Intrachain Contact Formation Research Articles

Coloring Invariant for Topological Circuits in Folded Linear Chains

Circuit topology is a mathematical approach that categorizes the arrangement of contacts within a folded linear chain, such as a protein molecule or the genome. Theses linear biomolecular chains often fold into complex 3D architectures with critical entanglements and local or global structural symmetries stabilised by formation of intrachain contacts. Here, we adapt and apply the algebraic structure of quandles to classify and distinguish chain topologies within the framework of circuit topology. We systematically study the basic circuit topology motifs and define quandle/bondle coloring for them. Next, we explore the implications of circuit topology operations that enable building complex topologies from basic motifs for the quandle coloring approach.

Study of conformational transitions of i-motif DNA using time-resolved fluorescence and multivariate analysis methods.

Recently, the presence of i-motif structures at C-rich sequences in human cells and their regulatory functions have been demonstrated. Despite numerous steady-state studies on i-motif at neutral and slightly acidic pH, the number and nature of conformation of this biological structure are still controversial. In this work, the fluorescence lifetime of labelled molecular beacon i-motif-forming DNA sequences at different pH values is studied. The influence of the nature of bases at the lateral loops and the presence of a Watson–Crick-stabilized hairpin are studied by means of time-correlated single-photon counting technique. This allows characterizing the existence of several conformers for which the fluorophore has lifetimes ranging from picosecond to nanosecond. The information on the existence of different i-motif structures at different pH values has been obtained by the combination of classical global decay fitting of fluorescence traces, which provides lifetimes associated with the events defined by the decay of each sequence and multivariate analysis, such as principal component analysis or multivariate curve resolution based on alternating least squares. Multivariate analysis, which is seldom used for this kind of data, was crucial to explore similarities and differences of behaviour amongst the different DNA sequences and to model the presence and identity of the conformations involved in the pH range of interest. The results point that, for i-motif, the intrachain contact formation and its dissociation show lifetimes ten times faster than for the open form of DNA sequences. They also highlight that the presence of more than one i-motif species for certain DNA sequences according to the length of the sequence and the composition of the bases in the lateral loop.

Expansion and Internal Friction in Unfolded Protein Chain

Similarities in global properties of homopolymers and unfolded proteins provide approaches to mechanistic description of protein folding. Here, hydrodynamic properties and relaxation rates of the unfolded state of carbonmonoxide-liganded cytochrome c (cyt-CO) have been measured using nuclear magnetic resonance and laser photolysis methods. Hydrodynamic radius of the unfolded chain gradually increases as the solvent turns increasingly better, consistent with theory. Curiously, however, the rate of intrachain contact formation also increases with an increasing denaturant concentration, which, by Szabo, Schulten, and Schulten theory for the rate of intramolecular contact formation in a Gaussian polymer, indicates growing intramolecular diffusion. It is argued that diminishing nonbonded atom interactions with increasing denaturant reduces internal friction and, thus, increases the rate of polypeptide relaxation. Qualitative scaling of the extent of unfolding with nonbonded repulsions allows for description of internal friction by a phenomenological model. The degree of nonbonded atom interactions largely determines the extent of internal friction.

Role of Ionic Liquid on the Conformational Dynamics in the Native, Molten Globule, and Unfolded States of Cytochrome C: A Fluorescence Correlation Spectroscopy Study

The role of a room temperature ionic liquid (RTIL, [pmim][Br]) on the size and conformational dynamics of a protein, horse heart cytochrome c (Cyt C) in its native, molten globule (MG-I and II), and unfolded states is studied using fluorescence correlation spectroscopy (FCS). For this purpose, the protein was covalently labeled by a fluorescent dye, Alexa Fluor 488. It is observed that the addition of the RTIL leads to an increase in the hydrodynamic radius (r(H)) of the protein, Cyt C in the native or MG-I state. In contrast, the addition of RTIL causes a decrease in the size (hydrodynamic radius, r(H)) of Cyt C unfolded by GdnHCl or MG-II state. The decrease in size indicates the formation of a relatively compact structure. We detected two types of conformational relaxation of the protein. The shorter relaxation time component (~3-5.5 μs) corresponds to the protein folding or intrachain contact formation, while the relatively longer time component (~63-122 μs) may be assigned to the motion of the protein side chains or concerted chain dynamics. The burst integrated fluorescence lifetime histograms indicate that the increase in size of the protein is accompanied by an increase in the contribution of the shorter component (~0.3-0.4 ns) with a concomitant decrease of the contribution of the longer component (~2.8-3.6 ns). An opposite trend is observed during the decrease in size of the protein.

