Simultaneous analysis of the cardiac electric and magnetic fields using the scalar multipole expansion

A theoretical analysis of electric and magnetic fields of the heart, based solely upon the scalar multipole expansion, is carried out in order to gain an insight into the interrelation of the data contained in electro- and magnetocardiological measurements. The usual multipole expansion is applied for the electric field, however corresp[nding equivalent multipoles are formulated as idealized generators, having not only flow sources, but also vortex sources of the field. Furthermore, the magnetic field in a homogeneous infinite volume conductor is expressed as a sum of two series, the first being the usual multipole expansion of the nonvortex component of the magnetic field, and the second being a sequence of magnetic fields set up by the aforementioned electric multipole generators reduced to axial form. The former term is uniquely defined by the electric multipole components, but the latter reflects properties of the cardiogenerator that can be revealed only by means of magnetic measurements. Features of the electric and magnetic multipole components as integral characteristics of the cardiogenerator are discussed and concepts of the magnetic centre and magnetic axis of the cardiogenerator are proposed. The analysis is illustrated by examples of simple generator configurations.     

Electromagnetic Field of Microtubules: Effects on Transfer of Mass Particles and Electrons

Biological polar molecules and polymer structures with energy supply (such as microtubules in the cytoskeleton) can get excited and generate an endogenous electromagnetic field with strong electrical component in their vicinity. The endogenous electrical fields through action on charges, on dipoles and multipoles, and through polarization (causing dielectrophoretic effect) exert forces and can drive charges and particles in the cell. The transport of mass particles and electrons is analyzed as a Wiener-Lévy process with inclusion of deterministic force (validity of the Bloch theorem is assumed for transport of electrons in molecular chains too). We compare transport driven by deterministic forces (together with an inseparable thermal component) with that driven thermally and evaluate the probability to reach the target. Deterministic forces can transport particles and electrons with higher probability than forces of thermal origin only. The effect of deterministic forces on directed transport is dominant.     

Novel mutations of the LolCDE complex causing outer membrane localization of lipoproteins despite their inner membrane-retention signals

In Gram-negative bacteria, lipoproteins are targeted to either the inner or outer membrane depending on their sorting signals. An ABC transporter LolCDE complex in Escherichia coli releases outer membrane-specific lipoproteins. Inner membrane-specific lipoproteins remain in the inner membrane because they each have a LolCDE-avoidance signal and therefore are not released by LolCDE. Only the LolC(A40P) mutation was previously found to cause outer membrane localization of lipoproteins despite their inner membrane-retention signals. Here, we isolated several new LolCDE mutants that cause outer membrane localization of lipoproteins possessing LolCDE-avoidance signals. Mutations were found in all three subunits of LolCDE, including the cytoplasmic ATPase subunit LolD. However, the extent of outer membrane sorting of inner membrane-specific lipoproteins differed depending on the mutation. Based on these observations, the molecular events underlying the recognition of lipoproteins by the LolCDE complex are discussed.     

Mammalian Oxa1 protein is useful for assessment of submitochondrial protein localization and mitochondrial membrane integrity

Taking advantage of the unique topology of oxidase assembly 1 (Oxa1) protein, a mitochondrial inner membrane protein with N (intermembrane space)-C (matrix) orientation, we explored the usefulness of the protein as a marker for submitochondrial protein localization. Mammalian Oxa1 protein exhibited different proteolytic patterns depending on mitochondrial membrane integrity, and in mitochondria with a disrupted outer membrane and outer and inner membranes, the proteolytic patterns of Oxa1 protein were consistent with those of mitochondrial intermembrane space and matrix marker proteins, respectively, suggesting that Oxa1 protein, a single molecule, can serve as a versatile submitochondrial localization marker that doubles as a membrane integrity marker.     

