Complementarities between mathematical and computational modeling: the case of the repeated Prisoners' Dilemma

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the mathematical model. Our main conclusion is that mathematical and computational models are good complements for research in social sciences. Indeed, while computational models are extremely useful to extend the scope of the analysis to complex scenarios hard to analyze mathematically, formal models can be useful to verify and to explain the outcomes of computational models.

Synchronous versus asynchronous modeling of gene regulatory networks.

MOTIVATION: In silico modeling of gene regulatory networks has gained some momentum recently due to increased interest in analyzing the dynamics of biological systems. This has been further facilitated by the increasing availability of experimental data on gene-gene, protein-protein and gene-protein interactions. The two dynamical properties that are often experimentally testable are perturbations and stable steady states. Although a lot of work has been done on the identification of steady states, not much work has been reported on in silico modeling of cellular differentiation processes. RESULTS: In this manuscript, we provide algorithms based on reduced ordered binary decision diagrams (ROBDDs) for Boolean modeling of gene regulatory networks. Algorithms for synchronous and asynchronous transition models have been proposed and their corresponding computational properties have been analyzed. These algorithms allow users to compute cyclic attractors of large networks that are currently not feasible using existing software. Hereby we provide a framework to analyze the effect of multiple gene perturbation protocols, and their effect on cell differentiation processes. These algorithms were validated on the T-helper model showing the correct steady state identification and Th1-Th2 cellular differentiation process. AVAILABILITY: The software binaries for Windows and Linux platforms can be downloaded from http://si2.epfl.ch/~garg/genysis.html.

Arterial properties in relation to genetic variations in the adducin subunits in a white population.

BACKGROUND: Adducin is a membrane skeleton protein, which consists of either alpha- and beta- or alpha- and gamma-subunits. We investigated whether arterial characteristics might be related to the genes encoding ADD1 (Gly460Trp-rs4961), ADD2 (C1797T-rs4984), and ADD3 (IVS11+386A>G-rs3731566). METHODS: We randomly recruited 1,126 Flemish subjects (mean age, 43.8 years; 50.3% women). Using a wall-tracking ultrasound system, we measured the properties of the carotid, femoral, and brachial arteries. We studied multivariate-adjusted phenotype-genotype associations, using a population- and family-based approach. RESULTS: In single-gene analyses, brachial diameter was 0.15 mm (P = 0.0022) larger, and brachial distensibility and cross-sectional compliance were 1.55 x 10(-3)/kPa (P = 0.013) and 0.017 mm(2)/kPa (P = 0.0029) lower in ADD3 AA than ADD3 GG homozygotes with an additive effect of the G allele. In multiple-gene analyses, the association of brachial diameter and distensibility with the ADD3 G allele occurred only in ADD1 GlyGly homozygotes. Otherwise, the associations between the arterial phenotypes in the three vascular beds and the ADD1 or ADD2 polymorphisms were not significant. In family-based analyses, the multivariate-adjusted heritability was 0.52, 0.38, and 0.30 for brachial diameter, distensibility, and cross-sectional compliance, respectively (P < 0.001). There was no evidence for population stratification (0.07 < or = P < or = 0.96). Transmission of the mutated ADD3 G allele was associated with smaller brachial diameter in 342 informative offspring (-0.12 +/- 0.04 mm; P = 0.0085) and in 209 offspring, who were ADD1 GlyGly homozygotes (-0.14 +/- 0.06 mm; P = 0.018). CONCLUSIONS: In ADD1 GlyGly homozygotes, the properties of the brachial artery are related to the ADD3 (A386G) polymorphism, but the underlying mechanism needs further clarification.

TRAF1/C5 but not PTPRC variants are potential predictors of rheumatoid arthritis response to anti-tumor necrosis factor therapy.

