects movements of the apical domain was missing in this mutant. This mutant also displayed several characteristics that suggested that the apical domains were behaving in an uncoordinated fashion.Conclusions/SignificanceThe loss of apical domain coordination and a concomitant decrease in functional ability highlights the importance of certain conformational signals that are relayed through domain interlinks in GroEL. We propose that circular permutation is a very versatile tool to probe chaperonin structure and function.

A Central Interdomain Protein Joint in Elongation Factor G Regulates Antibiotic Sensitivity, GTP Hydrolysis, and Ribosome Translocation

The antibiotic fusidic acid potently inhibits bacterial translation (and cellular growth) by lodging between domains I and III of elongation factor G (EF-G) and preventing release of EF-G from the ribosome. We examined the functions of key amino acid residues near the active site of EF-G that interact with fusidic acid and regulate hydrolysis of GTP. Alanine mutants of these residues spontaneously hydrolyzed GTP in solution, bypassing the normal activating role of the ribosome. A conserved phenylalanine in the switch II element of EF-G was important for suppressing GTP hydrolysis in solution and critical for catalyzing translocation of the ribosome along mRNA. These experimental results reveal the multipurpose roles of an interdomain joint in the heart of an essential translation factor that can both promote and inhibit bacterial translation.

Rapid binding and release of Hfq from ternary complexes during RNA annealing

The Sm protein Hfq binds small non-coding RNA (sRNAs) in bacteria and facilitates their base pairing with mRNA targets. Molecular beacons and a 16 nt RNA derived from the Hfq binding site in DsrA sRNA were used to investigate how Hfq accelerates base pairing between complementary strands of RNA. Stopped-flow fluorescence experiments showed that annealing became faster with Hfq concentration but was impaired by mutations in RNA binding sites on either face of the Hfq ring or by competition with excess RNA substrate. A fast bimolecular Hfq binding step (∼108 M−1s−1) observed with Cy3-Hfq was followed by a slow transition (0.5 s−1) to a stable Hfq–RNA complex that exchanges RNA ligands more slowly. Release of Hfq upon addition of complementary RNA was faster than duplex formation, suggesting that the nucleic acid strands dissociate from Hfq before base pairing is complete. A working model is presented in which rapid co-binding and release of two RNA strands from the Hfq ternary complex accelerates helix initiation 10 000 times above the Hfq-independent rate. Thus, Hfq acts to overcome barriers to helix initiation, but the net reaction flux depends on how tightly Hfq binds the reactants and products and the potential for unproductive binding interactions.

Distortion of tRNA upon Near-cognate Codon Recognition on the Ribosome

The accurate decoding of the genetic information by the ribosome relies on the communication between the decoding center of the ribosome, where the tRNA anticodon interacts with the codon, and the GTPase center of EF-Tu, where GTP hydrolysis takes place. In the A/T state of decoding, the tRNA undergoes a large conformational change that results in a more open, distorted tRNA structure. Here we use a real-time transient fluorescence quenching approach to monitor the timing and the extent of the tRNA distortion upon reading cognate or near-cognate codons. The tRNA is distorted upon codon recognition and remains in that conformation until the tRNA is released from EF-Tu, although the extent of distortion gradually changes upon transition from the pre- to the post-hydrolysis steps of decoding. The timing and extent of the rearrangement is similar on cognate and near-cognate codons, suggesting that the tRNA distortion alone does not provide a specific switch for the preferential activation of GTP hydrolysis on the cognate codon. Thus, although the tRNA plays an active role in signal transmission between the decoding and GTPase centers, other regulators of signaling must be involved.

Detection of a ternary complex of NF-κB and IκBα with DNA provides insights into how IκBα removes NF-κB from transcription sites

It has been axiomatic in the field of NF-κB signaling that the formation of a stable complex between NF-κB and the ankyrin repeat protein IκBα precludes the interaction of NF-κB with DNA. Contradicting this assumption, we present stopped-flow fluorescence and NMR experiments that give unequivocal evidence for the presence of a ternary DNA-NF-κB-IκBα complex in solution. Stepwise addition of a DNA fragment containing the κB binding sequence to the IκBα-NF-κB complex results in changes in the IκBα NMR spectrum that are consistent with dissociation of the region rich in proline, glutamate, serine, and threonine (PEST) and C-terminal ankyrin repeat sequences of IκBα from the complex. However, even at high concentrations of DNA, IκBα remains associated with NF-κB, indicated by the absence of resonances of the free N-terminal ankyrin repeats of IκBα. The IκBα-mediated release of NF-κB from its DNA-bound state may be envisioned as the reverse of this process. The initial step would consist of the coupled folding and binding of the intrinsically disordered nuclear localization sequence of the p65 subunit of NF-κB to the well-structured N-terminal ankyrin repeats of IκBα. Subsequently the poorly folded C-terminal ankyrin repeats of IκBα would fold upon binding to the p50 and p65 dimerization domains of NF-κB, permitting the negatively charged C-terminal PEST sequence of IκBα to displace the bound DNA through a process of local mass action.

