A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case. (C) 2000 Elsevier Science Ltd. All rights reserved.

Features of colorectal cancers with high-level microsatellite instability occurring in familial and sporadic settings

High-level microsatellite instability (AISI-H) is demonstrated in 10 to 15% of sporadic colorectal cancers and in most cancers presenting In the inherited condition hereditary nonpolyposis colorectal cancer (HNPCC). Distinction between these categories of MSI-H cancer is of clinical importance and the aim of this study was to assess clinical, pathological, and molecular features that might he discriminatory. One hundred and twelve MSI-H colorectal cancers from families fulfilling the Bethesda criteria were compared with 57 sporadic MSI-H colorectal cancers. HNPCC cancers presented at a lower age (P < 0.001) with no sporadic MSI-H cancer being diagnosed before the age of 57 years. MSI was less extensive in HNPCC cancers with 72% microsatellite markers showing band shifts compared with 87% in sporadic tumors (P < 0.001). Absent immunostaining for hMSH2 was only found in HNPCC tumors. Methylation of bMLH1 was observed in 87% of sporadic cancers but also in 55% of HNPCC tumors that showed loss of expression of hMLH1 (P = 0.02). HNPCC cancers were more frequently characterized by aberrant beta -catenin immunostaining as evidenced by nuclear positivity (P < 0.001). Aberrant p53 immunostaining was infrequent in both groups. There were no differences with respect to 5q loss of heterozygosity or codon 12 K-ras mutation, which were infrequent in both groups. Sporadic MSI-H cancers were more frequently heterogeneous (P < 0.001), poorly differentiated (P = 0.02), mucinous (P = 0.02), and proximally located (P = 0.04) than RNPCC tumors. In sporadic MSI-H cancers, contiguous adenomas were likely to be serrated whereas traditional adenomas were dominant in HNPCC. Lymphocytic infiltration was more pronounced in HNPCC but the results did not reach statistical significance. Overall, HNPCC cancers were more like common colorectal cancer in terms of morphology and expression of beta -catenin whereas sporadic MSI-H cancers displayed features consistent with a different morphogenesis. No individual feature was discriminatory for all RN-PCC cancers. However, a model based on four features was able to classify 94.5% of tumors as sporadic or HNPCC. The finding of multiple differences between sporadic and familial MSI-H colorectal cancer with respect to both genotype and phenotype is consistent with tumorigenesis through parallel evolutionary pathways and emphasizes the importance of studying the two groups separately.

Methylation of O-6-methylguanine DNA methyltransferase characterizes a subset of colorectal cancer with low-level DNA microsatellite instability

The significance of low-level DNA microsatellite instability (MSI-L) is not well understood. K-ras mutation is associated with MSI-L colorectal cancer and with the silencing of the DNA repair gene O-6-methylguanine DNA methyltransferase (MGMT) by methylation of its promoter region. MGMT methylation was studied in sporadic colorectal cancers stratified as DNA microsatellite instability-high (n = 23), MSI-L (n = 44), and microsatellite-stable (n = 23). Methylation-specific PCR was used to detect MGMT-promoter hypermethylation in 3 of 23 (13%) microsatellite instability-high, in 28 of 44 (64%) MSI-L, and in 6 of 23 (26%) microsatellite-stable cancers (P = 0.0001). K-ras was mutated in 20 of 29 (69%) methylated MSI-L cancers and in 2 of 15 (13%) unmethylated MSI-L cancers (P = 0.001), indicating a relationship between MGMT-methylation and mutation of K-ras. Loss of nuclear expression of MGMT was demonstrated immunohistochemically in 23 of 31 (74%) cancers with methylated MGMT and in 10 of 49 (20%) cancers with nonmethylated MGMT (P < 0.0001). Loss of expression of MGMT was also demonstrated in 9 of 31 serrated polyps. Silencing of MGMT may predispose to mutation by overwhelming the DNA mismatch repair system and occurs with greatest frequency in MSI-L colorectal cancers.

High frequency of low-level microsatellite instability in early colorectal cancer

Molecular events in early colorectal cancers (CRCs) have not been well elucidated because of the low incidence of early CRCs in clinical practice. Therefore, we studied 104 sporadic early CRCs with invasion limited to submucosa compared with 116 advanced CRCs. Loss of heterozygosity as well as microsatellite instability (MSI) status was examined. A significantly high frequency of low-level MSI (MSI-L) phenotype was detected in early CRCs (51.0%) compared with advanced CRCs (25.9%; P = 0.0001). In early and advanced CRCs, samples with MSI-L phenotype differed from microsatellite stable (MSS) phenotype with respect to loss of heterozygosity at 1p32 and 8p12-22. MSI-L is a frequent genetic event in early CRCs and may be a novel pathway in colorectal carcinogenesis distinct from both MSI-H and MSS.

