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Electron density calculations as an extension of protein structure refinement. Streptomyces griseus protease A at 1.5 A resolution.

Ab initio quantum mechanical calculations have been used to obtain details of the electron density distribution in a high-resolution refined protein structure. It is shown that with accurate atomic co-ordinates, electron density may be calculated with a quality similar to that which can be obtained directly from crystallographic studies of small organic molecules, and that this density contains information relevant to the understanding of catalysis. Atomic co-ordinates from the 1.8 A and 1.5 A resolution refinements of the crystal structure of protease A from Streptomyces griseus have been used to examine the influence of the environment on the electron density in the side-chain of the active site histidine (His57). The neighbouring aspartic acid 102 is the dominant factor in the environment, and quantum mechanical calculations have been performed on these two residues. Most interesting from the point of view of understanding the catalytic process is the effect that Asp102 has on the electron density in the region of the imidazole nitrogen (N epsilon 2) adjacent to the active site serine 195. In the positively charged imidazolium species, there is a polarization of the N epsilon 2-H bond, reducing the bonding density in a manner that may lower the height of the energy barrier for proton transfer. In the uncharged imidazole species, the proximity of Asp102 causes a movement of density from the lone pair region of the N epsilon 2 into the pi bonding region above and below the plane of the ring. Although it is shown that the primary effect of the aspartic acid is electrostatic, this movement is perpendicular to the direction of the electric field inducing it.

Amino Acid Sequence↗

A new algorithm for deriving pulsatile blood flow waveforms tested using stimulated dynamic angiographic data.

In vascular pathology the assessment of disease severity and monitoring of treatment requires quantitative and reproducible measurements of arterial blood flow. We have developed a new technique for processing sequences of dynamic digital X-ray angiographic images. We have tested it using computer simulated angiographic data which includes the effect of pulsatile blood flow and X-ray quantum noise. A parametric image was formed in which the image grey-level represents dye concentration as a function of time and distance along a vessel segment. Adjacent concentration--distance profiles in the parametric image were re-registered along the vessel axis until a match occurred. A match was defined as the point where the sum of squares of the differences in the two profiles was a minimum. The distance translated per frame interval is equal to the bolus velocity. We have tested several contrast medium injection methods including constant flow and a range of discrete pulses per second. The technique proved to be robust and independent of injection technique. Average blood flow was measured for simulated pulsatile waveforms with mean flows of up to 650 ml/min (peak velocities up to 186 cm/s) in a range of diameters from 2 mm to 6 mm. The standard deviation of the error in the mean flow estimates over the whole range of velocities and vessel sizes was +/- 1.4 cm/s.

Algorithms↗

Combined quantum mechanical and molecular mechanical reaction pathway calculation for aromatic hydroxylation by p-hydroxybenzoate-3-hydroxylase.

The reaction pathway for the aromatic 3-hydroxylation of p-hydroxybenzoate by the reactive C4a-hydroperoxyflavin cofactor intermediate in p-hydroxybenzoate hydroxylase (PHBH) has been investigated by a combined quantum mechanical and molecular mechanical (QM/MM) method. A structural model for the C4a-hydroperoxyflavin intermediate in the PHBH reaction cycle was built on the basis of the crystal structure coordinates of the enzyme-substrate complex. A reaction pathway for the subsequent hydroxylation step was calculated by imposing a reaction coordinate that involves cleavage of the peroxide oxygen-oxygen bond and formation of the carbon-oxygen bond between the C3 atom of the substrate and the distal oxygen of the peroxide moiety of the cofactor. The geometric changes and the Mulliken charge distributions along the calculated reaction pathway are in line with an electrophilic aromatic substitution type of mechanism. The energy barrier of the calculated reaction is considerably lower when the substrate hydroxyl moiety is deprotonated, in comparison with the barrier found with a protonated hydroxyl moiety. This effect of the protonation state of the substrate on the calculated energy barrier supports experimental observations that deprotonation is required for hydroxylation of the substrate. A notable event in the calculated reaction pathway is a lengthening of the peroxide oxygen-oxygen bond at an intermediate stage. Further analysis of the reaction pathway indicates that this oxygen-oxygen bond elongation is accompanied by an increase in electrophilic reactivity on the distal oxygen of the peroxide moiety, which may assist the C-O bond formation in the reaction of the C4a-hydroperoxyflavin intermediate with the substrate. Analysis of the effect of individual active site residues on the reaction reveals a specific transition state stabilization by the backbone carbonyl moiety of Pro293. The crystal water 717 appears to drive the hydroxylation step through a stabilizing hydrogen bond interaction to the proximal oxygen of the C4a-hydroperoxyflavin intermediate, which increases in strength as the hydroperoxyflavin cofactor converts to the anionic (deprotonated) hydroxyflavin.

