Weakly coupled map lattice models for multicellular patterning and collective normalization of abnormal single-cell states

We present a weakly coupled map lattice model for patterning that explores the effects exerted by weakening the local dynamic rules on model biological and artificial networks composed of two-state building blocks (cells). To this end, we use two cellular automata models based on (i) a smooth majority rule (model I) and (ii) a set of rules similar to those of Conway's Game of Life (model II). The normal and abnormal cell states evolve according to local rules that are modulated by a parameter κ. This parameter quantifies the effective weakening of the prescribed rules due to the limited coupling of each cell to its neighborhood and can be experimentally controlled by appropriate external agents. The emergent spatiotemporal maps of single-cell states should be of significance for positional information processes as well as for intercellular communication in tumorigenesis, where the collective normalization of abnormal single-cell states by a predominantly normal neighborhood may be crucial.

Digit replacement: A generic map for nonlinear dynamical systems

A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attractors and the hierarchical deposition of grains of different sizes on a surface.

Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling

We report a novel mechanism for the formation of chimera states, a peculiar spatiotemporal pattern with coexisting synchronized and incoherent domains found in ensembles of identical oscillators. Considering Stuart-Landau oscillators, we demonstrate that a nonlinear global coupling can induce this symmetry breaking. We find chimera states also in a spatially extended system, a modified complex Ginzburg-Landau equation. This theoretical prediction is validated with an oscillatory electrochemical system, the electro-oxidation of silicon, where the spontaneous formation of chimeras is observed without any external feedback control.

Origin of complexity and conditional predictability in cellular automata

A simple mechanism for the emergence of complexity in cellular automata out of predictable dynamics is described. This leads to introduce the concept of conditional predictability for systems whose trajectory can only be piecewise known. The mechanism is used to construct a cellular automaton model for discrete chimeralike states, where synchrony and incoherence in an ensemble of identical oscillators coexist. The incoherent region is shown to have a periodicity that is three orders of magnitude longer than the period of the synchronous oscillation.

Subharmonic phase clusters in the complex Ginzburg-Landau equation with nonlinear global coupling

A wide variety of subharmonic n -phase cluster patterns was observed in experiments with spatially extended chemical and electrochemical oscillators. These patterns cannot be captured with a phase model. We demonstrate that the introduction of a nonlinear global coupling (NGC) in the complex Ginzburg-Landau equation has subharmonic cluster pattern solutions in wide parameter ranges. The NGC introduces a conservation law for the oscillatory state of the homogeneous mode, which describes the strong oscillations of the mean field in the experiments. We show that the NGC causes a pronounced 2:1 self-resonance on any spatial inhomogeneity, leading to two-phase subharmonic clustering, as well as additional higher resonances. Nonequilibrium Ising-Bloch transitions occur as the coupling strength is varied.

Electrochemical properties of phospholipid monolayers at liquid-liquid interfaces

Biomembrane models built at the interface between two immiscible electrolytes (ITIES) are useful systems to study phenomena of biological relevance by means of their electrochemical processes. The unique properties of ITIES allow one either to control or measure the potential difference across the biomimetic membranes. Herein we focus on phospholipid monolayers adsorbed at liquid-liquid interfaces, and besides discussing recent developments on the subject, we describe electrochemical techniques that can be used to get insight on the interfacial processes and electrostatic properties of phospholipid membranes at the ITIES. In particular, we examine the electrochemical and physicochemical properties of (modified) phospholipid monolayers and their interaction with other biologically relevant compounds. The use of liquid-liquid electrochemistry as a powerful tool to characterize drug properties is outlined. Although this review is not a survey of all the work in the field, it provides a comprehensive referencing to current research.

Irregular subharmonic cluster patterns in an autonomous photoelectrochemical oscillator

Unusual subharmonic cluster patterns are observed during the oscillatory electro-oxidation of n-Si(111) under illumination. 2D in situ imaging of the electrode by means of an ellipsometric setup allows local variations in the oxide layer thickness to be monitored. The local oscillators exhibit an irregular distribution of the amplitude with the extrema locked to the constant base frequency of the total current. In addition, Ising 2-phase clustering occurs at half the base frequency. This intrinsic dynamics is described by means of a modified complex Ginzburg-Landau equation.

