Equilibrium constants and free energies in unfolding of proteins in urea solutions

A novel thermodynamic approach to the reversible unfolding of proteins in aqueous urea solutions has been developed based on the premise that urea ligands are bound cooperatively to the macromolecule. When successive stoichiometric binding constants have values larger than expected from statistical effects, an equation for moles of bound urea can be derived that contains imaginary terms. For a very steep unfolding curve, one can then show that the fraction of protein unfolded, B̄, depends on the square of the urea concentration, U, and is given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}\bar {B}=\frac{{\mathit{A}}^{{\mathit{2}}}_{{\mathit{1}}}{\mathit{e}}^{{\mathrm{{\lambda}}}n\bar {B}}{\mathit{U}}^{{\mathit{2}}}}{{\mathrm{1\hspace{.167em}+\hspace{.167em}}}{\mathit{A}}^{{\mathrm{2}}}_{{\mathrm{1}}}{\mathit{e}}^{{\mathrm{{\lambda}}}\bar {B}}{\mathit{U}}^{{\mathrm{2}}}}{\mathrm{.}}\end{equation*}\end{document} A12 is the binding constant as B̄→ 0, and λ is a parameter that reflects the augmentation in affinities of protein for urea as the moles bound increases to the saturation number, n. This equation provides an analytic expression that reproduces the unfolding curve with good precision, suggests a simple linear graphical procedure for evaluating A12 and λ, and leads to the appropriate standard free energy changes. The calculated ΔG° values reflect the coupling of urea binding with unfolding of the protein. Some possible implications of this analysis to protein folding in vivo are described.

Kinetic equilibrium of forces and molecular events in muscle contraction

In biomolecular systems, the mechanical transfer of free energy occurs with both high efficiency and high speed. It is shown here that such a transfer can be achieved only if the participating free-energy-storing elements exhibit opposing relationships between their content of free energy and the force they exert in the transfer direction. A kinetic equilibrium of forces (KEF) results, in which the transfer of free energy is mediated essentially by thermal molecular motion. On the basis of present evidence, KEF is used as a guiding principle in developing a mechanical model of the crossbridge cycle in muscle contraction. The model allows the basic features of molecular events to be visualized in terms of plausible structures. Real understanding of the process will require identification of the elements that perform the functions described here. Besides chemomechanical energy transduction, KEF may have a role in other biomolecular processes in which free energy is transferred mechanically over large distances.

Structure and function in rhodopsin: Kinetic studies of retinal binding to purified opsin mutants in defined phospholipid–detergent mixtures serve as probes of the retinal binding pocket

In the current standard procedure for preparation of mammalian rhodopsin mutants, transfected COS-1 cells expressing the mutant opsin genes are treated with 5 μM 11-cis-retinal before detergent solubilization for purification. We found that binding of 11-cis-retinal to opsin mutants with single amino acid changes at Trp-265 (W265F,Y,A) and a retinitis pigmentosa mutant (A164V) was far from complete and required much higher concentrations of 11-cis-retinal. By isolation of the expressed opsins in a stable form, kinetic studies of retinal binding to the opsins in vitro have been carried out by using defined phospholipid–detergent mixtures. The results show wide variation in the rates of 11-cis-retinal binding. Thus, the in vitro reconstitution procedure serves as a probe of the retinal-binding pocket in the opsins. Further, a method is described for purification and characterization of the rhodopsin mutants after retinal binding to the opsins in vitro.

