Free energy distributions in proteins.

The monomers or aggregates of protein molecules in protein crystallization solution at the initial stage of crystallization process are the basis of subsequent nucleation process. Tanaka et al (Tanaka S., et al, J. Cryst. Growth, 1996) concluded that there are units and clusters of lysozyme molecules in solution at the beginning of lysozyme crystallization process, and the decrease of clusters' amount showed the nucleation process comes up. Therefore, cluster of protein molecules in solution is one of important parameters, by which we can judge the crystallization process, in particular, nucleation process. However, the formation process of lysozyme clusters was not reported up to now. In this paper, we studied the aggregates of lysozyme molecules in solution 1 hr and 12 hrs after the mixture of lysozyme and NaCl (precipitant) solution, by atomic force microscopy (AFM) and dynamic light scattering (DLS). Moreover, we studied the effect of solution temperature on the aggregates in solution. Our results showed that, 1 hr after the mixture of lysozyme and NaCl solution, the mean size of aggregates in solution first increased and then decreased. Our results also showed that the aggregates of lysozyme molecules in solution gradually disassembled and clusters of lysozyme molecules appeared within 12 hrs after the mixture of lysozyme and NaCl solution. The decrease of solution temperature decreased the period for appearance of clusters of lysozyme molecules in solution.

Journal of Cellular and Comparative PhysiologyVolume 49, Issue S1 p. 59-62 Article The forces between protein molecules in solution: A summary† John G. Kirkwood, John G. Kirkwood Sterling Chemistry Laboratory, Yale University, New Haven, ConnecticutSearch for more papers by this author John G. Kirkwood, John G. Kirkwood Sterling Chemistry Laboratory, Yale University, New Haven, ConnecticutSearch for more papers by this author First published: May 1957 https://doi.org/10.1002/jcp.1030490406Citations: 7 † Summary of lecture given also at a Symposium on “Molecular Structure and Biological Specificity,” Washington, D. C., October 1955; sponsored by the American Institute of Biological Sciences and supported by the Office of Naval Research. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume49, IssueS1May 1957Pages 59-62 RelatedInformation

On the thermodynamics of adsorption on heterogeneous surfaces

DNA-stacking interactions Determine the Sequence Specificity of the Deoxyribonuclease Activity of 1,10-Phenanthroline-copper Ion

The solvent around protein molecules in solutions is structured and this structuring introduces a repulsion in the intermolecular interaction potential at intermediate separations. We use Monte Carlo simulations with isotropic, pair-additive systems interacting with such potentials. We test if the liquid-liquid and liquid-solid phase lines in model protein solutions can be predicted from universal curves and a pair of experimentally determined parameters, as done for atomic and colloid materials using several laws of corresponding states. As predictors, we test three properties at the critical point for liquid-liquid separation: temperature, as in the original van der Waals law, the second virial coefficient, and a modified second virial coefficient, all paired with the critical volume fraction. We find that the van der Waals law is best obeyed and appears more general than its original formulation: A single universal curve describes all tested nonconformal isotropic pair-additive systems. Published experimental data for the liquid-liquid equilibrium for several proteins at various conditions follow a single van der Waals curve. For the solid-liquid equilibrium, we find that no single system property serves as its predictor. We go beyond corresponding-states correlations and put forth semiempirical laws, which allow prediction of the critical temperature and volume fraction solely based on the range of attraction of the intermolecular interaction potential.

In general, materials with linear memory constitutive relations are characterized by a relaxation function. This leads to a situation where the free energy for most materials with memory is not unique. There is a convex set of free energy functionals with a minimum and a maximum element. An alternative procedure is proposed which characterizes a material by the kernel of the rate of dissipation functional. Using some recent results, we find that a unique free energy and relaxation function may then be deduced. An example is given for discrete spectrum materials. Also, the new results are used to show that a previously derived general representation of rate of dissipation and free energy functionals is not complete, in the sense that there are valid functionals which cannot be described by this general formula.

Solubility measurement, molecular simulation and thermodynamic analysis of guanidine hydrochloride in eleven neat solvents

We study a phase-field variational model for the solvaiton of charged molecules with an implicit solvent. The solvation free-energy functional of all phase fields consists of the surface energy, solute excluded volume and solute-solvent van der Waals dispersion energy, and electrostatic free energy. The surface energy is defined by the van der Waals--Cahn--Hilliard functional with squared gradient and a double-well potential. The electrostatic part of free energy is defined through the electrostatic potential governed by the Poisson--Boltzmann equation in which the dielectric coefficient is defined through the underlying phase field. We prove the continuity of the electrostatics---its potential, free energy, and dielectric boundary force---with respect to the perturbation of dielectric boundary. We also prove the $\Gamma$-convergence of the phase-field free-energy functionals to their sharp-interface limit, and the equivalence of the convergence of total free energies to that of all individual parts of free energy. We finally prove the convergence of phase-field forces to their sharp-interface limit. Such forces are defined as the negative first variations of the free-energy functional; and arise from stress tensors. In particular, we obtain the force convergence for the van der Waals--Cahn--Hilliard functionals with minimal assumptions.

We study the directed polymer of length t in a random potential with fixed endpoints in dimension 1+1 in the continuum and on the square lattice, by analytical and numerical methods. The universal regime of high temperature T is described, upon scaling “time”t∼T5/κ and space x=T3/κ (with κ=T for the discrete model) by a continuum model with δ-function disorder correlation. Using the Bethe Ansatz solution for the attractive boson problem, we obtain all positive integer moments of the partition function. The lowest cumulants of the free energy are predicted at small time and found in agreement with numerics. We then obtain the exact expression at any time for the generating function of the free-energy distribution, in terms of a Fredholm determinant. At large time we find that it crosses over to the Tracy-Widom distribution (TW) which describes the fixed-T infinite-t limit. The exact free-energy distribution is obtained for any time and compared with very recent results on growth and exclusion models.

