Matthew Johnson

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For a positive integer k and a graph G, the k-colour graph of G, Ck(G), is the graph that has the proper k-vertex-colourings of G as its vertex set, and two k-colourings are joined by an edge in Ck(G) if they differ in colour on just one vertex of G. In this note some results on the connectivity of Ck(G) are proved. In particular it is shown that if G has(More)
The glucocorticoid receptor (GR) is a ubiquitously expressed transcription factor present in most cell types. Upon ligand binding, the GR is activated and translocates into the nucleus where it transmits the anti-inflammatory actions of glucocorticoids. Here, we describe the ligand-independent activation of GR by the beta2-adrenergic receptor (beta2-AR)(More)
The actin cytoskeleton executes a broad range of essential functions within a living cell. The dynamic nature of the actin polymer is modulated to facilitate specific cellular processes at discrete locations by actin-binding proteins (ABPs), including the formins and tropomyosins (Tms). Formins nucleate actin polymers, while Tms are conserved dimeric(More)
Given a 3-colourable graph G and two proper vertex 3-colourings α and β of G, consider the following question : is it possible to transform α into β by recolouring vertices of G one at a time, making sure that all intermediate colourings are proper 3-colourings? We prove that this question is answerable in polynomial time. We do so by characterising the(More)
Understanding gene regulation and its adaptive significance requires not only a detailed knowledge of individual molecular interactions that give rise to changes in gene expression but also an overview of complete genetic networks and the ways in which components within them interact. Increasingly, such studies are being done using luminescent or(More)
The identification of small molecule aminoimidazoles as potent and selective human beta-secretase inhibitors is reported. These analogues demonstrate low nannomolar potency for BACE1 in a FRET assay, exhibit comparable activity in a cell-based (ELISA) assay, and show >100x selectivity for the other structurally related aspartyl proteases BACE2, cathepsin D,(More)
The $$k$$ k -colouring reconfiguration problem asks whether, for a given graph $$G$$ G , two proper $$k$$ k -colourings $$\alpha $$ α and $$\beta $$ β of $$G$$ G , and a positive integer $$\ell $$ ℓ , there exists a sequence of at most $$\ell +1$$ ℓ + 1 proper $$k$$ k -colourings of $$G$$ G which starts with $$\alpha $$ α and ends with $$\beta $$ β and(More)
For a positive integer k, a k-colouring of a graph G = (V,E) is a mapping c : V → {1, 2, . . . , k} such that c(u) 6= c(v) whenever uv ∈ E. The COLOURING problem is to decide, for a given G and k, whether a k-colouring of G exists. If k is fixed (that is, it is not part of the input), we have the decision problem k-COLOURING instead. We survey known results(More)