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Torque and rotation rate of the bacterial flagellar motor.

This paper describes an analysis of microscopic models for the coupling between ion flow and rotation of bacterial flagella. In model I it is assumed that intersecting half-channels exist on the rotor and the stator and that the driving ion is constrained to move together with the intersection site. Model II is based on the assumption that ion flow drives a cycle of conformational transitions in a channel-like stator subunit that are coupled to the motion of the rotor. Analysis of both mechanisms yields closed expressions relating the torque M generated by the flagellar motor to the rotation rate v. Model I (and also, under certain assumptions, model II) accounts for the experimentally observed linear relationship between M and v. The theoretical equations lead to predictions on the relationship between rotation rate and driving force which can be tested experimentally.

Bacterial Physiological Phenomena↗

Determination of electric field threshold for electrofusion of erythrocyte ghosts. Comparison of pulse-first and contact-first protocols.

Rabbit erythrocyte ghosts were fused by means of electric pulses to determine the electrofusion thresholds for these membranes. Two protocols were used to investigate fusion events: contact-first, and pulse-first. Electrical capacitance discharge (CD) pulses were used to induce fusion. Plots of fusion yield vs peak field strength yielded curves that intersected the field strength axis at positive values (pseudothresholds) which depended on the protocol and decay half time of the pulses. It was found that plots of pseudothreshold vs reciprocal half time were linear for each protocol; when extrapolated to reciprocal half time = 0 (i.e., t----infinity), these lines intersected the ordinate at values of the field strength considered to be the true electrofusion thresholds. In this fashion, the contact-first protocol gave an electrofusion threshold of 46.5 +/- 11.5 V/mm for hemoglobin-free ghosts (white ghosts) and 40.9 +/- 8.8 V/mm for ghosts with fractional hemoglobin (pink ghosts), while the threshold for the pulse-first protocol applied to pink ghosts was determined to be 93.4 +/- 11.0 V/mm. Although the thresholds depended on the electrofusion protocol, plots of critical field strength vs reciprocal time had the same slopes, i.e., approximately 24 Vs/mm. The results suggest that the fusogenic state induced by an electric pulse in either the contact-first protocol or the pulse-first protocol (long-lived fusogenic state) may in fact share a common mechanism, if the two states are not actually identical.

Animals↗

SIMS: computation of a smooth invariant molecular surface.

SIMS, a new method of calculating a smooth invariant molecular dot surface, is presented. The SIMS method generates the smooth molecular surface by rolling two probe spheres. A solvent probe sphere is rolled over the molecule and produces a Richards-Connolly molecular surface (MS), which envelops the solvent-excluded volume of the molecule. In deep crevices, Connolly's method of calculating the MS has two deficiencies. First, it produces self-intersecting parts of the molecular surface, which must be removed to obtain the correct MS. Second, the correct MS is not smooth, i.e., the direction of the normal vector of the MS is not continuous, and some points of the MS are singular. We present an exact method for removing self-intersecting parts and smoothing the singular regions of the MS. The singular MS is smoothed by rolling a smoothing probe sphere over the inward side of the singular MS. The MS in the vicinity of singularities is replaced with the reentrant surface of the smoothing probe sphere. The smoothing method does not disturb the topology of a singular MS, and the smooth MS is a better approximation of the dielectric border between high dielectric solvent and the low dielectric molecular interior. The SIMS method generates a smooth molecular dot surface, which has a quasi-uniform dot distribution in two orthogonal directions on the molecular surface, which is invariant with molecular rotation and stable under changes in the molecular conformation, and which can be used in a variety of implicit methods of modeling solvent effects. The SIMS program is faster than the Connolly MS program, and in a matter of seconds generates a smooth dot MS of a 200-residue protein. The program is available from the authors on request (see http:@femto.med.unc.edu/SIMS).

Algorithms↗

Three electronic state model of the primary phototransformation of bacteriorhodopsin.

