A mathematical model of the oscillations in the aphakic eye

In this paper we describe a mathematical model of the oscillations of the diaphragm which limits the vitreous body from the anterior segment of the human eye after the lens has been removed in a cataract operation. We study the motion of this diaphragm driven by movements of the eye. Firstly, a mathematical statement of the problem is given and then we solve the problem exactly for a given class of eye movements. From the analysis we deduce that significant oscillations of the membrane are driven by saccades and that it is the angular acceleration of the eye which causes these types of oscillations. A numerical example is given.     

Limit cycle model for brain waves

The extraordinary high sensitivity of certain biological systems to weak electromagnetic signals motivated Fröhlich to establish his brain wave model. Although the basic assumptions of such a model are still highly speculative, it seems worth while to investigate the quantitative dynamics of it. In this model coherent excitations in the 10¹¹ Hz region in combination with a collective enzyme-substrate reaction create and stabilize a limit cycle oscillation. In the present paper the existence of the limit cycle and its collapse due to external stimulation is studied. The bifurcation of this periodically oscillating resting state is analysed and the stability of additional steady states is proven. Approximations are discussed and a correspondence between the limit cycle model and nerve impulse generating models is established.     

Rapid amygdala gamma oscillations in response to eye gaze

Background

The eye gaze of other individuals conveys important social information and can trigger multiple psychological activities; some of which, such as emotional reactions and attention orienting, occur very rapidly. Although some neuroscientific evidence has suggested that the amygdala may be involved in such rapid gaze processing, no evidence has been reported concerning the speed at which the amygdala responds to eye gaze.

Methodology/Principal Findings

To investigate this issue, we recorded electrical activity within the amygdala of six subjects using intracranial electrodes. Subjects observed images of eyes and mosaics pointing in averted and straight directions. The amygdala showed higher gamma-band oscillations for eye gaze than for mosaics, which peaked at 200 ms regardless of the direction of the gaze.

Conclusion

These results indicate that the human amygdala rapidly processes eye gaze.     

Punctuated cyclin synthesis drives early embryonic cell cycle oscillations

Cyclin B activates cyclin-dependent kinase 1 (CDK1) at mitosis, but conflicting views have emerged on the dynamics of its synthesis during embryonic cycles, ranging from continuous translation to rapid synthesis during mitosis. Here we show that a CDK1-mediated negative-feedback loop attenuates cyclin production before mitosis. Cyclin B plateaus before peak CDK1 activation, and proteasome inhibition caused minimal accumulation during mitosis. Inhibiting CDK1 permitted continual cyclin B synthesis, whereas adding nondegradable cyclin stalled it. Cycloheximide treatment before mitosis affected neither cyclin levels nor mitotic entry, corroborating this repression. Attenuated cyclin production collaborates with its destruction, since excess cyclin B1 mRNA accelerated cyclin synthesis and caused incomplete proteolysis and mitotic arrest. This repression involved neither adenylation nor the 3' untranslated region, but it corresponded with a shift in cyclin B1 mRNA from polysome to nonpolysome fractions. A pulse-driven CDK1-anaphase-promoting complex (APC) model corroborated these results, revealing reduced cyclin levels during an oscillation and permitting more effective removal. This design also increased the robustness of the oscillator, with lessened sensitivity to changes in cyclin synthesis rate. Taken together, the results of this study underscore that attenuating cyclin synthesis late in interphase improves both the efficiency and robustness of the CDK1-APC oscillator.     

Resonance oscillations in the human arterial system]

The paper summarizes the results of the experiments aimed at obtaining sphygmograms of peripheral and carotid arteries with due regard to the values of longitudinal dimensions of body and extremities in healthy subjects. Mathematical equations expressing the fact that dicrotic waves recorded on sphygmograms are the reflections of blood eigentones coinciding with resonance oscillations have been derived. It is proved that at least two partial vibration systems oscillating with different own frequencies are present in human arteries. Conditions under which the resonance of constituent frequencies of pulsatile pressure waves and output waves in arteries occurs have been determined. From this point of view a new explanation for the well-known phenomenon of the pulsatile wave amplitude increase from the heart towards peripheric regions is proposed.     

