Dynamics of granzyme B-induced apoptosis: mathematical modeling

Apoptosis is mediated by an intracellular biochemical system that mainly includes proteins (procaspases, caspases, inhibitors, Bcl-2 protein family as well as substances released from mitochondrial intermembrane space). The dynamics of caspase activation and target cleavage in apoptosis induced by granzyme B in a single K562 cell was studied using a mathematical model of the dynamics of granzyme B-induced apoptosis developed in this work. Also the first application of optimization approach to determination of unknown kinetic constants of biochemical apoptotic reactions was presented. The optimization approach involves solving of two problems: direct and inverse. Solving the direct optimization problem, we obtain the initial (baseline) concentrations of procaspases for known kinetic constants through conditional minimization of a cost function based on the principle of minimum protein consumption by the apoptosis system. The inverse optimization problem is aimed at determination of unknown kinetic constants of apoptotic biochemical reactions proceeding from the condition that the optimal concentrations of procaspases resulting from the solution of the direct optimization problem coincide with the observed ones, that is, those determined by biochemical methods. The Multidimensional Index Method was used to perform numerical solution of the inverse optimization problem.     

Concerted simulations reveal how peroxidase compound III formation results in cellular oscillations

A major problem in mathematical modeling of the dynamics of complex biological systems is the frequent lack of knowledge of kinetic parameters. Here, we apply Brownian dynamics simulations, based on protein three-dimensional structures, to estimate a previously undetermined kinetic parameter, which is then used in biochemical network simulations. The peroxidase-oxidase reaction involves many elementary steps and displays oscillatory dynamics important for immune response. Brownian dynamics simulations were performed for three different peroxidases to estimate the rate constant for one of the elementary steps crucial for oscillations in the peroxidase-oxidase reaction, the association of superoxide with peroxidase. Computed second-order rate constants agree well with available experimental data and permit prediction of rate constants at physiological conditions. The simulations show that electrostatic interactions depress the rate of superoxide association with myeloperoxidase, bringing it into the range necessary for oscillatory behavior in activated neutrophils. Such negative electrostatic steering of enzyme-substrate association presents a novel control mechanism and lies in sharp contrast to the electrostatically-steered fast association of superoxide and Cu/Zn superoxide dismutase, which is also simulated here. The results demonstrate the potential of an integrated and concerted application of structure-based simulations and biochemical network simulations in cellular systems biology.     

Dynamics of muscle glycogenolysis modeled with pH time course computation and pH-dependent reaction equilibria and enzyme kinetics

Cellular metabolites are moieties defined by their specific binding constants to H+, Mg2+, and K+ or anions without ligands. As a consequence, every biochemical reaction in the cytoplasm has an associated proton stoichiometry that is generally noninteger- and pH-dependent. Therefore, with metabolic flux, pH is altered in a medium with finite buffer capacity. Apparent equilibrium constants and maximum enzyme velocities, which are functions of pH, are also altered. We augmented an earlier mathematical model of skeletal muscle glycogenolysis with pH-dependent enzyme kinetics and reaction equilibria to compute the time course of pH changes. Analysis shows that kinetics and final equilibrium states of the closed system are highly constrained by the pH-dependent parameters. This kinetic model of glycogenolysis, coupled to creatine kinase and adenylate kinase, simulated published experiments made with a cell-free enzyme mixture to reconstitute the network and to synthesize PCr and lactate in vitro. Using the enzyme kinetic and thermodynamic data in the literature, the simulations required minimal adjustments of parameters to describe the data. These results show that incorporation of appropriate physical chemistry of the reactions with accurate kinetic modeling gives a reasonable simulation of experimental data and is necessary for a physically correct representation of the metabolic network. The approach is general for modeling metabolic networks beyond the specific pathway and conditions presented here.     

