The nature of protein dipole moments: experimental and calculated permanent dipole of alpha-chymotrypsin

Comparison of Huggins Coefficients and Osmotic Second Virial Coefficients of Buffered Solutions of Monoclonal Antibodies

The Huggins coefficient kH is a well-known metric for quantifying the increase in solution viscosity arising from intermolecular interactions in relatively dilute macromolecular solutions, and there has been much interest in this solution property in connection with developing improved antibody therapeutics. While numerous kH measurements have been reported for select monoclonal antibodies (mAbs) solutions, there has been limited study of kH in terms of the fundamental molecular interactions that determine this property. In this paper, we compare measurements of the osmotic second virial coefficient B22, a common metric of intermolecular and interparticle interaction strength, to measurements of kH for model antibody solutions. This comparison is motivated by the seminal work of Russel for hard sphere particles having a short-range "sticky" interparticle interaction, and we also compare our data with known results for uncharged flexible polymers having variable excluded volume interactions because proteins are polypeptide chains. Our observations indicate that neither the adhesive hard sphere model, a common colloidal model of globular proteins, nor the familiar uncharged flexible polymer model, an excellent model of intrinsically disordered proteins, describes the dependence of kH of these antibodies on B22. Clearly, an improved understanding of protein and ion solvation by water as well as dipole-dipole and charge-dipole effects is required to understand the significance of kH from the standpoint of fundamental protein-protein interactions. Despite shortcomings in our theoretical understanding of kH for antibody solutions, this quantity provides a useful practical measure of the strength of interprotein interactions at elevated protein concentrations that is of direct significance for the development of antibody formulations that minimize the solution viscosity.

Constant-pH Brownian Dynamics Simulations of a Protein near a Charged Surface

We have developed a rigid-body Brownian dynamics algorithm that allows for simulations of a globular protein suspended in an ionic solution confined by a charged planar boundary, with an explicit treatment of pH-dependent protein protonation equilibria and their couplings to the electrostatic potential of the plane. Electrostatic interactions are described within a framework of the continuum Poisson-Boltzmann model, whereas protein-plane hydrodynamic interactions are evaluated based on analytical expressions for the position- and orientation-dependent near-wall friction tensor of a spheroid. The algorithm was applied to simulate near-surface diffusion of lysozyme in solutions having pH in the range 4-10 and ionic strengths of 10 and 150 mM. As a reference, we performed Brownian dynamics simulations in which the protein is assigned a fixed, most probable protonation state, appropriate for given solution conditions and unaffected by the presence of the charged plane, and Brownian dynamics simulations in which the protein probes possible protonation states with the pH-dependent probability, but these variations are not coupled to the electric field generated by the boundary. We show that electrostatic interactions with the negatively charged plane substantially modify probabilities of different protonation states of lysozyme and shift protonation equilibria of both acidic and basic amino acid side chains toward higher pH values. Consequently, equilibrium energy distributions, equilibrium position-orientation distributions, and functions that characterize rotational dynamics, which for a protein with multiple ionization sites, such as lysozyme, in the presence of a charged obstacle are pH-dependent, are significantly affected by the approach taken to incorporate the solution pH into simulations.

Does Ionic Screening Lower Activation Barriers for Conformational Transitions in Proteins?

In this work, we investigated the kinetics of binding of hen egg-white lysozyme with tri- N-acetylglucosamine in aqueous solutions, at two values of pH, 3.2 and 11, as a function of ionic strength, by a stopped-flow method with tryptophyl fluorescence observation of the transients. We analyzed registered reaction progress curves by employing numerical integration of appropriate chemical master equations. We discriminated between several binding models and established that the process observed in experiments follows a two-step mechanism, composed of four elementary stages: diffusional formation of an encounter complex, dissociation of the encounter complex, conformational transition of the encounter complex to the final complex, and the reverse transformation, i.e., from the final complex to the encounter complex. We evaluated rate constants of these elementary stages and determined their dependencies on solution ionic strength. Regardless of solution pH, rate constants of both forward and reverse conformational transitions increase with an increasing ionic strength. This suggests that ionic screening of intramolecular electrostatic interactions may act to lower the activation barrier for conformational transition in proteins.

Free energy calculations and molecular properties of substrate translocation through OccAB porins

We investigated with molecular modeling the translocation of simple substrates through four similar specific bacterial porins from the Acinetobacter baumannii pathogen providing structure–function analysis at the molecular level.

