Matrix stiffness affects endocytic uptake of MK2-inhibitor peptides.

In this study, the role of substrate stiffness on the endocytic uptake of a cell-penetrating peptide was investigated. The cell-penetrating peptide, an inhibitor of mitogen-activated protein kinase activated protein kinase II (MK2), enters a primary mesothelial cell line predominantly through caveolae. Using tissue culture polystyrene and polyacrylamide gels of varying stiffness for cell culture, and flow cytometry quantification and enzyme-linked immunoassays (ELISA) for uptake assays, we showed that the amount of uptake of the peptide is increased on soft substrates. Further, peptide uptake per cell increased at lower cell density. The improved uptake seen on soft substrates in vitro better correlates with in vivo functional studies where 10-100 µM concentrations of the MK2 inhibitor cell penetrating peptide demonstrated functional activity in several disease models. Additional characterization showed actin polymerization did not affect uptake, while microtubule polymerization had a profound effect on uptake. This work demonstrates that cell culture substrate stiffness can play a role in endocytic uptake, and may be an important consideration to improve correlations between in vitro and in vivo drug efficacy

On the effectiveness of spectral methods for the numerical solution of multi-frequency highly-oscillatory Hamiltonian problems

Multi-frequency, highly-oscillatory Hamiltonian problems derive from the mathematical modelling of many real life applications. We here propose a variant of Hamiltonian Boundary Value Methods (HBVMs), which is able to efficiently deal with the numerical solution of such problems.Comment: 28 pages, 4 figures (a few typos fixed

Efficient implementation of Radau collocation methods

In this paper we define an efficient implementation of Runge-Kutta methods of Radau IIA type, which are commonly used when solving stiff ODE-IVPs problems. The proposed implementation relies on an alternative low-rank formulation of the methods, for which a splitting procedure is easily defined. The linear convergence analysis of this splitting procedure exhibits excellent properties, which are confirmed by its performance on a few numerical tests.Comment: 19 pages, 3 figures, 9 table

On the Existence of Energy-Preserving Symplectic Integrators Based upon Gauss Collocation Formulae

We introduce a new family of symplectic integrators depending on a real parameter. When the paramer is zero, the corresponding method in the family becomes the classical Gauss collocation formula of order 2s, where s denotes the number of the internal stages. For any given non-null value of the parameter, the corresponding method remains symplectic and has order 2s-2: hence it may be interpreted as an order 2s-2 (symplectic) perturbation of the Gauss method. Under suitable assumptions, we show that the free parameter may be properly tuned, at each step of the integration procedure, so as to guarantee energy conservation in the numerical solution. The resulting symplectic, energy conserving method shares the same order 2s as the generating Gauss formula.Comment: 19 pages, 7 figures; Sections 1, 2, and 6 sliglthly modifie

Line Integral Methods for Conservative Problems

Line Integral Methods for Conservative Problems explains the numerical solution of differential equations within the framework of geometric integration, a branch of numerical analysis that devises numerical methods able to reproduce (in the discrete solution) relevant geometric properties of the continuous vector field. The book focuses on a large set of differential systems named conservative problems, particularly Hamiltonian systems. Assuming only basic knowledge of numerical quadrature and Runge–Kutta methods, this self-contained book begins with an introduction to the line integral methods. It describes numerous Hamiltonian problems encountered in a variety of applications and presents theoretical results concerning the main instance of line integral methods: the energy-conserving Runge–Kutta methods, also known as Hamiltonian boundary value methods (HBVMs). The authors go on to address the implementation of HBVMs in order to recover in the numerical solution what was expected from the theory. The book also covers the application of HBVMs to handle the numerical solution of Hamiltonian partial differential equations (PDEs) and explores extensions of the energy-conserving methods. With many examples of applications, this book provides an accessible guide to the subject yet gives you enough details to allow concrete use of the methods. MATLAB codes for implementing the methods are available online

Line Integral Methods for Conservative Problems

Line Integral Methods for Conservative Problems explains the numerical solution of differential equations within the framework of geometric integration, a branch of numerical analysis that devises numerical methods able to reproduce (in the discrete solution) relevant geometric properties of the continuous vector field. The book focuses on a large set of differential systems named conservative problems, particularly Hamiltonian systems. Assuming only basic knowledge of numerical quadrature and Runge–Kutta methods, this self-contained book begins with an introduction to the line integral methods. It describes numerous Hamiltonian problems encountered in a variety of applications and presents theoretical results concerning the main instance of line integral methods: the energy-conserving Runge–Kutta methods, also known as Hamiltonian boundary value methods (HBVMs). The authors go on to address the implementation of HBVMs in order to recover in the numerical solution what was expected from the theory. The book also covers the application of HBVMs to handle the numerical solution of Hamiltonian partial differential equations (PDEs) and explores extensions of the energy-conserving methods. With many examples of applications, this book provides an accessible guide to the subject yet gives you enough details to allow concrete use of the methods. MATLAB codes for implementing the methods are available online

Line Integral Solution of Differential Problems

In recent years, the numerical solution of differential problems, possessing constants of motion, has been attacked by imposing the vanishing of a corresponding line integral. The resulting methods have been, therefore, collectively named (discrete) line integral methods, where it is taken into account that a suitable numerical quadrature is used. The methods, at first devised for the numerical solution of Hamiltonian problems, have been later generalized along several directions and, actually, the research is still very active. In this paper we collect the main facts about line integral methods, also sketching various research trends, and provide a comprehensive set of references

High-order energy-conserving Line Integral Methods for charged particle dynamics

In this paper we study arbitrarily high-order energy-conserving methods for simulating the dynamics of a charged particle. They are derived and studied within the framework of Line Integral Methods (LIMs), previously used for defining Hamiltonian Boundary Value Methods (HBVMs), a class of energy-conserving Runge-Kutta methods for Hamiltonian problems. A complete analysis of the new methods is provided, which is confirmed by a few numerical tests.Comment: 24 pages, 3 figures, 2 tables - few typos fixe