The primary all-trans --> 13-cis photoisomerization of retinal in bacteriorhodopsin has been investigated by means of quantum chemical and combined classical/quantum mechanical simulations employing the density matrix evolution method. Ab initio calculations on an analog of a protonated Schiff base of retinal in vacuo reveal two excited states S1 and S2, the potential surfaces of which intersect along the reaction coordinate through an avoided crossing, and then exhibit a second, weakly avoided, crossing or a conical intersection with the ground state surface. The dynamics governed by the three potential surfaces, scaled to match the in situ level spacings and represented through analytical functions, are described by a combined classical/quantum mechanical simulation. For a choice of nonadiabatic coupling constants close to the quantum chemistry calculation results, the simulations reproduce the observed photoisomerization quantum yield and predict the time needed to pass the avoided crossing region between S1 and S2 states at tau1 = 330 fs and the S1 --> ground state crossing at tau2 = 460 fs after light absorption. The first crossing follows after a 30 degrees torsion on a flat S1 surface, and the second crossing follows after a rapid torsion by a further 60 degrees. tau1 matches the observed fluorescence lifetime of S1. Adjusting the three energy levels to the spectral shift of D85N and D212N mutants of bacteriorhodospin changes the crossing region of S1 and S2 and leads to an increase in tau1 by factors 17 and 10, respectively, in qualitative agreement with the observed increase in fluorescent lifetimes.

Amino Acid Substitution↗

Chronic (-) deprenyl administration alters dendritic morphology of layer III pyramidal neurons in the prefrontal cortex of adult Bonnett monkeys.

Chronic (-) deprenyl (0.2 mg/kg, b.wt; for 25 days) treatment induced alterations in the dendritic morphology of prefrontal cortical neurons in adult Bonnett monkeys were evaluated in the present study. The branching points and intersections in apical and basal dendrites were studied up to a distance of 400 and 200 micrometers, respectively, in Golgi impregnated layer III pyramidal neurons of the prefrontal cortex. Our results revealed a significant (p<0.001) increase in the number of branching points and intersections in both apical and basal dendrites in (-) deprenyl treated monkeys compared to controls. Such an enriched dendritic arborization in prefrontal cortical neurons may be responsible for the enhancement of cognitive functions in Alzheimer disease patients following (-) deprenyl treatment.

Analysis of Variance↗

Predictive action in infancy: tracking and reaching for moving objects.

Because action plans must anticipate the states of the world which will be obtained when the actions take place, effective actions depend on predictions. The present experiments begin to explore the principles underlying early-developing predictions of object motion, by focusing on 6-month-old infants' head tracking and reaching for moving objects. Infants were presented with an object that moved into reaching space on four trajectories: two linear trajectories that intersected at the center of a display and two trajectories containing a sudden turn at the point of intersection. In two studies, infants' tracking and reaching provided evidence for an extrapolation of the object motion on linear paths, in accord with the principle of inertia. This tendency was remarkably resistant to counter-evidence, for it was observed even after repeated presentations of an object that violated the principle of inertia by spontaneously stopping and then moving in a new direction. In contrast to the present findings, infants fail to extrapolate linear object motion in preferential looking experiments, suggesting that early-developing knowledge of object motion, like mature knowledge, is embedded in multiple systems of representation.

Child Development↗

On-chip definition of picolitre sample injection plugs for miniaturised liquid chromatography.

The fabrication of components for a miniaturised liquid chromatography system on silicon has recently been reported by our research group [J. Cap. Electrophoresis Microchip Technol. 6 (1999) 33; Analyst 125 (2000) 25]. To date, inlet and outlet connection ports, separation micro-channels (20-200 microm in width, 0.5-10 microm in depth, 15-60 cm in length), and an intersection for picolitre injection have been etched on a silicon wafer and then sealed with a Pyrex cover plate on which platinum electrodes for on-chip detection have been patterned. The platinum electrodes have been used for the amperometric detection of phenol, using 20 nl off-chip injection. In this work we present our latest results obtained with on-chip pressure driven picolitre injection, designed to realize the full capabilities of this micro-LC system. The injection volume is dependent on the micro-channel depth, width, and also on the intersection length, allowing injection in the low nanolitre to picolitre range.

