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.

Phase tracking and restoration of circadian rhythms by model-based optimal control.

Periodic cellular processes and especially circadian rhythms governed by the oscillating expression of a set of genes based on feedback regulation by their products have become an important issue in biology and medicine. The central circadian clock is an autonomous biochemical oscillator with a period close to 24 h. Research in chronobiology demonstrated that light stimuli can be used to delay or advance the phase of the oscillator, allowing it to influence the underlying physiological processes.

Approximation of slow attracting manifolds in chemical kinetics by trajectory-based optimization approaches.

Many common kinetic model reduction approaches are explicitly based on inherent multiple time scales and often assume and directly exploit a clear time scale separation into fast and slow reaction processes. They approximate the system dynamics with a dimension-reduced model after eliminating the fast modes by enslaving them to the slow ones. The corresponding restrictive assumption of full relaxation of fast modes often renders the resulting approximation of slow attracting manifolds inaccurate as a representation of the reduced model and makes the numerical solution of the nonlinear "reduction equations" particularly difficult in many cases where the gap in intrinsic time scales is not large enough.

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.

External optimal control of self-organisation dynamics in a chemotaxis reaction diffusion system.

Detailed quantitative understanding and specific external control of cellular behaviour are general long-term goals of modem bioscience research activities in systems biology. Pattern formation and self-organisation processes both in single cells and in distributed cell populations are phenomena which are highly significant for the functionality of life, because life requires to maintain a highly organised spatiotemporal system structure. In particular chemotaxis is crucial for various biological aspects of intercellular signalling and cell aggregation.

Derivation of a quantitative minimal model from a detailed elementary-step mechanism supported by mathematical coupling analysis.

Accurate experimental data increasingly allow the development of detailed elementary-step mechanisms for complex chemical and biochemical reaction systems. Model reduction techniques are widely applied to obtain representations in lower-dimensional phase space which are more suitable for mathematical analysis, efficient numerical simulation, and model-based control tasks. Here, we exploit a recently implemented numerical algorithm for error-controlled computation of the minimum dimension required for a still accurate reduced mechanism based on automatic time scale decomposition and relaxation of fast modes.

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.

Real-time nonlinear feedback control of pattern formation in (bio)chemical reaction-diffusion processes: a model study.

Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion.

Annihilation of limit-cycle oscillations by identification of critical perturbing stimuli via mixed-integer optimal control.

We present a novel model-based mixed-integer optimal control method to automatically identify the strength and timing of critical external stimuli leading to the transient annihilation of limit-cycle oscillators. Biochemical oscillators of this type play a central role in regulating cellular rhythms. Their specific manipulation is a promising perspective to control biological functions by drugs and tailored treatment strategies.

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.

Manipulation of surface reaction dynamics by global pressure and local temperature control: a model study.

Specific catalyst design and external manipulation of surface reactions by controlling accessible physical or chemical parameters may be of great benefit for improving catalytic efficiencies and energetics, product yield, and selectivities in the field of heterogeneous catalysis. Studying a realistic spatiotemporal one-dimensional model for CO oxidation on Pt(110) we demonstrate the value and necessity of mathematical modeling and advanced numerical methods for directed external multiparameter control of surface reaction dynamics. At the model stage we show by means of optimal control techniques that species coverages can be adjusted to desired values, aperiodic oscillatory behavior for distinct coupled reaction sites can be synchronized, and overall reaction rates can be optimized by varying the surface temperature in space and time and the CO and O2 gas phase partial pressure with time.