Entropic exponents of grafted lattice stars.

The surface entropic exponents of half-space lattice stars grafted at their central nodes in a hard wall are estimated numerically using the PERM algorithm. In the square half-lattice the exact values of the exponents are verified, including Barber's scaling relation and a generalization for 2-stars with one and two surface loops respectively. This is the relation γ_{211}=2γ_{21}-γ_{20}, where γ_{21} and γ_{211} are the surface entropic exponents of a grafted 2-star with one and two surface loops, respectively, and γ_{20} is the surface entropic exponent with no surface loops. This relation is also tested in the cubic half-lattice where surface entropic exponents are estimated up to 5-stars, including many with one or more surface loops. Barber's scaling relation and the relation γ_{3111}=γ_{30}-3γ_{31}+3γ_{311} are also tested, where the exponents {γ_{31},γ_{311},γ_{3111}} are of grafted 3-stars with one, two, or three surface loops, respectively, and γ_{30} is the surface exponent of grafted 3-stars.

Numerical estimates of square lattice star vertex exponents.

We implement parallel versions of the generalized atmospheric Rosenbluth methods and Wang-Landau algorithms for stars and for acyclic uniform branched networks in the square lattice. These are models of monodispersed branched polymers, and we estimate the star vertex exponents σ_{f} for f stars, and the entropic exponent γ_{G} for networks with comb and brush connectivity in two dimensions. Our results verify the predicted (but not rigorously proven) exact values of the vertex exponents and we test the scaling relation [B. Duplantier, J. Stat. Phys. 54, 581 (1989)JSTPBS0022-471510.1007/BF01019770]γ_{G}-1=[under ∑]f≥1m_{f}σ_{f}for several acyclic branched networks in two dimensions.

Phase diagrams of confined square lattice linked polygons.

The phase diagrams of two models of two confined and dense two-dimensional ring polymers are examined numerically. The ring polymers are modeled by square lattice polygons in a square cavity and are placed to be either unlinked or linked in the plane. The phase diagrams of the two models are found to be a function of the placement of the ring polymers and include multicritical points where first-order and continuous phase boundaries meet. We estimate numerically the critical exponents associated with the phase boundaries and the multicritical points.

Reply to "Comment on 'Osmotic pressure of compressed lattice knots' ".

The free energy of a model of uniformly weighted lattice knots of length n and knot type K confined to a lattice cube of side length L-1 is given by F_{L}(ϕ)=-1/Vlogp_{n,L}(K), where V=L^{3} and where ϕ=n/V is the concentration of monomers of the lattice knot in the confining cube. The limiting free energy of the model is F_{∞}(ϕ)=lim_{L→∞}F_{L}(ϕ) and the limiting osmotic pressure of monomers leaving the lattice knot to become solvent molecules is defined by Π_{∞}(ϕ)=ϕ^{2}d/dϕ[F_{∞}(ϕ)/ϕ]. I show that, under very mild assumptions, the functions P_{L}(ϕ)=ϕ^{2}d/dϕ[F_{L}(ϕ)/ϕ]|_{n} and Π_{L}(ϕ)=ϕ^{2}d/dϕ[F_{L}(ϕ)/ϕ]|_{L} are finite-size approximations of Π_{∞}(ϕ).

Osmotic pressure of compressed lattice knots.

A numerical simulation shows that the osmotic pressure of compressed lattice knots is a function of knot type, and so of entanglements. The osmotic pressure for the unknot goes through a negative minimum at low concentrations, but in the case of nontrivial knot types 3_{1} and 4_{1} it is negative for low concentrations. At high concentrations the osmotic pressure is divergent, as predicted by Flory-Huggins theory. The numerical results show that each knot type has an equilibrium length where the osmotic pressure for monomers to migrate into and out of the lattice knot is zero. Moreover, the lattice unknot is found to have two equilibria, one unstable, and one stable, whereas the lattice knots of type 3_{1} and 4_{1} have one stable equilibrium each.

Mean field analysis of algorithms for scale-free networks in molecular biology.

