Models in biology: 'accurate descriptions of our pathetic thinking'

Abstract

In this essay I will sketch some ideas for how to think about models in biology. I will begin by trying to dispel the myth that quantitative modeling is somehow foreign to biology. I will then point out the distinction between forward and reverse modeling and focus thereafter on the former. Instead of going into mathematical technicalities about different varieties of models, I will focus on their logical structure, in terms of assumptions and conclusions. A model is a logical machine for deducing the latter from the former. If the model is correct, then, if you believe its assumptions, you must, as a matter of logic, also believe its conclusions. This leads to consideration of the assumptions underlying models. If these are based on fundamental physical laws, then it may be reasonable to treat the model as 'predictive', in the sense that it is not subject to falsification and we can rely on its conclusions. However, at the molecular level, models are more often derived from phenomenology and guesswork. In this case, the model is a test of its assumptions and must be falsifiable. I will discuss three models from this perspective, each of which yields biological insights, and this will lead to some guidelines for prospective model builders.

Figure 1

Creation of non-identical compartments. Schematic of the Heinrich–Rapoport model, from [23, Figure one], with the distribution of SNAREs corresponding approximately to the steady state with non-identical compartments. Ⓒ2005 Heinrich and Rapoport. Originally published in Journal of Cell Biology, 168:271-280, doi:10.1083/jcb.200409087. SNARE, soluble N-ethyl-maleimide-sensitive factor attachment protein receptor.

Figure 2

Discrimination by the T-cell receptor. Schematic of the Altan-Bonnet–Germain model from [29, Figure two A], showing a kinetic proofreading scheme through a sequence of tyrosine phosphorylations, which is triggered by the binding of the TCR to pMHC, linked with a negative feedback loop through the tyrosine phosphatase SHP-1 and a positive feedback loop through MAPK. MAPK, mitogen-activated protein kinase; pMHC, peptide-major histocompatibility complex; P, singly phosphorylated; PP, multiply phosphorylated; SHP-1, SH2 domain-containing tyrosine phosphatase-1; TCR, T-cell receptor.

Figure 3

The somitogenesis clock. Top: A zebrafish embryo at the ten-somite stage, stained by in situ hybridization for mRNA of the Notch ligand DeltaC, taken from [47, Figure one]. Bottom left: Potential auto-regulatory mechanisms in the zebrafish, taken from [47, Figure three A,B]. In the upper mechanism, the Her1 protein dimerizes before repressing its own transcription. In the lower mechanism, Her1 and Her7 form a heterodimer, which represses transcription of both genes, which occur close to each other but are transcribed in opposite directions. Explicit transcription and translation delays are shown, which are incorporated in the corresponding models. Bottom right: Mouse embryos stained by in situ hybridization for Uncx4.1 mRNA, a homeobox gene that marks somites, taken from [52, Figure four].