The intraglobular electrostatic field of an enzyme. 1. The primary field created by the polypeptide core, functional groups and ions of the alpha-chymotrypsin molecule

The electric field set up by the dipoles of peptide groups ad other dipoles at the atoms of substrate and catalytic groups of alpha-chymotrypsin is considered. It is shown that substantial electric potentials reaching some tenths of volts exist in the active center of the enzyme, the fact which must influence significantly the reactivity of corresponding groups. In contrast to low molecular weight liquids, the contribution to the total potential of dipoles located at different distances from the point under consideration often changes nonmonotonically with the distance, sometimes the predominant influence being exerted not by the nearest polar groups but by the more distant ones. The existence of electric fields having a complex spatial configuration determined by the protein structure can be defined as the effect of the polar medium preorganization. Emphasis is placed on the necessity of taking into account the polarization of the external medium by charges of protein atoms and ions (the difference of primary and secondary electric fields).     

The catalytic mechanism of serine proteases II: The effect of the protein environment in the alpha-chymotrypsin proton relay system

The proton relay system of alpha-chymotrypsin is analyzed by the INDOISCRF method. The effects of the protein electric and polarization fields are explicitly introduced in the calculations. It is shown that the multicharged structure Ser-His+Asp- is the most sensitive, from an energetic view-point, towards the protein surrounding effects. Variations in the permanent and polarization fields are discussed, as well as the influence of the substrate and one water molecule localized in the active site of the enzyme. The catalytic role of such changes is conjectured.     

The surface layer of the protein globule. Hydration of the alpha-chymotrypsin molecule]

The surface of the alpha-chymotrypsin globule is investigated using a three-dimensional model of the molecule, constructed on the basis of X-ray data by sectioning the space of the protein globule in cubic elements with a step of 3 A. The surface layer contains about 55% of the overall globule volume. The atomic density of so defined surface was found to be approximately equal to that in the inner part of the globule. Topographical maps of the alpha-chymotrypsin surface were drawn and an analysis of the distribution of polar and unpolar atoms and groups on the surface and in the inner part of the globule was carried out. Some conclusions drawn from the atomic density, energetic and structural heterogeneity of the surface and concerning the conformational integrity and functional activity of alpha-chymotrypsin molecule are presented. Some aspects of the protein hydration problem are discussed and a structural model of the alpha-chymotrypsin hydratation shell is proposed, the main features of which are amorphism and the lack of long-range effect on the structure of water around the hydrated protein globule.     

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.     

About factors providing the fast protein-protein recognition in processes of complex formation

A package of programs for the examination of areas of subunit contacts (interface) in protein-protein (PP) complexes has been created and used for a detailed study of amino acid (AA) composition and interface structure in a large number of PP complexes from Brookhaven database (PBD). It appeared that in about 75% of the complexes, the AA composition of the subunit surface is not important. This suggests that, along with the surface AA composition, interactions between AA from the inner parts of protein globules may play a significant role in PP recognition. Such interactions between relatively distant AA residues can only be of electrostatic nature and contribute to the total electric field of the protein molecule. The configuration of the electric field itself appears to determine the PP recognition. The total electric field created by protein molecules can be calculated as a result of superimposition of the fields created by the protein multipole (i.e. by the totality of partial electric charges assigned to each atom of the molecule). We performed preliminary calculations for the distant electrostatic interaction of ribonuclease subunits in a vacuum. The results reveal that the effect of the electric fields of the protein multipole is strong enough to orient protein molecules prior to their Brown collision.     

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

The electric dichroism of alpha-chymotrypsin has been measured in buffers of various pH values and ion compositions. The stationary dichroism obtained as a function of the electric field strength is not compatible with an induced dipole mechanism and clearly shows that alpha-chymotrypsin is associated with a substantial permanent dipole moment. After correction for the internal directing electric field according to a sphere model, the dipole moment is 1.6 X 10(-27) C m at pH 8.3 (corresponding to 480 D). This value decreases with decreasing pH (to 1.2 X 10(-27) C m at pH 4.2), but is almost independent of the monovalent salt concentration in the range from 2 to 12 mM and of Mg2+ addition up to 1 mM. The assignment of the permanent dipole moment is confirmed by analysis of the dichroism rise curves. The dichroism decay time constants of (31 +/- 1) ns at 2 degrees C can be represented by a spherical model with a radius of 25-26 A, which is consistent with the known X-ray structure. The limiting linear dichroism is slightly dependent on the buffer composition and demonstrates subtle variations of the protein structure. As a complement to the experimental results, electric and hydrodynamic parameters of alpha-chymotrypsin have been calculated according to the known X-ray structure. Bead model simulations provide the center of diffusion, which is used to calculate dipole moments according to the equilibrium charge distribution evaluated from standard pK values.(ABSTRACT TRUNCATED AT 250 WORDS)     