Rapid local oscillations of the surface of the human erythrocyte

The transverse displacements of the human erythrocyte surface with amplitude 300-400 nm in the frequency range 0.2-30 Hz are recorded on the minimal area erythrocyte rim (approximately 0.5 X 0.5 microns). These local oscillations of the surface are diminished at hypoosmotic erythrocyte swelling, on addition of substances which increase the membrane rigidity (0.01% glutaraldehyde, 0.5 mM 4-hydroxymercuribenzoate, cell membrane stain--0.002% Heliogen Blue) and on discocyte--echinocyte transformation due to addition of 1-2 mM 2,4-dinitrophenol. The amplitude of transverse displacements is reduced by 1.7-2 times on erythrocytes of patients with inherent microspherocytosis. These erythrocytes have inherent defects in spectrin. It is suggested that spectrin is important for rapid local oscillations of the human erythrocyte surface.     

The torque-angle transfer function of the human eye

Zusammenfassung Sinusförmig wechselnde Kräfte werden am Auge angewandt, und die resultierenden Bewegungen werden mit Hilfe eines Beschleunigungsmessers gemessen. Dieser ist an einer Kontaktlinse befestigt. Die Veränderung der Größe und des Phasenwinkels der Augendrehung mit der Frequenz wird in Form eines Bode-Diagramms wiedergegeben. Ein mechanisches Modell, das aus linearen visco-elastischen Elementen besteht, wird verwendet, um das Augapfel-Muskel-System nachzuahmen. Die Parameter des Modells werden nach der Methode der besten Übereinstimmung aus den Übergangs-Charakteristika bestimmt. Die Beschleunigung-gegen-Zeit Kurve der Bewegung, die durch Anwendung einer stufenartigen Verdrehung am Auge verursacht wird, ist in guter Übereinstimmung mit der vom Modell vorausgesagten. Die Drehwinkel-Übergangsfunktion des unbelasteten Auges wird aus dem Modell durch Abzug des Trägheitsmoments der Kontaktlinse und ihrer Anhängsel abgeleitet. Ergebnisse für Horizontal- und Vertikalbewegungen werden gesondert diskutiert. Vier kanonische und eine nicht-kanonische Form des mechanischen Modells sind angegeben. Angesichts der bekannten mechanischen Eigenschaften freiwilliger Muskel wird vermutet, daß die nicht-kanonische Form am ehesten physikalischen Elementen in der Augenhöhle entspricht. Drei Arten der Augenbewegung, die für das Sehen wichtig sind, werden verglichen mit der Mechanik des Augapfel-Muskel-Systems. Es wird vorausgesagt, daß eine Rotationsresonanz des Augapfels in der Pfanne erzeugt werden kann, wenn der Kopf in geeigneter Weise in Schwingungen gebracht wird. Die Natur der Muskelkräfte, die für saccadische Bewegungen und unwillkürliche Fixierungstremore verantwortlich sind, wird aufgeklärt.     

Circadian oscillations of neuropeptide expression in the human biological clock

The mammalian suprachiasmatic nucleus is the principal component of a neural timing system implicated in the temporal organization of circadian and seasonal processes. The present study was performed to analyze the circadian profiles of two major neuropeptidergic cell groups in the human suprachiasmatic nucleus. To that end the brains of 40 human subjects collected at autopsy were investigated. The populations of arginine vasopressin- and vasoactive intestinal polypeptide-expressing neurons, located in the shell and core of the suprachiasmatic nucleus, respectively, showed marked circadian rhythms with an asymmetrical, bimodal waveform. Time series analysis revealed that these circadian cycles in neuronal activity could be described by a composite model consisting of a nonlinear periodic function, with mono- and diphasic cycles. The findings suggest that the 24-h biosynthesis of neuropeptides in the human suprachiasmatic nucleus, being part of the neural output pathway of the clock, is driven by a complex pacemaker system consisting of coupled nonlinear oscillators, in accordance with a multioscillator model of circadian timekeeping.Abbreviations AIC Akaikie's information criterion - ARMA autoregressive moving average - AVP arginine vasopressin - c-fos immediate early gene - Per period gene - SCN suprachiasmatic nucleus - VIP vasoactive intestinal polypeptide     

Endogenous cytokinin oscillations control cell cycle progression of tobacco BY-2 cells

