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. A two-compartment pharmacokinetic model was used to describe the MTX clearance. Response to treatment was assessed by MRI. We used multivariable models to investigate the association between MTX exposure and tumor response as well as survival. Dose normalized MTX peak serum levels [C (max), µmol/L g] and dose normalized area under the curve [AUC(dn), µmol h/L g] were higher in females than in males, respectively [59.4 (f) vs. 48.1 (m), P<0.001; 373.2 (f) vs. 271.9 (m), P=0.008]. Increasing AUC was inversely correlated with tumor response. AUC values above 2,126 h µmol/L were independently associated with shorter overall and progression-free survival [hazard ratio (HR), 4.56, 95 % CI 1.74-11.94; HR 2.87, 95 % CI 1.18-7.00]. Exceedingly high MTX AUC levels can have a negative impact on progression-free and overall survivals in elderly PCNSL patients.

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. Here, we show that the pathway robustness is further enhanced through the pairwise translational coupling of adjacent genes. Computer simulations predicted that the robustness of the pathway against the uncorrelated variations in protein levels can be enhanced by a selective pairwise coupling of individual chemotaxis genes on one mRNA, with the order of genes in E. coli ranking among the best in terms of noise compensation. Translational coupling between chemotaxis genes was experimentally confirmed, and coupled expression of these genes was shown to improve chemotaxis. Bioinformatics analysis further revealed that E. coli gene order corresponds to consensus in sequenced bacterial genomes, confirming evolutionary selection for noise reduction. Since polycistronic gene organization is common in bacteria, translational coupling between adjacent genes may provide a general mechanism to enhance robustness of their signaling and metabolic networks. Moreover, coupling between expression of neighboring genes is also present in eukaryotes, and similar principles of noise reduction might thus apply to all cellular networks.

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. The main goal now is to find the best suited model out of different hypotheses. The process of falsifying inappropriate candidate models is called model discrimination. RESULTS: We have developed a new computational tool to compute optimal experiments for biochemical kinetic systems with underlying ordinary differential equation (ODE) models for the purpose of model discrimination. We were inspired by the demands of biological experimentalists which perform one run measurement where perturbations to the system are possible. We provide a criterion which calculates the number and location of time points of optimal measurements as well as optimal initial conditions and optimal perturbations to the system. AVAILABILITY: The model discrimination algorithm described here is implemented in C++ in the package ModelDiscriminationToolkit. The source code can be downloaded from http://omnibus.unifreiburg.de/~ds500/_software.html.

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. Concentration differences are detected by a sensory system and transmitted to modulate rotation of flagellar motors, decreasing the probability of a tumble and reorientation if the perceived concentration change during a run is positive. Such regulation of tumble probability is of itself sufficient to explain chemotactic drift of a population up the gradient, and is commonly assumed to be the only navigation mechanism of chemotactic E. coli. Here we use computer simulations to predict existence of an additional mechanism of gradient navigation in E. coli. Based on the experimentally observed dependence of cell tumbling angle on the number of switching motors, we suggest that not only the tumbling probability but also the degree of reorientation during a tumble depend on the swimming direction along the gradient. Although the difference in mean tumbling angles up and down the gradient predicted by our model is small, it results in a dramatic enhancement of the cellular drift velocity along the gradient. We thus demonstrate a new level of optimization in E. coli chemotaxis, which arises from the switching of several flagellar motors and a resulting fine tuning of tumbling angle. Similar strategy is likely to be used by other peritrichously flagellated bacteria, and indicates yet another level of evolutionary development of bacterial chemotaxis.

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. All other chemotaxis proteins localize to clusters by binding either directly to receptors or to CheA. Here, we used fluorescence recovery after photobleaching (FRAP) to investigate the turnover of chemotaxis proteins at the cluster and their mobility in the cytoplasm. We found that cluster exchange kinetics were protein-specific and took place on several characteristic time scales that correspond to excitation, adaptation, and cell division, respectively. We further applied analytical and numerical data fitting to analyze intracellular protein diffusion and to estimate the rate constants of cluster equilibration in vivo. Our results indicate that the rates of protein turnover at the cluster have evolved to ensure optimal performance of the chemotaxis pathway.

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. Our modeling suggests the possibility of a calcium-controlled glucose influx as a driving force of metabolic oscillations and a potential role of polarized cell geometry and differential enzyme distribution for various NAD(P)H wave phenomena. The modeling results are supposed to stimulate further controversial discussions of such phenomena and potential mechanisms and experimental efforts to finally clarify the existence and biochemical basis of any kind of temporal and spatiotemporal patterns of calcium signals and metabolic dynamics in human neutrophils. Independent of Petty's observations, they present a general feasibility study of such phenomena in cells.

