Nonlinear diffusion and exclusion processes with contact interactions

Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C). We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.

Low formalin concentrations induce fine-tuned responses that are sex and age-dependent : a developmental study

The formalin test is increasingly applied as a model of inflammatory pain using high formalin concentrations (5–15%). However, little is known about the effects of low formalin concentrations on related behavioural responses. To examine this, rat pups were subjected to various concentrations of formalin at four developmental stages: 7, 13, 22, and 82 days of age. At postnatal day (PND) 7, sex differences in flinching but not licking responses were observed with 0.5% formalin evoking higher flinching in males than in females. A dose response was evident in that 0.5% formalin also produced higher licking responses compared to 0.3% or 0.4% formalin. At PND 13, a concentration of 0.8% formalin evoked a biphasic response. At PND 22, a concentration of 1.1% evoked higher flinching and licking responses during the late phase (10–30 min) in both males and females. During the early phase (0–5 min), 1.1% evoked higher licking responses compared to 0.9% or 1% formalin. 1.1% formalin produced a biphasic response that was not evident with 0.9 or 1%. At PND 82, rats displayed a biphasic pattern in response to three formalin concentrations (1.25%, 1.75% and 2.25%) with the presence of an interphase for both 1.75% and 2.25% but not for 1.25%. These data suggest that low formalin concentrations induce fine-tuned responses that are not apparent with the high formalin concentration commonly used in the formalin test. These data also show that the developing nociceptive system is very sensitive to subtle changes in formalin concentrations.

Asymptotic minimax robust and misspecified Lorden quickest change detection for dependent stochastic processes

The quick detection of an abrupt unknown change in the conditional distribution of a dependent stochastic process has numerous applications. In this paper, we pose a minimax robust quickest change detection problem for cases where there is uncertainty about the post-change conditional distribution. Our minimax robust formulation is based on the popular Lorden criteria of optimal quickest change detection. Under a condition on the set of possible post-change distributions, we show that the widely known cumulative sum (CUSUM) rule is asymptotically minimax robust under our Lorden minimax robust formulation as a false alarm constraint becomes more strict. We also establish general asymptotic bounds on the detection delay of misspecified CUSUM rules (i.e. CUSUM rules that are designed with post- change distributions that differ from those of the observed sequence). We exploit these bounds to compare the delay performance of asymptotically minimax robust, asymptotically optimal, and other misspecified CUSUM rules. In simulation examples, we illustrate that asymptotically minimax robust CUSUM rules can provide better detection delay performance at greatly reduced computation effort compared to competing generalised likelihood ratio procedures.

T. E. Harris and branching processes

T. E. Harris was a pioneer par excellence in many fields of probability theory. In this paper, we give a brief survey of the many fundamental contributions of Harris to the theory of branching processes, starting with his doctoral work at Princeton in the late forties and culminating in his fundamental book ``The Theory of Branching Processes,'' published in 1963.

Age-dependent decrease in glutamine synthetase expression in the hippocampal astroglia of the triple transgenic Alzheimer's disease mouse model : mechanism for deficient glutamatergic transmission?

Astrocytes are fundamental for brain homeostasis and the progression and outcome of many neuropathologies including Alzheimer's disease (AD). In the triple transgenic mouse model of AD (3xTg-AD) generalised hippocampal astroglia atrophy precedes a restricted and specific beta-amyloid (A beta) plaque-related astrogliosis. Astrocytes are critical for CNS glutamatergic transmission being the principal elements of glutamate homeostasis through maintaining its synthesis, uptake and turnover via glutamate-glutamine shuttle. Glutamine synthetase (GS), which is specifically expressed in astrocytes, forms glutamine by an ATP-dependent amination of glutamate. Here, we report changes in GS astrocytic expression in two major cognitive areas of the hippocampus (the dentate gyrus, DG and the CA1) in 3xTg-AD animals aged between 9 and 18 months. We found a significant reduction in Nv (number of cell/mm(3)) of GS immunoreactive (GS-IR) astrocytes starting from 12 months (28.59%) of age in the DG, and sustained at 18 months (31.65%). CA1 decrease of GS-positive astrocytes Nv (33.26%) occurs at 18 months. This Nv reduction of GSIR astrocytes is paralleled by a decrease in overall GS expression (determined by its optical density) that becomes significant at 18 months (21.61% and 19.68% in DG and CA1, respectively). GS-IR Nv changes are directly associated with the presence of A beta deposits showing a decrease of 47.92% as opposed to 23.47% in areas free of A beta. These changes in GS containing astrocytes and GS-immunoreactivity indicate AD-related impairments of glutamate homeostatic system, at the advanced and late stages of the disease, which may affect the efficacy of glutamatergic transmission in the diseased brain that may contribute to the cognitive deficiency.

