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We study equilibrium configurations of hexagonal columnar liquid crystals in the context of characterizing packing structures of bacteriophage viruses in a protein capsid. These are viruses that infect bacteria and are currently the focus of intense research efforts, with the goal of finding new therapies for bacteria-resistant antibiotics. The energy that we propose consists of the Oseen–Frank free energy of nematic liquid crystals that penalizes bending of the columnar directions, in addition to the cross-sectional elastic energy accounting for distortions of the transverse hexagonal structure; we also consider the isotropic contribution of the core and the energy of the unknown interface between the outer ordered region of the capsid and the inner disordered core. The problem becomes of free boundary type, with constraints. We show that the concentric, azimuthal, spool-like configuration is the absolute minimizer. Moreover, we present examples of toroidal structures formed by DNA in free solution and compare them with the analogous ones occurring in experiments with other types of lyotropic liquid crystals, such as food dyes and additives.This article is part of the theme issue ‘Topics in mathematical design of complex materials’.

Copy Number Aberrations, gains and losses of genomic regions, are a hallmark of cancer and can be experimentally detected using microarray comparative genomic hybridization (aCGH). In previous works, we developed a topology based method to analyze aCGH data whose output are regions of the genome where copy number is altered in patients with a predetermined cancer phenotype. We call this method Topological Analysis of array CGH (TAaCGH). Here we combine TAaCGH with machine learning techniques to build classifiers using copy number aberrations. We chose logistic regression on two different binary phenotypes related to breast cancer to illustrate this approach. The first case consists of patients with over-expression of the ERBB2 gene. Over-expression of ERBB2 is commonly regulated by a copy number gain in chromosome arm 17q. TAaCGH found the region 17q11-q22 associated with the phenotype and using logistic regression we reduced this region to 17q12-q21.31 correctly classifying 78% of the ERBB2 positive individuals (sensitivity) in a validation data set. We also analyzed over-expression in Estrogen Receptor (ER), a second phenotype commonly observed in breast cancer patients and found that the region 5p14.3-12 together with six full arms were associated with the phenotype. Our method identified 4p, 6p and 16q as the strongest predictors correctly classifying 76% of ER positives in our validation data set. However, for this set there was a significant increase in the false positive rate (specificity). We suggest that topological and machine learning methods can be combined for prediction of phenotypes using genetic data.

Bacteriophages densely pack their long dsDNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure. Experiments have confirmed that the details of the hexagonal packing depend on the electrochemistry of the capsid and its environment. In this work, we propose a biophysical model that quantifies the relationship between DNA configurations inside bacteriophage capsids and the types and concentrations of ions present in a biological system. We introduce an expression for the free energy which combines the electrostatic energy with contributions from bending of individual segments of DNA and Lennard-Jones-type interactions between these segments. The equilibrium points of this energy solve a partial differential equation that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach that allows us to simulate much larger systems than what is currently possible using the existing simulations, typically done at a molecular level. In particular, we are able to estimate bending and repulsion between DNA segments as well as the full electrochemistry of the solution, both inside and outside of the capsid. The numerical results show good agreement with existing experiments and molecular dynamics simulations for small capsids.

It is widely recognized that the three-dimensional (3D) architecture of eukaryotic chromatin plays an important role in processes such as gene regulation and cancer-driving gene fusions. Observing or inferring this 3D structure at even modest resolutions had been problematic, since genomes are highly condensed and traditional assays are coarse. However, recently devised high-throughput molecular techniques have changed this situation. Notably, the development of a suite of chromatin conformation capture (CCC) assays has enabled elicitation of contacts - spatially close chromosomal loci - which have provided insights into chromatin architecture. Most analysis of CCC data has focused on the contact level, with less effort directed toward obtaining 3D reconstructions and evaluating the accuracy and reproducibility thereof. While questions of accuracy must be addressed experimentally, questions of reproducibility can be addressed statistically - the purpose of this paper. We use a constrained optimization technique to reconstruct chromatin configurations for a number of closely related yeast datasets and assess reproducibility using four metrics that measure the distance between 3D configurations. The first of these, Procrustes fitting, measures configuration closeness after applying reflection, rotation, translation, and scaling-based alignment of the structures. The others base comparisons on the within-configuration inter-point distance matrix. Inferential results for these metrics rely on suitable permutation approaches. Results indicate that distance matrix-based approaches are preferable to Procrustes analysis, not because of the metrics per se but rather on account of the ability to customize permutation schemes to handle within-chromosome contiguity. It has recently been emphasized that the use of constrained optimization approaches to 3D architecture reconstruction are prone to being trapped in local minima. Our methods of reproducibility assessment provide a means for comparing 3D reconstruction solutions so that we can discern between local and global optima by contrasting solutions under perturbed inputs. © 2014 The Author.