Asymmetric electrostatic effects on the gating of rat brain sodium channels in planar lipid membranes.

The effects of ionic strength (10-1,000 mM) on the gating of batrachotoxin-activated rat brain sodium channels were studied in neutral and in negatively charged lipid bilayers. In neutral bilayers, increasing the ionic strength of the extracellular solution, shifted the voltage dependence of the open probability (gating curve) of the sodium channel to more positive membrane potentials. On the other hand, increasing the intracellular ionic strength shifted the gating curve to more negative membrane potentials. Ionic strength shifted the voltage dependence of both opening and closing rate constants of the channel in analogous ways to its effects on gating curves. The voltage sensitivities of the rate constants were not affected by ionic strength. The effects of ionic strength on the gating of sodium channels reconstituted in negatively charged bilayers were qualitatively the same as in neutral bilayers. However, important quantitative differences were noticed: in low ionic strength conditions (10-150 mM), the presence of negative charges on the membrane surface induced an extra voltage shift on the gating curve of sodium channels in relation to neutral bilayers. It is concluded that: (a) asymmetric negative surface charge densities in the extracellular (1e-/533A2) and intracellular (1e-/1,231A2) sides of the sodium channel could explain the voltage shifts caused by ionic strength on the gating curve of the channel in neutral bilayers. These surface charges create negative electric fields in both the extracellular and intracellular sides of the channel. Said electric fields interfere with gating charge movements that occur during the opening and closing of sodium channels; (b) the voltage shifts caused by ionic strength on the gating curve of sodium channels can be accounted by voltage shifts in both the opening and closing rate constants; (c) net negative surface charges on the channel's molecule do not affect the intrinsic gating properties of sodium channels but are essential in determining the relative position of the channel's gating curve; (d) provided the ionic strength is below 150 mM, the gating machinery of the sodium channel molecule is able to sense the electric field created by surface changes on the lipid membrane. I propose that during the opening and closing of sodium channels, the gating charges involved in this process are asymmetrically displaced in relation to the plane of the bilayer. Simple electrostatic calculations suggest that gating charge movements are influenced by membrane electrostatic potentials at distances of 48 and 28 A away from the plane of the membrane in the extracellular sides of the channel, respectively.     

What forces can determine the formation of highly specific protein-protein complexes?

A software package was designed and used in a detailed study of the contact regions (interfaces) of a large number of protein-protein complexes using the PDB data. It appeared that for about 75% of the complexes the amino acid composition of the subunit surface in the contact region is not essential. Thus one may suggest that, along with the amino acid residues at the interface, the residues in the interior of the globules substantially contribute to protein-protein recognition. Such interactions between quite remote residues are most probably of electrical nature, and are involved in recognition by contributing to the overall electric field created by the protein molecule; the configuration of this field is perhaps the definitive factor of recognition. The overall field of the protein molecule is additively built of the fields created by each constituent residue, and it can be calculated as a sum of the fields created by the protein multipole (aggregate of 'partial' electric charges assigned to every atom of the protein molecule). Preliminary calculations of the remote electrostatic interaction have been performed for ribonuclease subunits in vacuum. The results are indicative of a real possibility that the electric field created by the protein multipole can strongly influence the mutual orientation of molecules before Brownian collisions.     