BACKGROUND The aim of our work was to replicate, in a Southern European population, the association reported in Northern populations between PTPRC locus and response to anti-tumor necrosis factor (anti-TNF) treatment in rheumatoid arthritis (RA). We also looked at associations between five RA risk alleles and treatment response. METHODS We evaluated associations between anti-TNF treatment responses assessed by DAS28 change and by EULAR response at six months in 383 Portuguese patients. Univariate and multivariate linear and logistic regression analyses were performed. In a second step to confirm our findings, we pooled our population with 265 Spanish patients. RESULTS No association was found between PTPRC rs10919563 allele and anti-TNF treatment response, neither in Portuguese modeling for several clinical variables nor in the overall population combining Portuguese and Spanish patients. The minor allele for RA susceptibility, rs3761847 SNP in TRAF1/C5 region, was associated with a poor response in linear and logistic univariate and multivariate regression analyses. No association was observed with the other allellic variants. Results were confirmed in the pooled analysis. CONCLUSION This study did not replicate the association between PTPRC and the response to anti-TNF treatment in our Southern European population. We found that TRAF1/C5 risk RA variants potentially influence anti-TNF treatment response.

Hierarchical analyses of genetic differentiation in a hybrid zone of Sorex araneus (Insectivora : Soricidae)

Microsatellites are used to unravel the fine-scale genetic structure of a hybrid zone between chromosome races Valais and Cordon of the common shrew (Sorex araneus) located in the French Alps. A total of 269 individuals collected between 1992 and 1995 was typed for seven microsatellite loci. A modified version of the classical multiple correspondence analysis is carried out. This analysis clearly shows the dichotomy between the two races. Several approaches are used to study genetic structuring. Gene flow is clearly reduced between these chromosome races and is estimated at one migrant every two generations using X-statistics and one migrant per generation using F-statistics. Hierarchical F- and R-statistics are compared and their efficiency to detect inter- and intraracial patterns of divergence is discussed. Within-race genetic structuring is significant, but remains weak. F-ST displays similar values on both sides of the hybrid zone, although no environmental barriers are found on the Cordon side, whereas the Valais side is divided by several mountain rivers. We introduce the exact G-test to microsatellite data which proved to be a powerful test to detect genetic differentiation within as well as among races. The genetic background of karyotypic hybrids was compared with the genetic background of pure parental forms using a CRT-MCA. Our results indicate that, without knowledge of the karyotypes, we would not have been able to distinguish these hybrids from karyotypically pure samples.

Genetic and phenotypic population divergence on a microgeographic scale in brown trout.

Salmonid populations of many rivers are rapidly declining. One possible explanation is that habitat fragmentation increases genetic drift and reduces the populations' potential to adapt to changing environmental conditions. We measured the genetic and eco-morphological diversity of brown trout (Salmo trutta) in a Swiss stream system, using multivariate statistics and Bayesian clustering. We found large genetic and phenotypic variation within only 40 km of stream length. Eighty-eight percent of all pairwise F(ST) comparisons and 50% of the population comparisons in body shape were significant. High success rates of population assignment tests confirmed the distinctiveness of populations in both genotype and phenotype. Spatial analysis revealed that divergence increased with waterway distance, the number of weirs, and stretches of poor habitat between sampling locations, but effects of isolation-by-distance and habitat fragmentation could not be fully disentangled. Stocking intensity varied between streams but did not appear to erode genetic diversity within populations. A lack of association between phenotypic and genetic divergence points to a role of local adaptation or phenotypically plastic responses to habitat heterogeneity. Indeed, body shape could be largely explained by topographic stream slope, and variation in overall phenotype matched the flow regimes of the respective habitats.

A protocol describing the genetic correction of somatic human cells and subsequent generation of IPS cell

The generation of patient-specific induced pluripotent stem cells (iPSCPSCPSCs) offers unprecedented opportunities for modeling and treating human disease. In combination with gene therapy, the iPSCPSCPSC technology can be used to generate disease-free progenitor cells of potential interest for autologous cell therapy. We explain a protocol for the reproducible generation of genetically corrected iPSCPSCPSCs starting from the skin biopsies of Fanconi anemia patients using retroviral transduction with OCT4, SOX2 and KLF4. Before reprogramming, the fibroblasts and/or keratinocytes of the patients are genetically corrected with lentiviruses expressing FANCA. The same approach may be used for other diseases susceptible to gene therapy correction. Genetically corrected, characterized lines of patient-specific iPSCPSCPSCs can be obtained in 4–5 months.