Higher order multipole moments for molecular dynamics simulations

In conventional force fields, the electrostatic potential is represented by atom-centred point charges. This choice is in principle arbitrary, but technically convenient. Point charges can be understood as the first term of multipole expansions, which converge with an increasing number of terms towards the accurate representation of the molecular potential given by the electron density distribution. The use of multipole expansions can therefore improve the force field accuracy. Technically, the implementation of atomic multipoles is more involved than the use of point charges. Important points to consider are the orientation of the multipole moments during the trajectory, conformational dependence of the atomic moments and stability of the simulations which are discussed here.

On the calculation of magnetic fields based on multipole modeling of focal biological current sources.

Spatially restricted biological current distributions, like the primary neuronal response in the human somatosensory cortex evoked by electric nerve stimulation, can be described adequately by a current multipole expansion. Here analytic formulas are derived for computing magnetic fields induced by current multipoles in terms of an nth-order derivative of the dipole field. The required differential operators are given in closed form for arbitrary order. The concept is realized in different forms for an expansion of the scalar as well as the dyadic Green's function, the latter allowing for separation of those multipolar source components that are electrically silent but magnetically detectable. The resulting formulas are generally applicable for current sources embedded in arbitrarily shaped volume conductors. By using neurophysiologically relevant source parameters, examples are provided for a spherical volume conductor with an analytically given dipole field. An analysis of the signal-to-noise ratio for multipole coefficients up to the octapolar term indicates that the lateral extent of cortical current sources can be detected by magnetoencephalographic recordings.     

Libraries of atomic multipole moments for precise modeling of electrostatic properties of amino acids

Summary Contemporary theoretical models used in describing electrostatic properties of amino acids in polypeptides rely usually on atomic point charges. Recently noted defects of such models in reproducing protein folding originate from the inadequate representation of the electrostatic term, in particular inability of atomic charges to account for local anisotropy of molecular charge distribution. Such defects could be corrected by multicenter multipole moments derived directly from any high quality quantum chemical wavefunctions. This is illustrated by comparison of monopole and multipole electrostatic interactions between some amino acids within glutathione S-transferase.High quality Point Charge Models (PCM) can be derived analytically from multipole moment databases. Preliminary results suggest that torsional potentials are controlled by electrostatic interactions of atomic multipoles.Examples illustrating various uses of multicenter multipole moment databases of protein building blocks in modeling various properties of amino acids and polypeptides have been described, including calculation of molecular electrostatic potentials, electric fields, interactions between amino acid residues, estimates of pK_a shifts and changes in catalytic activity induced by amino acid substitutions in mutated enzymes.     

Structural determinants in addition to the amino-terminal sorting sequence influence membrane localization of Escherichia coli lipoproteins.

The lipid-modified nine-residue amino-terminal sequence of the mature form of the major outer membrane lipoprotein of Escherichia coli contains information that is responsible for sorting to either the inner or outer membrane. Fusion of this sorting sequence to beta-lactamase is sufficient for localization of the resultant lipo-beta-lactamase to the outer membrane (J. Ghrayeb and M. Inouye, J. Biol. Chem. 259:463-467, 1984). Substitution of the serine adjacent to the amino-terminal lipid-modified cysteine residue of the sorting sequence with the negatively charged residue aspartate causes inner membrane localization (K. Yamaguchi, F. Yu, and M. Inouye, Cell 53:423-432, 1988). Fusion of the aspartate-containing nine-residue inner membrane localization signal to the normally outer membrane lipoprotein bacteriocin release protein does cause partial localization to the inner membrane. However, a single replacement of the glutamine adjacent to the amino-terminal lipid-modified cysteine residue of bacteriocin release protein with aspartate causes no inner membrane localization. Therefore, an aspartate residue itself lacks the information necessary for inner membrane sorting when removed from the structural context provided by the additional eight residues of the sorting sequence. Although the aspartate-containing inner membrane sorting sequence causes an almost quantitative localization to the inner membrane when fused to the otherwise soluble protein beta-lactamase, this sequence cannot prevent significant outer membrane localization when fused to proteins (bacteriocin release protein and OmpA) normally found in the outer membrane. Therefore, structural determinants in addition to the amino-terminal sorting sequence influence the membrane localization of lipoproteins.     