[Locomotion and gait disorders]

INTRODUCTION

Human beings are characterised by the specialisation of certain functions, such as language or the ability to walk. We have achieved this capacity thanks to the development of multiple connections among different areas of the central and peripheral nervous system, together with adaptation of the musculoskeletal system. These are all essential to be able to walk correctly and to keep our balance.

DEVELOPMENT

Gait disorders are currently receiving a great deal of attention in neurology departments, and this fact is directly related to the phenomenon of the ageing of the population, since it is a pathology that is particularly prevalent among the elderly. One of the fundamental mainstays in the study of these disorders is being able to distinguish between the different clinical gait patterns and their classification according to the neural system that has been damaged. Observation, the use of different manoeuvres in the examination and the search for other associated clinical signs all enable us reach a good diagnostic approximation, which will later be confirmed with more specific complementary techniques.

CONCLUSIONS

From the therapeutic point of view, an early multidisciplinary intervention by the neurologist, primary care, specialists in rehabilitation and physiotherapists improves patients' quality of life and lowers the rate of associated comorbidity and mortality, which also results in a reduction in spending on community health resources.

Normal-form approach to spatiotemporal pattern formation in globally coupled electrochemical systems

We show that the experimental global coupling (GC) of spatially extended electrochemical oscillators is weak close to a supercritical Hopf bifurcation. A center manifold reduction allows then the normal form which comprises the GC and the naturally existing nonlocal (migration) coupling (NLC) to be derived. We show that the interaction between NLC and GC widens the spectrum of coherent structures found in globally coupled oscillatory media and allows for wavelength selection of standing waves, stabilization of phase clusters without breaking phase invariance, and creation of heteroclinic networks connecting families of oscillatory states characterized by different spatial symmetries.

Coherent structures emerging from turbulence in the nonlocal complex Ginzburg-Landau equation

The nonlocal complex Ginzburg-Landau equation (NCGLE) has been recently derived as a general model for electrochemical systems close to a supercritical Hopf bifurcation [V. Garcia-Morales and K. Krischer, Phys. Rev. Lett. 100, 054101 (2008)]. We carry out the stability analysis of plane waves for arbitrary Fourier numbers providing the generalized Eckhaus criterion for stability to long-wavelength fluctuations in the NCGLE. We also show that coherent structures (standing waves, heteroclinic orbits) arise in the NCGLE at intermediate coupling ranges from states which are turbulent under local coupling. These results are substantiated through simulations of the full NCGLE and bifurcation analysis of the truncated NCGLE which preserves the symmetry of the observed patterns. We briefly discuss the effect of the nonlocal coupling on other localized structures (Bekki-Nozaki holes) found in the NCGLE.

Nonlocal complex Ginzburg-Landau equation for electrochemical systems

By means of an extended center-manifold reduction, we derive the nonlocal complex Ginzburg-Landau equation (NCGLE) valid for electrochemical systems with migration coupling. We carry out the stability analysis of the uniform oscillation, elucidating the role of the nonlocal coupling in electrochemical systems at the vicinity of a supercritical Hopf bifurcation. We apply the NCGLE to an experimental system, an N-type negative differential resistance electrochemical oscillator, which is shown to exhibit electrochemical turbulence for wide parameter ranges.

Electrochemical Characterization of Polyelectrolyte/Gold Nanoparticle Multilayers Self-Assembled on Gold Electrodes

Polyelectrolyte/gold nanoparticle multilayers composed of poly(l-lysine) (pLys) and mercaptosuccinic acid (MSA) stabilized gold nanoparticles (Au NPs) were built up using the electrostatic layer-by-layer self-assembly technique upon a gold electrode modified with a first layer of MSA. The assemblies were characterized using UV-vis absorption spectroscopy, cyclic and square-wave voltammetry, electrochemical impedance spectroscopy, and atomic force microscopy. Charge transport through the multilayer was studied experimentally as well as theoretically by using two different redox pairs [Fe(CN)(6)](3-/4-) and [Ru(NH(3))(6)](3+/2+). This paper reports a large sensitivity to the charge of the outermost layer for the permeability of these assemblies to the probe ions. With the former redox pair, dramatic changes in the impedance response were obtained for thin multilayers each time a new layer was deposited. In the latter case, the multilayer behaves as a conductor exhibiting a strikingly lower impedance response, the electric current being enhanced as more layers are added for Au NP terminated multilayers. These results are interpreted quite satisfactorily by means of a capillary membrane model that encompasses the wide variety of behaviors observed. It is concluded that nonlinear slow diffusion through defects (pinholes) in the multilayer is the governing mechanism for the [Fe(CN)(6)](3-/4-) species, whereas electron transfer through the Au NPs is the dominant mechanism in the case of the [Ru(NH(3))(6)](3+/2+) pair.

