RNA-directed DNA methylation (RdDM) is a plant-specific de novo methylation pathway that is responsible for maintenance of asymmetric methylation (CHH, H = A, T or G) in euchromatin. Loci with CHH methylation produce 24 nucleotide (nt) short interfering (si) RNAs. These siRNAs direct additional CHH methylation to the locus, maintaining methylation states through DNA replication. To understand the necessary conditions to produce stable methylation, we developed a stochastic mathematical model of RdDM. The model describes DNA target search by siRNAs derived from CHH methylated loci bound by an Argonaute. Methylation reinforcement occurs either throughout the cell cycle (steady) or immediately following replication (bursty). We compare initial and final methylation distributions to determine simulation conditions that produce stable methylation. We apply this method to the low CHH methylation case. The resulting model predicts that siRNA production must be linearly proportional to methylation levels, that bursty reinforcement is more stable and that slightly higher levels of siRNA production are required for searching DNA, compared to RNA. Unlike CG methylation, which typically exhibits bi-modality with loci having either 100% or 0% methylation, CHH methylation exists across a range. Our model predicts that careful tuning of the negative feedback in the system is required to enable stable maintenance.
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.
Abstract How flexible developmental programs integrate information from internal and external factors to modulate stem cell behavior is a fundamental question in developmental biology. Cells of the Arabidopsis stomatal lineage modify the balance of stem cell proliferation and differentiation to adjust the size and cell type composition of mature leaves. Here, we report that meristemoids, one type of stomatal lineage stem cell, trigger the transition from asymmetric self-renewing divisions to commitment and terminal differentiation by crossing a critical cell size threshold. Through computational simulation, we demonstrate that this cell size-mediated transition allows robust, yet flexible termination of stem cell proliferation and we observe adjustments in the number of divisions before the differentiation threshold under several genetic manipulations. We experimentally evaluate several mechanisms for cell size sensing, and our data suggest that cell size is sensed via a chromatin ruler acting in the nucleus.
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.
In this paper, we construct a linear differential system in both continuous time and discrete time to model HIV transmission on the population level. The main question is the determination of parameters based on the posterior information obtained from statistical analysis of the HIV population. We call these parameters dynamic constants in the sense that these constants determine the behavior of the system in various models. There is a long history of using linear or nonlinear dynamic systems to study the HIV population dynamics or other infectious diseases. Nevertheless, the question of determining the dynamic constants in the system has not received much attention. In this paper, we take some initial steps to bridge such a gap. We study the dynamic constants that appear in the linear differential system model in both continuous and discrete time. Our computations are mostly carried out in Matlab.
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.
Abstract Grasses grow a series of phytomers during development. The distance between successive leaves is determined by internode lengths. Grasses exhibit genetic, developmental, and environmental variability in phytomer number, but how this affects internode length, biomass, and height is unknown. We hypothesized that a generalized mathematical model of phytomer development wherein between-phytomer competition influences internode length distributions would be sufficient to explain internode length patterns in two Setaria genotypes: weedy A10 and domesticated B100. Our model takes a novel approach that includes the vegetative growth of leaf blade, sheath, and internode at the individual phytomer level, and the shift to reproductive growth. To validate and test our mathematical model, we carried out a greenhouse experiment. We found that the rate of leaf emergence is consistent for both genotypes across development, and that the length of time spent elongating for the leaf and internode can be described as the ratio between the time of phytomer emergence and the elongation completion time. The validated model was simulated across all possible parameter values to predict the influence of phytomer number on internode length. This analysis predicts that different internode length distributions across different numbers of total phytomers are an emergent property, rather than a genotype-specific property requiring genotype-specific models. We applied the model to internode length only field data of S. italica accession B100, grown under both well-watered and drought conditions. The model predicts that droughted plants reduce leaf elongation time, reduce resource allocation to the internodes, and overall experience slower growth. Together, model and data suggest that allometric patterns are driven by competition for resources among phytomer and the shift to reproductive growth in Setaria . The resulting model enables us to predict growth dynamics and final allometries at the phytomer level.
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.
Abstract RNA-directed DNA Methylation (RdDM) is a plant-specific de novo methylation pathway that is responsible for maintenance of asymmetric methylation (CHH, where H=A, T, or G) in euchromatin. Loci with CHH methylation are transcriptionally silent and produce 24-nucleotide (nt) short interfering (si) RNAs. These siRNAs direct additional CHH methylation to the locus, thereby maintaining methylation states through DNA replication. To understand the necessary conditions to produce stable CHH methylation, we developed a stochastic mathematical model of RdDM. The model describes DNA target search of DNA or RNA by siRNAs derived from CHH-methylated loci. When the siRNA (bound by an Argonaute protein) finds the matching locus, the model uses the dwell time of the matched complex to determine the degree of CHH reinforcing methylation. Reinforcing methylation occurs either throughout the cell cycle (steady reinforcement), or immediately following replication (bursty reinforcement). Each simulation occurs over 10 cell cycles, and for 7 simulation replicates. We use nonparametric statistics to compare initial and final CHH methylation distributions to determine whether the simulation conditions produce stable maintenance. We apply this method to the low CHH methylation case, wherein the median is only 8%, and many loci have less than 8% methylation. The resulting model predicts that siRNA production must be linearly proportional to CHH methylation levels at each locus, that bursty reinforcement produces more stable systems, and that slightly higher levels of siRNA production are required for DNA target search, compared to RNA target search. Unlike CG methylation, which typically exhibits bi-modality, with loci having either 100% or 0% methylation, CHH methylation putatively exists at a range of methylation fractions. Our model predicts that careful tuning of the negative feedbacks in the system are required to balance the positive feedback loop of increasing CHH methylation and increasing siRNA production, enabling stable maintenance of a range of CHH methylation across replication events.
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.
