Automated mass action model space generation and analysis methods for two-reactant combinatorially complex equilibriums: An analysis of ATP-induced ribonucleotide reductase R1 hexamerization data

<p>Abstract</p> <p>Background</p> <p>Ribonucleotide reductase is the main control point of dNTP production. It has two subunits, R1, and R2 or p53R2. R1 has 5 possible catalytic site states (empty or filled with 1 of 4 NDPs), 5 possible <it>s</it>-site states (empty or filled with ATP, dATP, dTTP or dGTP), 3 possible <it>a</it>-site states (empty or filled with ATP or dATP), perhaps two possible <it>h</it>-site states (empty or filled with ATP), and all of this is folded into an R1 monomer-dimer-tetramer-hexamer equilibrium where R1 j-mers can be bound by variable numbers of R2 or p53R2 dimers. Trillions of RNR complexes are possible as a result. The problem is to determine which are needed in models to explain available data. This problem is intractable for 10 reactants, but it can be solved for 2 and is here for R1 and ATP.</p> <p>Results</p> <p>Thousands of ATP-induced R1 hexamerization models with up to three (<it>s</it>, <it>a </it>and <it>h</it>) ATP binding sites per R1 subunit were automatically generated via hypotheses that complete dissociation constants are infinite and/or that binary dissociation constants are equal. To limit the model space size, it was assumed that <it>s</it>-sites are always filled in oligomers and never filled in monomers, and to interpret model terms it was assumed that <it>a</it>-sites fill before <it>h</it>-sites. The models were fitted to published dynamic light scattering data. As the lowest Akaike Information Criterion (AIC) of the 3-parameter models was greater than the lowest of the 2-parameter models, only models with up to 3 parameters were fitted. Models with sums of squared errors less than twice the minimum were then partitioned into two groups: those that contained no occupied <it>h</it>-site terms (508 models) and those that contained at least one (1580 models). Normalized AIC densities of these two groups of models differed significantly in favor of models that did not include an <it>h</it>-site term (Kolmogorov-Smirnov p < 1 × 10^-15); consistent with this, 28 of the top 30 models (ranked by AICs) did not include an <it>h</it>-site term and 28/30 > 508/2088 with p < 2 × 10^-15. Finally, 99 of the 2088 models did not have any terms with ATP/R1 ratios >1.5, but of the top 30, there were 14 such models (14/30 > 99/2088 with p < 3 × 10^-16), i.e. the existence of R1 hexamers with >3 <it>a</it>-sites occupied by ATP is also not supported by this dataset.</p> <p>Conclusion</p> <p>The analysis presented suggests that three <it>a</it>-sites may not be occupied by ATP in R1 hexamers under the conditions of the data analyzed. If <it>a</it>-sites fill before <it>h</it>-sites, this implies that the dataset analyzed can be explained without the existence of an <it>h</it>-site.</p> <p>Reviewers</p> <p>This article was reviewed by Ossama Kashlan <it>(nominated by Philip Hahnfeldt)</it>, Bin Hu <it>(nominated by William Hlavacek) </it>and Rainer Sachs.</p

A two-way interface between limited Systems Biology Markup Language and R

BACKGROUND: Systems Biology Markup Language (SBML) is gaining broad usage as a standard for representing dynamical systems as data structures. The open source statistical programming environment R is widely used by biostatisticians involved in microarray analyses. An interface between SBML and R does not exist, though one might be useful to R users interested in SBML, and SBML users interested in R. RESULTS: A model structure that parallels SBML to a limited degree is defined in R. An interface between this structure and SBML is provided through two function definitions: write.SBML() which maps this R model structure to SBML level 2, and read.SBML() which maps a limited range of SBML level 2 files back to R. A published model of purine metabolism is provided in this SBML-like format and used to test the interface. The model reproduces published time course responses before and after its mapping through SBML. CONCLUSIONS: List infrastructure preexisting in R makes it well-suited for manipulating SBML models. Further developments of this SBML-R interface seem to be warranted

Modelling c-Abl Signalling in Activated Neutrophils: The Anti-inflammatory Effect of Seliciclib

When mammalian tissues are infected by bacteria or fungi, inflammatory cytokines are released that cause circulating neutrophils to invade the infected tissue. The cytosolic tyrosine kinase, c-Abl, in these tissue neutrophils is activated by TNFα. c-Abl then phosphorylates STAT transcription factors, which results in production of the antiapoptotic protein Mcl-1. The normally short-lived tissue neutrophils are then unable to enter apoptosis. c-Abl also causes release of reactive oxygen species (ROS) from the mitochondria of the activated neutrophils. These ROS, and ROS generated by NADPH oxidase, are bactericidal agents of the innate immune system. In some inflammatory diseases, such as chronic obstructive pulmonary disease (COPD), the invading neutrophils become permanently activated, and the resulting ROS overproduction causes severe tissue damage. The cyclin-dependent kinase inhibitor, seliciclib, blocks transcription through inhibition of cdk9. This results in a relatively rapid decline of antiapoptotic Mcl-1 transcripts in activated neutrophils, an increase in neutrophil apoptosis, and less ROS leakage and oxidative damage. We present here a model of neutrophil kinetics that simulates the principal pathways of c-Abl signalling and use it to explore possible treatment options for inflammatory lung disease