Direct interaction of lignin and lignin peroxidase from Phanerochaete chrysosporium

Binding properties of lignin peroxidase (LiP) from the basidiomycete Phanerochaete chrysosporium against a synthetic lignin (dehydrogenated polymerizate, DHP) were studied with a resonant mirror biosensor. Among several ligninolytic enzymes, only LiP specifically binds to DHP. Kinetic analysis revealed that the binding was reversible, and that the dissociation equilibrium constant was 330 μM. The LiP–DHP interaction was controlled by the ionization group with a pKa of 5.3, strongly suggesting that a specific amino acid residue plays a role in lignin binding. A one-electron transfer from DHP to oxidized intermediates LiP compounds I and II (LiPI and LiPII) was characterized by using a stopped-flow technique, showing that binding interactions of DHP with LiPI and LiPII led to saturation kinetics. The dissociation equilibrium constants for LiPI–DHP and LiPII–DHP interactions were calculated to be 350 and 250 μM, and the first-order rate constants for electron transfer from DHP to LiPI and to LiPII were calculated to be 46 and 16 s−1, respectively. These kinetic and spectral studies strongly suggest that LiP is capable of oxidizing lignin directly at the protein surface by a long-range electron transfer process. A close look at the crystal structure suggested that LiP possesses His-239 as a possible lignin-binding site on the surface, which is linked to Asp-238. This Asp residue is hydrogen-bonded to the proximal His-176. This His–Asp⋅⋅⋅proximal-His motif would be a possible electron transfer route to oxidize polymeric lignin.

Implications of macromolecular crowding for signal transduction and metabolite channeling

The effect of different total enzyme concentrations on the flux through the bacterial phosphoenolpyruvate:carbohydrate phosphotransferase system (PTS) in vitro was determined by measuring PTS-mediated carbohydrate phosphorylation at different dilutions of cell-free extract of Escherichia coli. The dependence of the flux on the protein concentration was more than linear but less than quadratic. The combined flux–response coefficient of the four enzymes constituting the glucose PTS decreased slightly from values of ≈1.8 with increasing protein concentrations in the assay. Addition of the macromolecular crowding agents polyethylene glycol (PEG) 6000 and PEG 35000 led to a sharper decrease in the combined flux–response coefficient, in one case to values of ≈1. PEG 6000 stimulated the PTS flux at lower protein concentrations and inhibited the flux at higher protein concentrations, with the transition depending on the PEG 6000 concentration. This suggests that macromolecular crowding decreases the dissociation rate constants of enzyme complexes. High concentrations of the microsolute glycerol did not affect the combined flux–response coefficient. The data could be explained with a kinetic model of macromolecular crowding in a two-enzyme group-transfer pathway. Our results suggest that, because of the crowded environment in the cell, the different PTS enzymes form complexes that live long on the time-scale of their turnover. The implications for the metabolic behavior and control properties of the PTS, and for the effect of macromolecular crowding on nonequilibrium processes, are discussed.

The role of zinc in the binding of killer cell Ig-like receptors to class I MHC proteins

The binding of killer cell Ig-like Receptors (KIR) to their Class I MHC ligands was shown previously to be characterized by extremely rapid association and dissociation rate constants. During experiments to investigate the biochemistry of receptor–ligand binding in more detail, the kinetic parameters of the interaction were observed to alter dramatically in the presence of Zn2+ but not other divalent cations. The basis of this phenomenon is Zn2+-induced multimerization of the KIR molecules as demonstrated by BIAcore, analytical ultracentrifugation, and chemical cross-linking experiments. Zn2+-dependent multimerization of KIR may be critical for formation of the clusters of KIR and HLA-C molecules, the “natural killer (NK) cell immune synapse,” observed at the site of contact between the NK cell and target cell.

Determination of the binding constants of the centromere protein Cbf1 to all 16 centromere DNAs of Saccharomyces cerevisiae

Cbf1p is a Saccharomyces cerevisiae chromatin protein belonging to the basic region helix–loop–helix leucine zipper (bHLHzip) family of DNA binding proteins. Cbf1p binds to a conserved element in the 5′-flanking region of methionine biosynthetic genes and to centromere DNA element I (CDEI) of S.cerevisiae centromeric DNA. We have determined the apparent equilibrium dissociation constants of Cbf1p binding to all 16 CDEI DNAs in gel retardation assays. Binding constants of full-length Cbf1p vary between 1.7 and 3.8 nM. However, the dissociation constants of a Cbf1p deletion variant that has been shown to be fully sufficient for Cbf1p function in vivo vary in a range between 3.2 and 12 nM. In addition, native polyacrylamide gel electrophoresis revealed distinct changes in the 3D structure of the Cbf1p/CEN complexes. We also show that the previously reported DNA binding stimulation activity of the centromere protein p64 functions on both the Cbf1 full-length protein and a deletion variant containing only the bHLHzip domain of Cbf1p. Our results suggest that centromeric DNA outside the consensus CDEI sequence and interaction of Cbf1p with adjacent centromere proteins contribute to the complex formation between Cbf1p and CEN DNA.

