Tyrosine phosphorylation of cortactin by the FAK-Src complex at focal adhesions regulates cell motility.

BackgroundCell migration plays an important role in many physiological and pathological processes, including immune cell chemotaxis and cancer metastasis. It is a coordinated process that involves dynamic changes in the actin cytoskeleton and its interplay with focal adhesions. At the leading edge of a migrating cell, it is the re-arrangement of actin and its attachment to focal adhesions that generates the driving force necessary for movement. However, the mechanisms involved in the attachment of actin filaments to focal adhesions are still not fully understood.ResultsSignaling by the FAK-Src complex plays a crucial role in regulating the formation of protein complexes at focal adhesions to which the actin filaments are attached. Cortactin, an F-actin associated protein and a substrate of Src kinase, was found to interact with FAK through its SH3 domain and the C-terminal proline-rich regions of FAK. We found that the autophosphorylation of Tyr(397) in FAK, which is necessary for FAK activation, was not required for the interaction with cortactin, but was essential for the tyrosine phosphorylation of the associated cortactin. At focal adhesions, cortactin was phosphorylated at tyrosine residues known to be phosphorylated by Src. The tyrosine phosphorylation of cortactin and its ability to associate with the actin cytoskeleton were required in tandem for the regulation of cell motility. Cell motility could be inhibited by truncating the N-terminal F-actin binding domains of cortactin or by blocking tyrosine phosphorylation (Y421/466/475/482F mutation). In addition, the mutant cortactin phosphorylation mimic (Y421/466/475/482E) had a reduced ability to interact with FAK and promoted cell motility. The promotion of cell motility by the cortactin phosphorylation mimic could also be inhibited by truncating its N-terminal F-actin binding domains.ConclusionsOur results suggest that cortactin acts as a bridging molecule between actin filaments and focal adhesions. The cortactin N-terminus associates with F-actin, while its C-terminus interacts with focal adhesions. The tyrosine phosphorylation of cortactin by the FAK-Src complex modulates its interaction with FAK and increases its turnover at focal adhesions to promote cell motility

Generating functions and short recursions, with applications to the moments of quadratic forms in noncentral normal vectors

Using generating functions, the top-order zonal polynomials that occur in much distribution theory under normality can be recursively related to other symmetric functions (power-sum and elementary symmetric functions, Ruben (1962), Hillier, Kan, and Wang (2009)). Typically, in a recursion of this type the k-th object of interest, dk say, is expressed in terms of all lower-order dj ’s. In Hillier, Kan, and Wang (2009) we pointed out that, in the case of top-order zonal polynomials (and generalizations of them), a shorter (i.e., fixed length) recursion can be deduced. The present paper shows that the argument in Hillier, Kan, and Wang (2009) generalizes to a large class of objects/generating functions. The results thus obtained are then applied to various problems involving quadratic forms in noncentral normal vectors Keywords; generating functions, invariant polynomials, non-central normal distribution, recursions, symmetric functions, zonal polynomials

Computationally efficient recursions for top-order invariant polynomials with applications

The top-order zonal polynomials Ck(A),and top-order invariant polynomials Ck1,...,kr(A1,...,Ar)in which each of the partitions of ki,i = 1,..., r,has only one part, occur frequently in multivariate distribution theory, and econometrics - see, for example Phillips (1980, 1984, 1985, 1986), Hillier (1985, 2001), Hillier and Satchell (1986), and Smith (1989, 1993). However, even with the recursive algorithms of Ruben (1962) and Chikuse (1987), numerical evaluation of these invariant polynomials is extremely time consuming. As a result, the value of invariant polynomials has been largely confined to analytic work on distribution theory. In this paper we present new, very much more efficient, algorithms for computing both the top-order zonal and invariant polynomials. These results should make the theoretical results involving these functions much more valuable for direct practical study. We demonstrate the value of our results by providing fast and accurate algorithms for computing the moments of a ratio of quadratic forms in normal random variables.