Fabrication of Sealed Nanostraw Microdevices for Oral Drug Delivery

The oral route is preferred for systemic drug administration and provides direct access to diseased tissue of the gastrointestinal (GI) tract. However, many drugs have poor absorption upon oral administration due to damaging enzymatic and pH conditions, mucus and cellular permeation barriers, and limited time for drug dissolution. To overcome these limitations and enhance oral drug absorption, micron-scale devices with planar, asymmetric geometries, termed microdevices, have been designed to adhere to the lining of the GI tract and release drug at high concentrations directly toward GI epithelium. Here we seal microdevices with nanostraw membranes-porous nanostructured biomolecule delivery substrates-to enhance the properties of these devices. We demonstrate that the nanostraws facilitate facile drug loading and tunable drug release, limit the influx of external molecules into the sealed drug reservoir, and increase the adhesion of devices to epithelial tissue. These findings highlight the potential of nanostraw microdevices to enhance the oral absorption of a wide range of therapeutics by binding to the lining of the GI tract, providing prolonged and proximal drug release, and reducing the exposure of their payload to drug-degrading biomolecules.

Aligned Immobilization of Proteins Using AC Electric Fields

Protein molecules are aligned and immobilized from solution by AC electric fields. In a single-step experiment, the enhanced green fluorescent proteins are immobilized on the surface as well as at the edges of planar nanoelectrodes. Alignment is found to follow the molecules' geometrical shape with their longitudinal axes parallel to the electric field. Simultaneous dielectrophoretic attraction and AC electroosmotic flow are identified as the dominant forces causing protein movement and alignment. Molecular orientation is determined by fluorescence microscopy based on polarized excitation of the proteins' chromophores. The chromophores' orientation with respect to the whole molecule supports X-ray crystal data.

Protein dielectrophoresis: advances, challenges, and applications

Protein dielectrophoresis (DEP) has the potential to play an important role as a manipulation, fractionation, preconcentration, and separation method in bioanalysis and as manipulation tool for nanotechnological applications. The first demonstrations of protein DEP have been reported almost 20 years ago. Since then various experimental realizations to manipulate proteins by DEP as well as more targeted applications employing protein DEP have been demonstrated. This review summarizes the experimental studies in the field of protein DEP trapping and focusing as well as specific applications in separation, molecular patterning, on bioprobes and biosensors. While a comprehensive theoretical model describing protein DEP is still lacking we also attempt to provide an overview of the factors influencing protein DEP and relate to currently available theoretical models. We further point out the variations in experimental conditions used in the past to study the somewhat 20 proteins as well as the implications of protein molecular structure to the DEP response.

PHEMTO: protein pH-dependent electric moment tools

PHEMTO (protein pH-dependent electric moment tools) is released in response to the high demand in protein science community for evaluation of electrostatic characteristics in relations to molecular recognition. PHEMTO will serve protein scientists with new advanced features for analysis of protein molecular interactions: Electric/dipole moments, their pH-dependence and in silico charge mutagenesis effects on these properties as well as alternative algorithms for electric/dipole moment computation--Singular value decomposition of electrostatic potential (EP) to account for reaction field. The implementation is based on long-term experience--PHEI mean field electrostatics and PHEPS server for evaluation of global and local pH-dependent properties. However, PHEMTO is not just an update of our PHEPS server. Besides standard electrostatics, we offer new, advanced and useful features for analysis of protein molecular interactions. In addition our algorithms are very fast. Special emphasis is given to the interface--intuitive and user-friendly. The input is comprised of the atomic coordinate file in Protein Data Bank format. The advanced user is provided with a special input section for addition of non-polypeptide charges. The output covers actually full electrostatic characteristics but special emphasis is given to electric/dipole moments and their interactive visualization. PHEMTO server can be accessed at http://phemto.orgchm.bas.bg/.

Protonation free energy levels in complex molecular systems

All proteins, nucleic acids, and other biomolecules contain residues capable of exchanging protons with their environment. These proton transfer phenomena lead to pH sensitivity of many molecular processes underlying biological phenomena. In the course of biological evolution, Nature has invented some mechanisms to use pH gradients to regulate biomolecular processes inside cells or in interstitial fluids. Therefore, an ability to model protonation equilibria in molecular systems accurately would be of enormous value for our understanding of biological processes and for possible rational influence on them, like in developing pH dependent drugs to treat particular diseases. This work presents a derivation, by thermodynamic and statistical mechanical methods, of an expression for the free energy of a complex molecular system at arbitrary ionization state of its titratable residues. This constitutes one of the elements of modeling protonation equilibria. Starting from a consideration of a simple acid-base equilibrium of a model compound with a single tritratable group, we arrive at an expression which is of general validity for complex systems. The only approximation used in this derivation is the postulating that the interaction energy between any pair of titratable sites does not depend on the protonation states of all the remaining ionizable groups.