Molecular modeling of peptide-MHC class I complexes : applications to peptide based immunotherapy

Summary The specific CD8+ T cell immune response against tumors relies on the recognition by the T cell receptor (TCR) on cytotoxic T lymphocytes (CTL) of antigenic peptides bound to the class I major histocompatibility complex (MHC) molecule. Such tumor associated antigenic peptides are the focus of tumor immunotherapy with peptide vaccines. The strategy for obtaining an improved immune response often involves the design of modified tumor associated antigenic peptides. Such modifications aim at creating higher affinity and/or degradation resistant peptides and require precise structures of the peptide-MHC class I complex. In addition, the modified peptide must be cross-recognized by CTLs specific for the parental peptide, i.e. preserve the structure of the epitope. Detailed structural information on the modified peptide in complex with MHC is necessary for such predictions. In this thesis, the main focus is the development of theoretical in silico methods for prediction of both structure and cross-reactivity of peptide-MHC class I complexes. Applications of these methods in the context of immunotherapy are also presented. First, a theoretical method for structure prediction of peptide-MHC class I complexes is developed and validated. The approach is based on a molecular dynamics protocol to sample the conformational space of the peptide in its MHC environment. The sampled conformers are evaluated using conformational free energy calculations. The method, which is evaluated for its ability to reproduce 41 X-ray crystallographic structures of different peptide-MHC class I complexes, shows an overall prediction success of 83%. Importantly, in the clinically highly relevant subset of peptide-HLAA*0201 complexes, the prediction success is 100%. Based on these structure predictions, a theoretical approach for prediction of cross-reactivity is developed and validated. This method involves the generation of quantitative structure-activity relationships using three-dimensional molecular descriptors and a genetic neural network. The generated relationships are highly predictive as proved by high cross-validated correlation coefficients (0.78-0.79). Together, the here developed theoretical methods open the door for efficient rational design of improved peptides to be used in immunotherapy. Résumé La réponse immunitaire spécifique contre des tumeurs dépend de la reconnaissance par les récepteurs des cellules T CD8+ de peptides antigéniques présentés par les complexes majeurs d'histocompatibilité (CMH) de classe I. Ces peptides sont utilisés comme cible dans l'immunothérapie par vaccins peptidiques. Afin d'augmenter la réponse immunitaire, les peptides sont modifiés de façon à améliorer l'affinité et/ou la résistance à la dégradation. Ceci nécessite de connaître la structure tridimensionnelle des complexes peptide-CMH. De plus, les peptides modifiés doivent être reconnus par des cellules T spécifiques du peptide natif. La structure de l'épitope doit donc être préservée et des structures détaillées des complexes peptide-CMH sont nécessaires. Dans cette thèse, le thème central est le développement des méthodes computationnelles de prédiction des structures des complexes peptide-CMH classe I et de la reconnaissance croisée. Des applications de ces méthodes de prédiction à l'immunothérapie sont également présentées. Premièrement, une méthode théorique de prédiction des structures des complexes peptide-CMH classe I est développée et validée. Cette méthode est basée sur un échantillonnage de l'espace conformationnel du peptide dans le contexte du récepteur CMH classe I par dynamique moléculaire. Les conformations sont évaluées par leurs énergies libres conformationnelles. La méthode est validée par sa capacité à reproduire 41 structures des complexes peptide-CMH classe I obtenues par cristallographie aux rayons X. Le succès prédictif général est de 83%. Pour le sous-groupe HLA-A*0201 de complexes de grande importance pour l'immunothérapie, ce succès est de 100%. Deuxièmement, à partir de ces structures prédites in silico, une méthode théorique de prédiction de la reconnaissance croisée est développée et validée. Celle-ci consiste à générer des relations structure-activité quantitatives en utilisant des descripteurs moléculaires tridimensionnels et un réseau de neurones couplé à un algorithme génétique. Les relations générées montrent une capacité de prédiction remarquable avec des valeurs de coefficients de corrélation de validation croisée élevées (0.78-0.79). Les méthodes théoriques développées dans le cadre de cette thèse ouvrent la voie du design de vaccins peptidiques améliorés.