Chromatography, High Pressure Liquid↗

Retention in reversed-phase liquid chromatography: solvatochromic investigation of homologous alcohol-water binary mobile phases.

The mechanism of retention in reversed-phase liquid chromatography (RPLC) has been further investigated using the ET(30) solvatochromic solvent polarity scale. The retention behavior of a variety of solutes was measured using a homologous series of normal alcohols as the organic modifiers in hydroorganic mobile phases. The results imply that a systematic change in the extent of solvation of the stationary phase occurs with respect to the size of the organic modifier. It was also found that a linear extrapolation of the log k' versus ET(30) plots for different mobile phases using methanol, ethanol and acetonitrile (but not n-propanol) as modifiers, intersected at approximately the ET(30) value of pure water. This intersection is further evidence that the ET(30) model of solute retention is a useful tool with which to study the mechanism of retention in RPLC. The extrapolated retention value in water, log k'w, from the ET(30) plots should then prove to be a more reliable means of estimating solute lipophilicity using RPLC than the percent organic modifier model.

Alcohols↗

How does an enzyme evolved in vitro compare to naturally occurring homologs possessing the targeted function? Tyrosine aminotransferase from aspartate aminotransferase.

Aspartate aminotransferase (AATase) and tyrosine aminotransferase (TATase) are Escherichia coli paralogs that share 43% sequence identity. A plausible model posits that TATase arose from a duplication of an ancestral AATase-like enzyme. Directed evolution of AATase to an enzyme having TATase activity was undertaken in order to compare the evolved AATase variants with homologous TATases. Eight rounds of DNA shuffling and in vivo selection followed by a backcross with WT AATase produced enzymes that exhibited 100-270-fold increases in k(cat)/K(m)(Phe) and had as much as 11% of the tyrosine aminotransferase activity of WT E.coli TATase. Amino acid substitutions in 11 clones from rounds 7 and 8 were compared with conserved residues in AATases and TATases. The findings are conveniently and compactly illustrated by the use of Venn diagrams and set theory notation. A statistically significant (0.001 or=75% identical) in AATases and variable (<75% identical) in TATases. Very few mutations occur in the intersection (set AAT intersection TAT) of amino acid residues that are conserved in both enzyme types. Seven mutations from set AAT-TAT were combined by site-directed mutagenesis to give a construct that is 60% as active as the best round 8 enzyme, which has 13 amino acid replacements. The Venn diagrams may provide a generally useful tool to highlight the most important specificity determinants for rational redesign. Amino acid replacements were mapped onto the crystal structure of a hydrocinnamate complex of a designed TATase. Five of the seven positions most frequently substituted in the evolved clones are within 15 A of the phenyl side-chain, but only six of the 48 positions that were mutated once or twice are within that radius. Context dependence, neutral mutations, different selective pressures, and stochastic components provide explanations for the observation that many of the substitutions found in the directly evolved enzymes differ from the corresponding amino acids found in the modern natural TATases.

Amino Acid Sequence↗

Physiological basis for mechanical time-variance in the heart: special consideration of non-linear function.

A relationship between ventricular pressure and volume is developed starting from basic cardiac muscle mechanics. The known and measurable properties of myocardium, such as the Hill law, the periodic excitation-contraction mechanism, and non-linear elasticity of the surrounding elastin and collagen structure, are formulated into a myofibril unit. A cylindrical geometry is chosen to represent the structure of the ventricle, using the myofibril unit as the basic building block. Pressure-volume isochrones computed from this model illustrate non-linear function in the heart which arises from both geometric effects and muscle effects. The above theory and model is linearized to provide a special study case. The behavior that resulted is that of a time-varying elastance, E(t), and, hence, can help in the interpretation of its meaning. It is found that the minimum in E(t) is the consequence of the stiffness of the myocardial fibrous network, adjusted by a geometric factor. In addition, the magnitude of E(t) is governed by myocardial contractility, a geometric factor, and the excitation-contraction mechanism, where time-dependency is imparted by periodic excitation. Since the elastic fibers are the only true elastic elements, the quantity of elastance is determined by controlled volume feedback. A circuit model is provided to illustrate this concept. The non-linear active and passive heart function curves are specified independently. These curves are required to intersect below the resting volume and result in a negative pressure at the intersection. This is found to explain the phenomenon of ventricular suction. In addition, they lead to a time-varying dead volume by virtue of time-dependent isochronal slope. Non-linear function is introduced to the model and is found to explain the variation in curvature of the ventricular isochrones.

