David B. A. Epstein

Protein Diffusion and Macromolecular Crowding in Thylakoid Membranes

The photosynthetic light reactions of green plants are mediated by chlorophyll-binding protein complexes located in the thylakoid membranes within the chloroplasts. Thylakoid membranes have a complex structure, with lateral segregation of protein complexes into distinct membrane regions known as the grana and the stroma lamellae. It has long been clear that some protein complexes can diffuse between the grana and the stroma lamellae, and that this movement is important for processes including membrane biogenesis, regulation of light harvesting, and turnover and repair of the photosynthetic complexes. In the grana membranes, diffusion may be problematic because the protein complexes are very densely packed (approximately 75% area occupation) and semicrystalline protein arrays are often observed. To date, direct measurements of protein diffusion in green plant thylakoids have been lacking. We have developed a form of fluorescence recovery after photobleaching that allows direct measurement of the diffusion of chlorophyll-protein complexes in isolated grana membranes from Spinacia oleracea. We show that about 75% of fluorophores are immobile within our measuring period of a few minutes. We suggest that this immobility is due to a protein network covering a whole grana disc. However, the remaining fraction is surprisingly mobile (diffusion coefficient 4.6 ± 0.4 × 10−11 cm2 s−1), which suggests that it is associated with mobile proteins that exchange between the grana and stroma lamellae within a few seconds. Manipulation of the protein-lipid ratio and the ionic strength of the buffer reveals the roles of macromolecular crowding and protein-protein interactions in restricting the mobility of grana proteins.

The use of Knuth-Bendix methods to solve the wordproblem in automatic groups

Certain classes of infinite groups arising from geometry and topology are known to have solvable word problem. We describe the development of practical methods for the solution of the word problem based on the reduction of words in the generators to a normal form. The Knuth-Bendix completion procedure is the principal tool used but, in the case that this process does not halt, we use alternative methods involving the construction of finite-state automata. A computer implementation of these procedures together with some performance statistics on some simple examples are also described.

Expanding endomorphisms of flat manifolds

LET h4 be a compact differentiable manifold without boundary. A Cl-endomorphism f: IV--+ M is expanding if for some (and hence any) Riemannian metric on M there exist c > 0, 1 > 1 such that ]/7’f”ul] 2 c/Z~]/U]I for all u E TM and all integers m > 0. In this paper we show that any compact manifold with a flat Riemannian metric admits an expanding endomorphism. The classification of expanding endomorphisms, up to topological conjugacy, was studied in [3]. It is of interest not only abstractly but also because the inverse limit of an expanding endomorphism can be considered as an indecomposable piece of the non-wandering set of diffeomorphism: see [4] and [5].

Toponome imaging system in situ protein network mapping in normal and cancerous colon from the same patient reveals more than five-thousand cancer specific protein clusters and their subcellular annotation by using a three symbol code

In a proof of principle study, we have applied an automated fluorescence toponome imaging system (TIS) to examine whether TIS can find protein network structures, distinguishing cancerous from normal colon tissue present in a surgical sample from the same patient. By using a three symbol code and a power of combinatorial molecular discrimination (PCMD) of 2(21) per subcellular data point in one single tissue section, we demonstrate an in situ protein network structure, visualized as a mosaic of 6813 protein clusters (combinatorial molecular phenotype or CMPs), in the cancerous part of the colon. By contrast, in the histologically normal colon, TIS identifies nearly 5 times the number of protein clusters as compared to the cancerous part (32 009). By subcellular visualization procedures, we found that many cell surface membrane molecules were closely associated with the cell cytoskeleton as unique CMPs in the normal part of the colon, while the same molecules were disassembled in the cancerous part, suggesting the presence of dysfunctional cytoskeleton-membrane complexes. As expected, glandular and stromal cell signatures were found, but interestingly also found were potentially TIS signatures identifying a very restricted subset of cells expressing several putative stem cell markers, all restricted to the cancerous tissue. The detection of these signatures is based on the extreme searching depth, high degree of dimensionality, and subcellular resolution capacity of TIS. These findings provide the technological rationale for the feasibility of a complete colon cancer toponome to be established by massive parallel high throughput/high content TIS mapping.

Non-β-cell progenitors of β-cells in pregnant mice

Pregnancy is a normal physiological condition in which the maternal β-cell mass increases rapidly about two-fold to adapt to new metabolic challenges. We have used a lineage tracing of β-cells to analyse the origin of new β-cells during this rapid expansion in pregnancy. Double transgenic mice bearing a tamoxifen-dependent Cre-recombinase construct under the control of a rat insulin promoter, together with a reporter Z/AP gene, were generated. Then, in response to a pulse of tamoxifen before pregnancy, β-cells in these animals were marked irreversibly and heritably with the human placental alkaline phosphatase (HPAP). First, we conclude that the lineage tracing system was highly specific for β-cells. Secondly, we scored the proportion of the β-cells marked with HPAP during a subsequent chase period in pregnant and non-pregnant females. We observed a dilution in this labelling index in pregnant animal pancreata, compared to non-pregnant controls, during a single pregnancy in the chase period. To extend these observations we also analysed the labelling index in pancreata of animals during the second of two pregnancies in the chase period. The combined data revealed statistically-significant dilution during pregnancy, indicating a contribution to new beta cells from a non-β-cell source. Thus for the first time in a normal physiological condition, we have demonstrated not only β-cell duplication, but also the activation of a non-β-cell progenitor population. Further, there was no transdifferentiation of β-cells to other cell types in a two and half month period following labelling, including the period of pregnancy.

