Optimal parameter settings for information processing in gene regulatory networks

Periodic synchronization of isolated network elements facilitates simulating and inferring gene regulatory networks including stochastic molecular kinetics

Background

The temporal progression of many fundamental processes in cells and organisms, including homeostasis, differentiation and development, are governed by gene regulatory networks (GRNs). GRNs balance fluctuations in the output of their genes, which trace back to the stochasticity of molecular interactions. Although highly desirable to understand life processes, predicting the temporal progression of gene products within a GRN is challenging when considering stochastic events such as transcription factor–DNA interactions or protein production and degradation.

Results

We report a method to simulate and infer GRNs including genes and biochemical reactions at molecular detail. In our approach, we consider each network element to be isolated from other elements during small time intervals, after which we synchronize molecule numbers across all network elements. Thereby, the temporal behaviour of network elements is decoupled and can be treated by local stochastic or deterministic solutions. We demonstrate the working principle of this modular approach with a repressive gene cascade comprising four genes. By considering a deterministic time evolution within each time interval for all elements, our method approaches the solution of the system of deterministic differential equations associated with the GRN. By allowing genes to stochastically switch between on and off states or by considering stochastic production of gene outputs, we are able to include increasing levels of stochastic detail and approximate the solution of a Gillespie simulation. Thereby, CaiNet is able to reproduce noise-induced bi-stability and oscillations in dynamically complex GRNs. Notably, our modular approach further allows for a simple consideration of deterministic delays. We further infer relevant regulatory connections and steady-state parameters of a GRN of up to ten genes from steady-state measurements by identifying each gene of the network with a single perceptron in an artificial neuronal network and using a gradient decent method originally designed to train recurrent neural networks. To facilitate setting up GRNs and using our simulation and inference method, we provide a fast computer-aided interactive network simulation environment, CaiNet.

Conclusion

We developed a method to simulate GRNs at molecular detail and to infer the topology and steady-state parameters of GRNs. Our method and associated user-friendly framework CaiNet should prove helpful to analyze or predict the temporal progression of reaction networks or GRNs in cellular and organismic biology. CaiNet is freely available at https://gitlab.com/GebhardtLab/CaiNet.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04541-6.

Gene switching rate determines response to extrinsic perturbations in the self-activation transcriptional network motif

Gene switching dynamics is a major source of randomness in genetic networks, also in the case of large concentrations of the transcription factors. In this work, we consider a common network motif - the positive feedback of a transcription factor on its own synthesis - and assess its response to extrinsic noises perturbing gene deactivation in a variety of settings where the network might operate. These settings are representative of distinct cellular types, abundance of transcription factors and ratio between gene switching and protein synthesis rates. By investigating noise-induced transitions among the different network operative states, our results suggest that gene switching rates are key parameters to shape network response to external perturbations, and that such response depends on the particular biological setting, i.e. the characteristic time scales and protein abundance. These results might have implications on our understanding of irreversible transitions for noise-related phenomena such as cellular differentiation. In addition these evidences suggest to adopt the appropriate mathematical model of the network in order to analyze the system consistently to the reference biological setting.

In silico evolution of diauxic growth

Background

The glucose effect is a well known phenomenon whereby cells, when presented with two different nutrients, show a diauxic growth pattern, i.e. an episode of exponential growth followed by a lag phase of reduced growth followed by a second phase of exponential growth. Diauxic growth is usually thought of as a an adaptation to maximise biomass production in an environment offering two or more carbon sources. While diauxic growth has been studied widely both experimentally and theoretically, the hypothesis that diauxic growth is a strategy to increase overall growth has remained an unconfirmed conjecture.

Methods

Here, we present a minimal mathematical model of a bacterial nutrient uptake system and metabolism. We subject this model to artificial evolution to test under which conditions diauxic growth evolves.

Results

As a result, we find that, indeed, sequential uptake of nutrients emerges if there is competition for nutrients and the metabolism/uptake system is capacity limited.

Discussion

However, we also find that diauxic growth is a secondary effect of this system and that the speed-up of nutrient uptake is a much larger effect. Notably, this speed-up of nutrient uptake coincides with an overall reduction of efficiency.

Conclusions

Our two main conclusions are: (i) Cells competing for the same nutrients evolve rapid but inefficient growth dynamics. (ii) In the deterministic models we use here no substantial lag-phase evolves. This suggests that the lag-phase is a consequence of stochastic gene expression.

Adaptation for protein synthesis efficiency in a naturally occurring self-regulating operon

The korAB operon in RK2 plasmids is a beautiful natural example of a negatively and cooperatively self-regulating operon. It has been particularly well characterized both experimentally and with mathematical models. We have carried out a detailed investigation of the role of the regulatory mechanism using a biologically grounded mechanistic multi-scale stochastic model that includes plasmid gene regulation and replication in the context of host growth and cell division. We use the model to compare four hypotheses for the action of the regulatory mechanism: increased robustness to extrinsic factors, decreased protein fluctuations, faster response-time of the operon and reduced host burden through improved efficiency of protein production. We find that the strongest impact of all elements of the regulatory architecture is on improving the efficiency of protein synthesis by reduction in the number of mRNA molecules needed to be produced, leading to a greater than ten-fold reduction in host energy required to express these plasmid proteins. A smaller but still significant role is seen for speeding response times, but this is not materially improved by the cooperativity. The self-regulating mechanisms have the least impact on protein fluctuations and robustness. While reduction of host burden is evident in a plasmid context, negative self-regulation is a widely seen motif for chromosomal genes. We propose that an important evolutionary driver for negatively self-regulated genes is to improve the efficiency of protein synthesis.

Negative feedback and physical limits of genes

This paper compares the auto-repressed gene to a simple one (a gene without auto-regulation) in terms of response time and output noise under the assumption of fixed metabolic cost. The analysis shows that, in the case of non-vanishing leak expression rate, the negative feedback reduces both the switching on and switching off times of a gene. The noise of the auto-repressed gene will be lower than the one of the simple gene only for low leak expression rates. Summing up, for low, but non-vanishing leak expression rates, the auto-repressed gene is both faster and less noisier compared to the simple one.