Animals↗

Electrical instability in cardiac muscle: phase singularities and rotors.

A dynamical system is "excitable" at some stage in its behavior (e.g. at a rest state or while it is nearly at rest prior to a spontaneous event) if a small, but not too small, stimulus of the right kind elicits an immediate big reaction that eventually leads back to the original state. During this return to excitability a typical system is not excitable. An excitable system need not have an attracting rest state; a spontaneous oscillator can be excitable, too, as is common in biological and in chemical excitable kinetics. In a medium characterized by such excitable dynamics at every point, the excitation can propagate as a travelling pulse. Undamaged cardiac muscle shares with other excitable media certain features of such pulse propagation in two and three dimensions. Among the new electrophysiological phenomena thus anticipated are paired mirror-image vortices ("rotors") organized around phase singularities. These should arise in the myocardium near the intersection of a moving critical contour of phase in the normal cycle of excitation and recovery with a momentary critical contour of local stimulus strength. Such intersections, and the corresponding aftermath of paired rotors, should only occur following certain combinations of stimulus size and stimulus timing. Plotting those combinations on a "vulnerability diagram", one delineates a domain for creation of rotors (corresponding to tachycardia) surrounded on all sides by a halo of combinations at which just a few repetitive responses follow stimulation. The experiments called for to check these implications have now been carried out in the special case of electrically-induced tachycardia in healthy canine ventricle. They support the two-dimensional theory, so a new experiment is suggested to demonstrate wholly intramural three-dimensional vortex filaments.

Animals↗

Multiple attractors and boundary crises in a tri-trophic food chain.

The asymptotic behaviour of a model of a tri-trophic food chain in the chemostat is analysed in detail. The Monod growth model is used for all trophic levels, yielding a non-linear dynamical system of four ordinary differential equations. Mass conservation makes it possible to reduce the dimension by 1 for the study of the asymptotic dynamic behaviour. The intersections of the orbits with a Poincaré plane, after the transient has died out, yield a two-dimensional Poincaré next-return map. When chaotic behaviour occurs, all image points of this next-return map appear to lie close to a single curve in the intersection plane. This motivated the study of a one-dimensional bi-modal, non-invertible map of which the graph resembles this curve. We will show that the bifurcation structure of the food chain model can be understood in terms of the local and global bifurcations of this one-dimensional map. Homoclinic and heteroclinic connecting orbits and their global bifurcations are discussed also by relating them to their counterparts for a two-dimensional map which is invertible like the next-return map. In the global bifurcations two homoclinic or two heteroclinic orbits collide and disappear. In the food chain model two attractors coexist; a stable limit cycle where the top-predator is absent and an interior attractor. In addition there is a saddle cycle. The stable manifold of this limit cycle forms the basin boundary of the interior attractor. We will show that this boundary has a complicated structure when there are heteroclinic orbits from a saddle equilibrium to this saddle limit cycle. A homoclinic bifurcation to a saddle limit cycle will be associated with a boundary crisis where the chaotic attractor disappears suddenly when a bifurcation parameter is varied. Thus, similar to a tangent local bifurcation for equilibria or limit cycles, this homoclinic global bifurcation marks a region in the parameter space where the top-predator goes extinct. The 'Paradox of Enrichment' says that increasing the concentration of nutrient input can cause destabilization of the otherwise stable interior equilibrium of a bi-trophic food chain. For a tri-trophic food chain enrichment of the environment can even lead to extinction of the highest trophic level.