Trypanosomatida parasites, such as Trypanosoma and Leishmania, are the cause of deadly diseases in many third world countries. The three dimensional structure of their mitochondrial DNA, known as kinetoplast DNA (kDNA), is unique since it is organized into several thousands of minicircles that are topologically linked. How and why the minicircles form such a network have remained unanswered questions. In our previous work we have presented a model of network formation that hypothesizes that the network is solely driven by the confinement of minicircles. Our model shows that upon confinement a percolation network forms. This network grows into a space filling network, called saturation network, upon further confinement of minicircles. Our model also shows, in agreement with experimental data, that the mean valence of the network (that is, the average number of minicircles topologically linked to any minicircle in the network) grows linearly with minicircle density. In our previous studies however we disregarded DNA flexibility and used rigid minicircles to model DNA, here we address this limitation by allowing minicircles to be flexible. Our numerical results show that the topological characteristics that describe the growth and topology of the minicircle networks have similar values to those observed in the case of rigid minicircles suggesting that these properties are robust and therefore a potentially adequate description of the networks observed in Trypanosomatid parasites.

The mitochondrial DNA of trypanosomes, called kinetoplast DNA (kDNA) contains thousands of minicircles that are topologically linked into a single structure that resembles a medieval chainmail. This biological chainmail is characterized by two parameters: the link type between minicircles, and the number of minicircles linked to each minicircle (i.e. the minicircle valence). In previous works, a protocol was proposed to determine the mean value of the minicircle valence. In these experiments, minicircles were excised from the network and the products compared with those obtained from fragmenting idealized structures. These idealized structures assumed a negligible variance in the distribution of valences of the initial network. It is therefore unclear to what extent this theoretical analysis captures the true topology of the kDNA network when kDNA samples are extracted from unsynchronized cells or from cells with silenced kDNA replication genes. Subsequent studies proposed that there is a critical percolation density during network formation. We asked whether this density can be estimated using fragmentation reactions. The goal of this work is to develop a mathematical method that can be used to estimate the mean valence of networks when the variance of the valence is non-negligible. We first show microscopy data on Crithidia fasciculata that, in agreement with the original experimental results, show a distribution of valences with nonzero variance. Second, we use computer simulations of network fragmentation to show that the predicted and actual mean valence are different when the valence distribution has nonzero variance. We propose a more general mathematical formulation and computer simulations of kDNA fragmentation to estimate this value. Last, we show that fragmentation experiments may lead to errors in the estimation of the critical percolation density since the collapsing density depends on the initial density of the network, and on the fragmentation reaction.

DNA copy number aberrations CNAs play an important role in cancer and can be experimentally detected using microarray comparative genomic hybridization CGH techniques. Amplicons, CNAs that extend over large sections of the genome, are difficult to study since they may contain multiple independent and dependent copy number changes. Here, we propose an algorithm to find the CNAs structure within a given amplicon. Our method relies on the observation that co-occurring CNAs can be encoded as 1-dimensional cycles. Applying this method to breast cancer patients known as ERBB2/HER2/NEU amplified we find three regions that can be co-occuring: the first region is in the cytoband 17q12, where the ERBB2 gene is located, the second region expands between 17q21.2 to 17q21.31 and includes the keratin genes, the third one is 17q21.33. We suggest that the first homology group helps uncovering the structure of amplicons.

A number of idealized models have been proposed to explain the long range organization of the DNA in bacteriophages. However, none of these models can account for the distributions of complex knots found when examining DNA extracted from bacteriophage P4 capsids. Furthermore, these models do not consider possible chirality biases in the arrangement of the DNA molecule inside the capsid. In this paper, we address these two issues by proposing a randomized version of one of the most popular models: the coaxially spooled model. We present analytical and numerical results for the properties of the random polygons (knots) generated using this model. We show that such model can easily generate complex knotted conformations and although it accounts for some chirality of the organization of the DNA molecules inside bacteriophage capsids does not fully explain the experimental data.