Side peak suppression in responses of an across-frequency integration model to stimuli of varying bandwidth as demonstrated analytically and by implementation

Multiplication-like sound localization models are subjected to phase ambiguities for high-frequency tonal stimuli as multiplication creates several equivalent response peaks in tuning curves. By increasing the bandwidth of the stimulus, phase ambiguities can be reduced, which is often referred to as side peak suppression. In this study we present a Jeffress-based sound localization model, and determine side peak suppression analytically. The results were verified with an implementation of the same model, and compared to physiological data of barn owls. Three types of stimuli were analyzed: pure-tone stimuli, two-tone complexes with varying frequency distances, and noise signals with variable bandwidths. As an additional parameter we also determined the half-width of the main response peak to examine the scaling of tuning curves in azimuth. Results showed that side peak suppression did not only depend on bandwidth, but also on the center frequency and the distance of the side peak to the main response peak. In particular, the analytical model predicted that side peak suppression is a function of relative bandwidth, whereas half-width is inversely proportional to center frequency, with a proportionality factor depending on relative bandwidth. The analytical approach and the implementation yielded equivalent tuning curves (deviation < 1 %). Moreover, the electrophysiological data recorded in barn owls closely matched the predicted tuning curves.     

Expert system for predicting protein localization sites in gram-negative bacteria

We have developed an expert system that makes use of various kinds of knowledge organized as "if-then" rules for predicting protein localization sites in Gram-negative bacteria, given the amino acid sequence information alone. We considered four localization sites: the cytoplasm, the inner (cytoplasmic) membrane, the periplasm, and the outer membrane. Most rules were derived from experimental observations. For example, the rule to recognize an inner membrane protein is the presence of either a hydrophobic stretch in the predicted mature protein or an uncleavable N-terminal signal sequence. Lipoproteins are first recognized by a consensus pattern and then assumed present at either the inner or outer membrane. These two possibilities are further discriminated by examining an acidic residue in the mature N-terminal portion. Furthermore, we found an empirical rule that periplasmic and outer membrane proteins were successfully discriminated by their different amino acid composition. Overall, our system could predict 83% of the localization sites of proteins in our database.     

Effects of dipole position,orientation and noise on the accuracy of EEG source localization

Background  

The electroencephalogram (EEG) reflects the electrical activity in the brain on the surface of scalp. A major challenge in this field is the localization of sources in the brain responsible for eliciting the EEG signal measured at the scalp. In order to estimate the location of these sources, one must correctly model the sources, i.e., dipoles, as well as the volume conductor in which the resulting currents flow. In this study, we investigate the effects of dipole depth and orientation on source localization with varying sets of simulated random noise in 4 realistic head models.     

Mapping the electrostatic potential within the ribosomal exit tunnel

Electrostatic potentials influence interactions among proteins and nucleic acids, the orientation of dipoles and quadrupoles, and the distribution of mobile charges. Consequently, electrostatic potentials can modulate macromolecular folding and conformational stability, as well as rates of catalysis and substrate binding. The ribosomal exit tunnel, along with its resident nascent peptide, is no less susceptible to these consequences. Yet, the electrostatics inside the tunnel have never been measured. Here we map both the electrostatic potential and accessibilities along the length of the tunnel and determine the electrostatic consequences of introducing a charged amino acid into the nascent peptide. To do this we developed novel probes and strategies. Our findings provide new insights regarding the dielectric of the tunnel and the dynamics of its local electric fields.     

Ultrafast,accurate, and robust localization of anisotropic dipoles

The resolution of single molecule localization imaging techniques largely depends on the precision of localization algorithms. However, the commonly used Gaussian function is not appropriate for anisotropic dipoles because it is not the true point spread function. We derived the theoretical point spread function of tilted dipoles with restricted mobility and developed an algorithm based on an artificial neural network for estimating the localization, orientation and mobility of individual dipoles. Compared with fitting-based methods, our algorithm demonstrated ultrafast speed and higher accuracy, reduced sensitivity to defocusing, strong robustness and adaptability, making it an optimal choice for both two-dimensional and threedimensional super-resolution imaging analysis.     

