ISIS INTERNATIONAL SYMPOSIUM ON INTERDISCIPLINARY SCIENCE

ISIS Opening Address: Complexity versus Simplicity
View Description Hide DescriptionThere are a lot of different concepts to cover all the meanings that we attach intuitively to the word complexity, and to its opposite simplicity. There is one kind of complexity that corresponds best to what is meant by the word complexity in ordinary conversation, and in most scientific dialog. It’s what I call effective complexity. Roughly, effective complexity refers to the length of a very precise description of the regularities of an entity. Not the features that are treated as random or incidental, but the features that are treated as regularities.

Superheavy Nuclei — Clusters of Matter and Antimatter
View Description Hide DescriptionThe extension of the periodic system into various new areas is investigated. Experiments for the synthesis of superheavy elements and the predictions of magic numbers with modern meson field theories are reviewed. Different channels of nuclear decay are discussed including cluster radioactivity, cold fission and cold multifragmentation Furthermore, we present the vacuum for the e ^{+}‐e ^{−} field of QED and show how it is modified for baryons in nuclear environment. Then we discuss the possibility of producing new types of nuclear systems by implanting an antibaryon into ordinary nuclei. The structure of nuclei containing one antiproton or antilambda is investigated within the framework of a relativistic mean‐field model. Self‐consistent calculations predict very enhanced binding and considerable compression in such systems as compared with normal nuclei. We present arguments that the life time of such nuclei with respect to the antibaryon annihilation might be long enough for their observation. A perspective for future research is given.

Heavy‐Ion Reactions in Time‐dependent Hartree‐Fock
View Description Hide DescriptionNuclear collisions at low energies present a unique opportunity for the study of degenerate Fermi systems far from equilibrium. Their behavior shows a rich variety: from complete fusion through highly nonelastic collisions to grazing situations with a complicated interplay of collective and single‐particle degrees of freedom. The time‐dependent Hartree‐Fock approximation assumes a dominance of Pauli exclusion, ignoring the two‐body collisions and instead using the mean field as the dominant dynamic quantity. For a class of zero‐range effective interactions (the so‐called Skyrme forces) it is possible to numerically solve the equations of motion to obtain a description of reactions that is parameter‐free in the sense that the forces are fitted exclusively to nuclear ground‐state properties. In this talk I give an overview of the theoretical issues, ignoring much of the technical detail of nuclear theory involved in such studies, and instead concentrating on the interesting consequences of the nonlinear coupling through the mean field: the spurious interaction between the different exit channels, the “one‐body dissipation” mechanism and the essential semiclassical nature of the approach.

Chaotic dynamics of modulational instability in optical fibers
View Description Hide DescriptionThe long distance dynamics of modulational instability in optical fibers is studied. A perturbed nonlinear Schrödinger equation which includes higher order dispersive and nonlinear terms as well as damping is investigated. When damping is significant, amplifiers are used to compensate for the fiber losses. Periodically modulated cw waves are shown to evolve chaotically for a variety of physical parameters. A nonlinear spectral analysis of the data shows that the chaotic evolution is characterized by homoclinic transitions in the spectrum.

Dynamics of Patterns on Elastic Hypersurfaces. Part I. Shear Waves in the Middle Surface
View Description Hide DescriptionThe shear motions in an incompressible elastic continuum are considered and it is shown that, when linearized, the governing equations can be rendered into Maxwell’s form. The trace of the deviator stress tensor is analogous to the electric field, while the vorticity (the curl of the velocity field) is interpreted as the magnetic field. We show that the analogy can be extended further to incorporate the so‐called Lorentz force as the counterpart of the advective nonlinearity of the elastic model. Localized shear dislocations are considered and shown to undergo Lorentz contraction in the direction of motion. Thus an interesting and far reaching analogy between the elastic continuum and the electrodynamics is established.

Dynamics of Patterns on Elastic Hypersurfaces. Part II. Wave Mechanics of Flexural Quasi‐Particles
View Description Hide DescriptionIn the first part of this work, the shear wave phenomena in an elastic 3D continuum are investigated and an analogy to Maxwellian electrodynamics is shown. In the present part, the model is extended assuming the continuum to be a momentum‐supporting hypersurface in 4D space (a hypershell). The transverse (flexural) deformations of the shell are governed by a Generalized Nonlinear Dispersive Wave Equation (GDWE) of Schrödinger type. The Hamiltonian structure of the model is discussed. The solitary wave solutions are shown to fit the concept of quasi‐particles. The concept of pseudo‐mass is introduced and the Newtonian mechanics for the centers of quasi‐particles/solitons is derived. Numerical examples of the shapes in 2D are presented. The presence of attractive force between the localized elevations of the surface is discussed and shown to depend on the distance between them as x⃗^{−2}.

Harmonic Oscillators as Bridges between Theories
View Description Hide DescriptionOther than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two‐by‐two matrices. If two oscillators are coupled, the problem combines both two‐by‐two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. It is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two‐by‐two matrices commonly called SL(2, c). Thus the coupled harmonic oscillators can therefore play the role of combining quantum mechanics with special relativity. Both Paul A. M. Dirac and Richard P. Feynman were fond of harmonic oscillators, while they used different approaches to physical problems. Both were also keenly interested in making quantum mechanics compatible with special relativity. It is shown that the coupled harmonic oscillators can bridge these two different approaches to physics.

