PROKARYO: an illustrative and interactive computational model of the lactose operon in the bacterium Escherichia coli

Abstract

BackgroundWe are creating software for agent-based simulation and visualization of bio-molecular processes in bacterial and eukaryotic cells. As a first example, we have built a 3-dimensional, interactive computer model of an Escherichia coli bacterium and its associated biomolecular processes. Our illustrative model focuses on the gene regulatory processes that control the expression of genes involved in the lactose operon. Prokaryo, our agent-based cell simulator, incorporates cellular structures, such as plasma membranes and cytoplasm, as well as elements of the molecular machinery, including RNA polymerase, messenger RNA, lactose permease, and ribosomes.ResultsThe dynamics of cellular ’agents’ are defined by their rules of interaction, implemented as finite state machines. The agents are embedded within a 3-dimensional virtual environment with simulated physical and electrochemical properties. The hybrid model is driven by a combination of (1) mathematical equations (DEQs) to capture higher-scale phenomena and (2) agent-based rules to implement localized interactions among a small number of molecular elements. Consequently, our model is able to capture phenomena across multiple spatial scales, from changing concentration gradients to one-on-one molecular interactions.We use the classic gene regulatory mechanism of the lactose operon to demonstrate our model’s resolution, visual presentation, and real-time interactivity. Our agent-based model expands on a sophisticated mathematical E. coli metabolism model, through which we highlight our model’s scientific validity.ConclusionWe believe that through illustration and interactive exploratory learning a model system like Prokaryo can enhance the general understanding and perception of biomolecular processes. Our agent-DEQ hybrid modeling approach can also be of value to conceptualize, illustrate, and—eventually—validate cell experiments in the wet lab.

Cis-Regulatory Logic Produces Gene-Expression Noise Describing Phenotypic Heterogeneity in Bacteria

“…It consists of four components: a regulatory gene, operator(s), promoter, and structural genes ( Conway et al, 2014 ). The discovery of the lac -operon model aided to decode complex coordination in bacteria ( Esmaeili et al, 2015 ). In bacteria, gene regulation primarily facilitates adjustment and adaptation to nutritional changes aiding their optimized growth ( Blake et al, 2006 ; Cheng et al, 2017 ).…”

“…CREs are regulatory DNA sequences that include enhancers and promoters that regulate gene expression on the same chromosome (Park and Wang, 2018). Noise can also be generated during translation when individual mRNAs within a cell fluctuate randomly (Bar-Even et al, 2006;Silander et al, 2012;Espinar et al, 2017). However, these are not gene-specific and, thus, do not directly regulate CREs.…”

Changes in students’ mental models from computational modeling of gene regulatory networks

“…Typically, students learn about the trp and lac operons, which have different regulatory mechanisms: the trp operon is repressible and the lac operon is inducible (Stefanski et al 2016). The long-term benefit for students is to establish a foundation about how molecular components work together to regulate gene expression and, as students advance in their curricula, allow students to apply this general mental model to other gene regulatory networks (Esmaeili et al 2015).…”

A toolbox for discrete modelling of cell signalling dynamics

“…The application of standard mathematical modelling, such as through stochastic or ordinary differential equations (ODEs), have been faithfully reproducing the interplay between genes and proteins in small regulatory networks with relative success. Prominent examples of ODE models include that of bacterial chemotaxis 1 , the lactose operon control system in Escherichia coli 2 and the process of X chromosome inactivation 3 , the cell cycle in yeast 4 , and the generation of amyloid fibrils 5 .Such models employ complex kinetic equations to describe relationships between proteins or genes over time, and require highly accurate and intensive experimental data for their development as input. The complexity of such equations and experimental data required can provide a lot of dynamical detail however this complexity also begs the question of whether this approach will scale well when constructing much larger, more intricate networks in the future.…”