Spatially resolved simulations of membrane reactions and dynamics: Multipolar reaction DPD

Biophysical chemistry of mesoscale systems and quantitative modeling in systems biology now require a simulation methodology unifying chemical reaction kinetics with essential collective physics. This will enable the study of the collective dynamics of complex chemical and structural systems in a spatially resolved manner with a combinatorially complex variety of different system constituents. In order to allow a direct link-up with experimental data (e.g. high-throughput fluorescence images) the simulations must be constructed locally, i.e. mesoscale phenomena have to emerge from local composition and interactions that can be extracted from experimental data. Under suitable conditions, the simulation of such local interactions must lead to processes such as vesicle budding, transport of membrane-bounded compartments and protein sorting, all of which result from a sophisticated interplay between chemical and mechanical processes and require the link-up of different length scales. In this work, we show that introducing multipolar interactions between particles in dissipative particle dynamics (DPD) leads to extended membrane structures emerging in a self-organized manner and exhibiting the necessary mechanical stability for transport, correct scaling behavior, and membrane fluidity so as to provide a two-dimensional self-organizing dynamic reaction environment for kinetic studies in the context of cell biology.     

Dissipative Structures,Organisms and Evolution

Self-organization in nonequilibrium systems has been known for over 50 years. Under nonequilibrium conditions, the state of a system can become unstable and a transition to an organized structure can occur. Such structures include oscillating chemical reactions and spatiotemporal patterns in chemical and other systems. Because entropy and free-energy dissipating irreversible processes generate and maintain these structures, these have been called dissipative structures. Our recent research revealed that some of these structures exhibit organism-like behavior, reinforcing the earlier expectation that the study of dissipative structures will provide insights into the nature of organisms and their origin. In this article, we summarize our study of organism-like behavior in electrically and chemically driven systems. The highly complex behavior of these systems shows the time evolution to states of higher entropy production. Using these systems as an example, we present some concepts that give us an understanding of biological organisms and their evolution.     

A Drive towards Thermodynamic Efficiency for Dissipative Structures in Chemical Reaction Networks

Dissipative accounts of structure formation show that the self-organisation of complex structures is thermodynamically favoured, whenever these structures dissipate free energy that could not be accessed otherwise. These structures therefore open transition channels for the state of the universe to move from a frustrated, metastable state to another metastable state of higher entropy. However, these accounts apply as well to relatively simple, dissipative systems, such as convection cells, hurricanes, candle flames, lightning strikes, or mechanical cracks, as they do to complex biological systems. Conversely, interesting computational properties—that characterize complex biological systems, such as efficient, predictive representations of environmental dynamics—can be linked to the thermodynamic efficiency of underlying physical processes. However, the potential mechanisms that underwrite the selection of dissipative structures with thermodynamically efficient subprocesses is not completely understood. We address these mechanisms by explaining how bifurcation-based, work-harvesting processes—required to sustain complex dissipative structures—might be driven towards thermodynamic efficiency. We first demonstrate a simple mechanism that leads to self-selection of efficient dissipative structures in a stochastic chemical reaction network, when the dissipated driving chemical potential difference is decreased. We then discuss how such a drive can emerge naturally in a hierarchy of self-similar dissipative structures, each feeding on the dissipative structures of a previous level, when moving away from the initial, driving disequilibrium.     

The Emergence of Temporal Structures in Dynamical Systems

Dynamical systems in classical, relativistic and quantum physics are ruled by laws with time reversibility. Complex dynamical systems with time-irreversibility are known from thermodynamics, biological evolution, growth of organisms, brain research, aging of people, and historical processes in social sciences. Complex systems are systems that compromise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations of which are the spontaneous emergence of distinctive temporal, spatial or functional structures. But, emergence is no mystery. In a general meaning, the emergence of macroscopic features results from the nonlinear interactions of the elements in a complex system. Mathematically, the emergence of irreversible structures is modelled by phase transitions in non-equilibrium dynamics of complex systems. These methods have been modified even for chemical, biological, economic and societal applications (e.g., econophysics). Emergence of irreversible structures can also be simulated by computational systems. The question arises how the emergence of irreversible structures is compatible with the reversibility of fundamental physical laws. It is argued that, according to quantum cosmology, cosmic evolution leads from symmetry to complexity of irreversible structures by symmetry breaking and phase transitions. Thus, arrows of time and aging processes are not only subjective experiences or even contradictions to natural laws, but they can be explained by quantum cosmology and the nonlinear dynamics of complex systems. Human experiences and religious concepts of arrows of time are considered in a modern scientific framework. Platonic ideas of eternity are at least understandable with respect to mathematical invariance and symmetry of physical laws. Heraclit’s world of change and dynamics can be mapped onto our daily real-life experiences of arrows of time.     