Cancer progression is due to the accumulation of recurrent genomic alterations that induce growth advantage and clonal expansion. Most of these genomic changes can be detected using the array comparative genomic hybridization (CGH) technique. The accurate classification of these genomic alterations is expected to have an important impact on translational and basic research. Here we review recent advances in CGH technology used in the characterization of different features of breast cancer. First, we present bioinformatics methods that have been developed for the analysis of CGH arrays; next, we discuss the use of array CGH technology to classify tumor stages and to identify and stratify subgroups of patients with different prognoses and clinical behaviors. We finish our review with a discussion of how CGH arrays are being used to identify oncogenes, tumor suppressor genes, and breast cancer susceptibility genes.

DNA copy number aberrations (CNAs) are of biological and medical interest because they help identify regulatory mechanisms underlying tumor initiation and evolution. Identification of tumor-driving CNAs (driver CNAs) however remains a challenging task, because they are frequently hidden by CNAs that are the product of random events that take place during tumor evolution. Experimental detection of CNAs is commonly accomplished through array comparative genomic hybridization (aCGH) assays followed by supervised and/or unsupervised statistical methods that combine the segmented profiles of all patients to identify driver CNAs. Here, we extend a previously-presented supervised algorithm for the identification of CNAs that is based on a topological representation of the data. Our method associates a two-dimensional (2D) point cloud with each aCGH profile and generates a sequence of simplicial complexes, mathematical objects that generalize the concept of a graph. This representation of the data permits segmenting the data at different resolutions and identifying CNAs by interrogating the topological properties of these simplicial complexes. We tested our approach on a published dataset with the goal of identifying specific breast cancer CNAs associated with specific molecular subtypes. Identification of CNAs associated with each subtype was performed by analyzing each subtype separately from the others and by taking the rest of the subtypes as the control. Our results found a new amplification in 11q at the location of the progesterone receptor in the Luminal A subtype. Aberrations in the Luminal B subtype were found only upon removal of the basal-like subtype from the control set. Under those conditions, all regions found in the original publication, except for 17q, were confirmed, all aberrations, except those in chromosome arms 8q and 12q were confirmed in the basal-like subtype. These two chromosome arms, however, were detected only upon removal of three patients with exceedingly large copy number values. More importantly, we detected 10 and 21 additional regions in the Luminal B and basal-like subtypes, respectively. Most of the additional regions were either validated on an independent dataset and/or using GISTIC. Furthermore, we found three new CNAs in the basal-like subtype: a combination of gains and losses in 1p, a gain in 2p and a loss in 14q. Based on these results, we suggest that topological approaches that incorporate multiresolution analyses and that interrogate topological properties of the data can help in the identification of copy number changes in cancer.

The circular chromosome of Escherichia coli is organized into independently supercoiled loops, or topological domains. We investigated the organization and size of these domains in vivo and in vitro. Using the expression of >300 supercoiling-sensitive genes to gauge local chromosomal supercoiling, we quantitatively measured the spread of relaxation from double-strand breaks generated in vivo and thereby calculated the distance to the nearest domain boundary. In a complementary approach, we gently isolated chromosomes and examined the lengths of individual supercoiled loops by electron microscopy. The results from these two very different methods agree remarkably well. By comparing our results to Monte Carlo simulations of domain organization models, we conclude that domain barriers are not placed stably at fixed sites on the chromosome but instead are effectively randomly distributed. We find that domains are much smaller than previously reported, ∼10 kb on average. We discuss the implications of these findings and present models for how domain barriers may be generated and displaced during the cell cycle in a stochastic fashion.

Analysing chromosome aberrations induced by low linear energy transfer (LET) radiation in order to characterize systematic spatial clustering among the 22 human autosomes in human lymphocytes and to compare their relative participation in interchanges.A multicolour fluorescence in situ hybridization (mFISH) data set, specifying colour junctions in metaphases of human peripheral blood lymphocytes 72 h after in vitro exposure to low LET radiation, was analysed separately and in combination with previously published results. Monte Carlo computer simulations and mathematical modelling guided data analysis.Statistical tests on aberration data confirmed two clusters of chromosomes, [1, 16, 17, 19, 22] and [13, 14, 15, 21, 22], as having their members being on average closer to each other than randomness would predict. The first set has been reported previously to be near the centre of the interphase nucleus and to be formed mainly by gene-rich chromosomes, while the second set comprises the nucleolus chromosomes. The results suggest a possible interplay between chromosome positioning and transcription. A number of other clusters suggested in the literature were not confirmed and considerable randomness of chromosome-chromosome juxtapositions was present. In addition, and consistent with previous results, it was found that chromosome participation in interchanges is approximately proportional to the two-thirds power of the DNA content.

