Publishing reproducible dynamic kinetic models

Signal integration and integral feedback control with biochemical reaction networks

Biochemical reaction networks perform a variety of signal processing functions, one of which is computing the integrals of signal values. This is often used in integral feedback control, where it enables a system's output to respond to changing inputs, but to then return exactly back to some pre-determined setpoint value afterward. To gain a deeper understanding of how biochemical networks are able to both integrate signals and perform integral feedback control, we investigated these abilities for several simple reaction networks. We found imperfect overlap between these categories, with some networks able to perform both tasks, some able to perform integration but not integral feedback control, and some the other way around. Nevertheless, networks that could either integrate or perform integral feedback control shared key elements. In particular, they included a chemical species that was neutrally stable in the open loop system (no feedback), meaning that this species does not have a unique stable steady-state concentration. Neutral stability could arise from zeroth order decay reactions, binding to a partner that was produced at a constant rate (which occurs in antithetic control), or through a long chain of covalent cycles. Mathematically, it arose from rate equations for the reaction network that were underdetermined when evaluated at steady-state.

Reproducibility and FAIR principles: the case of a segment polarity network model

The issue of reproducibility of computational models and the related FAIR principles (findable, accessible, interoperable, and reusable) are examined in a specific test case. I analyze a computational model of the segment polarity network in Drosophila embryos published in 2000. Despite the high number of citations to this publication, 23 years later the model is barely accessible, and consequently not interoperable. Following the text of the original publication allowed successfully encoding the model for the open source software COPASI. Subsequently saving the model in the SBML format allowed it to be reused in other open source software packages. Submission of this SBML encoding of the model to the BioModels database enables its findability and accessibility. This demonstrates how the FAIR principles can be successfully enabled by using open source software, widely adopted standards, and public repositories, facilitating reproducibility and reuse of computational cell biology models that will outlive the specific software used.

Probabilistic models of uORF-mediated ATF4 translation control

ATF4 is a key transcription factor that activates transcription of genes needed to respond to cellular stress. Although the mRNA encoding ATF4 is present at constant levels in the cell during the initial response, translation of ATF4 increases under conditions of cellular stress while the global translation rate decreases. We study two models for the control system that regulates the translation of ATF4, both based on the Vattem-Wek hypothesis. This hypothesis is based on a race to reload, following the translation of a small upstream open reading frame (uORF), the ternary complex that brings the initiator tRNA to the ribosome as the 40S subunit scans along the mRNA, encountering first a start codon for an inhibitory uORF whose reading frame overlaps the start of the ATF4 coding sequence. We develop a pair of simple, analytic, probabilistic models, one of which assumes all nucleotide triplets have identical kinetic properties, while the other recognizes the existence of triplets at which the ternary complex loads more efficiently. We also consider two different functions representing the dependence of the rate of initiation at uORF1 on the ternary complex concentration. In keeping with the theme of this Special Issue, we studied the properties of these models in a Maple document, which can easily be modified to consider different parameters, translation rate initiation functions, and so on.