Evaluation of rate law approximations in bottom-up kinetic models of metabolism.

BackgroundThe mechanistic description of enzyme kinetics in a dynamic model of metabolism requires specifying the numerical values of a large number of kinetic parameters. The parameterization challenge is often addressed through the use of simplifying approximations to form reaction rate laws with reduced numbers of parameters. Whether such simplified models can reproduce dynamic characteristics of the full system is an important question.ResultsIn this work, we compared the local transient response properties of dynamic models constructed using rate laws with varying levels of approximation. These approximate rate laws were: 1) a Michaelis-Menten rate law with measured enzyme parameters, 2) a Michaelis-Menten rate law with approximated parameters, using the convenience kinetics convention, 3) a thermodynamic rate law resulting from a metabolite saturation assumption, and 4) a pure chemical reaction mass action rate law that removes the role of the enzyme from the reaction kinetics. We utilized in vivo data for the human red blood cell to compare the effect of rate law choices against the backdrop of physiological flux and concentration differences. We found that the Michaelis-Menten rate law with measured enzyme parameters yields an excellent approximation of the full system dynamics, while other assumptions cause greater discrepancies in system dynamic behavior. However, iteratively replacing mechanistic rate laws with approximations resulted in a model that retains a high correlation with the true model behavior. Investigating this consistency, we determined that the order of magnitude differences among fluxes and concentrations in the network were greatly influential on the network dynamics. We further identified reaction features such as thermodynamic reversibility, high substrate concentration, and lack of allosteric regulation, which make certain reactions more suitable for rate law approximations.ConclusionsOverall, our work generally supports the use of approximate rate laws when building large scale kinetic models, due to the key role that physiologically meaningful flux and concentration ranges play in determining network dynamics. However, we also showed that detailed mechanistic models show a clear benefit in prediction accuracy when data is available. The work here should help to provide guidance to future kinetic modeling efforts on the choice of rate law and parameterization approaches

Efficiency of primary saliva secretion: an analysis of parameter dependence in dynamic single-cell and acinus models, with application to aquaporin knockout studies

Secretion from the salivary glands is driven by osmosis following the establishment of osmotic gradients between the lumen, the cell and the interstitium by active ion transport. We consider a dynamic model of osmotically driven primary saliva secretion and use singular perturbation approaches and scaling assumptions to reduce the model. Our analysis shows that isosmotic secretion is the most efficient secretion regime and that this holds for single isolated cells and for multiple cells assembled into an acinus. For typical parameter variations, we rule out any significant synergistic effect on total water secretion of an acinar arrangement of cells about a single shared lumen. Conditions for the attainment of isosmotic secretion are considered, and we derive an expression for how the concentration gradient between the interstitium and the lumen scales with water- and chloride-transport parameters. Aquaporin knockout studies are interpreted in the context of our analysis and further investigated using simulations of transport efficiency with different membrane water permeabilities. We conclude that recent claims that aquaporin knockout studies can be interpreted as evidence against a simple osmotic mechanism are not supported by our work. Many of the results that we obtain are independent of specific transporter details, and our analysis can be easily extended to apply to models that use other proposed ionic mechanisms of saliva secretion

Electron Accepting Units of the Diheme Cytochrome c TsdA, a Bifunctional Thiosulfate Dehydrogenase/Tetrathionate Reductase

The enzymes of the thiosulfate dehydrogenase (TsdA) family are wide-spread diheme c-type cytochromes. Here, redox carriers were studied mediating the flow of electrons arising from thiosulfate oxidation into respiratory or photosynthetic electron chains. In a number of organisms, including Thiomonas intermedia and Sideroxydans lithotrophicus the tsdA gene is immediately preceded by tsdB encoding for another diheme cytochrome. Spectrophotometric experiments in combination with enzymatic assays in solution showed that TsdB acts as an effective electron acceptor of TsdA in vitro when TsdA and TsdB originate from the same source organism. While TsdA covers a range from -300 mV to +150 mV, TsdB is redox active between -100 to +300 mV, thus enabling electron transfer between these hemoproteins. The three-dimensional structure of the TsdB-TsdA fusion protein from the purple sulfur bacterium Marichromatium purpuratum was solved by X-ray crystallography to 2.75 Å resolution providing insights into internal electron transfer. In the oxidized state, this tetraheme cytochrome c contains three hemes with axial His/Met ligation, while heme 3 exhibits the His/Cys coordination typical for TsdA active sites. Interestingly, thiosulfate is covalently bound to Cys330 on heme 3. In several bacteria including Allochromatium vinosum, TsdB is not present, precluding a general and essential role for electron flow. Both, AvTsdA and the MpTsdBA fusion react efficiently in vitro with high potential iron sulfur protein from A. vinosum (Em +350 mV). HiPIP not only acts as direct electron donor to the reaction center in anoxygenic phototrophs but can also be involved in aerobic respiratory chains