Functional and structural insight into the flexibility of cytochrome P450 reductases from Sorghum bicolor and its implications for lignin composition

Plant NADPH-dependent cytochrome P450 reductase (CPR) is a multidomain enzyme that donates electrons for hydroxylation reactions catalyzed by class II cytochrome P450 monooxygenases involved in the synthesis of many primary and secondary metabolites. These P450 enzymes include trans-cinnamate-4-hydroxylase, p-coumarate-3′-hydroxylase, and ferulate-5-hydroxylase involved in monolignol biosynthesis. Because of its role in monolignol biosynthesis, alterations in CPR activity could change the composition and overall output of lignin. Therefore, to understand the structure and function of three CPR subunits from sorghum, recombinant subunits SbCPR2a, SbCPR2b, and SbCPR2c were subjected to X-ray crystallography and kinetic assays. Steady-state kinetic analyses demonstrated that all three CPR subunits supported the oxidation reactions catalyzed by SbC4H1 (CYP73A33) and SbC3′H (CYP98A1). Furthermore, comparing the SbCPR2b structure with the well-investigated CPRs from mammals enabled us to identify critical residues of functional importance and suggested that the plant flavin mononucleotide–binding domain might be more flexible than mammalian homologs. In addition, the elucidated structure of SbCPR2b included the first observation of NADP⁺ in a native CPR. Overall, we conclude that the connecting domain of SbCPR2, especially its hinge region, could serve as a target to alter biomass composition in bioenergy and forage sorghums through protein engineering.     

RankAggreg, an R package for weighted rank aggregation

Background

Determining the parameters of a mathematical model from quantitative measurements is the main bottleneck of modelling biological systems. Parameter values can be estimated from steady-state data or from dynamic data. The nature of suitable data for these two types of estimation is rather different. For instance, estimations of parameter values in pathway models, such as kinetic orders, rate constants, flux control coefficients or elasticities, from steady-state data are generally based on experiments that measure how a biochemical system responds to small perturbations around the steady state. In contrast, parameter estimation from dynamic data requires time series measurements for all dependent variables. Almost no literature has so far discussed the combined use of both steady-state and transient data for estimating parameter values of biochemical systems.

Results

In this study we introduce a constrained optimization method for estimating parameter values of biochemical pathway models using steady-state information and transient measurements. The constraints are derived from the flux connectivity relationships of the system at the steady state. Two case studies demonstrate the estimation results with and without flux connectivity constraints. The unconstrained optimal estimates from dynamic data may fit the experiments well, but they do not necessarily maintain the connectivity relationships. As a consequence, individual fluxes may be misrepresented, which may cause problems in later extrapolations. By contrast, the constrained estimation accounting for flux connectivity information reduces this misrepresentation and thereby yields improved model parameters.

Conclusion

The method combines transient metabolic profiles and steady-state information and leads to the formulation of an inverse parameter estimation task as a constrained optimization problem. Parameter estimation and model selection are simultaneously carried out on the constrained optimization problem and yield realistic model parameters that are more likely to hold up in extrapolations with the model.     

Mathematical modeling of the microtubule detyrosination/tyrosination cycle for cell-based drug screening design

Microtubules and their post-translational modifications are involved in major cellular processes. In severe diseases such as neurodegenerative disorders, tyrosinated tubulin and tyrosinated microtubules are in lower concentration. We present here a mechanistic mathematical model of the microtubule tyrosination cycle combining computational modeling and high-content image analyses to understand the key kinetic parameters governing the tyrosination status in different cellular models. That mathematical model is parameterized, firstly, for neuronal cells using kinetic values taken from the literature, and, secondly, for proliferative cells, by a change of two parameter values obtained, and shown minimal, by a continuous optimization procedure based on temporal logic constraints to formalize experimental high-content imaging data. In both cases, the mathematical models explain the inability to increase the tyrosination status by activating the Tubulin Tyrosine Ligase enzyme. The tyrosinated tubulin is indeed the product of a chain of two reactions in the cycle: the detyrosinated microtubule depolymerization followed by its tyrosination. The tyrosination status at equilibrium is thus limited by both reaction rates and activating the tyrosination reaction alone is not effective. Our computational model also predicts the effect of inhibiting the Tubulin Carboxy Peptidase enzyme which we have experimentally validated in MEF cellular model. Furthermore, the model predicts that the activation of two particular kinetic parameters, the tyrosination and detyrosinated microtubule depolymerization rate constants, in synergy, should suffice to enable an increase of the tyrosination status in living cells.     