PH-Induced Intramolecular Folding Dynamics of i-Motif DNA

Using the combination of fluorescence resonance energy transfer (FRET) and fluorescence correlation spectroscopy (FCS) technique, we investigate the mechanism and dynamics of the pH-induced conformational change of i-motif DNA in the bulk phases and at the single-molecule level. Despite numerous studies on i-motif that is formed from cytosine (C)-rich strand at slightly acidic pH, its detailed conformational dynamics have been rarely reported. Using the FRET technique to provide valuable information on the structure of biomolecules such as a protein and DNA, we clearly show that the partially folded species as well as the single-stranded structure coexist at neutral pH, supporting that the partially folded species may exist substantially in vivo and play an important role in a process of gene expression. By measuring the FCS curves of i-motif, we observed the gradual decrease of the diffusion coefficient of i-motif with increasing pH. The quantitative analysis of FCS curves supports that the gradual decrease of diffusion coefficient (D) associated with the conformational change of i-motif is not only due to the change in the intermolecular interaction between i-motif and solvent accompanied by the increase of pH but also due to the change of the shape of DNA. Furthermore, FCS analysis showed that the intrachain contact formation and dissociation for i-motif are 5-10 times faster than that for the open form. The fast dynamics of i-motif with a compact tetraplex is due to the intrinsic conformational changes at the fluorescent site including the motion of alkyl chain connecting the dye to DNA, whereas the slow intrachain contact formation observed from the open form is due to the DNA motion corresponding to an early stage interaction in the folding process of the unstructured open form.

Empirical model of residue contact probabilities for polypeptides

An empirical theory for the probability of formation of intrachain contacts in denatured polypeptides is presented. Contact probabilities for arbitrary sequences are modeled by composition-weighted averages of the homopolypeptides contact probabilities. Homopolypeptide probabilities are obtained for each one of the 20 amino acids by Monte Carlo simulations. A multipower law model for the homopolypeptides fits very precisely the contact probabilities after optimization. Its asymptotic behavior for large contact loop lengths consist of three different exponents depending on where the contacts are located along the chain in general agreement with other theoretical models. The model for the heteropolypeptide contact probabilities is also able to reproduce the simulated probabilities of a set of denatured proteins but with less accuracy. Contact probabilities for heteropolypeptides are significantly similar, in particular for loop lengths above 20 residues, and the model does not have enough resolution to clearly distinguish between different proteins. Sequence order information seems necessary to increase the precision. Overall, contacts with loop lengths above 33 residues behave as those from random flight chains. One exception are polyproline chains for which this length seems to be much higher.

Conformations and Dynamics of Polypeptide Chains Revealed By Tryptophan-Cysteine Contact Formation Kinetics

Spectroscopic probes sensitive to intra-chain contact formation events in polypeptides are increasingly used to study the conformational and dynamical properties of different amino acid sequences. Quenching of the triplet state of tryptophan by close contact with cysteine enables the measure of contact formation rates without the need of extrinsic probes, thus being suitable for the study of natural proteins and peptides. We illustrate the use of this method to investigate the unfolded state of small proteins in conditions close to native and the kinetics of weakly structured protein fragments. The coexistence of different conformational states can be revealed from the non-exponential relaxation of the excited triplet, enabling the characterization of both the chain dynamics for each state and the transition kinetics. Moreover, the rate of contact formation measured for the least structured states is compared with those observed for model disordered peptides, allowing to estimate the strength of electrostatic and hydrophobic interactions between residues other than the probes. We test this approach with the widely studied GB1 15-residue C-terminal, which folds into a beta-hairpin structure. The kinetics of elementary conformational steps leading to the folded state is outlined, revealing the presence of misfolded states as proposed in recent computational works.