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. coli chemotaxis. We use the model to investigate chemotaxis in different gradients, and suggest a new, constant-activity type of gradient to systematically study chemotactic behavior of virtual bacteria. Using the unique properties of this gradient, we show that optimal chemotaxis is observed in a narrow range of CheA kinase activity, where concentration of the response regulator CheY-P falls into the operating range of flagellar motors. Our simulations also confirm that the CheB phosphorylation feedback improves chemotactic efficiency by shifting the average CheY-P concentration to fit the motor operating range. Our results suggest that in liquid media the variability in adaptation times among cells may be evolutionary favorable to ensure coexistence of subpopulations that will be optimally tactic in different gradients. However, in a porous medium (agar) such variability appears to be less important, because agar structure poses mainly negative selection against subpopulations with low levels of adaptation enzymes. RapidCell is available from the authors upon request.

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. The results are transferred back to the partial differential equation context and validated in numerical simulations. The whole procedure is applicable to any reaction-diffusion model.

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. We present results for the identification of network decompositions in a simple oscillatory chemical reaction, time scale separation based model reduction in a Michaelis-Menten enzyme system and network decomposition of a detailed model for the oscillatory peroxidase-oxidase enzyme system.

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 method takes into account parameter variabilities such that new experimental designs are robust against parameter changes while maintaining the optimal potential to discriminate between hypothetical models. In this contribution we present a newly developed software tool that offers a convenient graphical user interface for model discrimination. We demonstrate the beneficial operation of the discrimination approach and the usefulness of the software tool by analyzing a realistic benchmark experiment from literature. New robust optimal designs that allow to discriminate between the investigated model hypotheses of the benchmark experiment are successfully calculated and yield promising results. The involved robustification approach provides maximally discriminating experiments for the worst parameter configurations, which can be used to estimate the meaningfulness of upcoming experiments. A major benefit of the graphical user interface is the ability to interactively investigate the model behavior and the clear arrangement of numerous variables. In addition to a brief theoretical overview of the discrimination method and the functionality of the software tool, the importance of robustness of experimental designs against parameter variability is demonstrated on a biochemical benchmark problem. The software is licensed under the GNU General Public License and freely available at http://sourceforge.net/projects/mdtgui/.

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. We demonstrate exemplarily how mathematical modeling and numerical optimization can be used for the design of a circadian rhythm that is supposed to oscillate robustly with respect to uncertainty in system parameters.

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. For different parameter sets, scenarios, and objective functions optimal control problems are solved numerically with Bock's direct multiple shooting method. In particular, we show that an optimally controlled therapy can be the reason for the difference between a growing and a totally vanishing tumor in comparison to standard treatment schemes and untreated or wrongly treated tumors. Furthermore, we compare different objective functions. Eventually, we propose an optimization-driven indicator for the potential gain of optimal controls. Based on this indicator, we show that there is a high potential for optimization of chemotherapy schedules, although the currently available models are not yet appropriate for transferring the optimal therapies into medical practice due to patient-, cancer-, and therapy-specific components.

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. Several other papers reporting a similar phenomenon in a variety of cells were also published by the same lab and the phenomenon has been included in high profile reviews such as in Science. However, several groups have failed to reproduce this work and attempts to detect the Ca(2+) waves or the mechanism for their generation have failed. Now, the original report has been quietly retracted. In this short commentary, we give a brief account of the sorry story of the non-existent circulating Ca(2+) waves (z-waves) in the hope that the literature can be rectified and that future cell calcium biologists are not misled by these fantastic and spurious Ca(2+) reports.

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. In our model study we show that a propagating wave with certain shape and velocity and static symmetrical and asymmetrical patterns can be forced and manipulated by numerically computing open-loop optimal influx controls.

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. Furthermore, the influence of spin effects on the adsorption geometry as well as the adsorption energy is examined. It will be addressed why spin effects only have a minor influence on the behavior of NO on a rhodium surface.

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. The potential energy hypersurface (PES) for the dissociation of oxygen molecules adsorbed on a threefold fcc position perpendicular to the surface was calculated using a combined linear/quadratic synchronous transit method with conjugate gradient refinements. The results indicate that a minor amount of oxygen on the surface enhances the decomposition of further oxygen molecules, while this process is inhibited at higher coverage. Moreover, PES calculations of a single site jump of atomic oxygen on rhodium 111 indicate that the activation energy increases as well with increasing oxygen coverage. All results are discussed with respect to a rhodium based catalytic NOx reduction/decomposition system proposed by Nakatsuji, which decomposes nitrogen oxides in oxygen excess.

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. In addition, the activation energy and thermochemistry of this reaction were determined as a function of oxygen preoccupation/initial coverage. Steric and electronic effects and their influence on the dissociation reaction were examined. The results are discussed in the face of an NOx dissociation catalyst system proposed by Nakatsuji.

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.

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. But also from a general point of view external forcing of complex chemical reaction processes is important in many application areas ranging from chemical engineering to biomedicine. In order to study such control issues numerically, here, we choose a well characterized chemical system, the CO oxidation on Pt(110), which is interesting per se as an externally forced chemical oscillator model. We show numerically that tuning of temporal self-organization by input signals in this simple nonlinear chemical reaction exhibiting oscillatory behavior can in principle be exploited for both specific external control of dynamical system behavior and processing of complex information.

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. We formulate the control goal as an objective functional and apply numerical optimization for the solution of the resulting control problem.