Analysis and spatial modeling of the indoor radon Swiss data

The present research deals with an important public health threat, which is the pollution created by radon gas accumulation inside dwellings. The spatial modeling of indoor radon in Switzerland is particularly complex and challenging because of many influencing factors that should be taken into account. Indoor radon data analysis must be addressed from both a statistical and a spatial point of view. As a multivariate process, it was important at first to define the influence of each factor. In particular, it was important to define the influence of geology as being closely associated to indoor radon. This association was indeed observed for the Swiss data but not probed to be the sole determinant for the spatial modeling. The statistical analysis of data, both at univariate and multivariate level, was followed by an exploratory spatial analysis. Many tools proposed in the literature were tested and adapted, including fractality, declustering and moving windows methods. The use of Quan-tité Morisita Index (QMI) as a procedure to evaluate data clustering in function of the radon level was proposed. The existing methods of declustering were revised and applied in an attempt to approach the global histogram parameters. The exploratory phase comes along with the definition of multiple scales of interest for indoor radon mapping in Switzerland. The analysis was done with a top-to-down resolution approach, from regional to local lev¬els in order to find the appropriate scales for modeling. In this sense, data partition was optimized in order to cope with stationary conditions of geostatistical models. Common methods of spatial modeling such as Κ Nearest Neighbors (KNN), variography and General Regression Neural Networks (GRNN) were proposed as exploratory tools. In the following section, different spatial interpolation methods were applied for a par-ticular dataset. A bottom to top method complexity approach was adopted and the results were analyzed together in order to find common definitions of continuity and neighborhood parameters. Additionally, a data filter based on cross-validation was tested with the purpose of reducing noise at local scale (the CVMF). At the end of the chapter, a series of test for data consistency and methods robustness were performed. This lead to conclude about the importance of data splitting and the limitation of generalization methods for reproducing statistical distributions. The last section was dedicated to modeling methods with probabilistic interpretations. Data transformation and simulations thus allowed the use of multigaussian models and helped take the indoor radon pollution data uncertainty into consideration. The catego-rization transform was presented as a solution for extreme values modeling through clas-sification. Simulation scenarios were proposed, including an alternative proposal for the reproduction of the global histogram based on the sampling domain. The sequential Gaussian simulation (SGS) was presented as the method giving the most complete information, while classification performed in a more robust way. An error measure was defined in relation to the decision function for data classification hardening. Within the classification methods, probabilistic neural networks (PNN) show to be better adapted for modeling of high threshold categorization and for automation. Support vector machines (SVM) on the contrary performed well under balanced category conditions. In general, it was concluded that a particular prediction or estimation method is not better under all conditions of scale and neighborhood definitions. Simulations should be the basis, while other methods can provide complementary information to accomplish an efficient indoor radon decision making.

Dosage optimization of treatments using population pharmacokinetic modeling and simulation.

Pharmacokinetic variability in drug levels represent for some drugs a major determinant of treatment success, since sub-therapeutic concentrations might lead to toxic reactions, treatment discontinuation or inefficacy. This is true for most antiretroviral drugs, which exhibit high inter-patient variability in their pharmacokinetics that has been partially explained by some genetic and non-genetic factors. The population pharmacokinetic approach represents a very useful tool for the description of the dose-concentration relationship, the quantification of variability in the target population of patients and the identification of influencing factors. It can thus be used to make predictions and dosage adjustment optimization based on Bayesian therapeutic drug monitoring (TDM). This approach has been used to characterize the pharmacokinetics of nevirapine (NVP) in 137 HIV-positive patients followed within the frame of a TDM program. Among tested covariates, body weight, co-administration of a cytochrome (CYP) 3A4 inducer or boosted atazanavir as well as elevated aspartate transaminases showed an effect on NVP elimination. In addition, genetic polymorphism in the CYP2B6 was associated with reduced NVP clearance. Altogether, these factors could explain 26% in NVP variability. Model-based simulations were used to compare the adequacy of different dosage regimens in relation to the therapeutic target associated with treatment efficacy. In conclusion, the population approach is very useful to characterize the pharmacokinetic profile of drugs in a population of interest. The quantification and the identification of the sources of variability is a rational approach to making optimal dosage decision for certain drugs administered chronically.

