Reverse Automatic Differentiation for Optimum Design: from Adjoint State Assembly to Gradient Computation

The utilization of reverse mode Automatic Differentiation to the adjoint method for solving an Optimal Design problem is described. Using the reverse mode, we obtain the adjoint system residual in a rather efficient way. But memory requirements may be very large. The family of programs to differentiate involves many independant calculations, typically in parallel loops. Then we propose to apply a reverse differentiation «by iteration». This demands much less memory storage. This methods is used for the computing of the adjoint state and gradient related to the Optimal Design problem

Polymorphisms within the adenosine receptor 2a gene are associated with adverse events in RA patients treated with MTX

Objective. To examine the role of adenosine receptor 2a gene (ADORA2a) polymorphisms on outcome of MTX treatment in RA

AD-based perturbation methods for uncertainties and errors

International audienceThe progress of Automatic Differentiation ({\bf AD}) and its impact on perturbation methods is the object of this paper. AD studies show an important activity for developing methods addressing the management of modern CFD kernels, taking into account the language evolution, and intensive parallel computing. The evaluation of a posteriori error analysis and of resulting correctors will be addressed. Recents works in the AD-based contruction of second-derivatives for building reduced-order models based on a Taylor formula will be presented on the test case of a steady compressible flow around an aircraft

Mechanistic mathematical modelling of mercaptopurine effects on cell cycle of human acute lymphoblastic leukaemia cells

The antimetabolite mercaptopurine (MP) is widely used to treat childhood acute lymphoblastic leukaemia (ALL). To study the dynamics of MP on the cell cycle, we incubated human T-cell leukaemia cell lines (Molt-4 sensitive and resistant subline and P12 resistant) with 10 μM MP and measured total cell count, cell cycle distribution, percent viable, percent apoptotic, and percent dead cells serially over 72 h. We developed a mathematical model of the cell cycle dynamics after treatment with MP and used it to show that the Molt-4 sensitive controls had a significantly higher rate of cells entering apoptosis (2.7-fold, P<0.00001) relative to the resistant cell lines. Additionally, when treated with MP, the sensitive cell line showed a significant increase in the rate at which cells enter apoptosis compared to its controls (2.4-fold, P<0.00001). Of note, the resistant cell lines had a higher rate of antimetabolite incorporation into the DNA of viable cells (>1.4-fold, P<0.01). Lastly, in contrast to the other cell lines, the Molt-4 resistant subline continued to cycle, though at a rate slower relative to its control, rather than proceed to apoptosis. This led to a larger S-phase block in the Molt-4 resistant cell line, but not a higher rate of cell death. Gene expression of apoptosis, cell cycle, and repair genes were consistent with mechanistic dynamics described by the model. In summary, the mathematical model provides a quantitative assessment to compare the cell cycle effects of MP in cells with varying degrees of MP resistance

Modeling Mechanisms of In Vivo Variability in Methotrexate Accumulation and Folate Pathway Inhibition in Acute Lymphoblastic Leukemia Cells

Methotrexate (MTX) is widely used for the treatment of childhood acute lymphoblastic leukemia (ALL). The accumulation of MTX and its active metabolites, methotrexate polyglutamates (MTXPG), in ALL cells is an important determinant of its antileukemic effects. We studied 194 of 356 patients enrolled on St. Jude Total XV protocol for newly diagnosed ALL with the goal of characterizing the intracellular pharmacokinetics of MTXPG in leukemia cells; relating these pharmacokinetics to ALL lineage, ploidy and molecular subtype; and using a folate pathway model to simulate optimal treatment strategies. Serial MTX concentrations were measured in plasma and intracellular MTXPG concentrations were measured in circulating leukemia cells. A pharmacokinetic model was developed which accounted for the plasma disposition of MTX along with the transport and metabolism of MTXPG. In addition, a folate pathway model was adapted to simulate the effects of treatment strategies on the inhibition of de novo purine synthesis (DNPS). The intracellular MTXPG pharmacokinetic model parameters differed significantly by lineage, ploidy, and molecular subtypes of ALL. Folylpolyglutamate synthetase (FPGS) activity was higher in B vs T lineage ALL (p<0.005), MTX influx and FPGS activity were higher in hyperdiploid vs non-hyperdiploid ALL (p<0.03), MTX influx and FPGS activity were lower in the t(12;21) (ETV6-RUNX1) subtype (p<0.05), and the ratio of FPGS to γ-glutamyl hydrolase (GGH) activity was lower in the t(1;19) (TCF3-PBX1) subtype (p<0.03) than other genetic subtypes. In addition, the folate pathway model showed differential inhibition of DNPS relative to MTXPG accumulation, MTX dose, and schedule. This study has provided new insights into the intracellular disposition of MTX in leukemia cells and how it affects treatment efficacy

Drug-microbiota interactions and treatment response: Relevance to rheumatoid arthritis

Knowledge about associations between changes in the structure and/or function of intestinal microbes (the microbiota) and the pathogenesis of various diseases is expanding. However, interactions between the intestinal microbiota and different pharmaceuticals and the impact of these on responses to treatment are less well studied. Several mechanisms are known by which drug-microbiota interactions can influence drug bioavailability, efficacy, and/or toxicity. This includes direct activation or inactivation of drugs by microbial enzymes which can enhance or reduce drug effectiveness. The extensive metabolic capabilities of the intestinal microbiota make it a hotspot for drug modification. However, drugs can also influence the microbiota profoundly and change the outcome of interactions with the host. Additionally, individual microbiota signatures are unique, leading to substantial variation in host responses to particular drugs. In this review, we describe several known and emerging examples of how drug-microbiota interactions influence the responses of patients to treatment for various diseases, including inflammatory bowel disease, type 2 diabetes and cancer. Focussing on rheumatoid arthritis (RA), a chronic inflammatory disease of the joints which has been linked with microbial dysbiosis, we propose mechanisms by which the intestinal microbiota may affect responses to treatment with methotrexate which are highly variable. Furthering our knowledge of this subject will eventually lead to the adoption of new treatment strategies incorporating microbiota signatures to predict or improve treatment outcomes