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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

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

[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

Analysis of pairs of individual Ia-E.P.S.P.S in single motoneurones.

1. Recordings of individual e.p.s.p.s evoked by the action of single medial gastrocnemius Ia fibres have been made from medial gastrocnemius motoneurones. In many motoneurones the action of two Ia fibres has been observed and the properties of the e.p.s.p.s compared. 2. For sixty-three pairs of averaged e.p.s.p.s, each from the same motoneurone, the ratio of half-widths was plotted against the ratio of rise times. These results were compared with theoretical values derived from the Rall compartmental model. It was found that variations in synaptic current time courses and differences in the termination of localized synaptic terminals were not sufficient to account for all the data. 3. Amplitude and rise time were inversely related but the correlation coefficient was very low. For pairs of e.p.s.p.s in the same motoneurone the e.p.s.p. with the fast rise time was larger than that with the slow rise time in forty-eight of sixty-three cases. 4. In a given motoneurone individual e.p.s.p.s evoked by the action of different Ia fibres did not vary greatly in amplitude. The ratio of peak amplitudes was less than 3 for 86% of the pairs of e.p.s.p.s examined, and the maximum was 4-8. 5. Amplitude histograms were constructed for individual e.p.s.p.s at thirty-three synapses. Twenty-two of them could be shown to satisfy the Poisson law. The others satisfied the binomial law or neither. 6. Within a given motoneurone the amplitude of an e.p.s.p. is closely related to the mean number of quanta released but not to the amplitude of the unit e.p.s.p. produced by the action of a single quantum of transmitter.

Animals

[Organization of the background activity of rabbit visual cortex neurons].

Algorithm of calculation of consitent approximation to real entropy and redundancy which helps to understand the connection of two or more related states was realized by means of electronic computer BECM-6. Different laws of changes of information estimates dependeing on the number of approximation and the pitch of temporary quantum of messages corresponded to every type of cell impulsation of rabbits' visual cortex--arrhithimical, grouping and regular. The connections between the laws of impulse succession organization and some of its parameters were revealed. The results of studying the models of casual and deterministic pulse trains were compared.

Animals

Theoretical calculations on calcium channel drugs: is electron transfer involved mechanistically?

Theoretical studies were done on calcium channel drugs in order to gain insight into the mode of action. Empirical force field calculations with nifedipine, a calcium channel antagonist, indicate that the E-conformation at the ring juncture is lower in energy than the Z-conformation. This energy difference is only 0.2 kcal/mol when the esters in the 3- and 5-positions of the dihydropyridine (DHP) ring are both synperiplanar (sp, sp). Molecular orbital calculations on the ground and excited states in the Z-conformation with the esters in the (ap, sp) conformation show a low lying excited state with substantial intramolecular electron transfer (ET) character. This excited state is only 1.8 eV higher in energy than the ground state and corresponds to a transfer of approximately 0.3 electron from the DHP ring to the nitrobenzene moiety. We suggest that ET may play an important role in the mechanism of action, either intramolecular or, as previously proposed, intermolecular, along with lipophilicity and steric effects.

Calcium Channel Blockers

Solution behavior of methyl beta-xylobioside: conformational flexibility revealed by n.m.r. measurements and theoretical calculations.

The conformations of methyl beta-xylobioside in solution have been determined by n.m.r. spectroscopy. Interglycosidic 3JC,H values and the chemical shifts of the 13C resonances were measured at various temperatures in the range 238-378 K for solutions in 1,4-dioxane, methanol, methyl sulfoxide, and water. The temperature and solvent dependencies of the data obtained suggest conformational flexibility. Quantum-chemical PCILO calculations, with evaluation of the solvent effects, and molecular mechanics calculations revealed the existence of 7 low-energy regions for which the geometries and energies were determined. The computed abundances of conformers and averaged J values accord with the experimental data.

Carbohydrate Conformation

Molecular determinants for the agonist activity of 2-methylhistamine and 4-methylhistamine at H2-receptors.

A model for drug action at the histamine H2-receptor has been evaluated computationally for the agonists 2- and 4-methylhistamine. Based on molecular properties calculated for molecular structures optimized with ab initio quantum mechanical methods, the activities of these compounds and their potencies relative to histamine are found to be explained by the previously proposed model. Recognized in the N3-H tautomeric form of their monocations, both compounds exhibit a change in ring tautomeric preference when the cationic side chain is neutralized. This change makes possible their participation in a proposed proton relay event that was postulated to initiate the receptor response of H2-agonists. The relative concentrations of the mono- and dication forms of the molecules in equimolar concentrations of histamine and the two derivatives are calculated from the values of the molecular electrostatic potentials at the ring protonation sites. Because the monocation is the species recognized at the H2-receptor, the reduced potency of 2-methylhistamine relative to histamine and to the 4-methyl derivative is explained by the finding that 2-methylhistamine will have the lowest concentration of the recognized species. The rank order of potencies obtained from the ratio of monocationic species of the molecules is in agreement with experimental results.