Kinetic stability as a mechanism for protease longevity

The folding of the extracellular serine protease, α-lytic protease (αLP; EC 3.4.21.12) reveals a novel mechanism for stability that appears to lead to a longer functional lifetime for the protease. For αLP, stability is based not on thermodynamics, but on kinetics. Whereas this has required the coevolution of a pro region to facilitate folding, the result has been the optimization of native-state properties independent of their consequences on thermodynamic stability. Structural and mutational data lead to a model for catalysis of folding in which the pro region binds to a conserved β-hairpin in the αLP C-terminal domain, stabilizing the folding transition state and the native state. The pro region is then proteolytically degraded, leaving the active αLP trapped in a metastable conformation. This metastability appears to be a consequence of pressure to evolve properties of the native state, including a large, highly cooperative barrier to unfolding, and extreme rigidity, that reduce susceptibility to proteolytic degradation. In a test of survival under highly proteolytic conditions, homologous mammalian proteases that have not evolved kinetic stability are much more rapidly degraded than αLP. Kinetic stability as a means to longevity is likely to be a mechanism conserved among the majority of extracellular bacterial pro-proteases and may emerge as a general strategy for intracellular eukaryotic proteases subject to harsh conditions as well.

Unexpected signals in a system subject to kinetic proofreading

When multivalent ligands attach to IgEs bound to the receptors with high affinity for IgE on mast cells, the receptors aggregate, tyrosines on the receptors become phosphorylated, and a variety of cellular responses are stimulated. Prior studies, confirmed here, demonstrated that the efficiency with which later events are generated from earlier ones is inversely related to the dissociation rate of the aggregating ligand. This finding suggests that the cellular responses are constrained by a “kinetic proofreading” regimen. We have now observed an apparent exception to this rule. Doses of the rapidly or slowly dissociating ligands that generated equivalent levels of tyrosine-phosphorylated receptors comparably stimulated a putatively distal event: transcription of the gene for monocyte chemoattractant protein 1. Possible explanations of this apparent anomaly were explored.

Kinetic proofreading models for cell signaling predict ways to escape kinetic proofreading

In the context of cell signaling, kinetic proofreading was introduced to explain how cells can discriminate among ligands based on a kinetic parameter, the ligand-receptor dissociation rate constant. In the kinetic proofreading model of cell signaling, responses occur only when a bound receptor undergoes a complete series of modifications. If the ligand dissociates prematurely, the receptor returns to its basal state and signaling is frustrated. We extend the model to deal with systems where aggregation of receptors is essential to signal transduction, and present a version of the model for systems where signaling depends on an extrinsic kinase. We also investigate the kinetics of signaling molecules, “messengers,” that are generated by aggregated receptors but do not remain associated with the receptor complex. We show that the extended model predicts modes of signaling that exhibit kinetic discrimination for some range of parameters but for other parameter values show little or no discrimination and thus escape kinetic proofreading. We compare model predictions with experimental data.

