Conditional linearizability criteria for a system of third-order ordinary differential equations

We provide linearizability criteria for a class of systems of third-order ordinary differential equations (ODEs) that is cubically semi-linear in the first derivative, by differentiating a system of second-order quadratically semi-linear ODEs and using the original system to replace the second derivative. The procedure developed splits into two cases, those where the coefficients are constant and those where they are variables. Both cases are discussed and examples given

Implications of antimicrobial combinations in complex wound biofilms containing fungi

Diabetic foot ulcer treatment currently focuses on targeting bacterial biofilms, while dismissing fungi. To investigate this we used an in vitro biofilm model containing bacteria and fungi, reflective of the wound environment, to test the impact of antimicrobials. Here we showed that while mono-treatment approaches influenced biofilm composition it had no discernible effect on overall quantity. Only by combining bacterial and fungal specific antibiotics were we able to decrease the biofilm bioburden, irrespective of composition

Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - II: Partial Differential Equations

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible complex transformations can be used to obtain invertible real transformations that map a system of nonlinear partial differential equations into a system of linear partial differential equation. Explicit invariant criteria are given that provide procedures for writing down the solutions of the linearized equations. A few non-trivial examples are mentioned.Comment: This paper along with its first part ODE-I were combined in a single research paper "Linearizability criteria for systems of two second-order differential equations by complex methods" which has been published in Nonlinear Dynamics. Due to citations of both parts I and II these are not replaced with the above published articl

A General Method for Targeted Quantitative Cross-Linking Mass Spectrometry

Chemical cross-linking mass spectrometry (XL-MS) provides protein structural information by identifying covalently linked proximal amino acid residues on protein surfaces. The information gained by this technique is complementary to other structural biology methods such as x-ray crystallography, NMR and cryo-electron microscopy[1]. The extension of traditional quantitative proteomics methods with chemical cross-linking can provide information on the structural dynamics of protein structures and protein complexes. The identification and quantitation of cross-linked peptides remains challenging for the general community, requiring specialized expertise ultimately limiting more widespread adoption of the technique. We describe a general method for targeted quantitative mass spectrometric analysis of cross-linked peptide pairs. We report the adaptation of the widely used, open source software package Skyline, for the analysis of quantitative XL-MS data as a means for data analysis and sharing of methods. We demonstrate the utility and robustness of the method with a cross-laboratory study and present data that is supported by and validates previously published data on quantified cross-linked peptide pairs. This advance provides an easy to use resource so that any lab with access to a LC-MS system capable of performing targeted quantitative analysis can quickly and accurately measure dynamic changes in protein structure and protein interactions