Macrodipoles. Unusual electric properties of biological macromolecules

The wide range of different effects induced by electric fields in biological macromolecules is clearly due to the unusual quality and quantity of their electric parameters. A general concept for a quantitative description of the polarizability of macromolecules remains to be established. In the case of DNA, experimental data indicate the existence of an effective polarization length N(p); at chain lengths N < N(p) the polarizability increases with N(2), whereas saturation is approached at N > or = N(p). The polarization length decreases with increasing ionic strength in close analogy to the Debye length, but is approximately 10 times larger than the Debye length. The dynamics of DNA polarization at high field strengths has been observed in the ns time range and is consistent with biased field induced ion dissociation. In the range of chain lengths from approximately 400 to approximately 850 base pairs DNA molecules exhibit permanent dipole moments, which are in a preferentially perpendicular direction to the end-to-end-vector, leading to a positive electric dichroism. These results are consistent with a "frozen" ensemble of bent DNA configurations and provide evidence for the existence of slow, non-elastic bending transitions. The electric parameters of proteins are usually dominated by a permanent anisotropy of the charge distribution, corresponding to permanent dipole moments of the order of several hundred Debye up to about 1500 Debye. Relatively small dipole moments of protein monomers add up to millions of Debye, when these proteins are in a vectorial organization in membrane patches, as found for bacteriorhodopsin and Na (+)K (+)-ATPase . In these cases the dipole vector may support vectorial ion transport. It is remarkable that the dipole moments of proteins usually show a relatively small dependence on the salt concentration; a rational for these observations is provided by a dipole potential at the plane of shear for rotational diffusion, which is defined in close analogy to the zeta-potential for translational diffusion. Symmetry breaking leading to huge electric dipole moments may be expected for mixed lipid vesicles: according to model calculations the phase separation of lipid components with and without net charges may lead to very high dipole moments; the expectation has been verified experimentally for vesicles containing DMPA and DMPC. The state of these systems should be extremely sensitive to electric fields. In summary, there is an unusual wide variation of electric parameters associated with biological macromolecules and with biomolecular assemblies, which is the basis for the complexity of different phenomena induced by electric fields in biological systems.

A server and database for dipole moments of proteins

An Internet server at http://bip.weizmann.ac.il/dipol calculates the net charge, dipole moment and mean radius of any 3D protein structure or its constituent peptide chains, and displays the dipole vector superimposed on a ribbon backbone of the protein. The server can also display the angle between the dipole and a selected list of amino acid residues in the protein. When the net charges and dipole moments of ∼12 000 non-homologous PDB biological units (PISCES set), and their unique chains of length 50 residues or longer, were examined, the great majority of both charges and dipoles fell into a very narrow range of values, with long extended tails containing a few extreme outliers. In general, there is no obvious relation between a protein's charge or dipole moment and its structure or function, so that its electrostatic properties are highly specific to the particular protein, except that the majority of chains with very large positive charges or dipoles bind to ribosomes or interact with nucleic acids.

The pH-dependent conformational states of kyotorphin: a constant-pH molecular dynamics study

An extensive conformational study of the analgesic dipeptide kyotorphin (L-Tyr-L-Arg) at different pH values was performed using a constant-pH molecular dynamics method. This dipeptide showed a remarkable pH-dependent conformational variety. The protonation of the N-terminal amine was identified as a key element in the transition between the more extended and the more packed conformational states, as monitored by the dihedral angle defined by the atoms 1Cbeta-1Calpha-2Calpha-2Cbeta. The principal-component analysis of kyotorphin identified two major conformational populations (the extended trans and the packed cis) together with conformations that occur exclusively at extreme pH values. Other, less stable conformations were also identified, which help us to understand the transitions between the predominant populations. The fitting of kyotorphin's conformational space to the structure of morphine resulted in a set of conformers that were able to fulfill most of the constraints for the mu-receptor. These results suggest that there may be strong similarities between the kyotorphin receptor and the structural family of opioid receptors.

Constant-pH Molecular Dynamics with Ionic Strength Effects: Protonation−Conformation Coupling in Decalysine

A new implementation of the stochastic titration method for constant-pH molecular dynamics is presented, which introduces ionic strength effects in the simulations. In addition, the new implementation uses a faster molecular dynamics algorithm and an improved treatment of protonation events and of their effect on force field parameters. This new methodology is applied to a decalysine peptide, yielding very good quantitative agreement with experiments, both in terms of titration and helix-coil transition. The results show a significant dependence on ionic strength, illustrating the importance of including this parameter in constant-pH molecular dynamics simulations. Overall, the method seems to properly capture the protonation-conformation coupling and its dependence on ionic strength.