4-Hydroxybenzoate-3-Monooxygenase↗

Calculations of proton-binding thermodynamics in proteins.

Computational models of proton binding can range from the chemically complex and statistically simple (as in the quantum calculations) to the chemically simple and statistically complex. Much progress has been made in the multiple-site titration problem. Calculations have improved with the inclusion of more flexibility in regard to both the geometry of the proton binding and the larger scale protein motions associated with titration. This article concentrated on the principles of current calculations, but did not attempt to survey their quantitative performance. This is (1) because such comparisons are given in the cited papers and (2) because continued developments in understanding conformational flexibility and interaction energies will be needed to develop robust methods with strong predictive power. Nevertheless, the advances achieved over the past few years should not be underestimated: serious calculations of protonation behavior and its coupling to conformational change can now be confidently pursued against a backdrop of increasing understanding of the strengths and limitations of such models. It is hoped that such theoretical advances will also spur renewed experimental interest in measuring both overall titration curves and individual pKa values or pKa shifts. Exploration of the shapes of individual titration curves (as measured by Hill coefficients and other parameters) would also be useful in assessing the accuracy of computations and in drawing connections to functional behavior.

Hemoglobins↗

Molecular orbital calculations for parabens: a possible mechanism of action.

Molecular orbital calculations were carried out on the series benzoic acid, p-hydroxybenzoic acid, methylparaben, and ethylparaben. The characteristic trends of this entire series of preservatives are demonstrated by these members. The computer program used was Iterated Extended Hückel Theory. These systems were characterized in terms of atomic charge distributions, effect of hydroxyl and ester groups (both sterically and electronically), preferred molecular conformations, and distinguishing features of molecular orbitals. Through this approach, it was hoped that a common mode of action for all members of this series could be detected and that the trend(s) in this feature would correlate with known trends in activity of members of this series.

Chemical Phenomena↗

Three-dimensional reconstruction from reduced sets of very noisy images acquired following a single-axis tilt schema: application of a new three-dimensional reconstruction algorithm and objective comparison with weighted backprojection.

In this work we propose a reconstruction algorithm (ART with blobs) that has not been previously used in electron Tomography and we compare it with the standard method in the field (weighted back projection, WBP). We assume that only a limited set of very noisy images, collected around a single axis tilt, is available; which is a typical situation in Electron Tomography. In general, the reconstruction problem is underdetermined (due to the limited number of projections) and the data are inconsistent (due to the high level of noise). The evaluation of the results is performed in a rigorous way by a task-oriented approach which makes use of numerical observers. ART with blobs outperforms WBP for a number of key tasks. Results are presented both for simplified line integral data and for realistic simulations of macromolecular structures embedded in amorphous ice.

Algorithms↗

Classification of drugs by discriminant analysis using fragment molecular connectivity values.