The aim of this work is to determine what free energy functionals are expressible as quadratic forms of the state functional \(I^t\) which is discussed in earlier papers. The single integral form is shown to include the functional \(\psi _F\) proposed a few years ago, and also a further category of functionals which are easily described but more complicated to construct. These latter examples exist only for certain types of materials. The double integral case is examined in detail, against the background of a new systematic approach developed recently for double integral quadratic forms in terms of strain history, which was used to uncover new free energy functionals. However, while, in principle, the same method should apply to free energies which can be given by quadratic forms in terms of \(I^t\), it emerges that this requirement is very restrictive; indeed, only the minimum free energy can be expressed in such a manner.

We present calculations of the absolute and relative binding free energies of complexation of streptavidin with biotin and its analogs by means of a thermodynamic free energy perturbation method implemented with molecular dynamics. Using the recently solved crystal structure of the streptavidin-biotin complex, biotin was mutated into a dummy molecule as well as thiobiotin and iminobiotin both in the protein and in solution. The calculated absolute binding free energy was dependent on the simulation model used. Encouragingly, the "best models" provided a reasonable semiquantitative reproduction (-20 to -22 kcal/mol) of the experimental free energy (-18.3 kcal/mol). Furthermore, the calculated results give clear insights into the binding nature of the protein-ligand complex, showing that the van der Waals energy dominates the electrostatic and hydrogen bonding energies in the binding of biotin by streptavidin. Specifically, the mutation of biotin into a dummy molecule in solution has a delta G (van der Waals) approximately -4 kcal/mol, due to the cancellation of dispersion and repulsion "cavity" effects. On the other hand, in the protein, a very small free energy price must be paid to create a cavity since one already exists and the mutation of biotin into a dummy molecule has a delta G (van der Waals) approximately 15 kcal/mol. These results are also consistent with the interpretation that the entropy increase to be expected from hydrophobic interactions from desolvation of biotin is counterbalanced by a decrease in entropy accompanying the formation of buried hydrogen bonds, which have been derived from the apparently conflicting experimental data. They provide an alternative interpretation of the reason for the extremely high affinity of the biotin-streptavidin interaction than that recently proposed by Weber et al. (J. Am. Chem. Soc. 114:3197, 1992). In the case of the relative binding free energies, the calculated values of 3.8 +/- 0.6 and 7.2 +/- 0.6 kcal/mol compare well with the experimental values of 3.6 and 6.2 kcal/mol for the perturbation of biotin to thiobiotin and iminobiotin, respectively in the related protein avidin. The calculations indicate that desolvation of the ligand is important in understanding the relative affinity of the ligands with the protein. The above successful simulations suggest that the molecular dynamics/free energy perturbation method is useful for understanding the energetic features affecting the binding between proteins and ligands, since it is generally difficult to determine these factors unambiguously by experiment.(ABSTRACT TRUNCATED AT 400 WORDS)

Freeze-fracture study of water-soluble, standard proteins and of detergent-solubilized forms of sarcoplasmic reticulum Ca 2+-ATPase

Partial molecular alignment leads to an incomplete averaging of anisotropic magnetic interactions such as the magnetic dipole–dipole interaction, the chemical shift anisotropy, or the electric quadrupole interaction. The resulting so‐called “residual” anisotropic magnetic interactions currently become increasingly important in biomolecular NMR spectroscopy. In particular, residual dipolar couplings turn out to be extremely useful novel parameters for protein structure determination. The basic principles of this new methodology are discussed in the present review and recent applications are demonstrated. Different alignment mechanisms leading to partial orientation of protein molecules in solution are considered in detail. The influence of magnetic and electric fields applied to isotropic protein solutions is discussed. Various magnetically orienting media which can be admixed to protein solutions are described and compared. Experiments for the measurement of residual dipolar couplings in proteins and advantageous strategies for the use of residual dipolar couplings in structure calculations are reviewed. © 2001 John Wiley & Sons, Inc. Concepts Magn Reson 13: 238–259, 2001

A new approach is suggested to model the spatial structure of protein molecules in solution based on combined use of the methods of theoretical conformational analysis and NMR spectroscopy data. At the first stage, special means are used to convert d connectivity information into the most probable values of dihedral angles. This allows search for possible spatial structures in the limited regions of the conformational space at further stages using the methods of the theoretical conformational analysis. The suggested approach was verified in reconstructing the spatial backbone structure of the fragment 17-57 of the proteinase inhibitor BUSI IIA from the bull seminal plasma. The structural model parameters are compared with the corresponding characteristics obtained from the X-ray analysis data for the homologic proteinase inhibitor from the Japanese quail ovomucoid. The suggested approach is shown to correctly reproduce both the general molecule topology and the conformations of individual amino acid residues.

A chloroform solution of an anionic dye bound to polymethyl methacrylate having an amino endgroup is partitioned with an extremely dilute solution (< 0.001 per cent) of a protein at a suitable pH. The amount of dye which gets transferred to the aqueous layer is a measure of the available excess of carboxyl over amino group of the protein. This value increases considerably with age and also with heat denaturation of the protein and so this gives an insight into conformational change or unfolding of the protein molecule as due to thermal denaturation and ageing characteristics.The same method has also been applied with success to determine, the carboxyl content of polyacrylamide (partially hydrolysed), carboxymethyl cellulose, gum arabie, copolymers containing acrylic, methacrylic and crotonic acids, and graft polymers containing acrylic acid.