Electrochemical Study of Interfacial Composite Nanostructures: Polyelectrolyte/Gold Nanoparticle Multilayers Assembled on Phospholipid/Dextran Sulfate Monolayers at a Liquid−Liquid Interface

The build up and electrochemical characterization of interfacial composite nanostructures containing a cationic polyelectrolyte and negatively charged mercaptosuccinic acid stabilized gold nanoparticles (AuNPs) is reported. The nanostructures were formed at the interface between two immiscible electrolyte solutions in which the organic phase is an immobilized 2-nitrophenyl octyl ether/PVC gel. The growth of the multilayer was verified with UV-vis spectra, and approximately a linear increase in UV-vis absorbance with increasing number of layers was observed. The interfacial capacitance of the multilayers was measured as a function of the potential and a theoretical model was developed to explain the results. The excellent agreement between theoretical and experimental capacitance curves allows us to conclude that nanocomposites behave similarly to polyelectrolyte multilayers, with the outmost layer determining the alternating sign of the outer surface charge density. Cyclic voltammograms were used to evaluate the transfer rate constant across the multilayers of a model drug, metoprolol, and the standard probe tetraethylammonium cation. The apparent rate constants were slightly larger than in other studies in the literature and decrease with the increasing number of layers.

Interfacial interaction between dextran sulfate and lipid monolayers: an electrochemical study

The interaction between dextran sulfate (DS) with zwitterionic dipalmitoylphosphatidylcholine (DPPC) and negatively charged dipalmitoylphosphatidic acid monolayers at different surface pressures at air-liquid and liquid-liquid interfaces was studied using Langmuir-Blodgett (LB) and electrochemical techniques. The negatively charged DS can bind to phospholipids via calcium ions. To investigate the mechanism of the adsorption of DS on lipid monolayers, compression isotherms (pi-A) and capacitance-potential curves were measured, and a theoretical model was developed to interpret the capacitance data. The compression of lipid monolayers in the presence of DS led to a more condensed hybrid layer, removing the LE-LC phase transition of DPPC. Lower surface pressures improved the binding of DS on the lipid monolayers via calcium bridges due to the electrostatic attraction. Alternating current voltammetry and cyclic voltammetry were used to monitor the transfer of a cationic beta-blocker (metoprolol) across lipid monolayers in the absence and presence of the polyelectrolyte and to compare with the transfer of the standard probe, tetraethylammonium cation. Results showed a strong dependence on (i) the surface pressure, (ii) the applied potential, and, (iii) in the case of the hybrid layer, the charge of the phospholipid headgroup. Finally, results were also confirmed by attenuated total reflection Fourier transform infrared spectroscopy, performed after transferring lipid multilayers onto a solid substrate by the LB method.

Calculation of the wetting parameter from a cluster model in the framework of nanothermodynamics

The critical wetting parameter omega(c) determines the strength of interfacial fluctuations in critical wetting transitions. In this Brief Report, we calculate omega(c) from considerations on critical liquid clusters inside a vapor phase. The starting point is a cluster model developed by Hill and Chamberlin in the framework of nanothermodynamics [Proc. Natl. Acad. Sci. USA 95, 12779 (1998)]. Our calculations yield results for omega(c) between 0.52 and 1.00, depending on the degrees of freedom considered. The findings are in agreement with previous experimental results and give an idea of the universal dynamical behavior of the clusters when approaching criticality. We suggest that this behavior is a combination of translation and vortex rotational motion (omega(c)=0.84).