A comprehensive description of chromosome aberrations is introduced that is suitable for all cytogenetic protocols (e.g. solid staining, banding, FISH, mFISH, SKY, bar coding) and for mathematical analyses. "Aberration multigraphs" systematically characterize and interrelate three basic aberration elements: (1) the initial configuration of chromosome breaks; (2) the exchange process, whose cycle structure helps to describe aberration complexity; and (3) the final configuration of rearranged chromosomes, which determines the observed pattern but may contain cryptic misrejoinings in addition. New aberration classification methods and a far-reaching generalization of mPAINT descriptors, applicable to any protocol, emerge. The difficult problem of trying to infer actual exchange processes from cytogenetically observed final patterns is analyzed using computer algorithms, adaptations of known theorems on cubic graphs, and some new graph-theoretical constructs. Results include the following: (1) For a painting protocol, unambiguously inferring the occurrence of a high-order cycle requires a corresponding number of different colors; (2) cycle structure can be computed by a simple trick directly from mPAINT descriptors if the initial configuration has no more than one break per homologue pair; and (3) higher-order cycles are more frequent than the obligate cycle structure specifies. Aberration multigraphs are a powerful new way to describe, classify and quantitatively analyze radiation-induced chromosome aberrations. They pinpoint (but do not eliminate) the problem that, with present cytogenetic techniques, one observed pattern corresponds to many possible initial configurations and exchange processes.

To test quantitatively whether there are systematic chromosome–chromosome associations within human interphase nuclei, interchanges between all possible heterologous pairs of chromosomes were measured with 24-color whole-chromosome painting (multiplex FISH), after damage to interphase lymphocytes by sparsely ionizing radiation in vitro. An excess of interchanges for a specific chromosome pair would indicate spatial proximity between the chromosomes comprising that pair. The experimental design was such that quite small deviations from randomness (extra pairwise interchanges within a group of chromosomes) would be detectable. The only statistically significant chromosome cluster was a group of five chromosomes previously observed to be preferentially located near the center of the nucleus. However, quantitatively, the overall deviation from randomness within the whole genome was small. Thus, whereas some chromosome–chromosome associations are clearly present, at the whole-chromosomal level, the predominant overall pattern appears to be spatially random.

Exchange type chromosome aberrations (ETCAs) are rearrangements of the genome that occur when chromosomes break and the resulting fragments rejoin with fragments from other chromosomes or from other regions within the same chromosome. ETCAs are commonly observed in cancer cells and in cells exposed to radiation. The frequency of these chromosome rearrangements is correlated with their spatial proximity, therefore it can be used to infer the three dimensional organization of the genome. Extracting statistical significance of spatial proximity from cancer and radiation data has remained somewhat elusive because of the sparsity of the data. We here propose a new approach to study the three dimensional organization of the genome using algebraic statistics. We test our method on a published data set of irradiated human blood lymphocyte cells. We provide a rigorous method for testing the overall organization of the genome, and in agreement with previous results we find a random relative positioning of chromosomes with the exception of the chromosome pairs {1,22} and {13,14} that have a significantly larger number of ETCAs than the rest of the chromosome pairs suggesting their spatial proximity. We conclude that algebraic methods can successfully be used to analyze genetic data and have potential applications to larger and more complex data sets.