Electrostatics of proteins: Description in terms of two dielectric constants simultaneously

In the semi-continuum treatment of the energetics of charge formation (or transfer) inside a protein, two components of the energy are inevitably present: the energy of interaction of the ion with the pre-existing intraprotein electric field, and the energy due to polarization of the medium by the newly formed charge. The pre-existing field is set up by charges (partial or full) of the protein atoms fixed in a definite structure. The calculation of this field involves only the electronic polarization (the optical dielectric constant ϵ_o) of the protein because the polarization due to shifts of heavy atoms has already been accounted for by their equilibrium coordinates. At the same time, the aqueous surroundings should be described by the static constant ϵ_sw, as the positions of water molecules are not fixed. The formation of a new charge, absent in the equilibrium X-ray structure, results in shifts of electrons and polar atoms, i.e., it involves all kinds of medium polarization described by the static dielectric constant of protein ϵ_s. Thus, in calculations of the total energy, two different dielectric constants of the protein are operative simultaneously. This differs from a widely used algorithm employing one effective dielectric constant for both components of the ion's energy. Proteins: 28:174–182, 1997. © 1997 Wiley-Liss Inc.     

The Effect of Electrical Deformation Forces on the Electropermeabilization of Erythrocyte Membranes in Low- and High-Conductivity Media

Electrical breakdown of erythrocytes induces hemoglobin release which increases markedly with decreasing conductivity of the pulse medium. This effect presumably results from the transient, conductivity-dependent deformation forces (elongation or compression) on the cell caused by Maxwell stress. The deformation force is exerted on the plasma membrane of the cell, which can be viewed as a transient dipole induced by an applied DC electric field pulse. The induced dipole arises from the free charges that accumulate at the cell interfaces via the Maxwell-Wagner polarization mechanism. The polarization response of erythrocytes to a DC field pulse was estimated from the experimental data obtained by using two complementary frequency-domain techniques. The response is very rapid, due to the highly conductive cytosol. Measurements of the electrorotation and electrodeformation spectra over a wide conductivity range yielded the information and data required for the calculation of the deformation force as a function of frequency and external conductivity and for the calculation of the transient development of the deformation forces during the application of a DC-field pulse. These calculations showed that (i) electric force precedes and accompanies membrane charging (up to the breakdown voltage) and (ii) that under low-conductivity conditions, the electric stretching force contributes significantly to the enlargement of ``electroleaks' in the plasma membrane generated by electric breakdown. Received: 12 December 1997/Revised: 13 March 1998     

Energy of ion pairs in proteins

The energy of ions interaction in an ionic pair and the energy of ions transfer from water into protein at different ions disposition relative to the protein/water boundary has been considered. Ultimately, the ions transfer from aqueous phase into protein, i. e. in the medium with a low dielectric constant is energetically unfavorable and hence it cannot stabilize the protein structure by itself. For stabilization of ionic pairs in protein the action of some additional factors is necessary, in particular the action of the intraglobular electric field.     

Intraglobular electrostatic field of an enzyme. Calculation of the dissociation constant of a protein ionogenic group. Dissociation of Asp-102 chymotrypsin

Factors determining the change of dissociation constants of ionogenic groups upon their transfer from water into a protein globule are considered. The change of the short-range interaction is simulated with the aid of two model solvents: dimethylformamide (DMF) and formamide (FA). The change of Bornian solvation energy is calculated taking into account the interaction of ions situated inside a protein globule with the surrounding electrolyte solution. The change of ion energy due to the intraglobular electric field preexisting in the enzyme molecule is calculated. Each of the factors listed above gives a large contribution into the ion energy in the case of Asp-102 these contributions compensate each other to a great extent.     

An additional circulatory system: Vascular-Interstitial closed electric circuits (VICC)

The construction and activation of a previously described additional circulatory system for long-distance transport in tissue is summarized. Metabolism or injury produces electrochemical polarization of tissue. This driving force produces exchange of material by electrophoresis and dielectrophoresis in tissue and cellular matrices with fixed surface charges. These transports are described over vascular-intersititial closed electric circuits (VICC) because blood vessels function as relatively insulated conducting cables and connect with the conducting tissue fluids over capillaries. Necessary electron tranfer takes place at sites of segmental capillary contractions by the superimposed electric field via globular proteins known to exchange electrons in the endothelial cellular membranes. The effect of field-activated VICC is here demonstrated by accumulation of granulocytes in vivo as an electrophoretic process, which gives a mechanistic and energetic logical explanation of so-called leukotaxis.     