On Bioelectric Potentials in an Inhomogeneous Volume Conductor

Green's theorem is used to derive two sets of expressions for the quasi-static potential distribution in an inhomogeneous volume conductor. The current density in passive regions is assumed to be linearly related instantaneously to the electric field. Two equations are derived relating potentials to an arbitrary distribution of impressed currents. In one, surfaces of discontinuity in electrical conductivity are replaced by double layers and in the other, by surface charges. A multipole equivalent generator is defined and related both to the potential distribution on the outer surface of the volume conductor and to the current sources. An alternative result involves the electric field at the outer surface rather than the potential. Finally, the impressed currents are related to electrical activity at the membranes of active cells. The normal component of membrane current density is assumed to be equal at both membrane surfaces. One expression is obtained involving the potentials at the inner and outer surfaces of the membrane. A second expression involves the transmembrane potential and the normal component of membrane current.     

The interaction of arginine- and tryptophan-rich cyclic hexapeptides with Escherichia coli membranes.

Cyclization of R- and W-rich hexapeptides has been found to enhance specifically the antimicrobial activity against Gram-negative Escherichia coli. To gain insight into the role of the bacterial outer membrane in mediating selectivity, we assayed the activity of cyclic hexapeptides derived from the parent sequence c-(RRWWRF) against several E. coli strains and Bacillus subtilis, L-form bacteria, and E. coli lipopolysaccharide (LPS) mutant strains, and we also investigated the peptide-induced permeabilization of the outer and inner membrane of E. coli. Wall-deficient L-form bacteria were distinctly less susceptible than the wild type strain. The patterns of peptide-induced permeabilization of the outer and inner E. coli membranes correlated well with the antimicrobial activity, confirming that membrane permeabilization is a detrimental effect of the peptides upon bacteria. Truncation of LPS had no influence on the activity of the cyclic parent peptide, but the highly active c-(RRWFWR), with three adjacent aromatic residues, required the complete LPS for maximal activity. Furthermore, differences in the activity of the parent peptide and its all-D sequence indicated stereospecific interactions with the LPS mutant strains. We suggest that, depending on the primary sequence of the peptides, either hydrophobic interactions with the fatty acid chains of lipid A, or electrostatic interactions disturbing the polar core region and interference with saccharide-saccharide interactions prevail in the barrier-disturbing effect upon the outer membrane and thereby provide peptide accessibility to the inner membrane. The results underline the importance of tryptophan and arginine residues and their relative location for a high antimicrobial effect, and the activity-modulating function of the outer membrane of E. coli. In addition to membrane permeabilization, the data provided evidence for the involvement of other mechanisms in growth inhibition and killing of bacteria.     

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.     

High-resolution magnetoencephalography--studies with a small-volume phantom]

To investigate the spatiotemporal organisation of neuronal processes in an animal model using magnetoencephalography (MEG), a high temporal resolution (ms) and an appropriate spatial resolution of about 1 mm is necessary. With the aim of determining the localization error and the resolution power of high-resolution MEG systems, we developed a phantom capable of simulating the characteristics of animal models. The phantom enables us to variably position at least two magnetic field sources to within 0.1 mm. For source localization on the basis of the magnetic field data, a spatial filtering algorithm was used. The investigation of a 16-channel micro SQUID-MEG system with a current dipole orientated tangentially to the phantom surface produced the following localization data (min ... max, x, y--horizontal plane, z--depth); systematic localization error e(x) = 1.16 ... 1.67 mm, e(y) = -1.01 ... -1.28 mm, e(z) = -5.22 ... -7.64 mm, standard deviation of the individual measurements perpendicular to the dipole axis s(perp) = 0.05 ... 0.22 mm, along this axis s(long) = 0.20 ... 1.73 mm, in the depths sz = 0.17 ... 3.17 mm. The "goodness of fit" was > 95%. Separation of two dipoles was still possible for parallel dipoles at a distance apart of d(parallel) = 0.03 mm and for those oriented perpendicularly to each other at a distance apart of d(perp) = 0.10 mm. On the basis of these results we conclude that the MEG system can achieve a resolution sufficient to permit the investigation of neuronal microstructures. The spatial errors detected were related to sensor position in the cryostatic vessel as well as to external low-frequency noise.     