Tumour infiltrating lymphocytes and apoptosis are independent features in colorectal cancer stratified according to microsatellite instability status

Background-The presence of high level DNA microsatellite instability (MSI-H) in colorectal cancer is associated with an improved prognosis, as is the presence of tumour infiltrating lymphocytes (TILs). It is not clear if TILs contribute directly to the survival advantage associated with MSI-H cancers through activation of an antitumour immune response. Aims-To correlate TIL and apoptosis rates in colorectal cancer stratified by MSI status. Methods-The distribution of TILs was characterised and quantified in a selected series of 102 sporadic colorectal cancers classified according to levels of MSI as 32 MSI-H, 30 MSI-low (MSI-L), and 40 microsatellite stable (MSS). Archival blocks were immunostained using the T cell markers CD3 and CD8, and the B cell marker CD20. Apoptosis of malignant epithelial cells was quantified by immunohistochemistry with the M30 CytoDEATH antibody. Results-Positive staining with anti-CD3 and negative staining with anti-CD20 identified virtually all TILs as T cells. The majority of CD3(+) TILs (>75%) also stained with anti-CDS. TILs were most abundant in MSI-H colorectal cancers in which 23/32 (72%) scored as TIL positive. Only 5/40 (12.5%) MSS tumours and 9/30 (30%) MSI-L cancers were TIL positive (p

Stability of linear difference and differential inclusions

Any given n X n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N x N matrix B of spectral radius p(B) arbitrarily close to p(A). A difference inclusion x(k+1) is an element of Ax(k), where A is a compact set of matrices, is asymptotically stable if and only if A can be extended to a set B of nonnegative matrices B with \ \B \ \ (1) < 1 or \ \B \ \ (infinity) < 1. Similar results are derived for differential inclusions.

Estimates of the real structured radius of stability of linear dynamic systems

A question is examined as to estimates of the norms of perturbations of a linear stable dynamic system, under which the perturbed system remains stable in a situation R:here a perturbation has a fixed structure.

Noise-free scattering of the quantized electromagnetic field from a dispersive linear dielectric

We study the scattering of the quantized electromagnetic field from a linear, dispersive dielectric using the scattering formalism for quantum fields. The medium is modeled as a collection of harmonic oscillators with a number of distinct resonance frequencies. This model corresponds to the Sellmeir expansion, which is widely used to describe experimental data for real dispersive media. The integral equation for the interpolating field in terms of the in field is solved and the solution used to find the out field. The relation between the ill and out creation and annihilation operators is found that allows one to calculate the S matrix for this system. In this model, we find that there are absorption bands, but the input-output relations are completely unitary. No additional quantum-noise terms are required.

Linear models of simple cells: Correspondence to real cell responses and space spanning properties

Despite their limitations, linear filter models continue to be used to simulate the receptive field properties of cortical simple cells. For theoreticians interested in large scale models of visual cortex, a family of self-similar filters represents a convenient way in which to characterise simple cells in one basic model. This paper reviews research on the suitability of such models, and goes on to advance biologically motivated reasons for adopting a particular group of models in preference to all others. In particular, the paper describes why the Gabor model, so often used in network simulations, should be dropped in favour of a Cauchy model, both on the grounds of frequency response and mutual filter orthogonality.

The effect of channel geometry and wall boundary conditions on the formation of extrusion surface instabilities for LLDPE

It is believed that surface instabilities can occur during the extrusion of linear low density polyethylene due to high extensional stresses at the exit of the die. Local crack development can occur at a critical stress level when melt rupture is reached. This high extensional stress results from the rearrangement of the flow at the boundary transition between the wall exit and the free surface. The stress is highest at the extrudate surface and decreases into the bulk of the material. The location of the region where the critical level is reached can determine the amplitude of the extrudate surface distortion, This paper studies the effect of wall slip on the numerically simulated extensional stress level at the die exit and correlates this to the experimentally determined amplitude of the surface instability. The effect of die exit radius and die wall roughness on extrusion surface instabilities is also correlated to the exit stress level in the same way. Whereas full slip may completely suppress the surface instability, a reduction in the exit stress level and instability amplitude is also shown for a rounded die exit and a slight increase in instability is shown to result from a rough die wall. A surface instability map demonstrates how the shear rate for onset of extrusion surface instabilities can be predicted on the basis of melt strength measurements and simulated stress peaks at the exit of the die. (C) 2001 Elsevier Science B.V. All rights reserved.

Determination of breeding strategies for beef cattle bull breeders selling bulls into two competing markets on a non-linear price grid

Computer simulation was used to suggest potential selection strategies for beef cattle breeders with different mixes of clients between two potential markets. The traditional market paid on the basis of carcass weight (CWT), while a new market considered marbling grade in addition to CWT as a basis for payment. Both markets instituted discounts for CWT in excess of 340 kg and light carcasses below 300 kg. Herds were simulated for each price category on the carcass weight grid for the new market. This enabled the establishment of phenotypic relationships among the traits examined [CWT, percent intramuscular fat (IMF), carcass value in the traditional market, carcass value in the new market, and the expected proportion of progeny in elite price cells in the new market pricing grid]. The appropriateness of breeding goals was assessed on the basis of client satisfaction. Satisfaction was determined by the equitable distribution of available stock between markets combined with the assessment of the utility of the animal within the market to which it was assigned. The best goal for breeders with predominantly traditional clients was a CWT in excess of 330 kg, while that for breeders with predominantly new market clients was a CWT of between 310 and 329 kg and with a marbling grade of AAA in the Ontario carcass pricing system. For breeders who wished to satisfy both new and traditional clients, the optimal CWT was 310-329 kg and the optimal marbling grade was AA-AAA. This combination resulted in satisfaction levels of greater than 75% among clients, regardless of the distribution of the clients between the traditional and new marketplaces.