On the Use of Different Dielectric Constants for Computing Individual and Pairwise Terms in Poisson−Boltzmann Studies of Protein Ionization Equilibrium

Poisson-Boltzmann (PB) models are a fast and common tool for studying electrostatic processes in proteins, particularly their ionization equilibrium (protonation and/or reduction), often yielding quite good results when compared with more detailed models. Yet, they are conceptually very simple and necessarily approximate, their empirical character being most evident when it comes to the choice of the dielectric constant assigned to the protein region. The present study analyzes several factors affecting the ability of PB-based methods to model protein ionization equilibrium. We give particular attention to a suggestion made by Warshel and co-workers (e.g., Sham et al. J. Phys. Chem. B 1997, 101, 4458) of using different protein dielectric constants for computing the individual (site) and the pairwise (site-site) terms of the ionization free energies. Our prediction of pK(a) values for several proteins indicates that no advantage is obtained by such a procedure, even for sites that are buried and/or display large pK(a) shifts relative to the solution values. In particular, the present methodology gives the best predictions using a dielectric constant around 20, for shifted/buried and nonshifted/exposed sites alike. The similarities and differences between the PB model and Warshel's PDLD/S model are discussed, as well as the reasons behind their apparently discrepant results. The present PB model is shown to predict also good reduction potentials in redox proteins.

Noonan syndrome type I with PTPN11 3 bp deletion: Structure-function implications

Noonan syndrome was recently reported to be caused by mutations in the PTPN11 gene in 40% of the cases. This gene encodes the nonreceptor-type protein tyrosine phosphatase SHP-2 and has been shown to be self down-regulated with the concurrency of two SH2 domains. Insertion of a specific loop (D'EF) from N-terminal SH2 domain into the SHP-2 active-site is responsible for the reversible inhibition of the phosphatase activity. Here we report the first in frame trinucleotide deletion resulting in the removal of Aspartate 61 (D61del), a key residue of the N-terminal SH2 D'EF loop. Energetic-based structural analysis and electrostatic calculations carried out on the wild-type and mutant proteins predict lower stability of the D'EF loop for the D61del variant as compared to the wild type indicating better access to the active site and most likely an enzyme activated for longer extent. Similar computations were performed on the previously functionally characterized gain-of-function D61Y mutant and similar behaviors were observed. The simulation data for the D61del and D61Y mutants suggest that both variants could yield more catalytic cycles than the wild-type molecule in the same timespan because of the opening of the active site. It also supports the notion that D61 plays a major role for proper down-regulation of the protein tyrosine phosphatase activity of SHP-2.

Adsorption of alpha-chymotrypsin onto mica in laminar flow conditions. Adsorption kinetic constant as a function of tris buffer concentration at pH 8.6

We examined the adsorption kinetics of alpha-chymotrypsin (pH 8.6, 10(-2) to 0.5 M Tris buffer) on muscovite mica in conditions of laminar flow through a slit. The range of buffer concentrations is between two limits: (i) no adsorption in 1 M Tris and (ii) no desorption in 10(-3) M Tris. Studying the dependence of adsorption kinetics on the wall shear rate leads to the determination of the interfacial adsorption kinetic constant ka and the diffusion coefficient. The obtained value for the diffusion coefficient is close to the one expected from the molecular size of alpha-chymotrypsin. The interfacial adsorption kinetic constant of alpha-chymotrypsin decreases when ionic strength increases, while the initial desorption constant (over a part of all the adsorbed population) shows the contrary. Although alpha-chymotrypsin is almost at its isoelectric point, the effect of ionic strength on the adsorption kinetics suggests the importance of electrostatic interactions between the protein and mica. We observed an increase in the adsorption rate, at a surface coverage near 0.14 microg cm(-2), for adsorption in 10(-2) M Tris and the low wall shear rates (<300 s(-1)). This change in the adsorption rate suggests a structural transition, that we assume again to be due to electrostatic interactions, but between proteins. The large dipole moment of the protein may induce this transition, illustrated here by the ferroelectric/antiferroelectric pattern. The variation of the zeta potential with interfacial concentration seems to be in agreement with such a model.