Dielectric behavior of polyelectrolytes. IV. Electric polarizability of rigid biopolymers in electric fields

The equilibrium Kerr effect of a system of mobile charges constrained to the surface of biomacromolecules is calculated. Cylindrical and spherical geometries are considered. For the cylinder we determine the anisotropy of electric polarizability as a function of length, temperature, and number of charged species in the low-field regime, and the fraction of the maximum induced dipole in the field direction for higher electric fields. The results are compared to experimental data for DNA oligomers taken from the literature. With spherical geometry we calculate the fractional induced dipole moment as a function of electric field strength and from this deduce the orientation function. The field dependence of the orientation function is compared to experimental data in the literature for bovine disk membrane vesicles.     

Significance of Polarization Charges and Isomagnetic Surface in Magnetohydrodynamics

From the frozen-in field lines concept, a highly conducting fluid can move freely along, but not traverse to, magnetic field lines. We discuss this topic and find that in the study of the frozen-in field lines concept, the effects of inductive and capacitive reactance have been omitted. When admitted, the relationships among the motional electromotive field, the induced electric field, the eddy electric current, and the magnetic field becomes clearer. We emphasize the importance of isomagnetic surfaces and polarization charges, and show analytically that whether a conducting fluid can freely traverse magnetic field lines or not depends solely on the magnetic gradient along the path of the fluid. If a fluid does not change its density distribution and shape (can be regarded as a quasi-rigid body) and moves along isomagnetic surface, it can freely traverse magnetic field lines without any magnetic drag, no matter how strong the magnetic field is. Besides theoretical analysis, we also present experimental results to support our analysis. The main purpose of this work is to correct a fallacy among some astrophysicists.     

Electrorotation of colloidal particles and cells depends on surface charge.

The importance of surface conductivity to the frequency-dependent polarizability and the rotation of particles in circular electric fields (electrorotation) is emphasized by various theoretical and experimental investigations. Although surface conductivity seems to be naturally related to the ionic double layer, there is rare experimental evidence of a direct relationship. To highlight the role of surface charges in electrorotation, an apparatus was developed with a symmetrical three-electrode arrangement for field frequencies between 25 Hz and 80 MHz. The three-dimensional electrostatic field distribution between the electrodes was evaluated numerically. With this device, rotating, gradient, and homogeneous electric fields of defined precision and homogeneity could be applied to slightly conducting suspensions. Surface properties of monodisperse latex particles (O 9.67 microm), carrying weak acid groups, were characterized by suspension conductometric titration. This procedure determined the amount of carboxyl groups and showed that strong acid groups were missing on the surface of these particles. To obtain the electrophoretic mobility, the spheres were separated by free-flow electrophoresis, and the zeta-potential was calculated from these data. Single-particle rotation experiments on fractions of specified electrophoretic mobility were carried out at frequencies between 25 Hz and 20 MHz. By analyzing the pH dependence of the rotation velocity, it could be shown that the rotation rate is determined by surface charges, both at the peak in rotation rate near the Maxwell-Wagner frequency (MWF) and at low frequencies. The inversion of the rotation direction at the MWF peak for vanishing surface charges was demonstrated. An analytical model for the double layer and dissociation on a charged surface was developed that is valid for low and high zeta-potentials. This model could provide convincing evidence of the linear dependence of the MWF rotation velocity on surface charge.     

What Forces Can Determine the Formation of Highly Specific Protein–Protein Complexes?

A software package was designed and used in a detailed study of the contact regions (interfaces) of a large number of protein–protein complexes using the PDB data. It appeared that for about 75% of the complexes the amino acid composition of the subunit surface in the contact region is not essential. Thus one may suggest that, along with the amino acid residues at the interface, the residues in the interior of the globules substantially contribute to protein–protein recognition. Such interactions between quite remote residues are most probably of electrical nature, and are involved in recognition by contributing to the overall electric field created by the protein molecule; the configuration of this field is perhaps the definitive factor of recognition. The overall field of the protein molecule is additively built of the fields created by each constituent residue, and it can be calculated as a sum of the fields created by the protein multipole (aggregate of partial electric charges assigned to every atom of the protein molecule). Preliminary assessment of the remote electrostatic interaction has been performed for ribonuclease subunits in vacuum. The results are indicative of a real possibility that the electric field created by the protein multipole can strongly influence the mutual orientation of molecules before Brownian collision.