Simple mechanochemistry describes the dynamics of kinesin molecules

Recently, Block and coworkers [Visscher, K., Schnitzer, M. J., & Block, S. M. (1999) Nature (London) 400, 184–189 and Schnitzer, M. J., Visscher, K. & Block, S. M. (2000) Nat. Cell Biol. 2, 718–723] have reported extensive observations of individual kinesin molecules moving along microtubules in vitro under controlled loads, F = 1 to 8 pN, with [ATP] = 1 μM to 2 mM. Their measurements of velocity, V, randomness, r, stalling force, and mean run length, L, reveal a need for improved theoretical understanding. We show, presenting explicit formulae that provide a quantitative basis for comparing distinct molecular motors, that their data are satisfactorily described by simple, discrete-state, sequential stochastic models. The simplest (N = 2)-state model with fixed load-distribution factors and kinetic rate constants concordant with stopped-flow experiments, accounts for the global (V, F, L, [ATP]) interdependence and, further, matches relative acceleration observed under assisting loads. The randomness, r(F,[ATP]), is accounted for by a waiting-time distribution, ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{1}^{+}}}\end{equation*}\end{document}(t), [for the transition(s) following ATP binding] with a width parameter ν ≡ 〈t〉2/〈(Δt)2〉≃2.5, indicative of a dispersive stroke of mechanicity ≃0.6 or of a few (≳ν − 1) further, kinetically coupled states: indeed, N = 4 (but not N = 3) models do well. The analysis reveals: (i) a substep of d0 = 1.8–2.1 nm on ATP binding (consistent with structurally based suggestions); (ii) comparable load dependence for ATP binding and unbinding; (iii) a strong load dependence for reverse hydrolysis and subsequent reverse rates; and (iv) a large (≳50-fold) increase in detachment rate, with a marked load dependence, following ATP binding.

Force and kinetic barriers to unzipping of the DNA double helix

A theory of the unzipping of double-stranded DNA is presented and is compared to recent micromanipulation experiments. It is shown that the interactions that stabilize the double helix and the elastic rigidity of single strands simply determine the sequence-dependent ≈12-pN force threshold for DNA strand separation. Using a semimicroscopic model of the binding between nucleotide strands, we show that the greater rigidity of the strands when formed into double-stranded DNA, relative to that of isolated strands, gives rise to a potential barrier to unzipping. The effects of this barrier are derived analytically. The force to keep the extremities of the molecule at a fixed distance, the kinetic rates for strand unpairing at fixed applied force, and the rupture force as a function of loading rate are calculated. The dependence of the kinetics and of the rupture force on molecule length is also analyzed.

Kinetic analysis of peptide loading onto HLA-DR molecules mediated by HLA-DM.

The nonclassical major histocompatibility complex class II molecule HLA-DM (DM) has recently been shown to play a central role in the class II-associated antigen presentation pathway: DM releases invariant chain-derived CLIP peptides (class II-associated invariant chain protein peptide) from HLA-DR (DR) molecules and thereby facilitates loading with antigenic peptides. Some observations have led to the suggestion that DM acts in a catalytic manner, but so far direct proof is missing. Here, we investigated in vitro the kinetics of exchange of endogenously bound CLIP for various peptides on DR1 and DR2a molecules: we found that in the presence of DM the peptide loading process follows Michaelis-Menten kinetics with turnover numbers of 3-12 DR molecules per minute per DM molecule, and with KM values of 500-1000 nM. In addition, surface plasmon resonance measurements showed that DM interacts efficiently with DR-CLIP complexes but only weakly with DR-peptide complexes isolated from DM-positive cells. Taken together, our data provide evidence that DM functions as an enzyme-like catalyst of peptide exchange and favors the generation of long-lived DR-peptide complexes that are no longer substrates for DM.

Kinetic discrimination in T-cell activation.

We propose a quantitative model for T-cell activation in which the rate of dissociation of ligand from T-cell receptors determines the agonist and antagonist properties of the ligand. The ligands are molecular complexes between antigenic peptides and proteins of the major histocompatibility complex on the surfaces of antigen-presenting cells. Binding of ligand to receptor triggers a series of biochemical reactions in the T cell. If the ligand dissociates after these reactions are complete, the T cell receives a positive activation signal. However, dissociation of ligand after completion of the first reaction but prior to generation of the final products results in partial T-cell activation, which acts to suppress a positive response. Such a negative signal is brought about by T-cell ligands containing the variants of antigenic peptides referred to as T-cell receptor antagonists. Results of recent experiments with altered peptide ligands compare favorably with T-cell responses predicted by this model.