Theoretical and experimental study of the D2194G mutation in the C2 domain of coagulation factor V

Coagulation factor V (FV) is a large plasma glycoprotein with functions in both the pro- and anticoagulant pathways. In carriers of the so-called R2-FV haplotype, the FV D2194G mutation, in the C2 membrane-binding domain, is associated with low expression levels, suggesting a potential folding/stability problem. To analyze the molecular mechanisms potentially responsible for this in vitro phenotype, we used molecular dynamics (MD) and continuum electrostatic calculations. Implicit solvent simulations were performed on the x-ray structure of the wild-type C2 domain and on a model of the D2194G mutant. Because D2194 is located next to a disulfide bond (S-S bond), MD calculations were also performed on S-S bond depleted structures. D2194 is part of a salt-bridge network and investigations of the stabilizing/destabilizing role of these ionic interactions were carried out. Five mutant FV molecules were created and the expression levels measured with the aim of assessing the tolerance to amino acid changes in this region of molecule. Analysis of the MD trajectories indicated increased flexibility in some areas and energetic comparisons suggested overall destabilization of the structure due to the D2194G mutation. This substitution causes electrostatic destabilization of the domain by approximately 3 kcal/mol. Together these effects likely explain the lowered expression levels in R2-FV carriers.

A quantum mechanical study on phosphotyrosyl peptide binding to the SH2 domain of p56lck tyrosine kinase with insights into the biochemistry of intracellular signal transduction events

A study on the interaction between a phosphotyrosyl peptide with the SH2 domain of Lck kinase has been undertaken with the aid of semiempirical linear-scaling quantum mechanical methods. The structure of this complex has been solved at atomic resolution and, hence, it represents the ideal candidate for studying the charge deformation effects induced by the phosphopeptide on the binding site. Substantial changes in the charge of amino acid residues located in the binding pocket of the protein are observed upon ligand binding. More specifically, our quantum chemical calculations indicate that H-bonds involving charged side-chains are subject to consistent charge deformation effects whereas those forming salt bridges are unaffected by ligand binding. Furthermore, ligand binding has the effect of changing both the magnitude and direction of the protein's macrodipole, which rotates approximately 150 degrees with respect that of the unliganded protein. This suggests that a change in the polarization state of the protein might acts as a switch during the transmission of intracellular signals. The binding energy calculated with the aid of the COSMO solvation model corresponds to about -200 kcal/mol, most of which is attributed to the interaction of the phosphotyrosine head with the amino acid chains located in the binding site of the SH2 domain.

The dipole moment of membrane proteins: potassium channel protein and beta-subunit

The mechanism of ion channel opening is one of the most fascinating problems in membrane biology. Based on phenomenological studies, early researchers suggested that the elementary process of ion channel opening may be the intramembrane charge movement or the orientation of dipolar proteins in the channel. In spite of the far reaching significance of these hypotheses, it has not been possible to formulate a comprehensive molecular theory for the mechanism of channel opening. This is because of the lack of the detailed knowledge on the structure of channel proteins. In recent years, however, the research on the structure of channel proteins made marked advances and, at present, we are beginning to have sufficient information on the structure of some of the channel proteins, e.g. potassium-channel protein and beta-subunits. With these new information, we are now ready to have another look at the old hypothesis, in particular, the dipole moment of channel proteins being the voltage sensor for the opening and closing of ion channels. In this paper, the dipole moments of potassium channel protein and beta-subunit, are calculated using X-ray diffraction data. A large dipole moment was found for beta-subunits while the dipole moment of K-channel protein was found to be considerably smaller than that of beta-subunits. These calculations were conducted as a preliminary study of the comprehensive research on the dipolar structure of channel proteins in excitable membranes, above all, sodium channel proteins.

The structure and dipole moment of globular proteins in solution and crystalline states: use of NMR and X-ray databases for the numerical calculation of dipole moment

The large dipole moment of globular proteins has been well known because of the detailed studies using dielectric relaxation and electro-optical methods. The search for the origin of these dipolemoments, however, must be based on the detailed knowledge on protein structure with atomic resolutions. At present, we have two sources of information on the structure of protein molecules: (1) x-ray databases obtained in crystalline state; (2) NMR databases obtained in solution state. While x-ray databases consist of only one model, NMR databases, because of the fluctuation of the protein folding in solution, consist of a number of models, thus enabling the computation of dipole moment repeated for all these models. The aim of this work, using these databases, is the detailed investigation on the interdependence between the structure and dipole moment of protein molecules. The dipole moment of protein molecules has roughly two components: one dipole moment is due to surface charges and the other, core dipole moment, is due to polar groups such as N--H and C==O bonds. The computation of surface charge dipole moment consists of two steps: (A) calculation of the pK shifts of charged groups for electrostatic interactions and (B) calculation of the dipole moment using the pK corrected for electrostatic shifts. The dipole moments of several proteins were computed using both NMR and x-ray databases. The dipole moments of these two sets of calculations are, with a few exceptions, in good agreement with one another and also with measured dipole moments.