Trypanosomatida parasites, such as trypanosoma and lishmania, are the cause of deadly diseases in many third world countries. A distinctive feature of these organisms is the three dimensional organization of their mitochondrial DNA into maxi and minicircles. In some of these organisms minicircles are confined into a small disk volume and are topologically linked, forming a gigantic linked network. The origins of such a network as well as of its topological properties are mostly unknown. In this paper we quantify the effects of the confinement on the topology of such a minicircle network. We introduce a simple mathematical model in which a collection of randomly oriented minicircles are spread over a rectangular grid. We present analytical and computational results showing that a finite positive critical percolation density exists, that the probability of formation of a highly linked network increases exponentially fast when minicircles are confined, and that the mean minicircle valence (the number of minicircles that a particular minicircle is linked to) increases linearly with density. When these results are interpreted in the context of the mitochondrial DNA of the trypanosome they suggest that confinement plays a key role on the formation of the linked network. This hypothesis is supported by the agreement of our simulations with experimental results that show that the valence grows linearly with density. Our model predicts the existence of a percolation density and that the distribution of minicircle valences is more heterogeneous than initially thought.

Type II topoisomerases are enzymes that change the topology of DNA by performing strand-passage. In particular, they unknot knotted DNA very efficiently. Motivated by this experimental observation, we investigate transition probabilities between knots. We use the BFACF algorithm to generate ensembles of polygons in Z3 of fixed knot type. We introduce a novel strand-passage algorithm which generates a Markov chain in knot space. The entries of the corresponding transition probability matrix determine state-transitions in knot space and can track the evolution of different knots after repeated strand-passage events. We outline future applications of this work to DNA unknotting.

In recent years, knot theory and low-dimensional topology have been effectively used to study the topology and geometry of DNA under different spatial constraints, and to solve the topological mechanisms of enzymes such as site-specific recombinases and topoisomerases. Through continuous collaboration and close interaction with experimental biologists, many problems approached and the solutions proposed remain relevant to the biological community, while being mathematically and computationally interesting. In this paper, we illustrate the use of mathematical and computational methods in a variety of DNA topology problems. This is by no means an exhaustive description of techniques and applications, but is rather intended to introduce the reader to the exciting applications of topology to the study of DNA. Many more examples will be found throughout this book.

Kinetoplast DNA (kDNA) is the mitochondrial of DNA of disease causing organisms such as Trypanosoma Brucei (T. Brucei) and Trypanosoma Cruzi (T. Cruzi). In most organisms, KDNA is made of thousands of small circular DNA molecules that are highly condensed and topologically linked forming a gigantic planar network. In our previous work we have developed mathematical and computational models to test the confinement hypothesis, that is that the formation of kDNA minicircle networks is a product of the high DNA condensation achieved in the mitochondrion of these organisms. In these studies we studied three parameters that characterize the growth of the network topology upon confinement: the critical percolation density, the mean saturation density and the mean valence (i.e. the number of mini circles topologically linked to any chosen minicircle). Experimental results on insect-infecting organisms showed that the mean valence is equal to three, forming a structure similar to those found in medieval chain-mails. These same studies hypothesized that this value of the mean valence was driven by the DNA excluded volume. Here we extend our previous work on kDNA by characterizing the effects of DNA excluded volume on the three descriptive parameters. Using computer simulations of polymer swelling we found that (1) in agreement with previous studies the linking probability of two minicircles does not decrease linearly with the distance between the two minicircles, (2) the mean valence grows linearly with the density of minicircles and decreases with the thickness of the excluded volume, (3) the critical percolation and mean saturation densities grow linearly with the thickness of the excluded volume. Our results therefore suggest that the swelling of the DNA molecule, due to electrostatic interactions, has relatively mild implications on the overall topology of the network. Our results also validate our topological descriptors since they appear to reflect the changes in the physical properties of the polymeric chains and at the same time remain faithful to their description of kDNA.

© 2015 Diao et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Kinetoplast DNA (kDNA), a unique mitochondrial structure common to trypanosomatid parasites, contains thousands of DNA minicircles that are densely packed and can be topologically linked into a chain mail-like network. Experimental data indicate that every minicircle in the network is, on average, singly linked to three other minicircles (i.e., has mean valence 3) before replication and to six minicircles in the late stages of replication. The biophysical factors that determine the topology of the network and its changes during the cell cycle remain unknown. Using a mathematical modeling approach, we previously showed that volume confinement alone can drive the formation of the network and that it induces a linear relationship between mean valence and minicircle density. Our modeling also predicted a minicircle valence two orders of magnitude greater than that observed in kDNA. To determine the factors that contribute to this discrepancy we systematically analyzed the relationship between the topological properties of the network (i.e., minicircle density and mean valence) and its biophysical properties such as DNA bending, electrostatic repulsion, and minicircle relative position and orientation. Significantly, our results showed that most of the discrepancy between the theoretical and experimental observations can be accounted for by the orientation of the minicircles with volume exclusion due to electrostatic interactions and DNA bending playing smaller roles. Our results are in agreement with the three dimensional kDNA organization model, initially proposed by Delain and Riou, in which minicircles are oriented almost perpendicular to the horizontal plane of the kDNA disk. We suggest that while minicircle confinement drives the formation of kDNA networks, it is minicircle orientation that regulates the topological complexity of the network.