Animals↗

Can spatio-temporal energy models of motion predict feature motion?

Current "spatio-temporal energy" models of how we perceive pattern motion have been very successful in helping us to understand the mechanisms of motion perception. Although they have been supported by a large number of physiological and psychological studies, they have so far not provided a complete explanation for a number of results. These results emerge from experiments concerned with predicting perceived motion direction from patterns comprising two or more components. It has been suggested that these results are more consistent with an earlier type of model based on the motion of two-dimensional features. This paper briefly describes how three generic spatio-temporal energy models have been extended to predict motion derived from two-component stimuli. A new model is then presented that utilises similar architecture to the two-stage spatial-temporal energy model proposed by Adelson and Movshon (Nature 300 (1982) 523). The first stage is a spatial temporal filtering stage and the second stage computes the intersection of constraints (IOC), an important constraint used in combining motion information across two or more components. In the model presented here the second stage is different. A directional spatial second derivative is used to extract zero-crossings at the component level, i.e. gratings. If any zero-crossing falls in the same spatial position for two or more components its displacement is tracked using a nearest neighbour match. Tracking these 'intersecting zero-crossings' essentially computes the IOC but also provides other properties that predict non-IOC motion, and second-order component motion. Surprising new insights are described into how current spatio-temporal energy models may also account for these results. However, unlike the model presented here, they rely on operations carried out on the two-dimensional pattern.

Contrast Sensitivity↗

Attention and scintillation.

The scintillating grid is a recently discovered visual illusion, created by superimposing white discs on the intersections of orthogonal gray bars on a black background. Even though the entire display is stationary, observers perceive dark spots appearing and disappearing rapidly within some of the white discs. This scintillation effect is correlated with eye position and eye movements. Here we investigate whether covert shifts of attention, as revealed by cueing and visual search paradigms, can also affect the illusion. We find that the chance of a particular intersection scintillating is directly correlated with distance from the attentional focus, regardless of the location of the fixation point. This suggests that the dynamics of this illusion might reflect the distribution of attention in space and time.

Analysis of Variance↗

Measuring and modelling the airborne particulate matter mass concentration field in the street environment: model overview and evaluation.

This paper discusses the outline structure and preliminary evaluation of an emission-dispersion model for predicting the temporal and spatial distribution of vehicle-derived airborne particulate matter mass concentration in street canyons. The model is called Street Level Air Quality (SLAQ). SLAQ is semi-empirical, in that it uses not only results from field and wind tunnel experiments but also theory and models derived from multiple runs of numerical routines in order to simulate the basic physical processes within the street canyon. A combination of a plume model, for the direct contribution of vehicle exhaust, and a box model for the recirculating part of the pollutants in the street, is used to predict concentration for receptors within the canyon. Emission rates of vehicle-derived particulate matter are calculated within SLAQ, which serve as input to the dispersion module. Exhaust emission rates are scaled element by element along the street for each of the lanes according to the direction of traffic flow to account for modal operation of vehicles near signalised intersections. This refinement allows SLAQ to account for non-uniformity in along-canyon emission rates and to model a street that has several intersections along its length. Thermal turbulence due to environmental surface sensible heat and vehicle-generated heat is accounted for in the model. Other features of SLAQ include correction for the urban heat island effect, dry deposition, wet deposition, particle settling and estimation of wind direction standard deviation, when this latter data is not available. SLAQ has been evaluated in a street in Loughborough, Leicestershire, United Kingdom and correlation coefficient of 0.8 between the modelled and measured concentrations has been obtained.

Aerosols↗

In honour of Lothar Spillmann - filling-in, wiggly lines, adaptation, and aftereffects.