An investigation was made into the use of linear and quadratic discriminant analysis, along with K nearest-neighbor analysis, in the classification of a set of 51 compounds which were divided into five therapeutic categories. By superimposing each compound on a pattern structure, as first proposed by Cammarata, eight positions were assigned on the molecule. Each position was coded with the numerical value of a descriptor index. Relative molar refraction, which was the index used by Cammarata, was compared with a number of molecular connective indices. For each of the indices studied, it was found that only four of the eight positions contributed significantly to between-class differences. It was also found that first-order molecular connectivity, calculated as the sum of the contributions of each of the bonds joining a given position, resulted in consistently fewer misclassifications as compared with the other indices. Using first-order molecular connectivity, validation procedures were performed on the original set of compounds, on random samples drawn from this set, and on a set of ten compounds not included in the analysis. The results obtained were highly data dependent, but they, nevertheless, suggest that molecular connectivity indices should prove useful in structural classification procedures.

Analysis of Variance↗

Analysis of synaptic quantal depolarizations in smooth muscle using the wavelet transform.

The time-frequency characteristics of synaptic potentials contain valuable information about the process of neurotransmission between nerves and their target organs. For example, at the synapse between autonomic nerves and smooth muscle, two central issues of neurophysiology, i.e., 1) the probability of neurotransmitter release and 2) the quantal behavior of transmission can be deduced from analysis of the rising phases of evoked excitatory junction potentials (eEJP's) recorded from smooth muscle. eEJP rising phases are marked by prominent inflexions, which reflect these features of neuronal activity. Since these inflexions contain time-varying frequency information, we have applied recent techniques of time-frequency analysis based upon wavelet transforms to eEJP's recorded from the guinea-pig vas deferens in vitro. We find that these techniques allow accurate and convenient characterization of neuronal release sites, and that their probability of release falls between 0.001-0.004. We have also analyzed eEJP's recorded in the presence of the chemical 1-heptanol, which reveals quantal depolarizations. These results have helped clarify the nature of the quantal depolarizations that underly eEJP's. The present method offers significant advantages over those previously employed for these tasks, and holds promise as a novel approach to the analysis of synaptic potentials.

Animals↗

[A comparison of statistical methods for quantal analysis in computer and physiological experiments].

Amplitude distributions of postsynaptic potentials were simulated in computer experiments on the basis of binomial statistics. Influences of the sample size (N) and noise standard deviation (Sn) on the determination of the quantal content (m) and quantal size (v) were studied. Four methods of the quantal parameter estimation were modified and used: histogram, variance, failure and combined method. Three last methods gave satisfactory estimations (within +/- 10%) at N = 500-1000 and Sn less than 2v. The histogram method was adequate at Sn less than or equal to v. Similar results were obtained at N = 50-200, when the experiment was repeated about ten times. Applicability of similar methods was confirmed by the analysis of an intracellular record of inhibitory postsynaptic potentials (N = 1333) from the sensorimotor cortex of rabbit.

Action Potentials↗

Three-dimensional computerized tomography: a quantum leap in diagnostic imaging?

Ever since the discovery of radium by Madame Curie, men and women of vision and science have labored to improve radiation technology. Over a period of approximately 85 years, we have gone from this initial discovery to three-dimensional computerized transmission tomography; one of the latest techniques in modern day x-ray imaging. Its uses are vast and unparalleled in many facets of medicine and surgery, outlining pathology as never before seen, and possibly, never before completely understood. Three-dimensional computerized tomography is rapidly gaining popularity in cross-sectional imaging of the foot and ankle. It has proven invaluable in elucidating osseous and soft tissue pathology. Abnormalities of the musculoskeletal system that exhibit complex anatomy are often difficult to interpret using standard radiographic techniques. Overall, three-dimensional computerized tomography has established itself as a means by which clinicians may appreciate the three-dimensional disposition of anatomy and disease.

Ankle↗

Estimating the time course of evoked quantal release at the frog neuromuscular junction using end-plate current latencies.