Direct observation of ultrafast folding and denatured state dynamics in single protein molecules

Single-molecule fluorescence resonance energy transfer (smFRET) experiments are extremely useful in studying protein folding but are generally limited to time scales of greater than approximately 100 micros and distances greater than approximately 2 nm. We used single-molecule fluorescence quenching by photoinduced electron transfer, detecting short-range events, in combination with fluorescence correlation spectroscopy (PET-FCS) to investigate folding dynamics of the small binding domain BBL with nanosecond time resolution. The kinetics of folding appeared as a 10-micros decay in the autocorrelation function, resulting from stochastic fluctuations between denatured and native conformations of individual molecules. The observed rate constants were probe independent and in excellent agreement with values derived from conventional temperature-jump (T-jump) measurements. A submicrosecond relaxation was detected in PET-FCS data that reported on the kinetics of intrachain contact formation within the thermally denatured state. We engineered a mutant of BBL that was denatured under the reaction conditions that favored folding of the parent wild type ("D(phys)"). D(phys) had the same kinetic signature as the thermally denatured state and revealed segmental diffusion with a time constant of intrachain contact formation of 500 ns. This time constant was more than 10 times faster than folding and in the range estimated to be the "speed limit" of folding. D(phys) exhibited significant deviations from a random coil. The solvent viscosity and temperature dependence of intrachain diffusion showed that chain motions were slaved by the presence of intramolecular interactions. PET-FCS in combination with protein engineering is a powerful approach to study the early events and mechanism of ultrafast protein folding.

Dynamics of Unfolded Polypeptide Chains in Crowded Environment Studied by Fluorescence Correlation Spectroscopy

Proteins have evolved to fold and function within a cellular environment that is characterized by high macromolecular content. The earliest step of protein folding represents intrachain contact formation of amino acid residues within an unfolded polypeptide chain. It has been proposed that macromolecular crowding can have significant effects on rates and equilibria of biomolecular processes. However, the kinetic consequences on intrachain diffusion of polypeptides have not been tested experimentally, yet. Here, we demonstrate that selective fluorescence quenching of the oxazine fluorophore MR121 by the amino acid tryptophan (Trp) in combination with fast fluorescence correlation spectroscopy (FCS) can be used to monitor end-to-end contact formation rates of unfolded polypeptide chains. MR121 and Trp were incorporated at the terminal ends of polypeptides consisting of repetitive units of glycine (G) and serine (S) residues. End-to-end contact formation and dissociation result in “off” and “on” switching of MR121 fluorescence and underlying kinetics can be revealed in FCS experiments with nanosecond time resolution. We revisit previous experimental studies concerning the dependence of end-to-end contact formation rates on polypeptide chain length, showing that kinetics can be described by Gaussian chain theory. We further investigate effects of solvent viscosity and temperature on contact formation rates demonstrating that intrachain diffusion represents a purely diffusive, entropy-controlled process. Finally, we study the influence of macromolecular crowding on polypeptide chain dynamics. The data presented demonstrate that intrachain diffusion is fast in spite of hindered diffusion caused by repulsive interactions with macromolecules. Findings can be explained by effects of excluded volume reducing chain entropy and therefore accelerating the loop search process. Our results suggest that within a cellular environment the early formation of structural elements in unfolded proteins can still proceed quite efficiently in spite of hindered diffusion caused by high macromolecular content.