The sampling of scale-free networks in Molecular Biology is usually achieved by growing networks from a seed using recursive algorithms with elementary moves which include the addition and deletion of nodes and bonds. These algorithms include the Barabási-Albert algorithm. Later algorithms, such as the Duplication-Divergence algorithm, the Solé algorithm and the iSite algorithm, were inspired by biological processes underlying the evolution of protein networks, and the networks they produce differ essentially from networks grown by the Barabási-Albert algorithm. In this paper the mean field analysis of these algorithms is reconsidered, and extended to variant and modified implementations of the algorithms. The degree sequences of scale-free networks decay according to a powerlaw distribution, namely P(k) ∼ k-γ, where γ is a scaling exponent. We derive mean field expressions for γ, and test these by numerical simulations. Generally, good agreement is obtained. We also found that some algorithms do not produce scale-free networks (for example some variant Barabási-Albert and Solé networks).

Cancer prevalence in 129 breast-ovarian cancer families tested for BRCA1 and BRCA2 mutations.

BACKGROUND: Women who carry germline mutations in the breast-ovarian cancer susceptibility genes, BRCA1 and BRCA2, are at very high risk of developing breast and/or ovarian cancer. Both genes are tumour suppressor genes that protect all cells from deregulation, and there are reports of their involvement in other cancers that vary and seem to depend on the population investigated. It is therefore important to investigate the other associated cancers in different populations to assist with risk assessments. OBJECTIVES: To assess the cancer risk profile in BRCA-mutation-positive and negative South African breast-ovarian cancer families, mainly of Caucasian origin. DESIGN: Descriptive study in which the prevalence of all cancers in the pedigrees of BRCA1- and BRCA2-mutation-positive groups and a group of families without mutations in either gene were compared with the general population. RESULTS: As expected, female breast and ovarian cancer was significantly increased in all three groups. Furthermore, male breast cancer was significantly elevated in the BRCA2-positive and BRCA-negative groups. Stomach cancer prevalence was significantly elevated in the BRCA2-positive families compared with the general population. CONCLUSIONS: These results can be applied in estimation of cancer risks and may contribute to more comprehensive counselling of mutation-positive Caucasian breast and/or ovarian cancer families.

Strong association of de novo copy number mutations with sporadic schizophrenia.

Schizophrenia is an etiologically heterogeneous psychiatric disease, which exists in familial and nonfamilial (sporadic) forms. Here, we examine the possibility that rare de novo copy number (CN) mutations with relatively high penetrance contribute to the genetic component of schizophrenia. We carried out a whole-genome scan and implemented a number of steps for finding and confirming CN mutations. Confirmed de novo mutations were significantly associated with schizophrenia (P = 0.00078) and were collectively approximately 8 times more frequent in sporadic (but not familial) cases with schizophrenia than in unaffected controls. In comparison, rare inherited CN mutations were only modestly enriched in sporadic cases. Our results suggest that rare de novo germline mutations contribute to schizophrenia vulnerability in sporadic cases and that rare genetic lesions at many different loci can account, at least in part, for the genetic heterogeneity of this disease.

High precision canonical Monte Carlo determination of the growth constant of square lattice trees.

The number of lattice bond trees in the square lattice (counted modulo translations), t(n), is a basic quantity in lattice statistical mechanical models of branched polymers. This number is believed to have asymptotic behavior given by t(n) approximately Alambda(n)n(-theta), where A is an amplitude, lambda is the growth constant, and theta the entropic exponent. In this paper, we show that lambda and theta can be determined to high accuracy by using a canonical Monte Carlo algorithm; we find that lambda=5.1439+/-0.0025, theta=1.014+/-0.022, where the error bars are a combined 95% statistical confidence interval and an estimated systematic error due to uncertainties in modeling corrections to scaling. If one assumes the "exact value" theta=1 and then determines lambda, then the above estimate improves to lambda=5.143 39+/-0.000 72. In addition, we also determine the longest path exponent rho and the metric exponent nu from our data: rho=0.74000+/-0.00062, nu=0.6437+/-0.0035, with error bars similarly a combined 95% statistical confidence interval and an estimate of the systematic error.

PTEN mutations in uterine sarcomas.