The use of end-plate current (e.p.c.) latency measurements to estimate the time course of the stochastic probabilistic process governing evoked release was investigated in the sciatic nerve-sartorius muscle preparation of the frog, Rana pipiens. We also examined the possibility that the release of a quantum depresses or enhances the subsequent release of additional quanta. Muscle end-plates were voltage clamped at 3-4 degrees C. Quantal release was restricted to a short, or localized, region of the nerve terminal using Ca2+-free, EGTA Ringer solution and a Ca2+-filled micropipette. The number of e.p.c.s containing 0, 1, 2, etc. quanta were totalled and compared to numbers predicted using Poisson's theorem. The differences between the actual and predicted numbers of events were not significant at the nineteen junctions studied (P less than 0.05). The latency of the first quantum observed in several hundred e.p.c.s was measured and used to calculate an estimate, alpha 1(t), of the time-dependent, probabilistic process, alpha (t), governing all evoked quantal release (Barrett & Stevens, 1972b). In three experiments, all quantal latencies were measured to obtain the actual alpha (t). The alpha 1(t) function gave an excellent approximation of alpha (t) (P greater than 0.2), in real and simulated latency data. The latency of the second quantum in the e.p.c.s was measured and used to provide another estimate, alpha 2(t), of alpha (t). The alpha 2(t) function was lower (depressed) during the first few milliseconds of the evoked release period, relative to alpha 1(t). The difference was significant (P greater than 0.01) in all experiments. Our measurement procedures were tested using computer-generated 'e.p.c.s' containing randomly occurring 'quanta'. These tests showed that the early depression was due to inadequate detection of the second quantum in the e.p.c.s. The effect of Sr2+ on evoked release was examined using double-barrelled pipettes containing 1 M-SrCl2 and CaCl2 solutions. The major result was that the durations of alpha 1(t) and alpha 2(t) were equally lengthened in Sr2+, relative to Ca2+.

Animals↗

Mechanisms of post-traumatic seizures: a quantum pharmacological analysis of the molecular properties of an epileptogenic focus following iron-induced membrane peroxidation.

Late post-traumatic epilepsy following severe head trauma has been well documented. While there is increasing evidence suggesting that iron-induced lipid peroxidation of neural membranes may accompany cerebral haemorrhage, the pathogenic processes of post-traumatic epileptogenesis remain unknown. Furthermore, the effective prophylactic use of standard anticonvulsant drugs is unsubstantiated. The rational design of therapeutic agents specific for the prevention and treatment of post-traumatic epilepsy hinges on understanding the molecular membrane events at the epileptogenic focus. This study employs the techniques of theoretical quantum pharmacology to provide a structural analysis of neural phospholipid membranes, investigating changes in membrane integrity at the epileptogenic focus as the molecular basis for seizure activity. Molecular mechanics calculations and molecular dynamics simulations were used to model the biochemical events of the epileptogenic focus. We predict that applications of quantum pharmacological techniques to model biochemical events may provide an understanding of proconvulsive pathogenic mechanisms in post-traumatic epilepsy.

Aspartic Acid↗

Fractal and chaotic dynamics in nervous systems.

The chaotic aspects of brain structure and dynamics have been discussed. The relation of chaos to fractal processes in the brain from the neurosystems level down to the molecule has been explored. It is found that chaos appears to play an integral, though not necessarily exclusive role in function at all levels of organization from the neurosystems to the molecular and quantum levels. An interesting consequence involving the possible interface between chaotic dynamics and quantum physics has been discussed because of its potential significance is resolving several of the most intractable conceptual problems to do with computability, the brain and the mind (Blakemore and Greenfield, 1987; Hooper and Teresi, 1987; Rose, 1973; Searle, 1979; Penrose, 1986, 1989).

Action Potentials↗

Dendritic encoding: an alternative to temporal synaptic coding of conscious experience.