5 pages, 4 figures.-- PMID: 15958528 [PubMed].-- PMCID: PMC1166588., Icosahedral bacteriophages pack their double-stranded DNA genomes to near-crystalline density and achieve one of the highest levels of DNA condensation found in nature. Despite numerous studies, some essential properties of the packaging geometry of the DNA inside the phage capsid are still unknown. We present a different approach to the problems of randomness and chirality of the packed DNA. We recently showed that most DNA molecules extracted from bacteriophage P4 are highly knotted because of the cyclization of the linear DNA molecule confined in the phage capsid. Here, we show that these knots provide information about the global arrangement of the DNA inside the capsid. First, we analyze the distribution of the viral DNA knots by high-resolution gel electrophoresis. Next, we perform Monte Carlo computer simulations of random knotting for freely jointed polygons confined to spherical volumes. Comparison of the knot distributions obtained by both techniques produces a topological proof of nonrandom packaging of the viral DNA. Moreover, our simulations show that the scarcity of the achiral knot 41 and the predominance of the torus knot 51 over the twist knot 52 observed in the viral distribution of DNA knots cannot be obtained by confinement alone but must include writhe bias in the conformation sampling. These results indicate that the packaging geometry of the DNA inside the viral capsid is writhe-directed., This work was supported by grants from the Ministerio Español de Ciencia y Tecnología (BMC2002-03275), the National Institutes of Health (GM68423-01), and the National Science Foundation (DMS9971169) and by a Burroughs Wellcome Fund Interfaces grant to the Program in Mathematics and Molecular Biology.

Chromosome aberrations are large-scale illegitimate rearrangements of the genome. They are indicative of DNA damage and informative about damage processing pathways. Despite extensive investigations over many years, the mechanisms underlying aberration formation remain controversial. New experimental assays such as multiplex fluorescent in situ hybridyzation (mFISH) allow combinatorial "painting" of chromosomes and are promising for elucidating aberration formation mechanisms. Recently observed mFISH aberration patterns are so complex that computer and graph-theoretical methods are needed for their full analysis. An important part of the analysis is decomposing a chromosome rearrangement process into "cycles." A cycle of order n, characterized formally by the cyclic graph with 2n vertices, indicates that n chromatin breaks take part in a single irreducible reaction. We here describe algorithms for computing cycle structures from experimentally observed or computer-simulated mFISH aberration patterns. We show that analyzing cycles quantitatively can distinguish between different aberration formation mechanisms. In particular, we show that homology-based mechanisms do not generate the large number of complex aberrations, involving higher-order cycles, observed in irradiated human lymphocytes.

When linear double-stranded DNA is packed inside bacteriophage capsids, it becomes highly compacted. However, the phage is believed to be fully effective only if the DNA is not entangled. Nevertheless, when DNA is extracted from a tailless mutant of the P4 phage, DNA is found to be cyclic and knotted (probability of 0.95). The knot spectrum is very complex, and most of the knots have a large number of crossings. We quantified the frequency and crossing numbers of these knots and concluded that, for the P4 tailless mutant, at least half the knotted molecules are formed while the DNA is still inside the viral capsid rather than during extraction. To analyze the origin of the knots formed inside the capsid, we compared our experimental results to Monte Carlo simulations of random knotting of equilateral polygons in confined volumes. These simulations showed that confinement of closed chains to tightly restricted volumes results in high knotting probabilities and the formation of knots with large crossing numbers. We conclude that the formation of the knots inside the viral capsid is driven mainly by the effects of confinement., J.A. and M.V. were supported by the Program in Mathematics and Molecular Biology through a Burroughs Wellcome Fund Interfaces Grant and by National Science Foundation Grant DMS-9971169. M.V. was supported by a Dirección General de Asuntos del Personal Académico-Universidad Nacional Autónoma de México graduate fellowship. This research was supported also by Ministry of Science of Spain Grant PB98-0487