OBJECTIVE: Uterinesarcomas comprise three main types: carcinosarcomas, leiomyosarcomas, and endometrial stromal sarcomas. Carcinosarcomas are highly aggressive neoplasms with a biphasic histology of carcinomatous and sarcomatous elements. It is now generally accepted that carcinosarcomas are biphasic tumors that have to be regarded as endometrial carcinomas where metaplasia occurs. Mutations of the PTEN tumor suppressor gene, located on 10q23, play a significant role in the pathogenesis of the endometrioid type of endometrial carcinoma. Loss of heterozygosity of chromosome 10q has been reported in uterine leiomyosarcoma. Since little is known about the molecular pathobiology, our goal was to investigate the potential role of the PTEN gene in the carcinogenesis of uterine sarcomas. METHODS: We examined 21 carcinosarcomas, 21 leiomyosarcomas, and 5 endometrial stromal sarcomas using exon-by-exon polymerase chain reaction-single-strand conformation polymorphism analysis. RESULTS: Overall 8.5% (4/47) of uterine sarcomas were found to harbor somatic PTEN mutations. Of these, approximately 17% (3/18) were carcinosarcomas with endometrioid-type carcinoma components and approximately 5% (1/21) were leiomyosarcomas. No mutations were detected in carcinosarcomas with nonendometrioid carcinoma components (0/3) and in endometrial stromal sarcomas (0/5). CONCLUSIONS: These data suggest that intragenic PTEN mutations are involved in the genesis of uterine carcinosarcomas with endometrioid-type carcinoma components but rarely contribute to the pathobiology of uterine leiomyosarcomas.

Genetic analysis of the complete gag and env genes of HIV type 1 subtype C primary isolates from South Africa.

South Africa has one of the fastest growing HIV-1 epidemics, with an estimated 4.7 million people infected. To better understand the genetic diversity of this epidemic and its potential impact on vaccine development, we have cloned and sequenced the complete gag and env genes of 13 primary virus isolates. Phylogenetic analysis of our sequences and 69 complete env genes from the Los Alamos and GenBank databases revealed multiple subclusters within subtype C. The V3 loop region was relatively conserved in all our strains when compared with other subtypes, but the region immediately downstream was highly variable. No intersubtype recombinant forms were observed when comparing the gag and env sequences. Characterization of the complete gag and env genes enabled us to select specific strains for further vaccine development.

Adsorbing trees in two dimensions: a Monte Carlo study.

Branched polymers interacting with an impenetrable wall can be modeled by lattice trees confined to a half space with a fugacity kappa conjugate to the number of visits the tree makes in the wall. We adapt a cut-and-paste algorithm for lattice trees with an umbrella-style implementation to sample trees interacting with an impenetrable wall over a wide range of values for kappa. We report results about the thermodynamic and metric properties of the trees, and estimate the location of the adsorption transition kappa(+)(c) and crossover exponent straight phi.

FHIT RNA and protein expression in oral squamous cell carcinomas.

BACKGROUND: To investigate the possible role of FHIT, a possible tumour suppressor gene, in oral carcinogenesis, we examined 17 oral squamous cell carcinomas (OSCCs) for genetic alterations. MATERIALS AND METHODS: Fresh tissue was obtained during surgery, snap-frozen in liquid nitrogen and stored at -70 degrees C. Nested PCR amplification to examine the integrity of FHIT mRNA was performed on the reverse transcribed complementary DNA obtained from the frozen normal and tumour tissue. Immunohistochemistry was done on formal in-fixed paraffin-embedded tissue protein from the same cases using a polyclonal antiserum against the full length Fhit. RESULTS: Twelve out 17 (71%) OSCCs showed reduced or absent Fhit protein and half of the cases with reduced Fhit protein exhibited aberrant RT-PCR products. CONCLUSION: Immunohistochemical detection of Fhit protein expression in OSCCs is the more sensitive method to determine the status of Fhit in these tumours, in agreement with previous studies of other tumour types.

Microsatellite instability in uterine sarcomas.