In this commentary, arguments are made for a dendritic code being preferable to a temporal synaptic code as a model of conscious experience. A temporal firing pattern is a product of an ongoing neural computation; hence, it is based on a neural algorithm and an algorithm may not provide the most suitable model for conscious experience. Reiteration of a temporal firing code as suggested in a preceding article (Helekar, 1999) does not necessarily improve the situation. The alternative model presented here is that certain synaptic activity patterns, possibly those possessing universal features as suggested by Helekar, can become encoded in the dendritic structure. Following dendritic encoding, quantum phenomena in those specific dendrite sets could illuminate the static image of that encoded synaptic activity. It is the activation of the static image that would be equivalent to conscious experience; thus, conscious awareness would not be directly affiliated with synaptic activity. This dendrite encoding model may go farther than other models to explain the gestalt nature of consciousness, insofar as quantum entanglement could produce an interconnectedness between specific sets of dendrites-an interconnectedness that need not be based on neural computation or neural connections.

Consciousness↗

Profiles of evoked release along the length of frog motor nerve terminals.

In order to determine the relative probability of evoked transmitter release from different parts of frog motor nerve terminals, a technique has been developed in which single quantum end-plate potentials (e.p.p.s) are recorded by two intracellular electrodes, located at opposite ends of identified junctions. The log of the ratio of the amplitudes recorded simultaneously at the two electrodes is a linear function of the distance of the site of origin of the event from each of the two electrodes. Using online computer data acquisition and analysis, and current pulses at known locations for spatial calibration, it is possible to localize the site of single quantum e.p.p.s to within +/- 10-20 micron. Using the frog cutaneous pectoris neuromuscular preparation and a low calcium, high magnesium Ringer solution to ensure mostly single quantum events and failures, several thousand responses were recorded from each junction, allowing construction of a profile of the numbers of single quantum events arising from each portion of the junction. By comparison of junctional morphology and release profiles, it is possible to construct a probability of release per unit length profile for the entire junction. This technique has several advantages over localization of release events by measurements of extracellular synaptic currents. It was found that, for most junctions, the central 60-90% of the terminal exhibited relatively uniform probability of release, with highest levels typically near the point where the axon first contacted the muscle fibre, or in regions with many short terminal branches. However, no instances have been found in which a small region of terminal (10% or less) showed extraordinarily high release levels (30-50% of the total release from the junction). Characteristically, but not invariably, there is reduced release near the ends of terminal branches, especially the longer branches, where release per unit length could be as little as 5-10% of that in proximal portions. Some junctions had large regions of terminal that released very little transmitter. These also showed multiple myelineated axonal inputs, and may have been polyneuronally innervated junctions in which one of the inputs was much weaker than the other.

Animals↗

Theory of electrostatic interactions in macromolecules.

In the past year, substantial progress has been made in the modeling of electrostatic interactions in biomolecules. This review highlights advances in the following areas: first, the efficient computation of long-range electrostatic interactions in detailed molecular simulations; second, the application of the Poisson-Boltzmann electrostatic model in conformational analysis; third, the application of the Poisson-Boltzmann model in quantum chemistry calculations; fourth, the development of atomic parameters; and finally, the modeling of ionization equilibria in proteins.

Computer Simulation↗

[Cell molecular computer. VII. Cell biophysics and realistic or information physics (1)].

Living organisms measure many parameters in order to have orientation in the outer medium. That is why biophysics cannot use the ordinary laws of physics and must take into account the influence on the phenomena to be studied not only of a measurement but also of a calculation process in the real physical and biophysical device predicting the future. Science taking into account the effects of the calculating process-realistical or informative (RI) physics-has different (laws) for different times, distances and numbers of measuring and predicting parameters. RI-physics deals with unreproducible events and considers only such time intervals and distances for which the prediction can be made on the basis of earlier measurements and calculations according to the laws with optimal difficulty. It is suggested that the living cell uses the laws which are close to these optimal (limiting) laws of RI-physics. Physics and quantum mechanics can be considered as a limiting case of RI-physics. In this case values of distances and times are large enough and the number of simultaneously measured independent parameters is such that the heat effect of the calculating device would become negligible. Molecular cell computer (MCC) [I] cannot calculate the interaction of a great quantity of different molecules, using the equations of quantum mechanics because the expense of the (price of action) would be very large and both MCC and the surrounding world could change.

Cell Physiological Phenomena↗