Methylhistamines

Role of primary and secondary protein structure in neurotransmitter receptor activation mechanisms.

A proton transfer triggered by a ligand interacting with the receptor had been suggested as the initial step in the activation of a receptor for the neurotransmitter serotonin (5-hydroxy-tryptamine; 5-HT). To evaluate the role of the receptor macromolecule in modulating the primary molecular event in ligand-mediated activation, the process of proton transfer was analysed in the environment of a protein model for the 5-HT receptor. In the absence of a detailed receptor structure, the enzyme actinidin was chosen as the model for the receptor based on criteria obtained from structure-activity considerations on the ligands. The first simulation of a mechanism for receptor activation was performed on this model using methods of theoretical chemistry to study the effect of specific structural elements. The premise is that the role of the elements of secondary structure of soluble proteins (e.g. actinidin) in determining structure-function relations in these macromolecules is maintained when these elements are part of membrane-bound receptor proteins. Results from the calculations of the effects of the six alpha helices of actinidin on the proton transfer process from the imidazolium side chain of His 162 to the thiol side chain of Cys 25 in the protein show that the helices contribute in different ways to modulate the energy of proton transfer. The largest helix, A1, opposes the proton transfer through the effect of the helix dipole. The charged residues (primary structure) in helix A3 favor the proton transfer, and mask the effect of its helix dipole (secondary structure) which opposes the transfer. The direction of the proton transfer simulated for the activation mechanism is opposite to that assumed in the catalytic process of the thiol protease, and the entire protein environment opposes the transfer. This supports the specific role of the ligand in triggering the proton transfer as a response to its binding.

Computer Graphics

Three-dimensional imaging of neurons by confocal fluorescence microscopy.

The study of neuronal architecture by means of confocal laser microscopy is described. Optical serial sectioning has been performed on whole-mount specimens, and the resulting stacks of digitally recorded images have been processed with the help of a computer. Specimen preparation is described, as well as the instrument and its performance. It is shown that the limits in photometric quality are set by photon quantum noise. As both light absorption and scattering was low in the studied specimens, the maximum scanning depth was limited mainly by the working distance of the objectives. Compared with traditional methods, confocal microscopy in combination with digital image processing has the following advantages: (1) a truly three-dimensional (3-D) reconstruction is obtained, (2) the specimen remains intact, (3) a higher resolution can be obtained, (4) the process is automated and less time-consuming and (5) various kinds of data processing are possible.

Animals

Two-dimensional COSY and two-dimensional NOE spectroscopy of d(AC)4.d(GT)4: extraction of structural constraints.

Pure absorption phase, proton two-dimensional nuclear Overhauser effect (2D NOE) and double-quantum-filtered COSY (DQF-COSY) spectra were recorded for d(AC)4.d(GT)4. A full proton resonance assignment was made, except for the 5' and 5" protons. A new semiautomatic method for improved quantitation of 2D NOE peak intensities was developed, and its limitations and usefulness were examined. With this new method, 2D NOE intensity sets at several mixing times were obtained. Simulations of the 1'2', 1'2", and 2'3' DQF-COSY cross-peaks were compared with experimental data, establishing an alternating sugar pucker for the alternating purine-pyrimidine sequence. Scalar coupling constants for the sugar ring protons, derived from the fitting of the simulated spectra, are reported. Complete relaxation matrix analysis of the 2D NOE spectrum verified this alternating structure for all NOE interactions between nonexchangeable protons. Both the DQF-COSY and the 2D NOE results qualitatively indicate that the structure of d(AC)4.d(GT)4 resembles wrinkled D-DNA in aqueous solution.

Computer Simulation

Changes in the electron density of the cofactor NADPH on binding to E. coli dihydrofolate reductase.

Quantum-mechanical electron density calculations reveal that a significant polarization is induced in the cofactor NADPH (reduced nicotinamide adenine dinucleotide phosphate) on binding to the enzyme dihydrofolate reductase. The calculations indicate that electron density corresponding to approximately 0.7 electron charges is shifted within the molecule, extending over more than 20 A. Further calculations on proposed enzyme mutants show that the polarization of NADPH on binding to DHFR is, in large part, induced by a motif of three positively charged residues. This motif was also identified to be directly responsible for the positive electrostatic potential surrounding the cofactor binding site in the enzyme. The possibility of this long-range polarization of NADPH was originally proposed based on a previous study of ligand binding to DHFR where a conserved structural motif of three positively charged residues was found to play a major role in polarizing the substrate folate over its entire length of 18 A.

Arginine