Anionic biopolyelectrolytes of the syndecan/perlecan superfamily: physicochemical properties and medical significance

In the review article presented here, we demonstrate that the connective tissue is more than just a matrix for cells and a passive scaffold to provide physical support. The extracellular matrix can be subdivided into proteins (collagen, elastin), glycoconjugates (structural glycoproteins, proteoglycans) and glycosaminoglycans (hyaluronan). Our main focus rests on the anionic biopolyelectrolytes of the perlecan/syndecan superfamily which belongs to extracellular matrix and cell membrane integral proteoglycans. Though the extracellular domain of the syndecans may well be performing a structural role within the extracellular matrix, a key function of this class of membrane intercalated proteoglycans may be to act as signal transducers across the plasma membrane and thus be more appropriately included in the group of cell surface receptors. Nevertheless, there is a continuum in functions of syndecans and perlecans, especially with respect to their structural role and biomedical significance. HS/CS proteoglycans are receptor sites for lipoprotein binding thus intervening directly in lipid metabolism. We could show that among all lipoproteins, HDL has the highest affinity to these proteoglycans and thus instals a feedforward forechecking loop against atherogenic apoB100 lipoprotein deposition on surface membranes and in subendothelial spaces. Therefore, HDL is not only responsible for VLDL/IDL/LDL cholesterol exit but also controls thoroughly the entry. This way, it inhibits arteriosclerotic nanoplaque formation. The ternary complex 'lipoprotein receptor (HS/CS-PG) - lipoprotein (LDL, oxLDL, Lp(a)) - calcium' may be interpreted as arteriosclerotic nanoplaque build-up on the molecular level before any cellular reactivity, possibly representing the arteriosclerotic primary lesion combined with endothelial dysfunction. With laser-based ellipsometry we could demonstrate that nanoplaque formation is a Ca(2+)-driven process. In an in vitro biosensor application of HS-PG coated silica surfaces we tested nanoplaque formation and size in clinical trials with cardiovascular high-risk patients who underwent treatment with ginkgo or fluvastatin. While ginkgo reduced nanoplaque formation (size) by 14.3% (23.4%) in the isolated apoB100 lipid fraction at a normal blood Ca(2+) concentration, the effect of the statin with a reduction of 44.1% (25.4%) was more pronounced. In addition, ginkgo showed beneficial effects on several biomarkers of oxidative stress and inflammation. Besides acting as peripheral lipoprotein binding receptor, HS/CS-PG is crucially implicated in blood flow sensing. A sensor molecule has to fulfil certain mechanochemical and mechanoelectrical requirements. It should possess viscoelastic and cation binding properties capable of undergoing conformational changes caused both mechanically and electrostatically. Moreover, the latter should be ion-specific. Under no-flow conditions, the viscoelastic polyelectrolyte at the endothelium - blood interface assumes a random coil form. Blood flow causes a conformational change from the random coil state to the directed filament structure state. This conformational transition effects a protein unfurling and molecular elongation of the GAG side chains like in a 'stretched' spring. This configuration is therefore combined with an increase in binding sites for Na(+) ions. Counterion migration of Na(+) along the polysaccharide chain is followed by transmembrane Na(+) influx into the endothelial cell and by endothelial cell membrane depolarization. The simultaneous Ca(2+) influx releases NO and PGI2, vasodilatation is the consequence. Decrease in flow reverses the process. Binding of Ca(2+) and/or apoB100 lipoproteins (nanoplaque formation) impairs the flow sensor function. The physicochemical and functional properties of proteoglycans are due to their amphiphilicity and anionic polyelectrolyte character. Thus, they potently interact with cations, albeit in a rather complex manner. Utilizing (23)Na(+) and (39)K(+) NMR techniques, we could show that, both in HS-PG solutions and in native vascular connective tissue, the mode of interaction for monovalent cations is competition. Mg(2+) and Ca(2+) ions, however, induced a conformational change leading to an increased allosteric, cooperative K(+) and Na(+) binding, respectively. Since extracellular matrices and basement membranes form a tight-fitting sheath around the cell membrane of muscle and Schwann cells, in particular around sinus node cells of the heart, and underlie all epithelial and endothelial cell sheets and tubes, a release of cations from or an adsorption to these polyanionic macromolecules can transiently lead to fast and drastic activity changes in these tiny extracellular tissue compartments. The ionic currents underlying pacemaker and action potential of sinus node cells are fundamentally modulated. Therefore, these polyelectrolytic ion binding characteristics directly contribute to and intervene into heart rhythm.

