Mathematical modeling and synthetic biology

Abstract

Synthetic biology is an engineering discipline that builds on our mechanistic understanding of molecular biology to program microbes to carry out new functions. Such predictable manipulation of a cell requires modeling and experimental techniques to work together. The modeling component of synthetic biology allows one to design biological circuits and analyze its expected behavior. The experimental component merges models with real systems by providing quantitative data and sets of available biological 'parts' that can be used to construct circuits. Sufficient progress has been made in the combined use of modeling and experimental methods, which reinforces the idea of being able to use engineered microbes as a technological platform.

Figure 1

Enzyme-catalyzed reaction. The enzyme, E, converts the substrate, S, to the product, P. The enzyme and substrate form an intermediate complex, ES, which can dissociate back to E and S or form P and free the enzyme, E. This model treats the production of P from the ES complex as an irreversible reaction because the reversible reaction rate may be negligible.

Figure 2

Gene regulation. The transcription factor, TF, binds to the operator sequence and controls the production of the gene product, P. This model is similar to the one shown in Fig. 1; TF takes the place of E, the promoter takes the place of S, and the product, P, remains the same.

Figure 3

Standard BioBrick Assembly. Parts A and B are ligated together through a standard assembly protocol. The first plasmid is digested with EcoRI (E) and SpeI (S), while the second plasmid is digested with EcoRI (E) and XbaI (X). After ligation, a new plasmid is formed with both parts in tandem with a ‘scar’ which does not contain a restriction enzyme recognition site. The PstI site (P) is left unused in this scheme, but could be used if the parts were assembled in reverse order. (Figure adapted with permission from the MIT Registry of Standard Biological Parts.)

Figure 4

Screenshot of TinkerCell. The screenshot shows two models that are open. One (top left) is a feedback oscillator, and its simulated output is plotted below. The other window (bottom right) is a model consisting of a cell, membrane proteins, and gene regulation. See http://www.tinkercell.com/ for more information.

Figure 5

The repressilator constructed by Elowitz and Leibler [20]. Three genes produce repressor proteins. The cycle of repression causes the network to oscillate.

Figure 6

The robust oscillator constructed by Stricker et al. [18]. The combination of the negative and positive feedback causes the network to be robust to parameter changes. The strength of the repression (by lac inhibitor) can be controlled by the lactose analog, IPTG.

Figure 7

The incoherent feed-forward network constructed by Entus et al. [24]. The T7 RNA polymerase (RNAP) activates metJ and GFP, but metJ represses GFP. Thus, T7 RNAP directly activates GFP but indirectly repressed GFP, causing T7 RNAP to act as an activator or a repressor depending on its concentration.

Figure 8

A simplified design process for synthetic biology that would be possible in the future. Using computer-aided design (CAD) and database(s) of parts, a synthetic biologist can create multiple models that satisfy his or her idea. Using computational tools, the models can be analyzed in detail and modified as needed. Using efficient assembly procedures or DNA synthesis technology, the models can be built. If the design is modular, then the working product can be reused in another model.