skip to main content

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Diffeomorphic shape evolution coupled with a reaction-diffusion PDE on a growth potential
This paper studies a longitudinal shape transformation model in which shapes are deformed in response to an internal growth potential that evolves according to an advection reaction diffusion process. This model extends prior works that considered a static growth potential, i.e., the initial growth potential is only advected by diffeomorphisms. We focus on the mathematical study of the corresponding system of coupled PDEs describing the joint dynamics of the diffeomorphic transformation together with the growth potential on the moving domain. Specifically, we prove the uniqueness and long time existence of solutions to this system with reasonable initial and boundary conditions as well as regularization on deformation fields. In addition, we provide a few simple simulations of this model in the case of isotropic elastic materials in 2D.  more » « less
Award ID(s):
1945224
PAR ID:
10316563
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Quarterly of Applied Mathematics
Volume:
80
Issue:
1
ISSN:
0033-569X
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ( , Microbiology Spectrum)
    Cardona, Silvia T (Ed.)
    ABSTRACT

    The fastest replicating bacteriumVibrio natriegensis a rising workhorse for molecular and biotechnological research with established tools for efficient genetic manipulation. Here, we expand on the capabilities of multiplex genome editing by natural transformation (MuGENT) by identifying a neutral insertion site and showing how two selectable markers can be swapped at this site for sequential rounds of natural transformation. Second, we demonstrated that MuGENT can be used for complementation by gene insertion at an ectopic chromosomal locus. Additionally, we developed a robust method to cure the competence plasmid required to induce natural transformation. Finally, we demonstrated the ability of MuGENT to create massive deletions; the 280 kb deletion created in this study is one of the largest artificial deletions constructed in a single round of targeted mutagenesis of a bacterium. These methods each advance the genetic potential ofV. natriegensand collectively expand upon its utility as an emerging model organism for synthetic biology.

     IMPORTANCE

    Vibrio natriegensis an emerging model organism for molecular and biotechnological applications. Its fast growth, metabolic versatility, and ease of genetic manipulation provide an ideal platform for synthetic biology. Here, we develop and apply novel methods that expand the genetic capabilities of theV. natriegensmodel system. Prior studies developed a method to manipulate multiple regions of the chromosome in a single step. Here, we provide new resources that diversify the utility of this method. We also provide a technique to remove the required genetic tools from the cell once the manipulation is performed, thus establishing “clean” derivative cells. Finally, we show the full extent of this technique’s capability by generating one of the largest chromosomal deletions reported in the literature. Collectively, these new tools will be beneficial broadly to theVibriocommunity and specifically to the advancement ofV. natriegensas a model system.

     
    more » « less
  2. ; ( , Lab on a Chip)
    Patient derived organoids have emerged as robust preclinical models for screening anti-cancer therapeutics. Current 2D culturing methods do not provide physiological responses to therapeutics, therefore 3D models are being developed to better reproduce physiological responses. 3D culturing however often requires large initial cell populations and one week to one month to grow tumors ready for therapeutic testing. As a solution a 3D culturing system has been developed capable of producing physiologically relevant tumors in an expedited fashion while only requiring a small number of initial cancer cells. A bi-layer microfluidic system capable of facilitating active convective nutrient supply to populations of cancer cells facilitates expedited growth of cancer cells when starting with populations as small as 8 cells. The system has been shown to function well with adherent and non-adherent cell types by expediting cell growth by a factor ranging from 1.27 to 4.76 greater than growth under static conditions. Utilizing such an approach has enable to formation of tumors ready for therapeutic screening within 3 days and the ability to perform therapeutic screening within the microfluidic system is demonstrated. A mathematical model has been developed which allows for adjustments to be made to the dynamic delivery of nutrients in order to efficiently use culture media without excessive waste. We believe this work to be the first attempt to grow cancers in an expedited fashion utilizing only a convective nutrient supply within a microfluidic system which also facilitates on-device therapeutic screening. The developed microfluidic system and cancer growth method have the potential to offer improved drug screening for patients in clinical settings. 
    more » « less
  3. ; ; ; ; ; ; ( , Frontiers in Systems Biology)
    Sepsis is characterized by an overactive, dysregulated inflammatory response that drives organ dysfunction and often results in death. Mathematical modeling has emerged as an essential tool for understanding the underlying complex biological processes. A system of four ordinary differential equations (ODEs) was developed to simulate the dynamics of bacteria, the pro- and anti-inflammatory responses, and tissue damage (whose molecular correlate is damage-associated molecular pattern [DAMP] molecules and which integrates inputs from the other variables, feeds back to drive further inflammation, and serves as a proxy for whole-organism health status). The ODE model was calibrated to experimental data from E. coli infection in genetically identical rats and was validated with mortality data for these animals. The model demonstrated recovery, aseptic death, or septic death outcomes for a simulated infection while varying the initial inoculum, pathogen growth rate, strength of the local immune response, and activation of the pro-inflammatory response in the system. In general, more septic outcomes were encountered when the initial inoculum of bacteria was increased, the pathogen growth rate was increased, or the host immune response was decreased. The model demonstrated that small changes in parameter values, such as those governing the pathogen or the immune response, could explain the experimentally observed variability in mortality rates among septic rats. A local sensitivity analysis was conducted to understand the magnitude of such parameter effects on system dynamics. Despite successful predictions of mortality, simulated trajectories of bacteria, inflammatory responses, and damage were closely clustered during the initial stages of infection, suggesting that uncertainty in initial conditions could lead to difficulty in predicting outcomes of sepsis by using inflammation biomarker levels. 
    more » « less
  4. ; ; ; ( , Soft Matter)
    The construction of functional nano-/micro-architectures through self-assembly and self-organization of organic molecules and polymeric materials plays an important role in the development of many technologies. In this study, we report the spontaneous formation of uniform polymer microrods with lengths of up to a few tens of micrometers from paraffin wax. Through a solvent attrition approach, colloidal structures of paraffin wax are introduced into water. After the initial growth stage, the microrods undergo morphological transformation and end-to-end aggregation, processes likely driven by thermodynamics to create equilibrium structures with minimal interfacial energies. The polymer microrods can effectively absorb hydrophobic nanoparticles, indicating their potential to serve as host materials for functional components. The formation of polymer microrods from paraffin wax and their spontaneous growth mechanism discovered in this study may provide new insights to the self-assembly of microstructures. 
    more » « less
  5. ; ; ; ( , Applications in Plant Sciences)

    The past six years have seen the rapid growth of studies of CRISPR/Cas9 in plant genome editing, a method that enormously facilitates both basic research and practical applications. Most studies have focused on genetic model species, but plant species that are not genetic models may also be economically important or biologically significant, or both. However, developing the CRISPR/Cas9 system in a nongenetic model is challenging. Here, we summarize CRISPR/Cas9 applications in 45 plant genera across 24 families and provide a reference for practical application of CRISPR in nongenetic model plant systems. Suggestions for selecting plant species and target genes are given for proof‐of‐principle CRISPR studies, and the processes of vector construction are reviewed. We recommend using transient assays to identify a desired CRISPR/Cas9 system in a nongenetic model. We then review methods of plant transformation and describe approaches, using regenerated transgenic plants, for evaluating CRISPR editing results. Lastly, potential future applications of CRISPR in nongenetic model plant species are discussed. This review provides a road map for developing CRISPR in nongenetic models, an application that holds enormous potential in plant biology.

     
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email