Fourier‐Galerkin Method for Time Dependent Problems of Interacting Localized Waves
View Description Hide DescriptionWe develop a Fourier‐Galerkin spectral technique for computing solutions of type of interacting localized waves. We use a special complete orthonormal system of functions in L ^{2}(−∞, ∞). The rate of convergence of the coefficients is shown to be exponential. As a featured example we consider the Boussinesq Paradigm Equation (BPE). We obtain results for the head‐on and overtaking collisions of two or three solitons. We evaluate also the phase shifts of solitons.

Generalized Quasilinearization Method for Reaction Diffusion Equation with Numerical Applications
View Description Hide DescriptionWe have developed generalized quasilinearization method for reaction diffusion systems in [11], when the forcing functions are the sum of convex and concave functions. In this paper, we present theoretical result of the scalar case of reaction diffusion equation when the forcing function is the sum of a convex and concave function without proof. Further we demonstrate the application of the GQL method to reaction diffusion equation with numerical applications.

2D Solitary Waves of Boussinesq Equation
View Description Hide DescriptionIn this paper, the 2D stationary‐propagating localized solutions of Boussinesq’s equation are investigated numerically. An algorithm for treating the bifurcation and finding a nontrivial solution is created. The scheme is validated employing different grid sizes and different size of the box that contains the solution. The results obtained show that there is pseudo‐Lorentzian elongation of the scale of the solitons but it is only in the direction transverse to the propagation velocity. In longitudinal direction the scales are slightly contracted, so kind of “relative” contraction takes place. Results are shown graphically and discussed.

Nonlinear modeling of 3‐d flagellar dynamics
View Description Hide DescriptionWe develop exact equations formulas for the sliding between arbitrary filament pairs in a bundle subjected to a general 3‐d deformation. We introduce a classification of deformations, and we study particular examples for bending, twisting, helical and toroidal shapes. We prove that simultaneous combination of twisting and bending can produce a drastically drop in the sliding. These results can relate the geometry of shapes and motions with the distribution of molecular motors activity.

Symmetry Breaking in a Model for Nodal Cilia
View Description Hide DescriptionNodal cilia are very short cilia found in the embryonic node on the ventral surface of early mammalian embryos. They create a right to left fluid flow that is responsible for determining the normal asymmetry of the internal organs of the mammalian body. To do this, the distal end of the cilium must circle in a counterclockwise sense. Computer simulations with 3‐dimensional models of flagella allow examination of 3‐dimensional movements such as those of nodal cilia. 3‐dimensional circling motions of short cilia can be achieved with velocity controlled models, in which dynein activity is regulated by sliding velocity. If dyneins on one outer doublet are controlled by the sliding velocity experienced by that doublet, the system is symmetric, and the 3‐dimensional models can show either clockwise or counterclockwise circling. My computer simulations have examined two possible symmetry breaking mechanisms: 1) dyneins on doublet N are regulated by a mixture of the sliding velocities experienced by doublets N and N+1 (numbered in a clockwise direction, looking from the base). or 2) symmetry is broken by an off‐axis force that produces a right‐handed twist of the axoneme, consistent with observations that some dyneins can rotate their substrate microtubules in a clockwise direction.

What Organizes the Molecular Ballet that Promotes the Movement of the Axoneme in Such a Way that its Molecular Machinery Seems to be a Whole?
View Description Hide DescriptionThe axonemal machinery constitutes a highly organized structure whose mechanisms seem to be very simple but whose regulation remains unknown. This apparent simplicity is reinforced by the fact that many models are able to perfectly mimic the axonemal wave trains that propagate along cilia and flagella. However nobody knows what are the actual mechanisms that coordinate the molecular ballet that exist during the beat. Here we present some theoretical elements that show that if the radial spokes are one of the main elements that promote axonemal regulation, they must be involved in a complex mechanism that makes the axoneme a discrete structure whose regulation could depend on local entropy that promotes the emergence of new molecular properties.

Regulation of Eukaryotic Flagellar Motility
View Description Hide DescriptionThe central apparatus is essential for normal eukaryotic flagellar bend propagation as evidenced by the paralysis associated with mutations that prevent central pair (CP) assembly. Interactions between doublet‐associated radial spokes and CP projections are thought to modulate spoke‐regulated protein kinases and phosphatases on outer doublets, and these enzymes in turn modulate dynein activity. To better understand CP control mechanisms, we determined the three‐dimensional structure of the Chlamydomonas reinhardtii CP complex and analyzed CP orientation during formation and propagation of flagellar bending waves. We show that a single CP microtubule, C1, is near the outermost doublet in curved regions of the flagellum, and this orientation is maintained by twists between successive principal and reverse bends. The Chlamydomonas CP is inherently twisted; twists are not induced by bend formation, and do not depend on forces or signals transmitted through spoke‐central pair interactions. We hypothesize that CP orientation passively responds to bend formation, and that bend propagation drives rotation of the CP and maintains a constant CP orientation in bends, which in turn permits signal transduction between specific CP projections and specific doublet‐associated dyneins through radial spokes. The central pair kinesin, Klp1, although essential for normal motility, is therefore not the motor that drives CP rotation. The CP also acts as a scaffold for enzymes that maintain normal intraflagellar ATP concentration.

