The utility of simple mathematical models in understanding gene regulatory dynamics

Abstract

In this review, we survey work that has been carried out in the attempts of biomathematicians to understand the dynamic behaviour of simple bacterial operons starting with the initial work of the 1960’s. We concentrate on the simplest of situations, discussing both repressible and inducible systems and then turning to concrete examples related to the biology of the lactose and tryptophan operons. We conclude with a brief discussion of the role of both extrinsic noise and so-called intrinsic noise in the form of translational and/or transcriptional bursting.

Towards Simulating Carcinogenesis: Modeling and Simulating Carcinogenesis, Hematopoietic Tissue Homeostasis and Leukemogenesis

“…It comprises the analysis, visualization, and prediction of natural processes by collecting, cataloging, altering and modeling data employing algorithms and computation (Nature 2016). Computational analysis thereby allows the processing of huge amounts of data as well as the performance of highly theoretical studies and experiments under precise and selected conditions to avoid disturbance variables and to minimize the complexity of biological events (Mackey et al 2015).…”

“…First, they can serve as a tool to develop patterns derived from empirical measures and exploit the full information hidden in gathered data. Examples are the construction of probability functions for parameter inference or the examination of correlations between different parameters, for instance, via linear regression analysis (Mackey et al 2015;Blokh & Stambler 2016;Suthaharan 2016). Second, mathematical models can serve as "proof-of-concept tests" of logical predictions in verbal hypotheses and represent valid tests themselves to evolve further testable quantitative predictions.…”

“…At last, the described methods cannot only abstract complex data, but they can also provide new qualitative data to be further elaborated in empirical research. For instance, unknown or underestimated phenomena can be discovered, or assumptions hidden in a verbal hypothesis can be detected, as the synthetic system, different from a logical chain, can also show counterintuitive outcomes (Mackey et al 2015).…”

“…As Evolution is known to be a complex multi-parametric process with a large time scale, mathematical models are widely utilized as a solution to the analysis and simulation of evolutionary developments (Mackey et al 2015).…”

“…This way simulated organisms can be observed during competition and reproduction, while phenomena like "linkage, epistasis, demographic and environmental variability and behavior" (Mackey et al 2015) are considered. Total control is given by the possibility to apply random, handwritten or former evolved genomes and to set e.g.…”