The 15 SCR flexible extracellular domains of human complement receptor type 2 can mediate multiple ligand and antigen interactions

Complement receptor type 2 (CR2, CD21) is a cell surface protein that links the innate and adaptive immune response during the activation of B cells. The extracellular portion of CR2 comprises 15 or 16 short complement regulator (SCR) domains, for which the overall arrangement in solution is unknown. This was determined by constrained scattering and ultracentrifugation modelling. The radius of gyration of CR2 SCR 1-15 was determined to be 11.5 nm by both X-ray and neutron scattering, and that of its cross-section was 1.8 nm. The distance distribution function P(r) showed that the overall length of CR2 SCR 1-15 was 38 nm. Sedimentation equilibrium curve fits gave a mean molecular weight of 135,000 (+/- 13,000) Da, in agreement with a fully glycosylated structure. Velocity experiments using the g*(s) derivative method gave a sedimentation coefficient of 4.2 (+/- 0.1) S. In order to construct a model of CR2 SCR 1-15 for constrained fitting, homology models for the 15 SCR domains were combined with randomised linker peptides generated by molecular dynamics simulations. Using an automated procedure, the analysis of 15,000 possible CR2 SCR 1-15 models showed that only those models in which the 15 SCR domains were flexible but partially folded back accounted for the scattering and sedimentation data. The best-fit CR2 models provided a visual explanation for the versatile interaction of CR2 with four ligands C3d, CD23, gp350 and IFN-alpha. The flexible location of CR2 SCR 1-2 is likely to facilitate interactions of C3d-antigen complexes with the B cell receptor.     

Hyperdigraph-theoretic analysis of the EGFR signaling network: initial steps leading to GTP:Ras complex formation.

We construct an algebraic-combinatorial model of the SOS compartment of the EGFR biochemical network. A Petri net is used to construct an initial representation of the biochemical decision making network, which in turn defines a hyperdigraph. We observe that the linear algebraic structure of each hyperdigraph admits a canonical set of algebraic-combinatorial invariants that correspond to the information flow conservation laws governing a molecular kinetic reaction network. The linear algebraic structure of the hyperdigraph and its sets of invariants can be generalized to define a discrete algebraic-geometric structure, which is referred to as an oriented matroid. Oriented matroids define a polyhedral optimization geometry that is used to determine optimal subpaths that span the nullspace of a set of kinetic chemical reaction equations. Sets of constrained submodular path optimizations on the hyperdigraph are objectively obtained as a spanning tree of minimum cycle paths. This complete set of subcircuits is used to identify the network pinch points and invariant flow subpaths. We demonstrate that this family of minimal circuits also characteristically identifies additional significant biochemical reaction pattern features. We use the SOS Compartment A of the EGFR biochemical pathway to develop and demonstrate the application of our algebraic-combinatorial mathematical modeling methodology.     

Beta sheet 2–alpha helix C loop of cytochrome P450 reductase serves as a docking site for redox partners

As a promiscuous redox partner, the biological role of cytochrome P450 reductase (CPR) depends significantly on protein–protein interactions. We tested a hypothesized CPR docking site by mutating D113, E115, and E116 to alanine and assaying activity toward various electron acceptors as a function of ionic strength. Steady-state cytochrome c studies demonstrated the mutations improved catalytic efficiency and decreased the impact of ionic strength on catalytic parameters when compared to wild type. Based on activity toward 7-ethoxy-4-trifluoro-methylcoumarin, CYP2B1 and CPR favored formation of an active CYP2B1•CPR complex and inactive (CYP2B1)₂•CPR complex until higher ionic strength whereby only the binary complex was observed. The mutations increased dissociation constants only for the binary complex and suppressed the ionic strength effect. Studies with a non-binding substrate, 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) suggest changes in activity toward cytochrome c and CYP2B1 reflect alterations in the route of electron transfer caused by the mutations. Electrostatic modeling of catalytic and binding parameters confirmed the importance of D113 and especially the double mutant E115 and E116 as mediators in forming charge–charge interactions between CPR and complex partners.     