Sphingoid base metabolism in yeast: mapping gene expression patterns into qualitative metabolite time course predictions

Abstract Can qualitative metabolite time course predictions be inferred from measured mRNA expression patterns? Speaking against this possibility is the large number of &apos;decoupling&apos; control points that lie between these variables, i.e. translation, protein degradation, enzyme inhibition and enzyme activation. Speaking for it is the notion that these control points might be coordinately regulated such that action exerted on the mRNA level is informative of action exerted on the protein and metabolite levels. A simple kinetic model of sphingoid base metabolism in yeast is postulated. When the enzyme activities in this model are modulated proportional to mRNA expression levels measured in heat shocked yeast, the model yields a transient rise and fall in sphingoid bases followed by a permanent rise in ceramide. This finding is in qualitative agreement with experiments and is thus consistent with the aforementioned coordinated control system hypothesis

Rational polynomial representation of ribonucleotide reductase activity

BACKGROUND: Recent data suggest that ribonucleotide reductase (RNR) exists not only as a heterodimer R1(2)R2(2 )of R1(2 )and R2(2 )homodimers, but also as tetramers R1(4)R2(4 )and hexamers R1(6)R2(6). Recent data also suggest that ATP binds the R1 subunit at a previously undescribed hexamerization site, in addition to its binding to previously described dimerization and tetramerization sites. Thus, the current view is that R1 has four NDP substrate binding possibilities, four dimerization site binding possibilities (dATP, ATP, dGTP, or dTTP), two tetramerization site binding possibilities (dATP or ATP), and one hexamerization site binding possibility (ATP), in addition to possibilities of unbound site states. This large number of internal R1 states implies an even larger number of quaternary states. A mathematical model of RNR activity which explicitly represents the states of R1 currently exists, but it is complicated in several ways: (1) it includes up to six-fold nested sums; (2) it uses different mathematical structures under different substrate-modulator conditions; and (3) it requires root solutions of high order polynomials to determine R1 proportions in mono-, di-, tetra- and hexamer states and thus RNR activity as a function of modulator and total R1 concentrations. RESULTS: We present four (one for each NDP) rational polynomial models of RNR activity as a function of substrate and reaction rate modifier concentrations. The new models avoid the complications of the earlier model without compromising curve fits to recent data. CONCLUSION: Compared to the earlier model of recent data, the new rational polynomial models are simpler, adequately fitting, and likely better suited for biochemical network simulations

Sphingoid Base Metabolism in Yeast: Mapping Gene Expression Patterns Into Qualitative Metabolite Time Course Predictions

Can qualitative metabolite time course predictions be inferred from measured mRNA expression patterns? Speaking against this possibility is the large number of ‘decoupling’ control points that lie between these variables, i.e. translation, protein degradation, enzyme inhibition and enzyme activation. Speaking for it is the notion that these control points might be coordinately regulated such that action exerted on the mRNA level is informative of action exerted on the protein and metabolite levels. A simple kinetic model of sphingoid base metabolism in yeast is postulated. When the enzyme activities in this model are modulated proportional to mRNA expression levels measured in heat shocked yeast, the model yields a transient rise and fall in sphingoid bases followed by a permanent rise in ceramide. This finding is in qualitative agreement with experiments and is thus consistent with the aforementioned coordinated control system hypothesis

Gender effects on cytidine analogue metabolism and myelodysplastic syndrome treatment outcomes

In vivo, half-lives of cytidine analogues such as 5-azacytidine and decitabine, used to treat myelodysplastic syndromes (MDS), are determined largely by cytidine deaminase (CDA), an enzyme that rapidly metabolizes these drugs into inactive uridine counterparts. Genetic factors influence CDA activity, and hence, could impact 5-azacytidine/decitabine levels and efficacy, a possibility requiring evaluation. Using an HPLC assay, plasma CDA activity was confirmed to be decreased in individuals with the CDA SNP A79C. More interestingly, there was an even larger decrease in females. Explaining the decrease in enzyme activity, liver CDA expression was significantly lower in female versus male mice. As expected, decitabine plasma levels, measured by mass-spectrometry, were significantly higher in females. In mathematical modeling, the detrimental effect of shortening half-life of S-phase specific therapy was amplified in low S-phase fraction disease (e.g., MDS). Accordingly, in multivariate analysis of MDS patients treated with 5-azacytidine/decitabine, overall survival was significantly worse in males

p53 independent epigenetic-differentiation treatment in xenotransplant models of acute myeloid leukemia