The electric dipole moment of DNA-binding HU protein calculated by the use of an NMR database

Electric birefringence measurements indicated the presence of a large permanent dipole moment in HU protein-DNA complex. In order to substantiate this observation, numerical computation of the dipole moment of HU protein homodimer was carried out by using NMR protein databases. The dipole moments of globular proteins have hitherto been calculated with X-ray databases and NMR data have never been used before. The advantages of NMR databases are: (a) NMR data are obtained, unlike X-ray databases, using protein solutions. Accordingly, this method eliminates the bothersome question as to the possible alteration of the protein structure due to the transition from the crystalline state to the solution state. This question is particularly important for proteins such as HU protein which has some degree of internal flexibility; (b) the three-dimensional coordinates of hydrogen atoms in protein molecules can be determined with a sufficient resolution and this enables the N-H as well as C = O bond moments to be calculated. Since the NMR database of HU protein from Bacillus stearothermophilus consists of 25 models, the surface charge as well as the core dipole moments were computed for each of these structures. The results of these calculations show that the net permanent dipole moments of HU protein homodimer is approximately 500-530 D (1 D = 3.33 x 10(-30) Cm) at pH 7.5 and 600-630 D at the isoelectric point (pH 10.5). These permanent dipole moments are unusually large for a small protein of the size of 19.5 kDa. Nevertheless, the result of numerical calculations is compatible with the electro-optical observation, confirming a very large dipole moment in this protein.

Simulation of electron-proton coupling with a Monte Carlo method: application to cytochrome c3 using continuum electrostatics

A new method is presented for simulating the simultaneous binding equilibrium of electrons and protons on protein molecules, which makes it possible to study the full equilibrium thermodynamics of redox and protonation processes, including electron-proton coupling. The simulations using this method reflect directly the pH and electrostatic potential of the environment, thus providing a much closer and realistic connection with experimental parameters than do usual methods. By ignoring the full binding equilibrium, calculations usually overlook the twofold effect that binding fluctuations have on the behavior of redox proteins: first, they affect the energy of the system by creating partially occupied sites; second, they affect its entropy by introducing an additional empty/occupied site disorder (here named occupational entropy). The proposed method is applied to cytochrome c3 of Desulfovibrio vulgaris Hildenborough to study its redox properties and electron-proton coupling (redox-Bohr effect), using a continuum electrostatic method based on the linear Poisson-Boltzmann equation. Unlike previous studies using other methods, the full reduction order of the four hemes at physiological pH is successfully predicted. The sites more strongly involved in the redox-Bohr effect are identified by analysis of their titration curves/surfaces and the shifts of their midpoint redox potentials and pKa values. Site-site couplings are analyzed using statistical correlations, a method much more realistic than the usual analysis based on direct interactions. The site found to be more strongly involved in the redox-Bohr effect is propionate D of heme I, in agreement with previous studies; other likely candidates are His67, the N-terminus, and propionate D of heme IV. Even though the present study is limited to equilibrium conditions, the possible role of binding fluctuations in the concerted transfer of protons and electrons under nonequilibrium conditions is also discussed. The occupational entropy contributions to midpoint redox potentials and pKa values are computed and shown to be significant.

Future directions for combining molecular and continuum models in protein simulations

In order to perform useful computer simulations on protein molecules, models that combine atomistic and continuum approaches will be necessary. The use of continuum models will reduce the number of system variables and allow studies of longer time scales. On the other hand, one will still need to retain atomic detail in certain parts of the protein molecule, such as an enzyme active site. Most of the important advances to date have been continuum models of the surrounding solvent, but simplified descriptions of the protein itself also are being developed. Finally, in order to study these several different levels of complexity simultaneously in a single simulation, it will be necessary to use modern software engineering techniques.

pKa calculations for class A beta-lactamases: methodological and mechanistic implications

Beta-lactamases are responsible for resistance to penicillins and related beta-lactam compounds. Despite numerous studies, the identity of the general base involved in the acylation step is still unclear. It has been proposed, on the basis of a previous pKa calculation and analysis of structural data, that the unprotonated Lys73 in the active site could act as the general base. Using a continuum electrostatic model with an improved treatment of the multiple titration site problem, we calculated the pKa values of all titratable residues in the substrate-free TEM-1 and Bacillus licheniformis class A beta-lactamases. The pKa of Lys73 in both enzymes was computed to be above 10, in good agreement with recent experimental data on the TEM-1 beta-lactamase, but inconsistent with the proposal that Lys73 acts as the general base. Even when the closest titratable residue, Glu166, is mutated to a neutral residue, the predicted downward shift of the pKa of Lys73 shows that it is unlikely to act as a proton abstractor in either enzyme. These results support a mechanism in which the proton of the active Ser70 is transferred to the carboxylate group of Glu166.

