Mathematical Model of the Split Firefly Luciferase Assay

The firefly luciferase complementation assay is widely used as a bioluminescent reporter technology to detect protein-protein interactions in vitro and in vivo. Firefly luciferase oxidates its substrate, luciferin, resulting in the emission of light. A previous study suggests that the firefly luciferase complementation assay has different luminescence kinetics from full length luciferase. The mechanism behind this is still unknown. Although half of the previously published studies utilizing the firefly luciferase complementation assay consider it quantitative. To understand how the molecular reactions and the changes in the affinity of the protein pair affect experimental results, a mathematical model was constructed. This suggests that previously published studies should be considered qualitative, unless an additional experiment is performed. This new model demonstrates that the luminescence measured is not linearly correlated with the affinity of the protein pair. The model is then used to design a new experiment which allows the firefly luciferase complementation assay to be used quantitatively to detect changes of affinity

Parameter estimation and optimization for biological mathematical models using Bayesian statistics

In the field of biology, mathematical models are increasingly used to address biological questions and the large data sets generated in experimental studies. Mathematical models traditionally are simplified and structured to be analytically tractable, but computing power allows for more complex, larger models. Bayesian statistics lends itself naturally to address parameter estimation problems in these large models. Bayesian statistical inference is utilized in this thesis to obtain parameter estimates from a sparse data set on populations in the HIV epidemic. Current estimates of the HIV epidemic indicate a decrease in the incidence of the disease in the undiagnosed subpopulation over the past 10 years. A lack of access to care, however, has not been considered when modeling the population. Populations at high risk for contracting HIV are twice as likely to lack access to reliable medical care. In this thesis, we consider three contributors to the HIV population dynamics: susceptible pool exhaustion, lack of access to care, and usage of anti-retroviral therapy (ART) by diagnosed individuals. An extant problem in the mathematical study of this system is deriving parameter estimates due to a portion of the population being unobserved. We approach this problem by looking at the proportional change in the infected subpopulations. We obtain estimates for the proportional change of the infected subpopulations using hierarchical Bayesian statistics. The estimated proportional change is used to derive epidemic parameter estimates for a system of stochastic differential equations (SDEs). Model fit is quantified to determine the best parametric explanation for the observed dynamics in the infected subpopulations. Parameter estimates derived using these methods provide interpretability and recovery of the system. Simulations suggest that the undiagnosed population may be larger than currently estimated without significantly affecting the population dynamics

Dynamical Modeling in Cell Biology with Ordinary Differential Equations

Dynamical systems have been of interest to biologists and mathematicians alike. Many processes in biology lend themselves to dynamical study. Movement, change, and response to stimuli are dynamical characteristics that define what is \u27alive\u27. A scientific relationship between these two fields is therefore natural. In this thesis, I describe how my PhD research variously related to biological, mathematical, and computational problems in cell biology. In chapter 1 I introduce some of the current problems in the field. In chapter 2, my mathematical model of firefly luciferase in vivo shows the importance of dynamical models to understand systems. Data originally collected by other researchers led to apparently straight-forward conclusions based on experimental techniques. However, this is contradicted once a dynamical model is applied to the system. I show that interpretation of data that comes as a snapshot of a dynamical system is a dynamical modeling problem, even if one can fit a nice linear regression to that data. In chapters 2 and 3 I demonstrate the value of added complexity to mathematical models in firefly luciferase. Usually, a simple solution is considered best, but this may leave information behind. By expressing the simplified Michaelis-Menten model as a system of differential equations we are able to get valuable parameter estimates. These parameter estimates would be otherwise costly. In addition, the model allows us to quantify trends in the data that are visible but not interpretable by scientists without a mathematical framework. In chapter 4, a problem without experimental data is tackled regarding the plant cell cycle and its switch to endoreplication. In this case, much tedious hand-fitting is required to answer the research questions. Using this technique I was able to address biological questions, understand the validity of the model and the biological assumptions that went into that model. In chapter 5 I motivated the further development of educational tools to disseminate modeling and computational techniques to biologists. This type of training is necessary for the future of the field