Dynamics of Unfolded Polypeptide Chains as Model for the Earliest Steps in Protein Folding

The rate of formation of intramolecular interactions in unfolded proteins determines how fast conformational space can be explored during folding. Characterization of the dynamics of unfolded proteins is therefore essential for the understanding of the earliest steps in protein folding. We used triplet–triplet energy transfer to measure formation of intrachain contacts in different unfolded polypeptide chains. The time constants (1/ k) for contact formation over short distances are almost independent of chain length, with a maximum value of about 5 ns for flexible glycine-rich chains and of 12 ns for stiffer chains. The rates of contact formation over longer distances decrease with increasing chain length, indicating different rate-limiting steps for motions over short and long chain segments. The effect of the amino acid sequence on local chain dynamics was probed by using a series of host-guest peptides. Formation of local contacts is only sixfold slower around the stiffest amino acid (proline) compared to the most flexible amino acid (glycine). Good solvents for polypeptide chains like EtOH, GdmCl and urea were found to slow intrachain diffusion and to decrease chain stiffness. These data allow us to determine the time constants for formation of the earliest intrachain contacts during protein folding.

Non-Gaussian dynamics from a simulation of a short peptide: Loop closure rates and effective diffusion coefficients

Intrachain contact formation rates, fundamental to the dynamics of biopolymer self-organization such as protein folding, can be monitored in the laboratory through fluorescence quenching measurements. The common approximations for the intrachain contact rate given by the theory of Szabo, Schulten, and Schulten (SSS) [J. Chem. Phys. 72, 4350 (1980)] and Wilemski–Fixman (WF) [J. Chem. Phys. 60, 878 (1973)] are shown to be complementary variational bounds: The SSS and WF approximations are lower and upper bounds, respectively, on the mean first contact times. As reported in the literature, the SSS approximation requires an effective diffusion coefficient 10 to 100 times smaller than expected to fit experimentally measured quenching rates. An all atom molecular dynamics simulation of an eleven residue peptide sequence in explicit water is analyzed to investigate the source of this surprising parameter value. The simulated diffusion limited contact time is ≈6 ns for a reaction radius of 4 Å for solvent viscosity corresponding to that of water at 293 K and 1 atm (η=1.0 cP). In analytical work, the polymer is typically modeled by a Gaussian chain of effective monomers. Compared to Gaussian dynamics, the simulated end-to-end distance autocorrelation has a much slower relaxation. The long time behavior of the distance autocorrelation function can be approximated by a Gaussian model in which the monomer diffusion coefficient D0 is reduced to D0/6. This value of the diffusion coefficient brings the mean end-to-end contact time from analytical approximations and simulation into agreement in the sense that the SSS and WF approximations bracket the simulated mean first contact time.

Rate of intrachain contact formation in an unfolded protein: temperature and denaturant effects

We have measured the effect of temperature and denaturant concentration on the rate of intrachain diffusion in an unfolded protein. After photodissociating a ligand from the heme iron of unfolded horse cytochrome c, we use transient optical absorption spectroscopy to measure the time scale of the diffusive motions that bring the heme, located at His18, into contact with its native ligand, Met80. Measuring the rate at which this 62 residue intrachain loop forms under both folding and unfolding conditions, we find a significant effect of denaturant on the chain dynamics. The diffusion of the chain accelerates as denaturant concentration decreases, with the contact formation rate approaching a value near ∼6×10 5 s −1 in the absence of denaturant. This result agrees well with an extrapolation from recent loop formation measurements in short synthetic peptides. The temperature dependence of the rate of contact formation indicates an Arrhenius activation barrier, E a∼20 kJ/mol, at high denaturant concentrations, comparable to what is expected from solvent viscosity effects alone. Although E a increases by several k B T as denaturant concentration decreases, the overall rate of diffusion nevertheless increases. These results indicate that inter-residue energetic interactions do not control conformational diffusion in unfolded states, even under folding conditions.

A study of intermolecular interaction in aqueous solutions of polymers and cationic surfactants by polarized luminescence

The interaction of cationic surfactants with carboxyl containing polymers was studied by polarized luminescence. A high sensitivity of intramolecular mobility of the polymer to the formation of intra-chain contacts with the surfactant ions was demonstrated. The interaction of surfactant and polymer results in compacting of the polymeric coil and leads to intramolecular retardation.