Mathematical methods of electromagnetic theory

This text provides a mathematically precise but intuitive introduction to classical electromagnetic theory and wave propagation, with a brief introduction to special relativity. While written in a distinctive, modern style, Friedrichs manages to convey the physical intuition and 19th century basis of the equations, with an emphasis on conservation laws. Particularly striking features of the book include: (a) a mathematically rigorous derivation of the interaction of electromagnetic waves with matter, (b) a straightforward explanation of how to use variational principles to solve problems in e

The cancer glycocalyx mechanically primes integrin-mediated growth and survival

Malignancy is associated with altered expression of glycans and glycoproteins that contribute to the cellular glycocalyx. We constructed a glycoprotein expression signature, which revealed that metastatic tumours upregulate expression of bulky glycoproteins. A computational model predicted that these glycoproteins would influence transmembrane receptor spatial organization and function. We tested this prediction by investigating whether bulky glycoproteins in the glycocalyx promote a tumour phenotype in human cells by increasing integrin adhesion and signalling. Our data revealed that a bulky glycocalyx facilitates integrin clustering by funnelling active integrins into adhesions and altering integrin state by applying tension to matrix-bound integrins, independent of actomyosin contractility. Expression of large tumour-associated glycoproteins in non-transformed mammary cells promoted focal adhesion assembly and facilitated integrin-dependent growth factor signalling to support cell growth and survival. Clinical studies revealed that large glycoproteins are abundantly expressed on circulating tumour cells from patients with advanced disease. Thus, a bulky glycocalyx is a feature of tumour cells that could foster metastasis by mechanically enhancing cell-surface receptor function