The Individualized Genetic Barrier Predicts Treatment Response in a Large Cohort of HIV-1 Infected Patients.

The success of combination antiretroviral therapy is limited by the evolutionary escape dynamics of HIV-1. We used Isotonic Conjunctive Bayesian Networks (I-CBNs), a class of probabilistic graphical models, to describe this process. We employed partial order constraints among viral resistance mutations, which give rise to a limited set of mutational pathways, and we modeled phenotypic drug resistance as monotonically increasing along any escape pathway. Using this model, the individualized genetic barrier (IGB) to each drug is derived as the probability of the virus not acquiring additional mutations that confer resistance. Drug-specific IGBs were combined to obtain the IGB to an entire regimen, which quantifies the virus' genetic potential for developing drug resistance under combination therapy. The IGB was tested as a predictor of therapeutic outcome using between 2,185 and 2,631 treatment change episodes of subtype B infected patients from the Swiss HIV Cohort Study Database, a large observational cohort. Using logistic regression, significant univariate predictors included most of the 18 drugs and single-drug IGBs, the IGB to the entire regimen, the expert rules-based genotypic susceptibility score (GSS), several individual mutations, and the peak viral load before treatment change. In the multivariate analysis, the only genotype-derived variables that remained significantly associated with virological success were GSS and, with 10-fold stronger association, IGB to regimen. When predicting suppression of viral load below 400 cps/ml, IGB outperformed GSS and also improved GSS-containing predictors significantly, but the difference was not significant for suppression below 50 cps/ml. Thus, the IGB to regimen is a novel data-derived predictor of treatment outcome that has potential to improve the interpretation of genotypic drug resistance tests.

Genetic abnormalities and survival in multiple myeloma: the experience of the Intergroupe Francophone du Myélome.

Acquired genomic aberrations have been shown to significantly impact survival in several hematologic malignancies. We analyzed the prognostic value of the most frequent chromosomal changes in a large series of patients with newly diagnosed symptomatic myeloma prospectively enrolled in homogeneous therapeutic trials. All the 1064 patients enrolled in the IFM99 trials conducted by the Intergroupe Francophone du Myélome benefited from an interphase fluorescence in situ hybridization analysis performed on purified bone marrow plasma cells. They were systematically screened for the following genomic aberrations: del(13), t(11;14), t(4;14), hyperdiploidy, MYC translocations, and del(17p). Chromosomal changes were observed in 90% of the patients. The del(13), t(11;14), t(4;14), hyperdiploidy, MYC translocations, and del(17p) were present in 48%, 21%, 14%, 39%, 13%, and 11% of the patients, respectively. After a median follow-up of 41 months, univariate statistical analyses revealed that del(13), t(4;14), nonhyperdiploidy, and del(17p) negatively impacted both the event-free survival and the overall survival, whereas t(11;14) and MYC translocations did not influence the prognosis. Multivariate analyses on 513 patients annotated for all the parameters showed that only t(4;14) and del(17p) retained prognostic value for both the event-free and overall survivals. When compared with the currently used International Staging System, this prognostic model compares favorably. In myeloma, the genomic aberrations t(4;14) and del(17p), together with beta2-microglobulin level, are important independent predictors of survival. These findings have implications for the design of risk-adapted treatment strategies.

Combined effect of 25-OH vitamin D plasma levels and genetic vitamin D receptor (NR 1I1) variants on fibrosis progression rate in HCV patients.