Rapid simulation and analysis of isotopomer distributions using constraints based on enzyme mechanisms: an example from HT29 cancer cells

MOTIVATION: Addition of labeled substrates and the measurement of the subsequent distribution of the labels in isotopomers in reaction networks provide a unique method for assessing metabolic fluxes in whole cells. However, owing to insufficiency of information, attempts to quantify the fluxes often yield multiple possible sets of solutions that are consistent with a given experimental pattern of isotopomers. In the study of the pentose phosphate pathways, the need to consider isotope exchange reactions of transketolase (TK) and transaldolase (TA) (which in past analyses have often been ignored) magnifies this problem; but accounting for the interrelation between the fluxes known from biochemical studies and kinetic modeling solves it. The mathematical relationships between kinetic and equilibrium constants restrict the domain of estimated fluxes to the ones compatible not only with a given set of experimental data, but also with other biochemical information. METHOD: We present software that integrates kinetic modeling with isotopomer distribution analysis. It solves the ordinary differential equations for total concentrations (accounting for the kinetic mechanisms) as well as for all isotopomers in glycolysis and the pentose phosphate pathway (PPP). In the PPP the fluxes created in the TK and TA reactions are expressed through unitary rate constants. The algorithms that account for all the kinetic and equilbrium constant constraints are integrated with the previously developed algorithms, which have been further optimized. The most time-consuming calculations were programmed directly in assembly language; this gave an order of magnitude decrease in the computation time, thus allowing analysis of more complex systems. The software was developed as C-code linked to a program written in Mathematica (Wolfram Research, Champaign, IL), and also as a C++ program independent from Mathematica. RESULTS: Implementing constraints imposed by kinetic and equilibrium constants in the isotopomer distribution analysis in the data from the cancer cells eliminated estimates of fluxes that were inconsistent with the kinetic mechanisms of TK and TA. Fluxes measured experimentally in cells can be used to estimate better the kinetics of TK and TA as they operate in situ. Thus, our approach of integrating various methods for in situ flux analysis opens up the possibility of designing new types of experiments to probe metabolic interrelationships, including the incorporation of additional biochemical information. AVAILABILITY: Software is available freely at: http://www.bq.ub.es/bioqint/selivanov.htm CONTACT: martacascante@ub.edu     

A kinetic model of Escherichia coli core metabolism satisfying multiple sets of mutant flux data

In contrast to stoichiometric-based models, the development of large-scale kinetic models of metabolism has been hindered by the challenge of identifying kinetic parameter values and kinetic rate laws applicable to a wide range of environmental and/or genetic perturbations. The recently introduced ensemble modeling (EM) procedure provides a promising remedy to address these challenges by decomposing metabolic reactions into elementary reaction steps and incorporating all phenotypic observations, upon perturbation, in its model parameterization scheme. Here, we present a kinetic model of Escherichia coli core metabolism that satisfies the fluxomic data for wild-type and seven mutant strains by making use of the EM concepts. This model encompasses 138 reactions, 93 metabolites and 60 substrate-level regulatory interactions accounting for glycolysis/gluconeogenesis, pentose phosphate pathway, TCA cycle, major pyruvate metabolism, anaplerotic reactions and a number of reactions in other parts of the metabolism. Parameterization is performed using a formal optimization approach that minimizes the discrepancies between model predictions and flux measurements. The predicted fluxes by the model are within the uncertainty range of experimental flux data for 78% of the reactions (with measured fluxes) for both the wild-type and seven mutant strains. The remaining flux predictions are mostly within three standard deviations of reported ranges. Converting the EM-based parameters into a Michaelis–Menten equivalent formalism revealed that 35% of K_m and 77% of k_cat parameters are within uncertainty range of the literature-reported values. The predicted metabolite concentrations by the model are also within uncertainty ranges of metabolomic data for 68% of the metabolites. A leave-one-out cross-validation test to evaluate the flux prediction performance of the model showed that metabolic fluxes for the mutants located in the proximity of mutations used for training the model can be predicted more accurately. The constructed model and the parameterization procedure presented in this study pave the way for the construction of larger-scale kinetic models with more narrowly distributed parameter values as new metabolomic/fluxomic data sets are becoming available for E. coli and other organisms.     

A benzo[b]thiophene-based selective type 4 S1P receptor agonist

S1P receptors (S1PR1-5) are a group of GPCRs activated by a high affinity binding with S1P that have important roles in the regulation of the immune system. A potent S1PR agonist FTY720 is an immunomodulator used to treat multiple sclerosis and several ‘second generation’ drugs are under clinical development. Subtype-selective agonists have been reported for each S1PR isotype, some of which are used as pharmacological tools for functional studies. Here we report the discovery and initial characterization of compound 5c, a benzo[b]thiophene amino carboxylate which exhibits potent and selective agonist activity for S1PR4. Compound 5c has an EC₅₀ = 200 nM as an agonist in GTPγ³⁵S binding assay for S1PR4 and exhibits no activity against S1PR1,2,3,5. We confirmed its potent activity and decent S1PR subtype selectivity using biochemical and cellular assays.     