The interplay of intrinsic and extrinsic bounded noises in genetic networks

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a genetic network. The influence of intrinsic and extrinsic noises on genetic networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: $(i)$ the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, $(ii)$ a model of enzymatic futile cycle and $(iii)$ a genetic toggle switch. In $(ii)$ and $(iii)$ we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possibile functional role of bounded noises

Protein Pattern Formation

Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. A prominent example of intracellular patterns are the oscillatory pole-to-pole oscillations of Min proteins in \textit{E. coli} whose biological function is to ensure precise cell division. Cell polarization, a prerequisite for processes such as stem cell differentiation and cell polarity in yeast, is also mediated by a diffusion-reaction process. More generally, these functional modules of cells serve as model systems for self-organization, one of the core principles of life. Under which conditions spatio-temporal patterns emerge, and how these patterns are regulated by biochemical and geometrical factors are major aspects of current research. Here we review recent theoretical and experimental advances in the field of intracellular pattern formation, focusing on general design principles and fundamental physical mechanisms.Comment: 17 pages, 14 figures, review articl

Dynamic balance of pro‐ and anti‐inflammatory signals controls disease and limits pathology

Immune responses to pathogens are complex and not well understood in many diseases, and this is especially true for infections by persistent pathogens. One mechanism that allows for long‐term control of infection while also preventing an over‐zealous inflammatory response from causing extensive tissue damage is for the immune system to balance pro‐ and anti‐inflammatory cells and signals. This balance is dynamic and the immune system responds to cues from both host and pathogen, maintaining a steady state across multiple scales through continuous feedback. Identifying the signals, cells, cytokines, and other immune response factors that mediate this balance over time has been difficult using traditional research strategies. Computational modeling studies based on data from traditional systems can identify how this balance contributes to immunity. Here we provide evidence from both experimental and mathematical/computational studies to support the concept of a dynamic balance operating during persistent and other infection scenarios. We focus mainly on tuberculosis, currently the leading cause of death due to infectious disease in the world, and also provide evidence for other infections. A better understanding of the dynamically balanced immune response can help shape treatment strategies that utilize both drugs and host‐directed therapies.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146448/1/imr12671.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/146448/2/imr12671_am.pd

Balancing Robustness against the Dangers of Multiple Attractors in a Hopfield-Type Model of Biological Attractors

Background: Many chronic human diseases are of unclear origin, and persist long beyond any known insult or instigating factor. These diseases may represent a structurally normal biologic network that has become trapped within the basin of an abnormal attractor. Methodology/Principal Findings: We used the Hopfield net as the archetypical example of a dynamic biological network. By progressively removing the links of fully connected Hopfield nets, we found that a designated attractor of the nets could still be supported until only slightly more than 1 link per node remained. As the number of links approached this minimum value, the rate of convergence to this attractor from an arbitrary starting state increased dramatically. Furthermore, with more than about twice the minimum of links, the net became increasingly able to support a second attractor. Conclusions/Significance: We speculate that homeostatic biological networks may have evolved to assume a degree of connectivity that balances robustness and agility against the dangers of becoming trapped in an abnormal attractor

Dimensional analysis of MINMOD leads to definition of the disposition index of glucose regulation and improved simulation algorithm

BACKGROUND: Frequently Sampled Intravenous Glucose Tolerance Test (FSIVGTT) together with its mathematical model, the minimal model (MINMOD), have become important clinical tools to evaluate the metabolic control of glucose in humans. Dimensional analysis of the model is up to now not available. METHODS: A formal dimensional analysis of MINMOD was carried out and the degree of freedom of MINMOD was examined. Through re-expressing all state variable and parameters in terms of their reference scales, MINMOD was transformed into a dimensionless format. Previously defined physiological indices including insulin sensitivity, glucose effectiveness, and first and second phase insulin responses were re-examined in this new formulation. Further, the parameter estimation from FSIVGTT was implemented using both the dimensional and the dimensionless formulations of MINMOD, and the performances were compared utilizing Monte Carlo simulation as well as real human FSIVGTT data. RESULTS: The degree of freedom (DOF) of MINMOD was found to be 7. The model was maximally simplified in the dimensionless formulation that normalizes the variation in glucose and insulin during FSIVGTT. In the new formulation, the disposition index (Dl), a composite parameter known to be important in diabetes pathology, was naturally defined as one of the dimensionless parameters in the system. The numerical simulation using the dimensionless formulation led to a 1.5–5 fold gain in speed, and significantly improved accuracy and robustness in parameter estimation compared to the dimensional implementation. CONCLUSION: Dimensional analysis of MINMOD led to simplification of the model, direct identification of the important composite factors in the dynamics of glucose metabolic control, and better simulations algorithms