RAMTaB: Robust Alignment of Multi-Tag Bioimages

Background In recent years, new microscopic imaging techniques have evolved to allow us to visualize several different proteins (or other biomolecules) in a visual field. Analysis of protein co-localization becomes viable because molecules can interact only when they are located close to each other. We present a novel approach to align images in a multi-tag fluorescence image stack. The proposed approach is applicable to multi-tag bioimaging systems which (a) acquire fluorescence images by sequential staining and (b) simultaneously capture a phase contrast image corresponding to each of the fluorescence images. To the best of our knowledge, there is no existing method in the literature, which addresses simultaneous registration of multi-tag bioimages and selection of the reference image in order to maximize the overall overlap between the images. Methodology/Principal Findings We employ a block-based method for registration, which yields a confidence measure to indicate the accuracy of our registration results. We derive a shift metric in order to select the Reference Image with Maximal Overlap (RIMO), in turn minimizing the total amount of non-overlapping signal for a given number of tags. Experimental results show that the Robust Alignment of Multi-Tag Bioimages (RAMTaB) framework is robust to variations in contrast and illumination, yields sub-pixel accuracy, and successfully selects the reference image resulting in maximum overlap. The registration results are also shown to significantly improve any follow-up protein co-localization studies. Conclusions For the discovery of protein complexes and of functional protein networks within a cell, alignment of the tag images in a multi-tag fluorescence image stack is a key pre-processing step. The proposed framework is shown to produce accurate alignment results on both real and synthetic data. Our future work will use the aligned multi-channel fluorescence image data for normal and diseased tissue specimens to analyze molecular co-expression patterns and functional protein networks.

THE LINEARITY OF THE CONJUGACY PROBLEM IN WORD-HYPERBOLIC GROUPS

The main result proved in this paper is that the conjugacy problem in word-hyperbolic groups is solvable in linear time. This is using a standard RAM model of computation, in which basic arithmetical operations on integers are assumed to take place in constant time. The constants involved in the linear time solution are all computable explicitly. We also give a proof of the result of Mike Shapiro that in a word-hyperbolic group a word in the generators can be transformed into short-lex normal form in linear time. This is used in the proof of our main theorem, but is a significant theoretical result of independent interest, which deserves to be in the literature. Previously the best known result was a quadratic estimate.

Growth functions and automatic groups

In this paper we study growth functions of automatic and hyperbolic groups. In addition to standard growth functions, we also want to count the number of finite graphs isomorphic to a given finite graph in the ball of radius n around the identity element in the Cayley graph. This topic was introduced to us by K. Saito [1991]. We report on fast methods to compute the growth function once we know the automatic structure. We prove that for a geodesic automatic structure, the growth function for any fixed finite connected graph is a rational function. For a word-hyperbolic group, we show that one can choose the denominator of the rational function independently of the finite graph.

COMPUTATION IN WORD-HYPERBOLIC GROUPS

We describe two practical algorithms for computing with word-hyperbolic groups, both of which we have implemented. The first is a method for estimating the maximum width, if it exists, of geodesic bigons in the Cayley graph of a finitely presented group G. Our procedure will terminate if and only this maximum width exists, and it has been proved by Papasoglu that this is the case if and only if G is word-hyperbolic. So the algorithm amounts to a method of verifying the property of word-hyperbolicity of G. The aim of the second algorithm is to compute the thinness constant for geodesic triangles in the Cayley graph of G. This seems to be a much more difficult problem, but our implementation does succeed with straightforward examples. Both algorithms involve substantial computations with finite state automata.

Integrating semantic annotation and information visualization for the analysis of multichannel fluorescence micrographs from pancreatic tissue

The challenging problem of computational bioimage analysis receives growing attention from life sciences. Fluorescence microscopy is capable of simultaneously visualizing multiple molecules by staining with different fluorescent dyes. In the analysis of the result multichannel images, segmentation of ROIs resembles only a first step which must be followed by a second step towards the analysis of the ROIs signals in the different channels. In this paper we present a system that combines image segmentation and information visualization principles for an integrated analysis of fluorescence micrographs of tissue samples. The analysis aims at the detection and annotation of cells of the Islets of Langerhans and the whole pancreas, which is of great importance in diabetes studies and in the search for new anti-diabetes treatments. The system operates with two modules. The automatic annotation module applies supervised machine learning for cell detection and segmentation. The second information visualization module can be used for an interactive classification and visualization of cell types following the link-and-brush principle for filtering. We can compare the results obtained with our system with results obtained manually by an expert, who evaluated a set of example images three times to account for his intra-observer variance. The comparison shows that using our system the images can be evaluated with high accuracy which allows a considerable speed up of the time-consuming evaluation process.