Robust optimal design of experiments for model discrimination using an interactive software tool.

Mathematical modeling of biochemical processes significantly contributes to a better understanding of biological functionality and underlying dynamic mechanisms. To support time consuming and costly lab experiments, kinetic reaction equations can be formulated as a set of ordinary differential equations, which in turn allows to simulate and compare hypothetical models in silico. To identify new experimental designs that are able to discriminate between investigated models, the approach used in this work solves a semi-infinite constrained nonlinear optimization problem using derivative based numerical algorithms.

The prognostic value of serum methotrexate area under curve in elderly primary CNS lymphoma patients.

Studies on pharmacokinetics and pharmacodynamics of high-dose methotrexate chemotherapy (HD-MTX) in elderly primary central nervous system lymphoma (PCNSL) patients are rare. MTX exposure time has recently been proposed as an outcome determining factor in PCNSL. We investigated 49 immunocompetent PCNSL patients (female N=30, male N=19, median age 73 years) who were treated according to HD-MTX-based protocols.

Robust optimal design of synthetic biological networks.

In engineering, the use of mathematical modeling for design purposes has a long history. Long before any technical realization, a system is planned, simulated, and tested extensively on the computer. In biosciences, however, the application of model-based design before going to the wet lab is still rather rare but has particularly high potential in synthetic biology.

Optimal control for selected cancer chemotherapy ODE models: a view on the potential of optimal schedules and choice of objective function.

In this article, four different mathematical models of chemotherapy from the literature are investigated with respect to optimal control of drug treatment schedules. The various models are based on two different sets of ordinary differential equations and contain either chemotherapy, immunotherapy, anti-angiogenic therapy or combinations of these. Optimal control problem formulations based on these models are proposed, discussed and compared.

Predicted auxiliary navigation mechanism of peritrichously flagellated chemotactic bacteria.

Chemotactic movement of Escherichia coli is one of the most thoroughly studied paradigms of simple behavior. Due to significant competitive advantage conferred by chemotaxis and to high evolution rates in bacteria, the chemotaxis system is expected to be strongly optimized. Bacteria follow gradients by performing temporal comparisons of chemoeffector concentrations along their runs, a strategy which is most efficient given their size and swimming speed.

An optimal experimental design approach to model discrimination in dynamic biochemical systems.

Motivation: Finding suitable models of dynamic biochemical systems is an important task in systems biology approaches to the biosciences. On the one hand, a correct model helps to understand the underlying mechanisms and on the other hand, one can use the model to predict the behavior of a biological system under various circumstances. Typically, before the correct model of a biochemical system is found, different hypothetical models might be reasonable and consistent with previous knowledge and available data.

Role of translational coupling in robustness of bacterial chemotaxis pathway.

Chemotaxis allows bacteria to colonize their environment more efficiently and to find optimal growth conditions, and is consequently under strong evolutionary selection. Theoretical and experimental analyses of bacterial chemotaxis suggested that the pathway has been evolutionarily optimized to produce robust output under conditions of such physiological perturbations as stochastic intercellular variations in protein levels while at the same time minimizing complexity and cost of protein expression. Pathway topology in Escherichia coli apparently evolved to produce an invariant output under concerted variations in protein levels, consistent with experimentally observed transcriptional coupling of chemotaxis genes.

Fantastic Ca2+ "z-waves" fade out quietly.

The first report that high speed Ca(2+) waves travel in a restricted zone around the cell periphery in a clockwise manner and which can only be revealed by very high speed imaging has been quietly retracted. In the original report, a single small region of high Ca(2+) was seen to spin around the cell periphery and around phagosomes formed within phagocytes in a manner unlike anything reported previously. This consequently caused a lot of interest.

Oscillatory NAD(P)H waves and calcium oscillations in neutrophils? A modeling study of feasibility.

The group of Howard Petty has claimed exotic metabolic wave phenomena together with mutually phase-coupled NAD(P)H- and calcium-oscillations in human neutrophils. At least parts of these phenomena are highly doubtful due to extensive failure of reproducibility by several other groups and hints that unreliable data from the Petty lab are involved in publications concerning circular calcium waves. The aim of our theoretical spatiotemporal modeling approach is to propose a possible and plausible biochemical mechanism which would, in principle, be able to explain metabolic oscillations and wave phenomena in neutrophils.

Dependence of bacterial chemotaxis on gradient shape and adaptation rate.

Simulation of cellular behavior on multiple scales requires models that are sufficiently detailed to capture central intracellular processes but at the same time enable the simulation of entire cell populations in a computationally cheap way. In this paper we present RapidCell, a hybrid model of chemotactic Escherichia coli that combines the Monod-Wyman-Changeux signal processing by mixed chemoreceptor clusters, the adaptation dynamics described by ordinary differential equations, and a detailed model of cell tumbling. Our model dramatically reduces computational costs and allows the highly efficient simulation of E.

Protein exchange dynamics at chemoreceptor clusters in Escherichia coli.

