Memory and Friction: From the Nanoscale to the Macroscale.

Chapter 3 - A Review of Coarse-Grained Molecular Dynamics Techniques to Access Extended Spatial and Temporal Scales in Biomolecular Simulations

Chapter 8 - Subsurface Reactive Transport with High Performance Computing

Metabolic networks: biology meets engineering sciences

Chapter 16 - Molecular dynamics: An account of its evolution

Anomalous diffusion phenomena have been observed in many complex physical and biological systems. One significant advance recently is the physical extension of particle's motion in a static medium to a uniformly and even nonuniformly expanding medium. The dynamic mechanism of the anomalous diffusion in the nonuniformly expanding medium has only been investigated by the approach of continuous-time random walk. To study more physical observables and to supplement the physical models of the anomalous diffusion in the expanding mediums, we characterize the nonuniformly expanding medium with a spatiotemporal dependent scale factor a(x,t) and build the Langevin picture describing the particle's motion in the nonuniformly expanding medium. Besides the existing comoving and physical coordinates, by introducing a new coordinate and assuming that a(x,t) is separable at a long-time limit, we build the relation between the nonuniformly expanding medium and the uniformly expanding one and further obtain the moments of the comoving and physical coordinates. Different forms of the scale factor a(x,t) are considered to uncover the combined effects of the particle's intrinsic diffusion and the nonuniform expansion of medium. The theoretical analyses and simulations provide the foundation for studying more anomalous diffusion phenomena in the expanding mediums.

The Nobel Prize in Chemistry, 2013 has been awarded to Martin Karplus, Michael Levitt and Arieh Warshel for their studies on development of multi-scale models for complex chemical systems. This article introduces the readers to the theoreticalmethods developed for the study of complex chemical and biological systems and connects the works of the awardees to this vast area of research. The development of quantum chemistry (QC or QM) to study molecules at electronic level is briefly mentioned. The growth of methods based on classical physics to study large systems at the molecular level (MM) is discussed. The origin of hybridQM/MM techniques to perform multi-scale modelling is then presented. Further, the parallel development of molecular simulations, which connects the macroscopic and the microscopic world elucidating the dynamical properties of molecules, is introduced. Finally, the impact of theoretical chemistry on the advancement of our understanding of complex chemical and biological systems is highlighted.

Equilibrium fluctuation relations for voltage coupling in membrane proteins

Although progress has been made in high-performance computing, there are still limitations on temporal and spatial scales of molecular dynamic calculations. A major issue in molecular dynamic (MD) simulations is the computational cost, and coarse-grained methods can save computational costs and accelerate calculations by reducing the degrees of freedom in the system. This method takes a selected group of representative atoms in the atomic microstructure as a bead and uses the proportional relationship of atomic scale atomic potentials in MD simulation to define the interaction between beads and solve the motion equation of beads. This article proposed a coarse-grained potential for graphite based on the modification of Airebo potential, with an n3: 1 mapping, and established a corresponding n3: 1 coarse-grained model, where one bead represents the number of n3 atoms. The results indicated that the coarse-grained model well reflected the basic thermal and mechanical properties of graphite. In addition, this article also proposed a coarsening method for the Lennard–Jones (L–J) potential function parameters and established a coarse-grained wetting model with n = 2. The results indicate that the coarse-grained wetting model can effectively predict the wetting performance of copper droplets on graphite in only 60% of the time using the all-atom model. The coarsening potential function and model proposed in this article are also applicable to graphite with rough surfaces. It can be anticipated that coarse-grained molecular dynamics methods will have more applications in the future, as they can handle large-scale calculations more quickly.

This work presents a few variational multiscale models for charge transport in complex physical, chemical and biological systems and engineering devices, such as fuel cells, solar cells, battery cells, nanofluidics, transistors and ion channels. An essential ingredient of the present models, introduced in an earlier paper (Bulletin of Mathematical Biology, 72, 1562-1622, 2010), is the use of differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain from the microscopic domain, meanwhile, dynamically couple discrete and continuum descriptions. Our main strategy is to construct the total energy functional of a charge transport system to encompass the polar and nonpolar free energies of solvation, and chemical potential related energy. By using the Euler-Lagrange variation, coupled Laplace-Beltrami and Poisson-Nernst-Planck (LB-PNP) equations are derived. The solution of the LB-PNP equations leads to the minimization of the total free energy, and explicit profiles of electrostatic potential and densities of charge species. To further reduce the computational complexity, the Boltzmann distribution obtained from the Poisson-Boltzmann (PB) equation is utilized to represent the densities of certain charge species so as to avoid the computationally expensive solution of some Nernst-Planck (NP) equations. Consequently, the coupled Laplace-Beltrami and Poisson-Boltzmann-Nernst-Planck (LB-PBNP) equations are proposed for charge transport in heterogeneous systems. A major emphasis of the present formulation is the consistency between equilibrium LB-PB theory and non-equilibrium LB-PNP theory at equilibrium. Another major emphasis is the capability of the reduced LB-PBNP model to fully recover the prediction of the LB-PNP model at non-equilibrium settings. To account for the fluid impact on the charge transport, we derive coupled Laplace-Beltrami, Poisson-Nernst-Planck and Navier-Stokes equations from the variational principle for chemo-electro-fluid systems. A number of computational algorithms is developed to implement the proposed new variational multiscale models in an efficient manner. A set of ten protein molecules and a realistic ion channel, Gramicidin A, are employed to confirm the consistency and verify the capability. Extensive numerical experiment is designed to validate the proposed variational multiscale models. A good quantitative agreement between our model prediction and the experimental measurement of current-voltage curves is observed for the Gramicidin A channel transport. This paper also provides a brief review of the field.