Studies have shown a 15-30% frequency of microsatellite instability in endometrial cancer. In addition, we found a 21% frequency of microsatellite instability in endometrial cancer. Our aim was to investigate the presence of microsatellite instability and loss of heterozygosity in uterine sarcomas. The records of 69 women referred to Kalafong Academic and Pretoria Academic Hospital with a primary diagnosis of uterine sarcoma were reviewed. At histological review of 43 cases with a primary diagnosis of leiomyosarcoma, diagnosis of mitotically active leiomyoma was made in 21. Diagnosis of carcinosarcoma was made in 21 cases and endometrial stromal sarcoma in five. In all cases, genomic DNA was extracted from normal myometrium and tumor and analyzed for microsatellite instability and loss of heterozygosity. High-frequency microsatellite instability was absent in leiomyosarcoma, endometrial stromal sarcoma, and mitotically active leiomyomas and was observed in 1 (5%) carcinosarcoma. Loss of heterozygosity for chromosome 11 was present in 8/48 (17%) of uterine sarcomas, equally distributed between leiomyosarcomas (4/22 = 18%) and carcinosarcomas (4/21 = 19%). There was no loss of alleles in endometrial stromal sarcoma nor mitotically active leiomyomas. In conclusion, it is suggested that tumor suppressor genes may play a role in the tumorigenesis of uterine mesenchymal cells, whereas mismatch repair genes contribute to the carcinogenesis of endometrial cancer.

Characterization and phylogenetic analysis of South African HIV-1 subtype C accessory genes.

To acquire new knowledge about the genetic diversity and potential impact on vaccine strategies of HIV-1 subtype C in South Africa, we have characterized the vif, vpr, and vpu genes of 15 isolates. Phylogenetic analysis of the genomic fragment encompassing these genes revealed subtype C subclusters, suggesting close relatedness with subtype C strains from other geographic locations and excluded isolation of South African strains. The putative T155 phosphorylation site in the C terminal of Vif was absent in all subtype C sequences. Variation in the predicted amino acid sequences of the three genes further showed strong correlation with other subtype C sequences.

Novel mutations identified using a comprehensive CCR5-denaturing gradient gel electrophoresis assay.

BACKGROUND: Most mutations detected for the gene for CC chemokine receptor 5 (CCR5) are either relatively specific to different population groups or rarely observed in Africans. OBJECTIVES: To develop a comprehensive mutation detection assay for the entire coding region of CCR5 and to identify novel mutations that may play a role in genetic susceptibility to HIV-1 infection, within the diverse South African population. DESIGN: The study cohort consisted of 103 HIV-seropositive patients and 146 HIV-seronegative controls of predominantly African descent. METHODS: A mutation detection assay for the entire coding region of CCR5 was designed; this included amplification of part of the coding region of CCR2. The assay was based on denaturing gradient gel electrophoresis (DGGE) and allowed the complete analysis of samples from 10 individuals per denaturing gel. RESULTS: The use of the CCR5-DGGE assay led to the identification of seven novel and six previously reported mutations. All novel mutations, including a common polymorphism at codon 35, occurred exclusively in non-Caucasians, indicating possible African origin. CONCLUSION: A comprehensive DGGE mutation detection assay has been developed for the entire coding region of CCR5. Application of this assay resulted in the identification of novel CCR5 mutations, which may have a significant effect on the normal functioning of CCR5 and thus contribute to host variability and susceptibility to HIV-1 infection and/or progression to AIDS within this population.

The extent of linkage disequilibrium in four populations with distinct demographic histories.

The design and feasibility of whole-genome-association studies are critically dependent on the extent of linkage disequilibrium (LD) between markers. Although there has been extensive theoretical discussion of this, few empirical data exist. The authors have determined the extent of LD among 38 biallelic markers with minor allele frequencies >.1, since these are most comparable to the common disease-susceptibility polymorphisms that association studies aim to detect. The markers come from three chromosomal regions-1,335 kb on chromosome 13q12-13, 380 kb on chromosome 19q13.2, and 120 kb on chromosome 22q13.3-which have been extensively mapped. These markers were examined in approximately 1,600 individuals from four populations, all of European origin but with different demographic histories; Afrikaners, Ashkenazim, Finns, and East Anglian British. There are few differences, either in allele frequencies or in LD, among the populations studied. A similar inverse relationship was found between LD and distance in each genomic region and in each population. Mean D' is.68 for marker pairs <5 kb apart and is.24 for pairs separated by 10-20 kb, and the level of LD is not different from that seen in unlinked marker pairs separated by >500 kb. However, only 50% of marker pairs at distances <5 kb display sufficient LD (delta>.3) to be useful in association studies. Results of the present study, if representative of the whole genome, suggest that a whole-genome scan searching for common disease-susceptibility alleles would require markers spaced < or = 5 kb apart.