Signal processing in bacterial chemotaxis relies on large sensory complexes consisting of thousands of protein molecules. These clusters create a scaffold that increases the efficiency of pathway reactions and amplifies and integrates chemotactic signals. The cluster core in Escherichia coli comprises a ternary complex composed of receptors, kinase CheA, and adaptor protein CheW.

Targeting characteristic wave properties in reaction-diffusion systems by optimization of external forcing.

We consider the targeted manipulation of reaction-diffusion waves by optimization of an external forcing parameter. As an example, we present numerical results for the FitzHugh-Nagumo system exploiting model-based optimization capable of targeting characteristic wave properties such as wavelength, shape, and propagation speed by spatiotemporally controlling electric current. The conceptual basis of our approach is optimal control of periodic orbits in a wave-variable coordinate system.

Automatic network coupling analysis for dynamical systems based on detailed kinetic models.

We introduce a numerical complexity reduction method for the automatic identification and analysis of dynamic network decompositions in (bio)chemical kinetics based on error-controlled computation of a minimal model dimension represented by the number of (locally) active dynamical modes. Our algorithm exploits a generalized sensitivity analysis along state trajectories and subsequent singular value decomposition of sensitivity matrices for the identification of these dominant dynamical modes. It allows for a dynamic coupling analysis of (bio)chemical species in kinetic models that can be exploited for the piecewise computation of a minimal model on small time intervals and offers valuable functional insight into highly nonlinear reaction mechanisms and network dynamics.

Influence of coadsorbates on the NO dissociation on a rhodium(311) surface.

Density functional theory (DFT) studies were performed to investigate the influence of coadsorbates on the nitrogen oxide dissociation on the vicinal rhodium(311) surface. This study amplifies prior studies on the dissociation of oxygen and nitrogen oxide on the (111) facet of rhodium. The influence of coadsorbates on the kinetic parameters and thermochemistry of the NO dissociation on Rh311 was studied.

Linear relationship between activation energies and reaction energies for coverage-dependent dissociation reactions on rhodium surfaces.

Evidence of a relationship between activation energies and enthalpy changes of various dissociation reactions on transition metals has been reported recently. A reconsideration of density functional theory results for dissociation energies of oxygen and NO on different rhodium surfaces (low-index and stepped) and their dependencies on oxygen precoverage reveal that also here a linear Brønsted-Evans-Polanyi (BEP) relationship exists. The establishment of such a general concept would be of tremendous importance for the development of detailed, elementary-step reaction mechanisms, because the activation energies of reaction steps as well as their coverage dependencies could be estimated based on the adsorption energies calculated by means of DFT.

Specific external forcing of spatiotemporal dynamics in reaction-diffusion systems.

Self-organization behavior and in particular pattern forming spatiotemporal dynamics play an important role in far from equilibrium chemical and biochemical systems. Specific external forcing and control of self-organizing processes might be of great benefit in various applications ranging from technical systems to modern biomedical research. We demonstrate that in a cellular chemotaxis system modeled by one-dimensional reaction-diffusion equations particular forms of spatiotemporal dynamics can be induced and stabilized by controlling spatially distributed influx patterns of a chemical species as a function of time.

Influence of initial oxygen coverage and magnetic moment on the NO decomposition on rhodium (111).

In this study, density functional theory calculations were performed to investigate the influence of oxygen preoccupation on the nitrogen oxide decomposition on rhodium. Besides gauging the coverage dependence of the adsorption energy of NO on the (111) rhodium facet, the influence of the initial oxygen coverage on the kinetics and thermodynamics of the nitrogen oxide decomposition reaction was also studied. The results are discussed with respect to a novel NOx decomposition catalyst.

Coverage dependence of oxygen decomposition and surface diffusion on rhodium 111: a DFT study.

A systematic study of oxygen adsorption, decomposition and diffusion on Rh111 and its dependence on coadsorbed oxygen molecules has been performed using density functional theory calculations. First, the bonding strength between metal surface and adsorbed oxygen molecules has been studied as a function of initial oxygen coverage. The bonding strength decreases with increasing oxygen coverage, which points towards a self-inhibition of the adsorption process.

Dynamic control and information processing in chemical reaction systems by tuning self-organization behavior.

Specific external control of chemical reaction systems and both dynamic control and signal processing as central functions in biochemical reaction systems are important issues of modern nonlinear science. For example nonlinear input-output behavior and its regulation are crucial for the maintainance of the life process that requires extensive communication between cells and their environment. An important question is how the dynamical behavior of biochemical systems is controlled and how they process information transmitted by incoming signals.

Manipulation of self-aggregation patterns and waves in a reaction-diffusion system by optimal boundary control strategies.

Reaction-diffusion systems are of considerable importance in many areas of physical sciences. For many reasons, an external manipulation of the dynamics of these processes is desirable. Here we show numerically how spatiotemporal behavior like pattern formation and wave propagation in a two component nonlinear reaction-diffusion model of bacterial chemotaxis can be externally controlled.