We propose a new analytical technique, cycle length analysis (CLA), which quantifies all intermittent periodic modes of a data set. CLA is especially well suited to the treatment of extended measurements of complex physical, chemical, and biological systems when subjected to variations in underlying dynamical parameters which cannot be controlled precisely or monitored accurately. We demonstrate the application of CLA using (1) a coupled oscillator model under the conditions of continuously varying control parameters and (2) clinical cardiac rhythm data.

Synchronization of one system with another is very important process in the control of complex physical, chemical and biological systems. Many researchers have focused on this topic and have developed several efficient synchronization techniques for chaotic systems. Chua's oscillator, which is one of the most studied chaotic systems, is a simple electronic circuit that exhibits nonlinear dynamical phenomena such as bifurcation and chaos. In this work the master-slave and mutual methods of synchronization are used in order to synchronize the Chua modified systems. In addition the amplification of chaos using mismatch is achieved for the same chaotic system.

A unified type of response experiment is suggested for complex systems made up of individual species (atoms, molecules, quasi-particles, biological organisms, etc.). We make the following assumptions: (i) some of the species may exist in two forms, labeled and unlabeled, respectively; (ii) the kinetic and transport properties of the labeled and unlabeled species are the same, respectively (neutrality assumption); (iii) the experiment preserves the total input and output fluxes; only the fractions of the labeled compounds in the input and output fluxes are varied. Under these circumstances a linear integral superposition law connects the fractions of labeled species in the input and output fluxes. This linear superposition law is valid for homogeneous and inhomogeneous systems and for systems with intrinsic (hidden) state variables; it arises from the neutrality condition and holds even though the underlying dynamics of the process may be highly nonlinear. Because this response law does not involve the linearization of the evolution equations it has great potential for the analysis of complex physical, chemical, and biological systems. We compare our approach with the linearization techniques used in biochemistry and genetics. We consider a simple reaction network involving replication, transformation, and disappearance steps and study the influence of experimental (measurement) and linearization errors on the evaluated values of rate coefficients. We show that the method involving the linearization of the kinetic equations leads to unpredictable results; because of the interference between measurement and linearization errors, either error compensation or error amplification occurs. Although our approach does not eliminate the effects of measurement errors, it leads to more consistent results. For a broad range of input fractions no error amplification or compensation occurs, and the error range for the rate coefficients is about the same as the error range of the measurements.

The goal of this article is not to answer a specific question but to analyse some ways to ask questions in relation to highly complex systems. The point of departure is a controversy between PARSONS and LUHMANN about the relationship between parts and wholes, between action units and systems. In the first part (I and II) the positions are presented to point out the problem: can we analyse complex social systems within the frame of action theory on the basis of action units and the functional preconditions of coordinating contingent interactions; or do the emergent properties of complex systems call for a subordination of action theory under the concept of processual prerequisites of system guidance? The second part (II and III) deals with a possibility to revise LUHMANN’s program of an “analysis of complexity” (a program which also is increasingly important for the analysis of complex physical, chemical or biological systems). The classificatorial constraints of LUHMANN’s program are discussed under the perspective of a more adequate theory of generalized media of system guidance.

In the last fifteen years a controversial new theory of the origins of biological complexity and the nature of the universe has been fomenting bitter debates in education and science policy across North America, Europe, and Australia. Backed by intellectuals at respectable universities, Intelligent Design theory (ID) proposes an alternative to accepted accounts of evolutionary theory: that life is so complex, and that the universe is so fine-tuned for the appearance of life, that the only plausible explanation is the existence of an intelligent designer. For many ID theorists, the designer is taken to be the god of Christianity. Niall Shanks has written the first accessible introduction to, and critique of, this controversial new intellectual movement. Shanks locates the growth of ID in the last two decades of the twentieth century in the growing influence of the American religious right. But, as he shows, its roots go back beyond Aquinas to Ancient Greece. After looking at the historical roots of ID, Shanks takes a hard look at its intellectual underpinnings, discussing modern understandings of thermodynamics, and how self-organizing processes lead to complex physical, chemical, and biological systems. He considers cosmological arguments for ID rooted in so-called anthropic coincidences and also tackles new biochemical arguments for ID based on irreducible biological complexity. Throughout he shows how arguments for ID lack cohesion, rest on errors and unfounded suppositions, and generally are grossly inferior to evolutionary explanations. While ID has been proposed as a scientific alternative to evolutionary biology, Shanks argues that ID is in fact old creationist wine in new designer label bottles and moreover is a serious threat to the scientific and democratic values that are our cultural and intellectual inheritance from the Enlightenment.

Reaction–diffusion models are commonly used to describe dynamical processes in complex physical, chemical and biological systems. Applications of these models range from pattern formation or epidemic spreads to natural selection through ecological systems and percolation systems. Reaction refers to phenomena where two or more entities become in contact and modify their state as a consequence of this fact. Diffusion implies the existence of a space where the involved entities are situated and can move. The Reaction–Diffusion Machine is a computational model we previously introduced inspired by reaction diffusion phenomena. In this work, we prove that a Deterministic Turing Machine can be simulated by a Reaction-Diffusion Machine.