Nonlinearly saturated dynamical state of a three-wave mode-coupled dissipative system with linear instability

Linearly unstable dissipative systems with quadratic nonlinearity occurring in plasma physics, optics, fluid mechanics, etc. are often modeled by a general set of three-wave mode-coupled ordinary differential equations for complex variables. Bounded attractors of the set approximate nonlinearly saturated turbulent states of real physical systems. Exact criteria for boundedness of the attractors are found. Fundamentally different kinds of asymptotic behavior of the wave triad are classified in the parameter space and quantitatively assessed.     

On the formation of dissipative spatial patterns of charge carriers in biosystems

Summary It is shown that in systems like large aggregates of biological molecules, population inversion of charge carriers, for example as produced by photoexcitation processes, may have competitive advantage beyond critical levels of excitation to produce ordered spatial structures (morphological transitions). In our analysis electromagnetic radiation transfers electrons from bonding states into a continuum of itinerant antibonding states in ap-type doped sample. In this system, in which energy is pumped continuously by an external source, the interplay of collective and dissipative processes can be responsible for the condensation of a self-organized spatially ordered structure. The study we present here is carried out resorting to the powerful nonequilibrium statistical operator method, thus showing that it can be provide a mechano-statistical formalism at the microscopic level for the treatment of Prigogine's synergetic dissipative structures. The authors of this paper have agreed to not receive the proofs for correction     

The Mathematical Universe

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Gödel incompleteness. I hypothesize that only computable and decidable (in Gödel’s sense) structures exist, which alleviates the cosmological measure problem and may help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.     

Self-organized critical model for protein folding

The major factor that drives a protein toward collapse and folding is the hydrophobic effect. At the folding process a hydrophobic core is shielded by the solvent-accessible surface area of the protein. We study the fractal behavior of 5526 protein structures present in the Brookhaven Protein Data Bank. Power laws of protein mass, volume and solvent-accessible surface area are measured independently. The present findings indicate that self-organized criticality is an alternative explanation for the protein folding. Also we note that the protein packing is an independent and constant value because the self-similar behavior of the volumes and protein masses have the same fractal dimension. This power law guarantees that a protein is a complex system. From the analyzed data, q-Gaussian distributions seem to fit well this class of systems.     

Critical behavior and 1/f noise in lumped systems undergoing two phase transitions

It is shown that the interaction of order parameters when subcritical and supercritical phase transitions take place simultaneously may result in a self-organized critical state and cause a 1/f ^α fluctuation spectrum, where 1≤α≤2. Such behavior is inherent in potential and nonpotential systems of nonlinear Langevin equations. A numerical analysis of the solutions to the proposed systems of stochastic differential equations showed that the solutions correlate with fractional integration and differentiation of white noise. The general behavior of such a system has features in common with self-organized criticality.     

Self-organized criticality in the hysteresis of the Sherrington–Kirkpatrick model

We study hysteretic phenomena in random ferromagnets. We argue that the angle-dependent magnetostatic (dipolar) terms introduce frustration and long-range interactions in these systems. This makes it plausible that the Sherrington–Kirkpatrick model may be able to capture some of the relevant physics of these systems. We use scaling arguments, replica calculations and large scale numerical simulations to characterize the hysteresis of the zero temperature SK model. By constructing the distribution functions of the avalanche sizes, magnetization jumps and local fields, we conclude that the system exhibits self-organized criticality everywhere on the hysteresis loop.     

Rotating bound states of dissipative solitons in systems of reaction-diffusion type

We report on the formation of stable rotating bound states consisting of self-organized well localized solitary structures with particle-like behaviour in systems of reaction-diffusion type. These dissipative solitons are detected in an experimental planar d.c. gas-discharge system with a high ohmic barrier, as well as in numerical solutions of related three-component reaction-diffusion equations where the formation of rotating bound states is investigated in the context of a particle ansatz.Received: 15 July 2003, Published online: 15 March 2004PACS: 89.75.Fb Structures and organization in complex systems - 82.40.Ck Pattern formation in reactions with diffusion, flow and heat transfer - 52.80.Tn Other gas discharges     

Bistability,autowaves and dissipative structures in semiconductor fibers with anomalous resistivity properties