Flagellar Bend Dynamics in African Trypanosomes
View Description Hide DescriptionThe flagellated protozoa are highly dependent on flagellar dynamics for environmental sensing, reproduction, cell morphology, and disease progression. Functional and structural nuances amongst the different flagellated cells create the need to quantify the flagellar dynamics in each organism. In the African trypanosomes, specialized cellular and flagellar architecture sutures the flagellum to the cell body along its length, which results in a unique auger‐like cell motility. In this paper, we provide a quantitative description of flagellar bends in procyclic Trypanosoma brucei. We used digital video microscopy to describe the geometry and dynamics of trypanosome flagellar bends. We present a formula that demonstrates trypanosome flagellar bends have a conserved and predictable shape that is related to conic functions. We also investigate the local dynamics of individual flagellar bends and show that trypanosome flagellar bends can dilate, constrict, and travel bidirectionally along the flagellum. The implications of this data in modeling trypanosome cell motility are discussed.

MSP Dynamics and Retraction in Nematode Sperm
View Description Hide DescriptionMost eukaryotic cells can crawl over surfaces. In general, this motility requires three distinct actions: polymerization at the leading edge, adhesion to the substrate, and retraction at the rear. Recent in vitro experiments with extracts from spermatozoa from the nematode Ascaris suum suggest that retraction forces are generated by depolymerization of the Major Sperm Protein (MSP) cytoskeleton. Combining polymer entropy with a simple kinetic model for disassembly I propose a model for disassembly‐induced retraction that fit the in vitro experimental data. This model explains the mechanism by which deconstruction of the cytoskeleton produces the force necessary to pull the cell body forward and suggest further experiments that can test the validity of the model.

Divalent Cation Control of Flagellar Motility in African Trypanosomes
View Description Hide DescriptionChanges in calcium concentration have been shown to dynamically affect flagellar motility in several eukaryotic systems. The African trypanosome is a monoflagellated protozoan parasite and the etiological agent of sleeping sickness. Although cell motility has been implicated in disease progression, very little is currently known about biochemical control of the trypanosome flagellum. In this study, we assess the effects of extracellular changes in calcium and nickel concentration on trypanosome flagellar movement. Using a flow through chamber, we determine the relative changes in motility in individual trypanosomes in response to various concentrations of calcium and nickel, respectively. Extracellular concentrations of calcium and nickel (as low as 100 micromolar) significantly inhibit trypanosome cell motility. The effects are reversible, as indicated by the recovery of motion after removal of the calcium or nickel from the chamber. We are currently investigating the specific changes in flagellar oscillation and coordination that result from calcium and nickel, respectively. These results verify the presence of a calcium‐responsive signaling mechanism(s) that regulates flagellar beat in trypanosomes.

Non‐equilibrium Studies of Voltage‐Gated Ion Channels
View Description Hide DescriptionIon channels are proteins specializing in transport of certain ions across cellular membranes. They play a crucial role in physiological processes such as: excitability of brain or cardiac cells, cell volume control, messenger ion flow. Understanding and control of the ion channel functioning (their gating and selectivity) is one of the major goals of cellular biophysics. Ion channels are studied using molecular biology and electrophysiology techniques. Among the latter a standard method is patch clamping where currents across a whole cell membrane or a patch of it, sometimes containing only one channel, are recorded. These currents reveal changes in membrane conductance due to changes in gating variables. In our lab we study voltage‐gated ion channels. We develop a new electrophysiological technique that involves applying specially designed, rapidly fluctuating voltage waveforms to the cell membrane, thus driving the channel molecules far from equilibrium. The method probes new details of the channel kinetics inaccessible to the standard techniques. It aids the development of new mathematical models of the ion channel gating and the testing and refinement of existing models.

Phenomenological Energetics for Molecular Motors
View Description Hide DescriptionThe phenomenological consideration on the energetics of molecular motor that are working at non‐equilibrium conditions, is presented in this paper. First, a phenomenological equation of motion for a motor molecule is suggested, in which the physical properties of the motor are incorporated. Based on this equation of motion, the energetics of the system were considered. It is found that the energy fluxes can be expressed in terms of several mechanical observables, so that we can directly calculate the energetic efficiency of the motor experimentally. The present framework can adequately explain the recent experimental data on the energetic efficiency of kinesin. In order to gain further insight, we examined the theory by employing a well‐known ratchet model, which demonstrated that the present framework is consistent with an already known framework of energetics, referred to as stochastic energetics, provided that the nonlinearity of the system is not so high. The present framework provides an easy procedure to estimate the energy fluxes on a molecular motor, with mechanical experiments at a single‐molecule level.