Towards Modular, Scalable and Optimal Design of Transcriptional Logic Systems

Living organisms can perform computations through various mechanisms. Understanding the limitations of these computations is not only of practical relevance (for example in the context of synthetic biology) but will most of all provide new insights into the design principles of living systems. This thesis investigates the conditions under which genes can perform logical computations and how this behaviour can be enhanced. In particular, we identified three properties which characterise genes as computational units, namely: the noise of the gene expression, the slow response times and the energy cost of the logical operation. This study examined how biological parameters control the computational properties of genes and what is the functional relationship between various computational properties. Specifically, we found that there is a three-way trade-off between speed, accuracy and metabolic cost, in the sense that under fixed metabolic cost the speed can be increased only by reducing the accuracy and vice-versa. Furthermore, higher metabolic cost resulted in better trade-offs between speed and accuracy. In addition, we showed that genes with leak expression are sub-optimal compared with leak-free genes. However, the cost to reduce the leak rate can be significant and, thus, genes prefer to handle poorer speed-accuracy behaviour than to increase the energy cost. Moreover, we identified another accuracy-speed trade-off under fixed metabolic cost, but this time the trade-off is controlled by the position of the switching threshold of the gene. In particular, there are two optimal configurations, one for speed and another one for accuracy, and all configurations in between lie on an optimal trade-off curve. Finally, we showed that a negatively auto-regulated gene can display better trade-offs between speed and accuracy compared with a simple one (a gene without feedback) when the two systems have equal metabolic cost. This optimality of the negative auto-regulation is controlled by the leak rate of the gene, in the sense that higher leak rates lead to faster systems and lower leak rates to more accurate ones. This in conjunction with the fact that many genes display low but non-vanishing leak rates can indicate the reason why negative auto-regulation is a network motif (has high occurrence in genetic networks). These trade-offs that we identified in this thesis indicate that there are some physical limits which constrain the computations performed by genes and further enhancement usually comes at the cost of impairing at least one property.