On the complete integrability and linearization of nonlinear ordinary differential equations. IV. Coupled second-order equations

Coupled second-order nonlinear differential equations are of fundamental importance in dynamics. In this part of our study on the integrability and linearization of nonlinear ordinary differential equations (ODEs), we focus our attention on the method of deriving a general solution for two coupled second-order nonlinear ODEs through the extended Prelle–Singer procedure. We describe a procedure to obtain integrating factors and the required number of integrals of motion so that the general solution follows straightforwardly from these integrals. Our method tackles both isotropic and non-isotropic cases in a systematic way. In addition to the above-mentioned method, we introduce a new method of transforming coupled second-order nonlinear ODEs into uncoupled ones. We illustrate the theory with potentially important examples.

Multivariable harmonic balance analysis of the neuronal oscillator for leech swimming

Biological systems, and particularly neuronal circuits, embody a very high level of complexity. Mathematical modeling is therefore essential for understanding how large sets of neurons with complex multiple interconnections work as a functional system. With the increase in computing power, it is now possible to numerically integrate a model with many variables to simulate behavior. However, such analysis can be time-consuming and may not reveal the mechanisms underlying the observed phenomena. An alternative, complementary approach is mathematical analysis, which can demonstrate direct and explicit relationships between a property of interest and system parameters. This paper introduces a mathematical tool for analyzing neuronal oscillator circuits based on multivariable harmonic balance (MHB). The tool is applied to a model of the central pattern generator (CPG) for leech swimming, which comprises a chain of weakly coupled segmental oscillators. The results demonstrate the effectiveness of the MHB method and provide analytical explanations for some CPG properties. In particular, the intersegmental phase lag is estimated to be the sum of a nominal value and a perturbation, where the former depends on the structure and span of the neuronal connections and the latter is roughly proportional to the period gradient, communication delay, and the reciprocal of the intersegmental coupling strength.

Network structure for control of coupled multiple nonlinear oscillators

In recent research, the morphological effect is widely discussed from walking to the Internet, and its mechanism for generating the functionality has been discovered. In this paper, a module that employs the structural effect for controlling behavior is constructed using coupled nonuniform van der Pol oscillators. We first examine the synchrony of two types of oscillators focusing on number; then, an oscillator module that changes its synchrony from structural disposition is constructed. Oscillators are mutually arranged on a ring-shaped network, and an additional connection is used for transformation. The stability of this system is also discussed, and finally, the procedure for designing this structure-sensitive module using more than three types of oscillators is described.

Spatial coupling in cyclic population dynamics: models and data

We use a dynamic random field to model a spatial collection of coupled oscillators with discrete time stochastic dynamics. At each time step the phase of each cyclic local population is subject to random noise, incremented by a common dynamic, and pulled by a coupling force in the direction of some collective mean phase. We define asynchrony and derive expressions for its measurement in this model. We describe robust methods for phase estimation of cyclic population time series, for estimating strength of coupling between local populations, and for measuring variance of locally acting noise from field data. Proposed methods allow intermittently acting phase synchronizing events operating over large spatial scales to be distinguished from more continuous and possibly locally acting coupling, both of which could result in elevated levels of phase synchronization. We demonstrate the utility of this approach by applying it to classical spatial time series data of Canadian lynx. Analysis confirms findings of previous studies and reveals evidence to suggest that interpopulation coupling was weaker over the 20th century than for the 1800s. Analysis supports the notion that synchrony in these populations is maintained by a continuous and locally acting coupling between adjacent regions with large phase adjustments occurring only infrequently. When this coupling is absent, asynchrony develops between populations.

