Browsing by Author "Davis, Lisa"

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Discontinuous Galerkin calculations for a nonlinear PDE model of DNA transcription with short, transient and frequent pausing
(2014-09) Davis, Lisa; Gedeon, Tomas; Thorenson, Jennifer R.
A discontinuous Galerkin finite element method is used to approximate solutions to a classical traffic flow PDE. This PDE is used to model the biological process of transcription; the process of transferring genetic information from DNA either to mRNA or to rRNA. The transcription process is punctuated by short, frequent RNAP pauses which are incorporated into the model as traffic lights. These pauses cause a delay in the average transcription process. The DG solution of the nonlinear model is used to calculate the delay and to determine the effect of the pauses on the average transcription time. Numerical error measurements between the DG solution and the true solution (derived by the method of characteristics) are given for a simple model problem. It shows an excellent agreement in a neighborhood away from the shocks as well as O(Δx) convergence for the delay calculation. Preliminary parameter studies indicate that in a system with multiple pauses both the location and time duration of the pauses can significantly affect the average delay experienced by an RNAP.
A Mechanistic Model for Cooperative Behavior of Co-transcribing RNA Polymerases
(2016-08) Davis, Lisa; Gedeon, Tomas; Heberling, Tamra; Gedeon, Jakub; Morgan, Charles
In fast-transcribing prokaryotic genes, such as an rrn gene in Escherichia coli, many RNA polymerases (RNAPs) transcribe the DNA simultaneously. Active elongation of RNAPs is often interrupted by pauses, which has been observed to cause RNAP traffic jams; yet some studies indicate that elongation seems to be faster in the presence of multiple RNAPs than elongation by a single RNAP. We propose that an interaction between RNAPs via the torque produced by RNAP motion on helically twisted DNA can explain this apparent paradox. We have incorporated the torque mechanism into a stochastic model and simulated transcription both with and without torque. Simulation results illustrate that the torque causes shorter pause durations and fewer collisions between polymerases. Our results suggest that the torsional interaction of RNAPs is an important mechanism in maintaining fast transcription times, and that transcription should be viewed as a cooperative group effort by multiple polymerases.
Reconstructing Full-Field Flapping Wing Dynamics from Sparse Measurements
(IOP Publishing, 2020-11) Johns, William; Davis, Lisa; Jankauski, Mark
Flapping insect wings deform during flight. This deformation benefits the insect’s aerodynamic force production as well as energetic efficiency. However, it is challenging to measure wing displacement field in flying insects. Many points must be tracked over the wing’s surface to resolve its instantaneous shape. To reduce the number of points one is required to track, we propose a physics-based reconstruction method called System Equivalent Reduction Expansion Processes (SEREP) to estimate wing deformation and strain from sparse measurements. Measurement locations are determined using a Weighted Normalized Modal Displacement (NMD) method. We experimentally validate the reconstruction technique by flapping a paper wing from 5-9 Hz with 45° and measuring strain at three locations. Two measurements are used for the reconstruction and the third for validation. Strain reconstructions had a maximal error of 30% in amplitude. We extend this methodology to a more realistic insect wing through numerical simulation. We show that wing displacement can be estimated from sparse displacement or strain measurements, and that additional sensors spatially average measurement noise to improve reconstruction accuracy. This research helps overcome some of the challenges of measuring full-field dynamics in flying insects and provides a framework for strain-based sensing in insect-inspired flapping robots.
Ribosome Abundance Control in Prokaryotes
(Springer Science and Business Media LLC, 2023-10) Shea, Jacob; Davis, Lisa; Quaye, Bright; Gedeon, Tomas
Cell growth is an essential phenotype of any unicellular organism and it crucially depends on precise control of protein synthesis. We construct a model of the feedback mechanisms that regulate abundance of ribosomes in E. coli, a prototypical prokaryotic organism. Since ribosomes are needed to produce more ribosomes, the model includes a positive feedback loop central to the control of cell growth. Our analysis of the model shows that there can be only two coexisting equilibrium states across all 23 parameters. This precludes the existence of hysteresis, suggesting that the ribosome abundance changes continuously with parameters. These states are related by a transcritical bifurcation, and we provide an analytic formula for parameters that admit either state.
When a Traffic Light Turns Green, a Study of Traffic Flow Using Partial Differential Equations
(2013-03) Dupree, William; Davis, Lisa
Partial differential equations, PDEs, are used in many applied mathematical models. In the summer research performed, PDEs were used to model traffic flow and the theoretical behavior of cars on simple roadways. As with ordinary differential equations, partial differential equations have many different forms of a variety of orders. The PDE used for traffic flow, and the focus of the current research, was the homogeneous advection equation involving the traffic density as the spacial and time varying function. Methods to solve this equation, and how it related to traffic flow, were studied out of Richard Haberman's text titled Mathematical Models. Only solutions to the linear advection equation were sought, leading to one of the most fundamental wave function solutions to PDEs.