The self-assembly and evolution of homomeric protein complexes

We introduce a simple "patchy particle" model to study the thermodynamics and dynamics of self-assembly of homomeric protein complexes. Our calculations allow us to rationalize recent results for dihedral complexes. Namely, why evolution of such complexes naturally takes the system into a region of interaction space where (i) the evolutionarily newer interactions are weaker, (ii) subcomplexes involving the stronger interactions are observed to be thermodynamically stable on destabilization of the protein-protein interactions and (iii) the self-assembly dynamics are hierarchical with these same subcomplexes acting as kinetic intermediates.Comment: 4 pages, 4 figure

Conditional gene expression in the mouse using a Sleeping Beauty gene-trap transposon

BACKGROUND: Insertional mutagenesis techniques with transposable elements have been popular among geneticists studying model organisms from E. coli to Drosophila and, more recently, the mouse. One such element is the Sleeping Beauty (SB) transposon that has been shown in several studies to be an effective insertional mutagen in the mouse germline. SB transposon vector studies have employed different functional elements and reporter molecules to disrupt and report the expression of endogenous mouse genes. We sought to generate a transposon system that would be capable of reporting the expression pattern of a mouse gene while allowing for conditional expression of a gene of interest in a tissue- or temporal-specific pattern. RESULTS: Here we report the systematic development and testing of a transposon-based gene-trap system incorporating the doxycycline-repressible Tet-Off (tTA) system that is capable of activating the expression of genes under control of a Tet response element (TRE) promoter. We demonstrate that the gene trap system is fully functional in vitro by introducing the "gene-trap tTA" vector into human cells by transposition and identifying clones that activate expression of a TRE-luciferase transgene in a doxycycline-dependent manner. In transgenic mice, we mobilize gene-trap tTA vectors, discover parameters that can affect germline mobilization rates, and identify candidate gene insertions to demonstrate the in vivo functionality of the vector system. We further demonstrate that the gene-trap can act as a reporter of endogenous gene expression and it can be coupled with bioluminescent imaging to identify genes with tissue-specific expression patterns. CONCLUSION: Akin to the GAL4/UAS system used in the fly, we have made progress developing a tool for mutating and revealing the expression of mouse genes by generating the tTA transactivator in the presence of a secondary TRE-regulated reporter molecule. A vector like the gene-trap tTA could provide a means for both annotating mouse genes and creating a resource of mice that express a regulable transcription factor in temporally- and tissue-specific patterns for conditional gene expression studies. These mice would be a valuable resource to the mouse genetics community for purpose of dissecting mammalian gene function

Splaying Preorders and Postorders

Let $T$ be a binary search tree. We prove two results about the behavior of the Splay algorithm (Sleator and Tarjan 1985). Our first result is that inserting keys into an empty binary search tree via splaying in the order of either $T$'s preorder or $T$'s postorder takes linear time. Our proof uses the fact that preorders and postorders are pattern-avoiding: i.e. they contain no subsequences that are order-isomorphic to $(2,3,1)$ and $(3,1,2)$, respectively. Pattern-avoidance implies certain constraints on the manner in which items are inserted. We exploit this structure with a simple potential function that counts inserted nodes lying on access paths to uninserted nodes. Our methods can likely be extended to permutations that avoid more general patterns. Second, if $T'$ is any other binary search tree with the same keys as $T$ and $T$ is weight-balanced (Nievergelt and Reingold 1973), then splaying $T$'s preorder sequence or $T$'s postorder sequence starting from $T'$ takes linear time. To prove this, we demonstrate that preorders and postorders of balanced search trees do not contain many large "jumps" in symmetric order, and exploit this fact by using the dynamic finger theorem (Cole et al. 2000). Both of our results provide further evidence in favor of the elusive "dynamic optimality conjecture.