Mechanistic mathematical modeling

P. C. R. Fontes, S. A. Barber, and G. E. Wilcox, Prediction of phosphorus uptake by two tomato cultivars growing under sufficient and insufficient phosphorus soil conditions using a mechanistic mathematical model. Plant Soil. 94 81 (1986). 

Stephens, N., Flynn, K. J., and Gallon, J. R. (2003). Interrelationships between the pathways of inorganic nitrogen assimilation in the cyanobacterium Gloeothece can be described using a mechanistic mathematical model. New Phytol. 160, 545—555. 

The fundamental concepts used to mathematically represent mechanistic mathematical models are borrowed from chemical reaction kinetics and transport phenomena.1920 However, the application of these concepts in biology requires an understanding of the biological literature. The biological data to build a mechanistic model of mAh action typically include... 

The application of mechanistic mathematical models for determining the properties of the therapeutic mAbs can help in maximizing the efficacy of the mAb. 

Inhibition of the biological function of the target antigen is a general safety concern and mechanistic mathematical modeling can help in optimally designing dosage and affinity of the therapeutic mAb. A mechanistic... 

In addition to injection-site reactions, other mild to moderate reactions include fever, dizziness, sweating, and nausea. Low incidences of severe infusion reactions (e.g., hypotension, cardiac dysfunction, anaphylaxis, and bron-chospasms) have also been reported with Rituximab, Cetuximab, and even with humanized mAb Trastuzumab.46 Once again, the underlying mechanisms are poorly understood, limiting the application of mechanistic mathematical modeling for predicting infusion site reactions. 

In conclusion, mechanistic mathematical modeling can help testing the feasibility of a mAb approach to treat a disease and picking the mAb properties for optimal therapeutic index. As a result, the use of mechanistic mathematical models in drug discovery will lead to reduction in clinical attrition by increasing the chance of producing a safe and effective drug. 

ModEst (from Model Estimation) is another software (Figure 10.28) that has been designed for parameter estimation of mechanistic mathematical models as well as for experimental design. 

Due to the central role of caspases in cancer, and in nem odegenerative and autoimmune disorders, they ai e subject to intense studies. A mechanistic mathematical model was formulated on the basis of newly emerging information, describing key elements of receptor-mediated and stress-induced caspase activation. Mass-conservation principles were used in conjunction witli kinetic rate laws to formulate ordinaiy differential equations that describe the temporal evolution of caspase activation. Qualitative strategies for the prevention of... 

Howell BA, Yang Y, Kumar R, Woodhead JL, Harrill AH, Clewell HJ in, Andersen ME, SUer SQ, Watkins PB. 2012. In vitro to in vivo extrapolation and species response comparisons for drug-induced liver injury (DILI) using DILIsym a mechanistic, mathematical model of DILI. J Pharmacokinet Pharmacodyn 39 527-541. 

Yang Y, Nadanaciva S, Will Y, Woodhead JL, Howell BA, Watkins PB, Siler SQ (2015) MITOsym a mechanistic, mathematical model of hepatocellnlar respiration and bioenergetics. Pharm Res 32, 1975-92. 

To determine the extent of bloating or expansion in an industrial rotary kiln, one must carry out laboratory tests using bench scale furnaces for the evolution kinetics and further correlation tests in a pilot rotary kiln for appropriate temperature profiles. The temporal events determined are, in turn, used to plan quarry operations for product quality control. The same data may also be useful in developing a mechanistic mathematical model that can predict temperature distribution and density changes in the raw material as they journey through the kiln (Boateng et al., 1997). Such tools have proven to be useful for the control of product quality as new mines are explored or even as different strata of the existing mine are explored for feedstock. Some of these time-temperature histories are discussed herein. 

Fortunately, the literature discusses that creep lifetime for p-aramid (Kevlar ), a cousin to PBO, may be represented by a mechanistic mathematical model of the material failure phenomenon. Although the failure mechanism(s) may be different for PBO, the... 

---