Maximizing average throughput in oscillatory biochemical synthesis systems: an optimal control approach

Perfect control for nonminimum-phase unstable systems defined in the multivariable continuous-time state-space framework - An inverse-based approach

In this paper, a new perfect control law dedicated to nonminimum-phase unstable LTI MIMO systems governed in the continuous-time state-space domain is proposed. Two algorithms are investigated, one of which has turned out to be definitely accurate. Henceforth, the inverse model control-based formula can be applied to any right-invertible plants having more input than output variables. Last, not least, through the application of some generalized inverses, the perfect control procedure guarantees the structural stability behavior even for unstable systems. Thus, the notion of the nonminimum-phase property should be understood in terms of a possible achieveability covering the entire class of LTI MIMO continuous-time plants. Theoretical and practical simulation examples performed in the Matlab/Simulink environment confirm the feasibility of the newly introduced approach.

On the gain of entrainment in the n-dimensional ribosome flow model

The ribosome flow model (RFM) is a phenomenological model for the flow of particles along a one-dimensional chain of n sites. It has been extensively used to study ribosome flow along the mRNA molecule during translation. When the transition rates along the chain are time-varying and jointly T-periodic the RFM entrains, i.e. every trajectory of the RFM converges to a unique T-periodic solution that depends on the transition rates, but not on the initial condition. In general, entrainment to periodic excitations like the 24 h solar day or the 50 Hz frequency of the electric grid is important in numerous natural and artificial systems. An interesting question, called the gain of entrainment (GOE) in the RFM, is whether proper coordination of the periodic translation rates along the mRNA can lead to a larger average protein production rate. Analysing the GOE in the RFM is non-trivial and partial results exist only for the RFM with dimensions n = 1, 2. We use a new approach to derive several results on the GOE in the general n-dimensional RFM. Perhaps surprisingly, we rigorously characterize several cases where there is no GOE, so to maximize the average production rate in these cases, the best choice is to use constant transition rates all along the chain.

Translation in the cell under fierce competition for shared resources: a mathematical model

During translation, mRNAs 'compete' for shared resources. Under stress conditions, during viral infection and also in high-throughput heterologous gene expression, these resources may become scarce, e.g. the pool of free ribosomes is starved, and then the competition may have a dramatic effect on the global dynamics of translation in the cell. We model this scenario using a network that includes m ribosome flow models (RFMs) interconnected via a pool of free ribosomes. Each RFM models ribosome flow along an mRNA molecule, and the pool models the shared resource. We assume that the number of mRNAs is large, so many ribosomes are attached to the mRNAs, and the pool is starved. Our analysis shows that adding an mRNA has an intricate effect on the total protein production. The new mRNA produces new proteins, but the other mRNAs produce less proteins, as the pool that feeds these mRNAs now has a smaller abundance of ribosomes. As the number of mRNAs increases, the marginal utility of adding another mRNA diminishes, and the total protein production rate saturates to a limiting value. We demonstrate our approach using an example of insulin protein production in a cell-free system.

A theoretical framework to analyse the flow of particles in a dynamical system with stochastic transition rates and site capacities

We study the stochasticity in a dynamical model: ribosome flow model with different site sizes that models the unidirectional movement of particles controlled by transition rates along a lattice having different site sizes. Our work models the parameters as random variables with known distributions and investigates the steady-state flow rate under this notion by using tools from the random matrix theory. Some closed-form theoretical results are derived for the steady-state flow rate under some restrictive assumptions such as random variables being independent and identically distributed. Furthermore, for arbitrary but bounded stochastic transition rates, stochastic site capacities, or both, we establish bounds for the steady-state flow rate. Our analysis can be generalized and applied to study the flow of particles in numerous transport systems in the stochastic environment.

Large-scale mRNA translation and the intricate effects of competition for the finite pool of ribosomes

We present a new theoretical framework for large-scale mRNA translation using a network of models called the ribosome flow model with Langmuir kinetics (RFMLK), interconnected via a pool of free ribosomes. The input to each RFMLK depends on the pool density, and it affects the initiation rate and potentially also the internal ribosome entry rates along each RFMLK. Ribosomes that detach from an RFMLK owing to termination or premature drop-off are fed back into the pool. We prove that the network always converges to a steady state, and study its sensitivity to variations in the parameters. For example, we show that if the drop-off rate at some site in some RFMLK is increased then the pool density increases and consequently the steady-state production rate in all the other RFMLKs increases. Surprisingly, we also show that modifying a parameter of a certain RFMLK can lead to arbitrary effects on the densities along the modified RFMLK, depending on the parameters in the entire network. We conclude that the competition for shared resources generates an indirect and intricate web of mutual effects between the mRNA molecules that must be accounted for in any analysis of translation.