The influence of conductivity changes in boundary element compartments on the forward and inverse problem in electroencephalography and magnetoencephalography.

Source localization based on magnetoencephalographic and electroencephalographic data requires knowledge of the conductivity values of the head. The aim of this paper is to examine the influence of compartment conductivity changes on the neuromagnetic field and the electric scalp potential for the widely used three compartment boundary element models. Both the analysis of measurement data and the simulations with dipoles distributed in the brain produced two significant results. First, we found the electric potentials to be approximately one order of magnitude more sensitive to conductivity changes than the magnetic fields. This was valid for the field and potential topology (and hence dipole localization), and for the amplitude (and hence dipole strength). Second, changes in brain compartment conductivity yield the lowest change in the electric potentials topology (and hence dipole localization), but a very strong change in the amplitude (and hence in the dipole strength). We conclude that for the magnetic fields the influence of compartment conductivity changes is not important in terms of dipole localization and strength estimation. For the electric potentials however, both dipole localization and strength estimation are significantly influenced by the compartment conductivity.     

Crystal structures of bacterial lipoprotein localization factors,LolA and LolB

Lipoproteins having a lipid-modified cysteine at the N-terminus are localized on either the inner or the outer membrane of Escherichia coli depending on the residue at position 2. Five Lol proteins involved in the sorting and membrane localization of lipoprotein are highly conserved in Gram-negative bacteria. We determined the crystal structures of a periplasmic chaperone, LolA, and an outer membrane lipoprotein receptor, LolB. Despite their dissimilar amino acid sequences, the structures of LolA and LolB are strikingly similar to each other. Both have a hydrophobic cavity consisting of an unclosed beta barrel and an alpha-helical lid. The cavity represents a possible binding site for the lipid moiety of lipoproteins. Detailed structural differences between the two proteins provide significant insights into the molecular mechanisms underlying the energy-independent transfer of lipoproteins from LolA to LolB and from LolB to the outer membrane. Furthermore, the structures of both LolA and LolB determined from different crystal forms revealed the distinct structural dynamics regarding the association and dissociation of lipoproteins. The results are discussed in the context of the current model for the lipoprotein transfer from the inner to the outer membrane through a hydrophilic environment.     

Characterization of the LolA-LolB system as the general lipoprotein localization mechanism of Escherichia coli.

The major outer membrane lipoprotein (Lpp) of Escherichia coli requires LolA for its release from the cytoplasmic membrane, and LolB for its localization to the outer membrane. We examined the significance of the LolA-LolB system as to the outer membrane localization of other lipoproteins. All lipoproteins possessing an outer membrane-directed signal at the N-terminal second position were efficiently released from the inner membrane in the presence of LolA. Some lipoproteins were released in the absence of externally added LolA, albeit at a slower rate and to a lesser extent. This LolA-independent release was also strictly dependent on the outer membrane sorting signal. A lipoprotein-LolA complex was formed when the release took place in the presence of LolA, whereas lipoproteins released in the absence of LolA existed as heterogeneous complexes, suggesting that the release and the formation of a complex with LolA are distinct events. The release of LolB, an outer membrane lipoprotein functioning as the receptor for a lipoprotein-LolA complex, occurred with a trace amount of LolA, and therefore was extremely efficient. The LolA-dependent release of lipoproteins was found to be crucial for the specific incorporation of lipoproteins into the outer membrane, whereas lipoproteins released in the absence of LolA were nonspecifically and inefficiently incorporated into the membrane. The outer membrane incorporation of lipoproteins including LolB per se was dependent on LolB in the outer membrane. From these results, we conclude that lipoproteins in E. coli generally utilize the LolA-LolB system for efficient release from the inner membrane and specific localization to the outer membrane.