Mathematical Model of the Firefly Luciferase Complementation Assay Reveals a Non-Linear Relationship between the Detected Luminescence and the Affinity of the Protein Pair Being Analyzed

Overcoming the Challenges to Enhancing Experimental Plant Biology With Computational Modeling

The study of complex biological systems necessitates computational modeling approaches that are currently underutilized in plant biology. Many plant biologists have trouble identifying or adopting modeling methods to their research, particularly mechanistic mathematical modeling. Here we address challenges that limit the use of computational modeling methods, particularly mechanistic mathematical modeling. We divide computational modeling techniques into either pattern models (e.g., bioinformatics, machine learning, or morphology) or mechanistic mathematical models (e.g., biochemical reactions, biophysics, or population models), which both contribute to plant biology research at different scales to answer different research questions. We present arguments and recommendations for the increased adoption of modeling by plant biologists interested in incorporating more modeling into their research programs. As some researchers find math and quantitative methods to be an obstacle to modeling, we provide suggestions for easy-to-use tools for non-specialists and for collaboration with specialists. This may especially be the case for mechanistic mathematical modeling, and we spend some extra time discussing this. Through a more thorough appreciation and awareness of the power of different kinds of modeling in plant biology, we hope to facilitate interdisciplinary, transformative research.

Non-Steady State Analysis of Enzyme Kinetics in Real Time Elucidates Substrate Association and Dissociation Rates: Demonstration with Analysis of Firefly Luciferase Mutants

Firefly luciferase has been widely used in biotechnology and biophotonics due to photon emission during enzymatic activity. In the past, the effect of amino acid substitutions (mutants) on the enzymatic activity of firefly luciferase has been characterized by the Michaelis constant, KM. The KM is obtained by plotting the maximum relative luminescence units (RLU) detected for several concentrations of the substrate (luciferin or luciferyl-adenylate). The maximum RLU is used because the assay begins to violate the quasi-steady state approximation when RLU decays as a function of time. However, mutations also affect the time to reach and decay from the maximum RLU. These effects are not captured when calculating the KM. To understand changes in the RLU kinetics of firefly luciferase mutants, we used a Michaelis-Menten model with the non-steady state approximation. In this model, we do not assume that the amount of enzyme-substrate complex is at equilibrium throughout the course of the experiment. We found that one of the two mutants analyzed in this study decreases not only the dissociation rate ( koff) but also the association rate ( kon) of luciferyl-adenylate, suggesting the narrowing of the structural pocket containing the catalytic amino acids. Furthermore, comparative analysis of the nearly complete oxidation of luciferyl-adenylate with wild-type and mutant firefly luciferase reveals that the total amount of photons emitted with the mutant is 50-fold larger than that with the wild type, on average. These two results together indicate that the slow supply of luciferyl-adenylate to the enzyme increases the total number of photons emitted from the substrate, luciferyl-adenylate. Analysis with the non-steady state approximation model is generally applicable when enzymatic production kinetics are monitored in real time.

Techniques for the Analysis of Protein-Protein Interactions in Vivo

Identifying key players and their interactions is fundamental for understanding biochemical mechanisms at the molecular level. The ever-increasing number of alternative ways to detect protein-protein interactions (PPIs) speaks volumes about the creativity of scientists in hunting for the optimal technique. PPIs derived from single experiments or high-throughput screens enable the decoding of binary interactions, the building of large-scale interaction maps of single organisms, and the establishment of cross-species networks. This review provides a historical view of the development of PPI technology over the past three decades, particularly focusing on in vivo PPI techniques that are inexpensive to perform and/or easy to implement in a state-of-the-art molecular biology laboratory. Special emphasis is given to their feasibility and application for plant biology as well as recent improvements or additions to these established techniques. The biology behind each method and its advantages and disadvantages are discussed in detail, as are the design, execution, and evaluation of PPI analysis. We also aim to raise awareness about the technological considerations and the inherent flaws of these methods, which may have an impact on the biological interpretation of PPIs. Ultimately, we hope this review serves as a useful reference when choosing the most suitable PPI technique.