Simulation of electrostatic and hydrodynamic properties of Serratia endonuclease

We analyze the electrostatic and hydrodynamic properties of a nuclease from the pathogenic gram-negative bacterium Serratia marcescens using finite-difference Poisson-Boltzmann methods for electrostatic calculations and a bead-model approach for diffusion coefficient calculations. Electrostatic properties are analyzed for the enzyme in monomeric and dimeric forms and also in the context of DNA binding by the nuclease. Our preliminary results show that binding of a double-stranded DNA dodecamer by nuclease causes an overall shift in the charge of the protein by approximately three units of elementary charge per monomer, resulting in a positively charged protein at physiologic pH. In these calculations, the free enzyme was found to have a negative (-1 e) charge per monomer at pH 7. The most dramatic shift in pKa involves His 89 whose pKa increases by three pH units upon DNA binding. This shift leads to a protonated residue at pH 7, in contrast to the unprotonated form in the free enzyme. DNA binding also leads to a decrease in the energetic distances between the most stable protonation states of the enzyme. Dimerization has no significant effect on the electrostatic properties of each of the monomers for both free enzyme and that bound to DNA. Results of hydrodynamic calculations are consistent with the dimeric form of the enzyme in solution. The computed translational diffusion coefficient for the dimer model of the enzyme is in very good agreement with measurements from light scattering experiments. Preliminary electrooptical calculations indicate that the dimer should possess a large dipole moment (approximately 600 Debye units) as well as substantial optical anisotropy (limiting reduced linear electric dichroism of about 0.3). Therefore, this system may serve as a good model for investigation of electric and hydrodynamic properties by relaxation electrooptical experiments.

Electrostatics and electrodynamics of bacteriorhodopsin

The stationary electric dichroism of bacteriorhodopsin is in qualitative, but not quantitative, agreement with the orientation function for disks having a permanent dipole directed perpendicular to the plane and an induced dipole in the plane. Fits of the orientation function to data measured at low field strengths demonstrate: an increase of the permanent dipole moment mu with the square of the disk radius r2, whereas the polarizability alpha increases with r4; the ionic strength dependence is small for mu and clearly stronger for alpha; the permanent dipole moment is 4x10(6) D at r = 0.5 micron. According to the risetime constants, the induced dipole does not saturate and increases to 4x10(8) D at 40 kV/cm and r = 0.5 micron. The data indicate that the permanent dipole is not of some interfacial character but is due to a real assymetry of the charge distribution. The experimental dipole moment per protein monomer is approximately 55 D, whereas calculations based on the structure of Grigorieff et al. (Grigorieff, N., T.A. Ceska, K.H. Downing, J.M. Baldwin, and R. Henderson. 1996. Electron-crystallographic refinement of the structure of bacteriorhodopsin. J. Mol. Biol. 259:393-421) provide a dipole moment of approximately 570 D. The difference is probably due to a nonsymmetric distribution of charged lipid residues. It is concluded that experimental dipole moments reflect the mu-potential at the plane of shear for rotational diffusion, in analogy to the sigma-potential used for translational diffusion. It is suggested that the permanent dipole of bacteriorhodopsin supports proton transport by attraction of protons inside and repulsion of protons outside of the cell. Dichroism rise curves at field strengths between E = 150 and 800 V/cm reveal an exponential component with time constants tau 3r in the range between 1 and 40 ms, which is not found in Brownian dynamics simulations on a disk structure using hydrodynamic and electric parameters characteristic of bacteriorhodopsin disks. The experimental data suggest that this process reflects a cooperative change of the bacteriorhodopsin structure, which is induced already at a remarkably low field strength of approximately 150 V/cm.

Electrooptical measurements demonstrate a large permanent dipole moment associated with acetylcholinesterase

Acetylcholinesterase (AChE) from krait (Bungarus fasciatus) venom is a soluble, nonamphiphilic monomer of 72 kDa. This snake venom AChE has been analyzed by measurements of the stationary and the transient electric dichroism at different field strengths. The stationary values of the dichroism are consistent with the orientation function for permanent dipoles and are not consistent with the orientation function for induced dipoles. The permanent dipole moment obtained by least-squares fits for a buffer containing 5 mM MES is 1000 D, after correction for the internal directing field, assuming a spherical shape of the protein. The dipole moment decreases with increasing buffer concentration to 880 D at 10 mM MES and 770 D at 20 mM MES. The dichroism decay time constant is 90 ns (+/- 10%) which is clearly larger than the value expected from the size/shape of the protein and indicates contributions from sugar residues attached to the protein. The dichroism rise times observed at low field strengths are larger than the decay times and, thus, support the assignment of a permanent dipole moment, although it has not been possible to approach the limit where the energy of the dipole in the electric field is sufficiently low compared to kT. The experimental value of the permanent dipole moment is similar to that calculated for a model structure of Bungarus fasciatus AChE, which has been constructed from its amino and acid sequence, in analogy to the crystal structure of AChE from Torpedo californica.