A reactive coordination scheme for a many-robot system

This paper presents a novel approach for coordinating a homogeneous system of mobile robots using implicit communication in the form of broadcasts. The broadcast-based coordination scheme was developed for the Army Ant swarm-a system of small, relatively inexpensive mobile robots that can accomplish complex tasks by cooperating as a team. The primary drawback, however, of the Army Ant system is that the absence of a central supervisor poses difficulty in the coordination and control of the agents. Our coordination scheme provides a global "group dynamic" that controls the actions of each robot using only local interactions. Coordination of the swarm is achieved with signals we call "heartbeats". Each agent broadcasts a unique heartbeat and responds to the collective behavior of all other heartbeats. We generate heartbeats with van der Pol oscillators. In this application, we use the known properties of coupled van der Pol oscillators to create predictable group behavior. Some of the properties and behaviors of coupled van der Pol oscillators are discussed in detail. We emphasize the use of this scheme to allow agents to simultaneously perform an action such as lifting, steering, or changing speed. The results of experiments performed on three actual heartbeat circuits are presented and the behavior of the realized system is compared to simulated results. We also demonstrate the application of the coordination scheme to global speed control.

A group-theoretic approach to rings of coupled biological oscillators

In this paper, a general approach for studying rings of coupled biological oscillators is presented. This approach, which is group-theoretic in nature, is based on the finding that symmetric ring networks of coupled non-linear oscillators possess generic patterns of phase-locked oscillations. The associated analysis is independent of the mathematical details of the oscillators' intrinsic dynamics and the nature of the coupling between them. The present approach thus provides a framework for distinguishing universal dynamic behaviour from that which depends upon further structure. In this study, the typical oscillation patterns for the general case of a symmetric ring of n coupled non-linear oscillators and the specific cases of three- and five-membered rings are considered. Transitions between different patterns of activity are modelled as symmetry-breaking bifurcations. The effects of one-way coupling in a ring network and the differences between discrete and continuous systems are discussed. The theoretical predictions for symmetric ring networks are compared with physiological observations and numerical simulations. This comparison is limited to two examples: neuronal networks and mammalian intestinal activity. The implications of the present approach for the development of physiologically meaningful oscillator models are discussed.

The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: a mathematical model

We present a theoretical model which is used to explain the intersegmental coordination of the neural networks responsible for generating locomotion in the isolated spinal cord of lamprey. A simplified mathematical model of a limit cycle oscillator is presented which consists of only a single dependent variable, the phase theta(t). By coupling N such oscillators together we are able to generate stable phase locked motions which correspond to traveling waves in the spinal cord, thus simulating "fictive swimming". We are also able to generate irregular "drifting" motions which are compared to the experimental data obtained from cords with selective surgical lesions.

A thermal entrainment device for cardiovascular investigation

Information on the temperature control mechanism of the body can be obtained from several body parameters such as the irregularities of the heart beat. Entrainment of the temperature control mechanism occurs when air is alternately heated and cooled as it passes over a subject's limb. The fluid flow, timing circuits and measuring devices for this experiment are described in detail. Experiments were carried out on normal healthy adults resting and during recovery from heavy exercise. Electrocardiogram and optical plethysmography of the little finger were analysed by Fast Fourier Transform. Entrainment occurs with period times between 8s and 80s with the best entrainment occurring at a period time of 30s. The value of the work and the areas presently under investigation are outlined.

Coupled Van der Pol oscillators---a model of excitatory and inhibitory neural interactions

A system of mutually coupled Van der Pol equations is derived from an extended version of the Wilson and Cowan model for the dynamics of a number of excitatory and inhibitory neural subsets. In the lowest order of approximation, interactions between excitatory and inhibitory subsets appear as linear elastic coupling, while those within and between excitatory and excitatory subsets appear as nonlinear frictional coupling. The case of two coupled oscillators is investigated by the method of averaging and the stability conditions for two mode oscillations are obtained. Internal resonance is also discussed briefly in the case of identical oscillators.