Thermodynamic Theory of Site-Specific Binding Processes in Biological Macromolecules

Calculation of equilibrium formation constants of complexes with a polydentate oligomer

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Acritical regulatory pathway of the blood coagulation cascade is provided by antithrombin, a serine protease inhibitor serpin that specifically shuts down the activity of factor Xa and thrombin.

GAGs have anticoagulant activity, but they often lack the heparin pentasaccharide unit required for antithrombin activation, which has raised important questions about their precise mechanism of action. See page In the extracellular matrix, GAGs are anchored to proteoglycans and feature different degrees of sulfation that can affect both ion distribution and the water content of the environment.

Versican is the most abundant proteoglycan present in the arteries and uses long chains of CS as GAG appendices. Because of the ionic nature of GAGs and their spatial arrangement in the extracellular matrix, several possible mechanisms may be at the basis of their anticoagulant activity. Electrostatic forces generated by the sulfated components of GAGs may steer antithrombin and target proteases to facilitate productive collision. Another possibility is that the variability in pattern of sulfation of GAGs may affect the water balance of the extracellular environment by sequestering solvent that could otherwise abundantly hydrate protein surfaces.

In an article appearing in this issue of the Journal, McGee and Wagner 4 use an osmotic stress technique to demonstrate that the oversulfated CS, CSE, present in versican has an anticoagulant activity linked to water transfer. Importantly, the amount of oversulfated versican in advanced type IV atherosclerosis lesions is reduced significantly compared with healthy aorta, presaging an increased thrombogenic risk due to reduction of antithrombin activity. As a result, the reduction of oversulfated versican in atherosclerosis lesions reduces the availability of cofactor for antithrombin activation and, in addition, alters the homeostatic water balance of the extracellular milieu by compromising all interactions linked to water release.

An interesting new paradigm emerges from these studies: GAGs may regulate protein-protein interactions in the blood coagulation cascade by altering water homeostasis in the extracellular matrix. The role of water in macromolecular interactions has long captivated the interest of physical chemists and has helped shape our mechanistic understanding of protein folding, ligand binding and linkage.

When two proteins come together to form a complex, some of the waters on their hydration shell are released into the bulk solvent. The amount of water bound to the complex is less than the sum of the water content of the free proteins, meaning that formation of the complex is linked to a net release of water from the hydration shells to the bulk solvent.

This transfer occurs unnoticed under standard investigations of the interaction of the two proteins. When the cosolute is added to the system at high enough concentrations, the amount of free water available for protein hydration decreases. The cosolute forces the proteins to partially dehydrate and indirectly drives the equilibrium toward formation of the complex that bears a smaller number of bound waters in its hydration shell. This is a consequence of thermodynamic stability and the linkage between water binding and complex formation causes a rebalancing of the equilibrium resulting in an apparent increase in affinity.

Download figure Download PowerPoint Schematic representation of the role of water in protein-protein interactions. Two proteins left form a complex by releasing the waters yellow balls absorbed on their surface of recognition. The water transfer in the reaction affects the energetics of the binding equilibrium. When a cosolute green is added to the solution right , some of the waters yellow and blue balls in the bulk solvent are sequestered.

Biomolecule

Thermodynamic stability 5 drives the equilibrium toward the state with reduced number of water molecules bound, which is the protein-protein complex. Another reason for overlooking this mechanism could have been the fact that multiple local optima can also exist via other mechanisms see for example [ Klebe, ] , and measurements that allow inference of entropy and enthalpy separately are not commonly performed in studies of macromolecular interactions. In addition, simple additive binding models such as position weight matrices PWMs can hide the effect, as they can only describe a single optimal state.

A—B Schematic cartoon illustrations of the binding mechanism driven by the low enthalpy A and by high entropy B are presented in the left panels. The DNA bases are presented as pyrimidine and purine rings, protein is represented as ellipsoid, N-terminus is shown bound to the minor groove created by A-stretch, and water molecules are shown schematically and colored blue. The dashed lines represent hydrogen bonds observed in the low enthalpy state; the solid line represents direct interactions between amino acids and bases.