This work provides a discussion of bistability conditions, switching autowave properties and emergence of dissipative structures in semiconducting fibers with anomalous positive dependence of electrical resistivity on temperature of sigmoid type, (1?+?e ^?T )^?1. An open system thermodynamics approach is utilized for the analysis of this dissipative solid-state system. The approach aims to represent the structure of the solution space of its governing equation in the form of physical phase diagrams, known as non-equilibrium phase diagrams, and two specific binary diagrams have been obtained here. One of the diagrams, where the electrical power density and ambient temperature represent external parameters, shows a wide region with dissipative structures as non-uniform steady-state temperature profiles on the fiber. The possibility of efficient external control over the dissipative structure geometry is also demonstrated.     

The vacuum fluctuation theorem: Exact Schrödinger equation via nonequilibrium thermodynamics

Assuming that a particle of energy ?ω is actually a dissipative system maintained in a nonequilibrium steady state by a constant throughput of energy (heat flow), one obtains the shortest derivation of the Schrödinger equation from (modern) classical physics in the literature, and the only exact one, too.     

Coexisting structural phases in a two-dimensional vanadium oxide/surfactant nanostructure

A structural study employing X-ray diffraction has been made on a two-dimensional (2D) self-organized compound VO_x(C₁₂H₂₈N)_y comprising inorganic vanadium oxides and organic dodecylammonium surfactants. Coexisting periodic phases of a 2D centered rectangular structure and a lamellar structure have thus been identified and closely followed as a function of temperature, elucidating the changes in the distinct structures and their interplay in the system.     

Shocks in an electronegative plasma with Boltzmann negative ions and κ-distributed trapped electrons

We derived a Schamel-Burgers equation to study the dynamics of nonlinear structures in dissipative electronegative plasma having Boltzmann negative ions and κ-distributed trapped electrons. A recently introduced Tangent hyperbolic method has been employed to get the solutions of the differential equations which contain fractional nonlinearity. The effects of different physical parameters particularly, the kinematic viscosity, the superthermality, the trapping efficiency and the electronegativity factor on the ion acoustic (IA) shock profiles have been elaborated. In case of non-dissipative electronegative plasma, the small amplitude double layers (DLs) have also been investigated. It has been elaborated that the DLs strongly depend on the system parameters. The results illustrate that the superthermality index and trapping parameter play disruptive role in the formation of DLs. Likewise, the electronegativity factor plays a dominant role in the shaping of the compressive DLs. The study can be supportive to understand the behavior of nonlinear structures as observed in the nature and laboratory plasmas.     

Self-organized epitaxial growth on spontaneously nano-patterned templates

Self-ordering at crystal surfaces has been the subject of intense efforts during the last ten years, since it has been recognized as a promising way for growing uniform nanostructures with regular sizes and spacings in the 1–100 nm range. In this article we give an overview of the self-organized nanostructures growth on spontaneously nano-patterned templates. A great variety of surfaces exhibits a nano-scale order at thermal equilibrium, including adsorbate-induced reconstruction, surface dislocations networks, vicinal surfaces or more complex systems. Continuum models have been proposed where long-range elastic interactions are responsible for spontaneous periodic domain formation. Today the comparison between experiments such as Grazing Incidence X-Ray Diffraction experiments and calculations has lead to a great improvement of our fundamental understanding of the physics of self-ordering at crystal surfaces. Then, epitaxial growth on self-ordered surfaces leads to nanostructures organized growth. The present knowledge of modelization of such an heterogeneous growth using multi-scaled calculations is discussed. Such a high quality of both long-range and local ordered growth opens up the possibility of making measurements of physical properties of such nanostructures by macroscopic integration techniques. To cite this article: S. Rousset et al., C. R. Physique 6 (2005).     

Goldstone Modes in Driven Diffusion Systems

By analyzing the dynamical equations of dissipative diffusion systems with the help of Feynman diagrams, we explicitly show that Goldstone modes exist in these systems and how these Goldstone modes are related to the origin of self-organized criticality. The analysis gives a clear statistical field theory picture of self-organized criticality.     

Reaction-diffusion system with self-organized critical behavior

We describe the construction of a conserved reaction-diffusion system that exhibits self-organized critical (avalanche-like) behavior under the action of a slow addition of particles. The model provides an illustration of the general mechanism to generate self-organized criticality in conserving systems. Extensive simulations in d = 2 and 3 reveal critical exponents compatible with the universality class of the stochastic Manna sandpile model. Received 16 November 2000