Stable spike clusters for the one-dimensional Gierer-Meinhardt system

We consider the Gierer-Meinhardt system with precursor inhomogeneity in a one-dimensional interval. A spike cluster is the combination of several spikes which all approach the same point in the singular limit of small activator diffusivity. We rigorously prove the existence of a steady-state spike cluster consisting of N spikes near a non-degenerate local minimum point of the smooth inhomogeneity, where N is an arbitrary positive integer. Further, we show that this solution is linearly stable. We explicitly compute all eigenvalues, both large (of order O(1)) and small (of order o(1)). The main features of studying the Gierer-Meinhardt system in this setting are as follows: (i) it is biologically relevant since it models a hierarchical process (pattern formation of small-scale structures induced by a pre-existing large-scale inhomogeneity), (ii) it contains three different spatial scales two of which are small. (iii) all the expressions can be made explicit and often have a particularly simple form.

Investigation of the functional roles of host cell proteins involved in Coronavirus infection using highly specific and scalable RNA interference (RNAi) approach

Since its identification in the 1990s, the RNA interference (RNAi) pathway has proven extremely useful in elucidating the function of proteins in the context of cells and even whole organisms. In particular, this sequence-specific and powerful loss-of-function approach has greatly simplified the study of the role of host cell factors implicated in the life cycle of viruses. Here, we detail the RNAi method we have developed and used to specifically knock down the expression of ezrin, an actin binding protein that was identified by yeast two-hybrid screening to interact with the Severe Acute Respiratory Syndrome Coronavirus (SARS-CoV) spike (S) protein. This method was used to study the role of ezrin, specifically during the entry stage of SARS-CoV infection.