The significance of cytokinins for the progression of the cell cycle is well known. Cytokinins contribute to the control of the expression of D-cyclins and other cell cycle genes, but knowledge as to how they affect the progression of the cell cycle is still limited. Highly synchronized tobacco BY-2 cells with clearly defined cell cycle stages were employed to determine cytokinin patterns in detail throughout the entire cycle. Concentrations of trans-zeatin, and of some other cytokinins, oscillated during the course of the cell cycle, increasing substantially at all four phase transitions and decreasing again to a minimum value during the course of each subsequent phase. Addition of exogenous cytokinins or inhibition of cytokinin biosynthesis promoted the progression of the cell cycle when the effects of these manipulations intensified the endogenous fluctuations, whereas the progression of the cycle was retarded when the amplitude of the fluctuations was decreased. The results show that the attainment of low concentrations of cytokinins is as important as the transient increases in concentration for a controlled progression from one phase of the cell cycle to the next. Cytokinin oxidase/dehydrogenase activity also showed fluctuations during the course of the cell cycle, the timing of which could at least partly explain oscillations of cytokinin levels. The activities of the enzyme were sufficient to account for the rates of cytokinin disappearance observed subsequent to a phase transition.     

Identification of possible two-reactant sources of oscillations in the Calvin photosynthesis cycle and ancillary pathways

A systematic search for possible sources of experimentally observed oscillations in the photosynthetic reaction system has been performed by application of recent theoretical results characterizing the transient-state rate behaviour of metabolic reactions involving two independent concentration variables. All subsystems involving two independent reactants in metabolically fundamental parts of the Calvin cycle and the ancillary pathways of starch and sucrose synthesis have been examined in order to decide on basis of their kinetic and stoichiometric structure whether or not they may trigger oscillations. The results show that no less than 20 possible oscillators can be identified in the examined reaction system, only three of which have been previously considered as potential sources of experimentally observed oscillations. This illustrates the superiority of the method now applied over those previously used to identify possible two-reactant sources of metabolic oscillations and indicates that there should be no difficulty in complex metabolic pathways to point to a multitude of interactions that may trigger an oscillatory rate behaviour of the system.     

Natural images from the birthplace of the human eye

Here we introduce a database of calibrated natural images publicly available through an easy-to-use web interface. Using a Nikon D70 digital SLR camera, we acquired about six-megapixel images of Okavango Delta of Botswana, a tropical savanna habitat similar to where the human eye is thought to have evolved. Some sequences of images were captured unsystematically while following a baboon troop, while others were designed to vary a single parameter such as aperture, object distance, time of day or position on the horizon. Images are available in the raw RGB format and in grayscale. Images are also available in units relevant to the physiology of human cone photoreceptors, where pixel values represent the expected number of photoisomerizations per second for cones sensitive to long (L), medium (M) and short (S) wavelengths. This database is distributed under a Creative Commons Attribution-Noncommercial Unported license to facilitate research in computer vision, psychophysics of perception, and visual neuroscience.     

Operant control of human eye movements

Saccade and smooth pursuit are the eye movements used by primates to shift gaze. In this article we review evidence for the effects of reinforcement on several dimensions of these responses such as their latencies, velocities or amplitudes. We propose that these responses are operant behaviours controlled by their consequences on performance of visually guided tasks. Studying the conditions under which particular eye movement patterns might emerge from the cumulative effects of reinforcement provides critical insights about how motor responses are attuned to environmental exigencies.     

Computer simulation of hydraulic flows in the human eye

A two-dimensional computer model was developed to describe hydraulic flows inside the human eye. The flow field was described by coupled Navier-Stokes and Darcy equations. The velocity and pressure profiles in the chambers, the wall, and the vitreous body of the normal eye were obtained using the finite-element method. The model includes filtration of fluid from the retinal capillary and its drainage through the choroid. The applications of this model include estimation of the contribution of convection and diffusion to the transport of drugs and study of the kinetics of biodistribution in the eye.     

Adaptive wavelet analysis of oscillations in the human peripheral blood flow

The main principles are outlined for spectral timing analysis of the peripheral blood flow oscillations obtained by laser Doppler flowmetry. The oscillations can be studied in a wide frequency range both in stationary and nonstationary conditions during functional tests. The potential of the method has been demonstrated in experiments with the reaction of the microvascular bed to transcutaneous iontophoretic introduction of acetylcholine chloride. The major advantage of the method over conventional wavelet analysis is a significant increase in the “effective” length of the signal analyzed, which allows correct analysis of low-frequency components in much shorter LDF recordings than those commonly used.