Role of Ser-257 in the Sliding Mechanism of NADP(H) in the Reaction Catalyzed by the Aspergillus fumigatus Flavin-dependent Ornithine N5-Monooxygenase SidA

SidA (siderophore A) is a flavin-dependent N-hydroxylating monooxygenase that is essential for virulence in Aspergillus fumigatus. SidA catalyzes the NADPH- and oxygen-dependent formation of N⁵-hydroxyornithine. In this reaction, NADPH reduces the flavin, and the resulting NADP⁺ is the last product to be released. The presence of NADP⁺ is essential for activity, as it is required for stabilization of the C4a-hydroperoxyflavin, which is the hydroxylating species. As part of our efforts to determine the molecular details of the role of NADP(H) in catalysis, we targeted Ser-257 for site-directed mutagenesis and performed extensive characterization of the S257A enzyme. Using a combination of steady-state and stopped-flow kinetic experiments, substrate analogs, and primary kinetic isotope effects, we show that the interaction between Ser-257 and NADP(H) is essential for stabilization of the C4a-hydroperoxyflavin. Molecular dynamics simulation results suggest that Ser-257 functions as a pivot point, allowing the nicotinamide of NADP⁺ to slide into position for stabilization of the C4a-hydroperoxyflavin.     

The partly folded back solution structure arrangement of the 30 SCR domains in human complement receptor type 1 (CR1) permits access to its C3b and C4b ligands

Human complement receptor type 1 (CR1, CD35) is a type I membrane-bound glycoprotein that belongs to the regulators of complement activity (RCA) family. The extra-cellular component of CR1 is comprised of 30 short complement regulator (SCR) domains, whereas complement receptor type 2 (CR2) has 15 SCR domains and factor H (FH) has 20 SCR domains. The domain arrangement of a soluble form of CR1 (sCR1) was studied by X-ray scattering and analytical ultracentrifugation. The radius of gyration R_G of sCR1 of 13.4(±1.1) nm is not much greater than those for CR2 and FH, and its R_G/R₀ anisotropy ratio is 3.76, compared to ratios of 3.67 for FH and 4.1 for CR2. Unlike CR2, but similar to FH, two cross-sectional R_G ranges were identified that gave R_XS values of 4.7(±0.2) nm and 1.2(±0.7) nm, respectively, showing that the SCR domains adopt a range of conformations including folded-back ones. The distance distribution function P(r) showed that the most commonly occurring distance in sCR1 is at 11.5 nm. Its maximum length of 55 nm is less than double those for CR2 or FH, even though sCR1 has twice the number of SCR domains compared to CR2 Sedimentation equilibrium experiments gave a mean molecular weight of 235 kDa for sCR1. This is consistent with the value of 245 kDa calculated from its composition including 14 N-linked oligosaccharide sites, and confirmed that sCR1 is a monomer in solution. Sedimentation velocity experiments gave a sedimentation coefficient of 5.8 S. From this, the frictional ratio (f/f₀) of sCR1 was calculated to be 2.29, which is greater than those of 1.96 for CR2 and 1.77 for FH. The constrained scattering modelling of the sCR1 solution structure starting from homologous SCR domain structures generated 5000 trial conformationally randomised models, 43 of which gave good scattering fits to show that sCR1 has a partly folded-back structure. We conclude that the inter-SCR linkers show structural features in common with those in FH, but differ from those in CR2, and the SCR arrangement in CR1 will permit C3b or C4b to access all three ligand sites.     