Suppression of apoptosis by TP53 mutation contributes to resistance of acute myeloid leukemia (AML) to conventional cytotoxic treatment. Using differentiation to induce irreversible cell cycle exit in AML cells could be a p53-independent treatment alternative, however, this possibility requires evaluation. In vitro and in vivo regimens of the cytosine analogue decitabine that deplete the chromatin modifying enzyme DNA methyl-transferase 1 (DNMT1) without phosphorylating p53 or inducing early apoptosis were determined. These decitabine regimens but not equimolar DNA-damaging cytarabine up regulated the key late differentiation factors CEBP&#x3b5; and p27/CDKN1B, induced cellular differentiation, and terminated AML cell-cycle, even in cytarabine-resistant p53- and p16/CDKN2A-null AML cells. Leukemia initiation by xeno-transplanted AML cells was abrogated but normal hematopoietic stem cell (HSC) engraftment was preserved. In vivo, the low toxicity allowed frequent drug administration to increase exposure, an important consideration for S-phase specific decitabine therapy. In xeno-transplant models of p53-null and relapsed/refractory AML, the non-cytotoxic regimen significantly extended survival compared to conventional cytotoxic cytarabine. Modifying in vivo dose and schedule to emphasize this pathway of decitabine action can bypass a mechanism of resistance to standard therapy

Equilibrium model selection: dTTP induced R1 dimerization

<p>Abstract</p> <p>Background</p> <p>Biochemical equilibria are usually modeled iteratively: given one or a few fitted models, if there is a lack of fit or over fitting, a new model with additional or fewer parameters is then fitted, and the process is repeated. The problem with this approach is that different analysts can propose and select different models and thus extract different binding parameter estimates from the same data. An alternative is to first generate a comprehensive standardized list of plausible models, and to then fit them exhaustively, or semi-exhaustively.</p> <p>Results</p> <p>A framework is presented in which equilibriums are modeled as pairs (<it>g</it>, <it>h</it>) where <it>g </it>= 0 maps total reactant concentrations (system inputs) into free reactant concentrations (system states) which <it>h </it>then maps into expected values of measurements (system outputs). By letting dissociation constants <it>K</it>_{<it>d </it>}be either freely estimated, infinity, zero, or equal to other <it>K</it>_<it>d</it>, and by letting undamaged protein fractions be either freely estimated or 1, many <it>g </it>models are formed. A standard space of <it>g </it>models for ligand-induced protein dimerization equilibria is given. Coupled to an <it>h </it>model, the resulting (<it>g</it>, <it>h</it>) were fitted to dTTP induced R1 dimerization data (R1 is the large subunit of ribonucleotide reductase). Models with the fewest parameters were fitted first. Thereafter, upon fitting a batch, the next batch of models (with one more parameter) was fitted only if the current batch yielded a model that was better (based on the Akaike Information Criterion) than the best model in the previous batch (with one less parameter). Within batches models were fitted in parallel. This semi-exhaustive approach yielded the same best models as an exhaustive model space fit, but in approximately one-fifth the time.</p> <p>Conclusion</p> <p>Comprehensive model space based biochemical equilibrium model selection methods are realizable. Their significance to systems biology as mappings of data into mathematical models warrants their development.</p

On systems and control approaches to therapeutic gain

BACKGROUND: Mathematical models of cancer relevant processes are being developed at an increasing rate. Conceptual frameworks are needed to support new treatment designs based on such models. METHODS: A modern control perspective is used to formulate two therapeutic gain strategies. RESULTS: Two conceptually distinct therapeutic gain strategies are provided. The first is direct in that its goal is to kill cancer cells more so than normal cells, the second is indirect in that its goal is to achieve implicit therapeutic gains by transferring states of cancer cells of non-curable cases to a target state defined by the cancer cells of curable cases. The direct strategy requires models that connect anti-cancer agents to an endpoint that is modulated by the cause of the cancer and that correlates with cell death. It is an abstraction of a strategy for treating mismatch repair (MMR) deficient cancers with iodinated uridine (IUdR); IU-DNA correlates with radiation induced cell killing and MMR modulates the relationship between IUdR and IU-DNA because loss of MMR decreases the removal of IU from the DNA. The second strategy is indirect. It assumes that non-curable patient outcomes will improve if the states of their malignant cells are first transferred toward a state that is similar to that of a curable patient. This strategy is difficult to employ because it requires a model that relates drugs to determinants of differences in patient survival times. It is an abstraction of a strategy for treating BCR-ABL pro-B cell childhood leukemia patients using curable cases as the guides. CONCLUSION: Cancer therapeutic gain problem formulations define the purpose, and thus the scope, of cancer process modeling. Their abstractions facilitate considerations of alternative treatment strategies and support syntheses of learning experiences across different cancers