Aim The success of kidney transplantation relies heavily upon the compatibility of the HLA genes between donor and recipient, but the high degree of polymorphism among these genes in the population makes finding an ideal match difficult. However, it is unclear whether specific amino acids are particularly critical in determining histocompatibility. To investigate this possibility, we introduce a novel method of comparing donor and recipient genotypes and explore its efficacy in predicting transplant rejection. Methods Using typing data of the HLA-A, -B, -C, and -DRB1 genes for 580 paired donors and recipients of a kidney transplant, we developed a method of allele estimation that used population frequency information to estimate amino acid sequence information. Using this sequence data we tested a number of metrics for measuring differences between donor and recipient genotypes, and looked for associations between mismatched residues and chronic rejection. Results Preliminary analysis of a cohort of 348 transplants with Caucasian recipients indicate a high association between residue mismatches in HLA-B and chronic rejection, primarily in residues 69 and 71 with p α p α Conclusions Association between HLA residue mismatches and chronic rejection was observed in cases where the residues’ properties differed significantly, and when the value of the residue is linked to broader motif changes. Future investigations will consider the impact of functional changes in residues in addition to statistical characterization of these predictive sites, and how these factors relate to transplant compatibility assessment.

4 pages, 3 figures.-- PMID: 11433043 [PubMed].-- PMCID: PMC55791., We describe a two-dimensional agarose gel electrophoresis procedure that improves the resolution of knotted DNA molecules. The first gel dimension is run at low voltage, and DNA knots migrate according to their compactness. The second gel dimension is run at high voltage, and DNA knots migrate according to other physical parameters such as shape and flexibility. In comparison with one-dimensional gel electrophoresis, this procedure segregates the knotted DNA molecules from other unknotted forms of DNA, and partially resolves populations of knots that have the same number of crossings. The two-dimensional display may allow quantitative and qualitative characterization of different types of DNA knots simply by gel velocity., This work was supported by grant PB98-0487 of the Ministry of Science of Spain (to J.R.). S.T. was the recipient of a predoctoral fellowship of the Ministry of Science of Spain. J.A., M.E.V. and D.W.S. were supported by the Program in Mathematics and Molecular Biology (PMMB) through a Burroughs Wellcome Fund Interfaces Grant

Motivation: The position of chromosomes in the interphase nucleus is believed to be associated with a number of biological processes. Here, we present a web-based application that helps analyze the relative position of chromosomes during interphase in human cells, based on observed radiogenic chromosome aberrations. The inputs of the program are a table of yields of pairwise chromosome interchanges and a proposed chromosome geometric cluster. Each can either be uploaded or selected from provided datasets. The main outputs are P-values for the proposed chromosome clusters. SCHIP is designed to be used by a number of scientific communities interested in nuclear architecture, including cancer and cell biologists, radiation biologists and mathematical/computational biologists. Availability: http://cramer.stat.ub.es/schip Contact: jarsuaga@cc.ucsf.edu Supplementary information: http://cramer.stat.ub.es/schip/help.htm

The chromosome of Escherichia coli is maintained in a negatively supercoiled state, and supercoiling levels are affected by growth phase and a variety of environmental stimuli. In turn, supercoiling influences local DNA structure and can affect gene expression. We used microarrays representing nearly the entire genome of Escherichia coli MG1655 to examine the dynamics of chromosome structure. We measured the transcriptional response to a loss of supercoiling caused either by genetic impairment of a topoisomerase or addition of specific topoisomerase inhibitors during log-phase growth and identified genes whose changes are statistically significant. Transcription of 7% of the genome (306 genes) was rapidly and reproducibly affected by changes in the level of supercoiling; the expression of 106 genes increased upon chromosome relaxation and the expression of 200 decreased. These changes are most likely to be direct effects, as the kinetics of their induction or repression closely follow the kinetics of DNA relaxation in the cells. Unexpectedly, the genes induced by relaxation have a significantly enriched AT content in both upstream and coding regions. The 306 supercoiling-sensitive genes are functionally diverse and widely dispersed throughout the chromosome. We propose that supercoiling acts as a second messenger that transmits information about the environment to many regulatory networks in the cell.