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

© 2016 Dale et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The firefly luciferase complementation assay is widely used as a bioluminescent reporter technology to detect protein-protein interactions in vitro, in cellulo, and in vivo. Upon the interaction of a protein pair, complemented firefly luciferase emits light through the adenylation and oxidation of its substrate, luciferin. Although it has been suggested that kinetics of light production in the firefly luciferase complementation assay is different from that in full length luciferase, the mechanism behind this is still not understood. To quantitatively understand the different kinetics and how changes in affinity of a protein pair affect the light emission in the assay, a mathematical model of the in vitro firefly luciferase complementation assay was constructed. Analysis of the model finds that the change in kinetics is caused by rapid dissociation of the protein pair, low adenylation rate of luciferin, and increased affinity of adenylated luciferin to the enzyme. The model suggests that the affinity of the protein pair has an exponential relationship with the light detected in the assay. This relationship causes the change of affinity in a protein pair to be underestimated. This study underlines the importance of understanding the molecular mechanism of the firefly luciferase complementation assay in order to analyze protein pair affinities quantitatively

Functional analysis of short linear motifs in the plant cyclin-dependent kinase inhibitor SIAMESE

© 2018 American Society of Plant Biologists. All rights reserved. Endoreplication, a modified cell cycle in which DNA is replicated without subsequent cell division, plays an important but poorly understood role in plant growth and in plant responses to biotic and abiotic stress. The Arabidopsis (Arabidopsis thaliana) SIAMESE (SIM) gene encodes the first identified member of the SIAMESE-RELATED (SMR) family of cyclin-dependent kinase inhibitors. SIM controls endoreplication during trichome development, and sim mutant trichomes divide several times instead of endoreplicating their DNA. The SMR family is defined by several short linear amino acid sequence motifs of largely unknown function, and family members have little sequence similarity to any known protein functional domains. Here, we investigated the roles of the conserved motifs in SIM site-directed Arabidopsis mutants using several functional assays. We identified a potential cyclin-dependent kinase (CDK)-binding site, which bears no resemblance to other known CDK interaction motifs. We also identified a potential site of phosphorylation and two redundant nuclear localization sequences. Surprisingly, the only motif with similarity to the other family of plant CDK inhibitors, the INHIBITOR/INTERACTOR OF CDC2 KINASE/KIP-RELATED PROTEIN proteins, is not required for SIM function in vivo. Because even highly divergent members of the SMR family are able to replace SIM function in Arabidopsis trichomes, it is likely that the results obtained here for SIM will apply to other members of this plant-specific family of CDK inhibitors

Tailoring Enterprise Systems Engineering Policy for Project Scale and Complexity

No abstract availabl

The Raf-like kinase ILK1 and the high affinity K\u3csup\u3e+\u3c/sup\u3e transporter HAK5 are required for innate immunity and abiotic stress response

© 2016 American Society of Plant Biologists. All rights reserved. Plant perception of pathogen-associated molecular patterns (PAMPs) and other environmental stresses trigger transient ion fluxes at the plasma membrane. Apart from the role of Ca2+ uptake in signaling, the regulation and significance of PAMPinduced ion fluxes in immunity remain unknown. We characterized the functions of INTEGRIN-LINKED KINASE1 (ILK1) that encodes a Raf-like MAP2K kinase with functions insufficiently understood in plants. Analysis of ILK1 mutants impaired in the expression or kinase activity revealed that ILK1 contributes to plant defense to bacterial pathogens, osmotic stress sensitivity, and cellular responses and total ion accumulation in the plant upon treatment with a bacterial-derived PAMP, flg22. The calmodulin-like protein CML9, a negative modulator of flg22-triggered immunity, interacted with, and suppressed ILK1 kinase activity. ILK1 interacted with and promoted the accumulation of HAK5, a putative (H+)/K+ symporter that mediates a high-affinity uptake during K+ deficiency. ILK1 or HAK5 expression was required for several flg22 responses including gene induction, growth arrest, and plasma membrane depolarization. Furthermore, flg22 treatment induced a rapid K+ efflux at both the plant and cellular levels in wild type, while mutants with impaired ILK1 or HAK5 expression exhibited a comparatively increased K+ loss. Taken together, our results position ILK1 as a link between plant defense pathways and K+ homeostasis