BACKGROUND: Decreased vitamin D levels have been described in various forms of chronic liver disease and associated with advanced fibrosis. Whether this association is a cause or consequence of advanced fibrosis remains unclear to date. AIMS: To analyse combined effects of 25-OH vitamin D plasma levels and vitamin D receptor gene (VDR; NR1I1) polymorphisms on fibrosis progression rate in HCV patients. METHODS: 251 HCV patients underwent VDR genotyping (bat-haplotype: BsmI rs1544410 C, ApaI rs7975232 A and TaqI rs731236 A). Plasma 25-OH vitamin D levels were quantified in a subgroup of 97 patients without advanced fibrosis. The VDR haplotype and genotypes as well as plasma 25-OH vitamin D levels were associated with fibrosis progression. RESULTS: The bAt[CCA]-haplotype was significantly associated with fibrosis progression >0.101 U/year (P = 0.007; OR = 2.02) and with cirrhosis (P = 0.022; OR = 1.84). Forty-five percent of bAt[CCA]-haplotype patients were rapid fibrosers, 21.1% were cirrhotic. Likewise, ApaI rs7975232 CC genotype was significantly associated with fibrosis progression and cirrhosis. Lower plasma 25-OH vitamin D levels were significantly associated with fibrosis progression >0.101 U/year in F0-2 patients (P = 0.013). Combined analysis of both variables revealed a highly significant additive effect on fibrosis progression with 45.5% rapid fibrosers for bAt[CCA]-haplotype and 25-OH vitamin D < 20 μg/L compared with only 9.1% for the most favourable combination (P = 0.006). In multivariate analysis, the bAt-haplotype was an independent risk factor for fibrosis progression (P = 0.001; OR = 2.83). CONCLUSION: Low 25-OH vitamin D plasma levels and the unfavourable VDR bAt[CCA]-haplotype are associated with rapid fibrosis progression in chronic HCV patients. In combination, both variables exert significant additive effects on fibrosis progression.

Multivariate analyses of genotype x environment interaction of popcorn

The objectives of this work were to evaluate the genotype x environment (GxE) interaction for popcorn and to compare two multivariate analyses methods. Nine popcorn cultivars were sown on four dates one month apart during each of the agricultural years 1998/1999 and 1999/2000. The experiments were carried out using randomized block designs, with four replicates. The cv. Zélia contributed the least to the GxE interaction. The cv. Viçosa performed similarly to cv. Rosa-claro. Optimization of GxE was obtained for cv. CMS 42 for a favorable mega-environment, and for cv. CMS 43 for an unfavorable environment. Multivariate analysis supported the results from the method of Eberhart & Russell. The graphic analysis of the Additive Main effects and Multiplicative Interaction (AMMI) model was simple, allowing conclusions to be made about stability, genotypic performance, genetic divergence between cultivars, and the environments that optimize cultivar performance. The graphic analysis of the Genotype main effects and Genotype x Environment interaction (GGE) method added to AMMI information on environmental stratification, defining mega-environments and the cultivars that optimized performance in those mega-environments. Both methods are adequate to explain the genotype x environment interactions.

Divergence and genetic variability among superior rubber tree genotypes

The objective of this work was to estimate the genetic variability and divergence among 22 superior rubber tree (Hevea sp.) genotypes of the IAC 400 series. Univariate and multivariate analyses were performed using eight quantitative traits (descriptors), including yield. In the univariate analyses, the estimated parameters were: genetic and environmental variances; genetic and environmental coefficients of variation; and the variation index. The Mahalanobis generalized distance, the Tocher agglomerative method and canonical variables were used for the multivariate analyses. In the univariate analyses, variability was verified among the genotypes for all the variables evaluated. The Tocher method grouped the genotypes into 11 clusters of dissimilarity. The first four canonical variables explained 87.93% of the cumulative variation. The highest genetic variability was found in rubber yield-related traits, which contributed the most to the genetic divergence. The most divergent pairs of genotypes are suggested for crossbreeding. The genotypes evaluated are suitable for breeding and may be used to continue the IAC rubber tree breeding program.