I have studied a number of visual phenomena that Lothar Spillmann has already elucidated. These include: Neon spreading: when a small red cross is superimposed on intersecting black lines, the red cross seems to spread out into an illusory disk. Unlike the Hermann grid, neon spreading is relatively unaffected when the black lines are curved or wiggly. This suggests that the Hermann grid, but not neon spreading, involves long-range interactions. Neon spreading can be shown in random-dot patterns, even without intersections. It is strongest when the red crosses are equiluminous with the gray background. Adaptation, aftereffects, and filling-in: direct and induced aftereffects of color, motion, and dimming. Artificial scotomata and filling-in: the "dam" theory is false. Staring at wiggly lines or irregularly scattered dots makes them gradually appear straighter, or more regularly spaced. I present evidence that irregularity is actually a visual dimension to which the visual system can adapt. Conjectures on the nature of peripheral fading and of motion-induced blindness. Some failed experiments on correlated visual inputs and cortical plasticity.

Adaptation, Physiological↗

FGF and Shh signals control dopaminergic and serotonergic cell fate in the anterior neural plate.

During development, distinct classes of neurons are specified in precise locations along the dorso-ventral and anterior-posterior axes of the neural tube. We provide evidence that intersections of Shh, which is expressed along the ventral neural tube, and FGF8, which is locally produced at the mid/hindbrain boundary and in the rostral forebrain, create induction sites for dopaminergic neurons in the midbrain and forebrain. The same intersection, when preceded by a third signal, FGF4, which is expressed in the primitive streak, defines an inductive center for hindbrain 5-HT neurons. These findings illustrate that cell patterning in the neural plate is a multistep process in which early inducers, which initially divide the neural plate into crude compartments, are replaced by multiple local organizing centers, which specify distinct neuronal cell types within these compartments.

Animals↗

Increasing the cervical lordosis with chiropractic biophysics seated combined extension-compression and transverse load cervical traction with cervical manipulation: nonrandomized clinical control trial.

BACKGROUND: Cervical lordosis has been shown to be an important outcome of care; however, few conservative methods of rehabilitating sagittal cervical alignment have been reported. OBJECTIVE: To study whether a seated, retracted, extended, and compressed position would cause tension in the anterior cervical ligament, anterior disk, and muscle structures, and thereby restore cervical lordosis or increase the curvature in patients with loss of the cervical lordosis. STUDY DESIGN: Nonrandomized, prospective, clinical control trial. METHODS: Thirty preselected patients, after diagnostic screening for tolerance to cervical extension with compression, were treated for the first 3 weeks of care using cervical manipulation and a new type of cervical extension-compression traction (vertical weight applied to the subject's forehead in the sitting position with a transverse load at the area of kyphosis). Pretreatment and posttreatment Visual Analogue Scale (VAS) pain ratings were compared along with pretreatment and posttreatment lateral cervical radiographs analyzed with the posterior tangent method for changes in alignment. Results are compared to a control group of 33 subjects receiving no treatment and matched for age, sex, weight, height, and pain. RESULTS: Control subjects reported no change in VAS pain ratings and had no statistical significant change in segmental or global cervical alignment on comparative lateral cervical radiographs (difference in all angle mean values < 1.3 degrees ) repeated an average of 8.5 months later. For the traction group, VAS ratings were 4.1 pretreatment and 1.1 posttreatment. On comparative lateral cervical radiographs repeated after an average of 38 visits over 14.6 weeks, 10 angles and 2 distances showed statistically significant improvements, including anterior head weight bearing (mean improvement of 11 mm), Cobb angle at C2-C7 (mean improvement of -13.6 degrees ), and the angle of intersection of the posterior tangents at C2-C7 (mean improvement of 17.9 degrees ). Twenty-one (70%) of the treatment group subjects were followed for an additional 14 months; improvements in cervical lordosis and anterior weight bearing were maintained. CONCLUSIONS: Chiropractic biophysics (CBP) technique's extension-compression 2-way cervical traction combined with spinal manipulation decreased chronic neck pain intensity and improved cervical lordosis in 38 visits over 14.6 weeks, as indicated by increases in segmental and global cervical alignment. Anterior head weight-bearing was reduced by 11 mm; Cobb angles averaged an increase of 13 degrees to 14 degrees; and the angle of intersection of posterior tangents on C2 and C7 averaged 17.9 degrees of improvement.

Adult↗