Kinetics of ATP and TNP-ATP Binding to the Active Site of CheA from Thermotoga maritima

The mechanism of nucleotide binding to the active site of Thermotoga maritima CheA was investigated using stopped-flow fluorescence experiments that monitored binding of ATP and TNP-ATP to the catalytic domain (P4) of CheA that had been engineered to include a tryptophan residue as a fluorescent reporter group at the active site (P4(F487W)). Rapid decreases in protein intrinsic fluorescence and increases in TNP-ATP fluorescence were observed during binding reactions, and time courses were analyzed to define the kinetic mechanisms for ATP and TNP-ATP binding. This analysis indicated that binding of ATP(Mg(2+)) to P4(F487W) involves a single reversible step with a k(on) of 0.92 +/- 0.09 microM(-1) s(-1), a k(off) of 1.9 +/- 0.4 s(-1), and a K(d) of 1.5-2.1 microM (all values determined at 4 degrees C). Binding of TNP-ATP(Mg(2+)) to P4(F487W) involves a more complicated mechanism, requiring at least three sequential steps. Computer simulations and nonlinear regression analysis were used to estimate the rate constants of the forward and reverse reactions for each of the three steps in the reaction scheme [Formula: see text] Similar analysis indicated that an alternative reaction scheme, involving a rate-limiting conformational change in P4 prior to TNP-ATP binding, did an equally good job of accounting for all of the kinetics results:[Formula: see text] In both models, steps 2 and 3 have slow reversal rates that contribute to the high affinity of the active site for TNP-ATP (K(d) = 0.015 microM). These results highlight the dramatic effect of the TNP moieties on CheA-nucleotide interactions, and they provide the first detailed information about the kinetic mechanism underlying interaction of a protein histidine kinase with this tight-binding inhibitor.

ADP but Not Pi Dissociation Contributes to Rate Limitation for Escherichia coli Rho

To define the molecular mechanism by which ATP hydrolysis powers the 5'-->3' travel of homohexameric Escherichia coli transcription termination factor Rho along RNA, rates for association and dissociation of non-RNA substrates and products were measured. Rapid mix/chemical quench and stopped-flow spectrofluorometry measurements were carried out with Rho and [gamma-(32)P]ATP, mantADP, or fluorescently tagged E. coli phosphate-binding protein. The results indicate that the P(i) off-rate is not rate limiting, but at approximately 90 s(-1), the ADP dissociation rate is comparable to the 30 s(-1) k(cat). Previous results indicate that the chemistry step of ATP hydrolysis by Rho is at least 10-fold faster than the overall catalytic cycle. The as yet unmeasured RNA dissociation step, which could be associated with a protein conformation change, might also be a rate-limiting factor.

Characterization of the Cofactor-Induced Folding Mechanism of a Zinc-Binding Peptide Using Computationally Designed Mutants

Metals are the most commonly encountered protein cofactors, and they play important structural and functional roles in biology. In many cases, metal binding provides a major driving force for a polypeptide chain to fold. While there are many studies on the structure, stability, and function of metal-binding proteins, there are few studies focusing on understanding the kinetic mechanism of metal-induced folding. Herein, the Zn2+-induced folding kinetics of a small zinc-binding protein are studied; the CH11 peptide is derived from the first cysteine/histidine-rich region (CH1 domain) of the protein interaction domains of the transcriptional coregulator CREB-binding protein. Computational design is used to introduce tryptophan and histidine mutations that are structurally consistent with CH11; these mutants are studied using stopped-flow tryptophan fluorescence experiments. The Zn2+-induced CH11 folding kinetics are consistent with two parallel pathways, where the initial binding of Zn2+ occurs at two sites. However, the initially formed Zn2+-bound complexes can proceed either directly to the folded state where zinc adopts a tetrahedral coordination or to an off-pathway misligated intermediate. While elimination of those ligands responsible for misligation simplifies the folding kinetics, it also leads to a decrease in the zinc binding constant. Therefore, these results suggest why these nonnative zinc ligands in the CH11 motif are conserved in several distantly related organisms and why the requirement for function can lead to kinetic frustration in folding. In addition, the loop closure rate of the CH11 peptide is determined based on the proposed model and temperature-dependent kinetic measurements.