The blurred water molecules indicate the high entropy state. Hydrogen bonds that are common to both complexes are omitted for clarity. As DNA is composed of only four bases, only discrete positions along this axis are possible indicated by dots.

Example models of shape and charge distribution of different DNA sequences from Figure 1C are shown as surface representation above the scheme. The surfaces are colored according to the charge distribution: positively charged atoms are in blue, negatively charged are in red and neutral atoms are in green. Shaded boxes on the right show simplified dinucleotide binding models that illustrate how this leads to two distinct locally optimal sequences.

Because we selected for this study cases with two almost equally strong binding sequences, the effect is likely to be stronger here than in most other interactions. Thus, the relative importance of the phenomenon across other types of interactions needs to be evaluated experimentally. The phenomenon we observed exists due to the fact that entropy and enthalpy of binding vary as a function of the shape of the interacting macromolecules.

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Both functions will have optima, commonly at different exact positions. The binding free energy will also vary as a function of the shape, but is likely to have more optima than its constituent functions because they are partially independent of each other. Thus, it is likely that many other biologically relevant examples of this effect will be identified. In addition, it is likely that in most cases one of the local optima is located at lower affinity than the other.

This would manifest as a minor peak or a shoulder in the affinity landscape away from the optimal sequence. In each case, the measured affinities would deviate from those predicted from a single PWM model. Our results and the underlying theory suggest that the ability of TFs to bind to distinct sequences could thus be widespread, and that the importance of the optimal states in determining TF-DNA binding preferences should be reinvestigated.

Moreover, models for TF binding that are used to identify TF sites should also be adjusted to include features that allow two or more optima. In a broader sense, our results are potentially relevant to all macromolecular interactions, particularly in the presence of a polar solvent such as water that can contribute to bridging interactions, whose contributions to the enthalpy and entropy of binding are in the same order of magnitude.

Therefore, in addition to explaining the observed epistasis in protein-DNA interactions, the presence of two optima is likely to also explain the molecular mechanisms behind other types of genetic epistasis. Savitsky et al. For each complex, the purified and concentrated protein was first mixed with a solution of annealed DNA duplex at a molar ratio The crystallization conditions for all complexes were optimized using an in house developed crystal screening kit of different PEGs.

Complexes were crystalized in sitting drops by vapor diffusion technique from solution containing 50 mM Tris buffer pH 8. Statistics of data collection are presented in Table 1. All structures were solved by molecular replacement using program Phaser McCoy et al. The manual rebuilding of the model was done using COOT. The refinement statistics are presented in Table 1. The first seven amino acids from N-termini and the last seven from C-termini were found disordered and were not built in the maps.

The starting structure was placed in a cubic solvent box with 8 nm side length containing water Jorgensen et al. After energy minimization to relax initial strain the systems were heated from K to K over 0. Particle mesh Ewald summation was used to treat the long range electrostatic interactions, using a sixth order cubic spline interpolation for the charge distribution on the 0. The same 0. In the free energy perturbation calculations Zwanzig, we changed the three base pairs in the TCG sequence into those of the CAA sequence using a total of 43 intermediate states, where the order of change was: turn off charges, change Lennard-Jones parameters, turn on charges.

In each state, a 10 ns equilibration was followed by 10 ns production. The free energies were calculated using the Bennett Acceptance Ratio method Bennett, The ITC experiments were carried similarly to described in Ref. Yin et al. To measure binding affinity, a solution of 0. A total of 23 injections were made with s between injections. Each experiment was repeated three times for the reliability of the results. All data were evaluated using the OriginPro 7. In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses.

Structure, Function and Interactions

A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included. Thank you for submitting your article "Two distinct DNA sequences recognized by transcription factors represent enthalpy and entropy optima" for consideration by eLife.

Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Naama Barkai as the Senior Editor.

The following individuals involved in review of your submission have agreed to reveal their identity: Gary Stormo Reviewer 1 ; Thomas D Tullius Reviewer 3.

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