Measurement and computation of the dipole moment of globular proteins III: Chymotrypsin

The dipole moments of alpha- and gamma-chymotrypsin are determined experimentally using the dielectric constant measuring method. The values thus obtained are compared with the results of the electric dichroism measurements for alpha-chymotrypsins by other investigators. The agreement is reasonably good, if not satisfactory. The cause of difference appears to be due to the difficulty of finding the correct internal field. The interaction between two neighboring dipoles is found to be a minor component of the local fields. Secondly, the dipole moment of alpha-chymotrypsin was computed using Protein Data Bases. The dipole moment of proteins consists of two major components, the moment due to fixed surface charges and the core moment due to polar chemical bonds. The method of calculation was described in detail in previous papers. The pK shifts of polar side chains were calculated using the methods of Tanford et al. and its modification by Warshel et al. The agreement between measured and calculated dipole moments is satisfactory.

Electrooptical analysis of α-chymotrypsin at physiological salt concentration

The electric dichroism of alpha-chymotrypsin has been measured in a buffer containing 0.1 M Na(+), 10 mM Mg(2+) and 25 mM Tris-cacodylate pH 7.2. The reduced dichroism as a function of the electric field strength can be represented by the orientation function for permanent dipoles and is not consistent with the orientation function for induced dipoles. After correction for the internal directing field, the dipole moment is 1.1 x 10(-27) Cm (+/- 10%), corresponding to 340 D, at 20 degrees C. The assignment of the permanent dipole moment is confirmed by the shape of the dichroism rise curves, which require two exponentials with amplitudes of opposite sign for fitting. The dichroism decay time constants measured in the range of temperatures between 2 and 30 degrees C indicate a temperature induced change of the structure, which is equivalent to an increase of the hydrodynamic radius from r = 26.6 A at 2 degrees C to 28.5 A at 30 degrees C. Our results demonstrate that electrooptical investigations of proteins with a high time resolution can be extended to physiological salt concentrations without serious problems by use of appropriate instruments.

Computation of the dipole moments of proteins

A simple and computationally feasible procedure for the calculation of net charges and dipole moments of proteins at arbitrary pH and salt conditions is described. The method is intended to provide data that may be compared to the results of transient electric dichroism experiments on protein solutions. The procedure consists of three major steps: (i) calculation of self energies and interaction energies for ionizable groups in the protein by using the finite-difference Poisson-Boltzmann method, (ii) determination of the position of the center of diffusion (to which the calculated dipole moment refers) and the extinction coefficient tensor for the protein, and (iii) generation of the equilibrium distribution of protonation states of the protein by a Monte Carlo procedure, from which mean and root-mean-square dipole moments and optical anisotropies are calculated. The procedure is applied to 12 proteins. It is shown that it gives hydrodynamic and electrical parameters for proteins in good agreement with experimental data.

Electrostatics of hemoglobins from measurements of the electric dichroism and computer simulations

Hemoglobins from normal human cells, from sickle cells, and from horse were investigated by electrooptical methods in their oxy and deoxy forms. The reduced linear dichroism measured as a function of the electric field strength demonstrates the existence of permanent dipole moments in the range of 250-400 Debye units. The reduced limiting dichroism is relatively small (< or = 0.1); it is negative for hemoglobin from sickle cells and positive for the hemoglobins from normal human cells and from horse. The dichroism decay time constants are in the range from about 55 to 90 ns. Calculations of the electrooptical data from available crystal structures are given according to models of various complexity, including Monte Carlo simulations of proton fluctuations with energies evaluated by a finite difference Poisson-Boltzmann procedure. The experimental dipole moments are shown to be consistent with the results of the calculations. In the case of human deoxyhemoglobin, the root mean square dipole is higher than the mean dipole by a factor of about 4.5, indicating a particularly large relative contribution due to proton fluctuations. The ratio of the root mean square dipole to the mean dipole is much smaller (approximately 1.1 to approximately 1.5) for the other hemoglobin molecules. The calculations demonstrate that the dichroism decay time constants are not simply determined by the size/shape of the proteins, but are strongly influenced by the orientation of the dipole vector with respect to the axis of maximal absorbance. The comparison of experimental and calculated electrooptical data provides a useful test for the accuracy of electrostatic calculations and/or for the equivalence of structures in crystals and in solutions.