Fides: Reliable trust-region optimization for parameter estimation of ordinary differential equation models

Ordinary differential equation (ODE) models are widely used to study biochemical reactions in cellular networks since they effectively describe the temporal evolution of these networks using mass action kinetics. The parameters of these models are rarely known a priori and must instead be estimated by calibration using experimental data. Optimization-based calibration of ODE models on is often challenging, even for low-dimensional problems. Multiple hypotheses have been advanced to explain why biochemical model calibration is challenging, including non-identifiability of model parameters, but there are few comprehensive studies that test these hypotheses, likely because tools for performing such studies are also lacking. Nonetheless, reliable model calibration is essential for uncertainty analysis, model comparison, and biological interpretation.We implemented an established trust-region method as a modular Python framework (fides) to enable systematic comparison of different approaches to ODE model calibration involving a variety of Hessian approximation schemes. We evaluated fides on a recently developed corpus of biologically realistic benchmark problems for which real experimental data are available. Unexpectedly, we observed high variability in optimizer performance among different implementations of the same mathematical instructions (algorithms). Analysis of possible sources of poor optimizer performance identified limitations in the widely used Gauss-Newton, BFGS and SR1 Hessian approximation schemes. We addressed these drawbacks with a novel hybrid Hessian approximation scheme that enhances optimizer performance and outperforms existing hybrid approaches. When applied to the corpus of test models, we found that fides was on average more reliable and efficient than existing methods using a variety of criteria. We expect fides to be broadly useful for ODE constrained optimization problems in biochemical models and to be a foundation for future methods development.     

Electron transfer between the two photosystems. II. Equilibrium constants

(1) The equilibrium constants for the redox reactions occurring between Photosystem (PS) I donors were measured on chloroplasts, dark-adapted in the presence of sodium ascorbate and 3-(3′,4′-dichlorophenyl)-1,1-dimethylurea (DCMU) and then illuminated by d.c. light. The equilibrium constant for the electron transfer between plastocyanin and P-700 is close to 1 and the overall equilibrium constant between cytochrome f and P-700 is about 2.3. As these equilibrium constants do not depend upon the intensity of the d.c. beam, the low values we measured cannot be due to kinetic limitations. (2) The equilibrium constants were measured also in the absence of DCMU using chloroplasts in oxidizing conditions (ferricyanide or far red illumination) illuminated by a saturating flash. During the course of the reduction of PS I donors by plastoquinol molecules formed by the flash, the equilibrium constants are higher than in the preceding conditions: the value for plastocyanin to P-700 is close to 5, and that for cytochrome f to P-700 is about 25. (3) The variations of these equilibrium constants are tentatively interpreted as being due to mutual electrostatic interactions between cytochrome b and f which are included in the same complex. This model implies that the perturbation of the redox properties of cytochrome f by a positive charge located on cytochrome b is identical to the perturbation of the redox properties of cytochrome b by a positive charge located on cytochrome f.     

Simulating Metabolism with Statistical Thermodynamics

New methods are needed for large scale modeling of metabolism that predict metabolite levels and characterize the thermodynamics of individual reactions and pathways. Current approaches use either kinetic simulations, which are difficult to extend to large networks of reactions because of the need for rate constants, or flux-based methods, which have a large number of feasible solutions because they are unconstrained by the law of mass action. This report presents an alternative modeling approach based on statistical thermodynamics. The principles of this approach are demonstrated using a simple set of coupled reactions, and then the system is characterized with respect to the changes in energy, entropy, free energy, and entropy production. Finally, the physical and biochemical insights that this approach can provide for metabolism are demonstrated by application to the tricarboxylic acid (TCA) cycle of Escherichia coli. The reaction and pathway thermodynamics are evaluated and predictions are made regarding changes in concentration of TCA cycle intermediates due to 10- and 100-fold changes in the ratio of NAD⁺:NADH concentrations. Finally, the assumptions and caveats regarding the use of statistical thermodynamics to model non-equilibrium reactions are discussed.     

Schistosoma mansoni: Role in vivo of complement in primary infection of mice

The role of complement in the control of the primary Schistosoma mansoni infection in mice was investigated in vivo. The number of recovered adult schistosomes 6–7 weeks postinfection was used as a parasitological criterion of immunity. No significant difference in the worm burden was observed between C5-sufficient and C5-deficient mice. In contrast, when cobra venom factor (CVF) was injected into normal or C5-deficient mice 24 hr before challenge, a significant increase of the worm burden was noticed in comparison to the untreated mice. These results indicated that, although C5 and probably the late complement components are not essential for the control of the primary infection, the alternative pathway and some of its components are involved. In fact, the injection of C3 2 hr before infection of CVF-treated mice completely restored the immunity. A role for C3, in association with effector cells, in the nonspecific immunity occurring in the first hours after a primary S. mansoni infection is suggested.