Interactions of age-dependent mortality and selectivity functions in age-based stock assessment models

The natural mortality rate (M) of fish varies with size and age, although it is often assumed to be constant in stock assessments. Misspecification of M may bias important assessment quantities. We simulated fishery data, using an age-based population model, and then conducted stock assessments on the simulated data. Results were compared to known values. Misspecification of M had a negligible effect on the estimation of relative stock depletion; however, misspecification of M had a large effect on the estimation of parameters describing the stock recruitment relationship, age-specific selectivity, and catchability. If high M occurs in juvenile and old fish, but is misspecified in the assessment model, virgin biomass and catchability are often poorly estimated. In addition, stock recruitment relationships are often very difficult to estimate, and steepness values are commonly estimated at the upper bound (1.0) and overfishing limits tend to be biased low. Natural mortality can be estimated in assessment models if M is constant across ages or if selectivity is asymptotic. However if M is higher in old fish and selectivity is dome-shaped, M and the selectivity cannot both be adequately estimated because of strong interactions between M and selectivity.

Generalized Markov branching processes

A generalized Markov Brnching Process (GMBP) is a Markov branching model where the infinitesimal branching rates are modified with an interaction index. It is proved that there always exists only one GMBP. An associated differential-integral equation is derived. The extinction probalility and the mean and conditional mean extinction times are obtained. Ergodicity and stability of GMBP with resurrection are also considered. Easy checking criteria are established for ordinary and strong ergodicty. The equilibrium distribution is given in an elegant closed form. The probability meaning of our results is clear and thus explained.

Age-dependent accumulation of lipofuscin in perivascular and subretinal microglia in experimental mice

Fundus autofluorescence (AF) imaging by confocal scanning laser ophthalmoscopy has been widely used by ophthalmologists in the diagnosis/monitoring of various retinal disorders. It is believed that fundus AF is derived from lipofuscin in retinal pigment epithelial (RPE) cells; however, direct clinicopathological correlation has not been possible in humans. We examined fundus AF by confocal scanning laser ophthalmoscopy and confocal microscopy in normal C57BL/6 mice of different ages. Increasingly strong AF signals were observed with age in the neuroretina and subretinal/RPE layer by confocal scanning laser ophthalmoscopy. Unlike fundus AF detected in normal human subjects, mouse fundus AF appeared as discrete foci distributed throughout the retina. Most of the AF signals in the neuroretina were distributed around retinal vessels. Confocal microscopy of retinal and choroid/RPE flat mounts demonstrated that most of the AF signals were derived from Iba-1+ perivascular and subretinal microglia. An age-dependent accumulation of Iba-1+ microglia at the subretinal space was observed. Lipofuscin granules were detected in large numbers in subretinal microglia by electron microscopy. The number of AF+ microglia and the amount of AF granules/cell increased with age. AF granules/lipofuscin were also observed in RPE cells in mice older than 12 months, but the number of AF+ RPE cells was very low (1.48 mm-2 and 5.02 mm-2 for 12 and 24 months, respectively) compared to the number of AF+ microglial cells (20.63 mm-2 and 76.36 mm-2 for 6 and 24 months, respectively). The fluorescence emission fingerprints of AF granules in subretinal microglia were the same as those in RPE cells. Our observation suggests that perivascular and subretinal microglia are the main cells producing lipofuscin in normal aged mouse retina and are responsible for in vivo fundus AF. Microglia may play an important role in retinal aging and age-related retinal diseases.

Age-dependent increase in ortho-tyrosine and methionine sulfoxide in human skin collagen is not accelerated in diabetes. Evidence against a generalized increase in oxidative stress in diabetes

The glycoxidation products Nepsilon-(carboxymethyl)lysine and pentosidine increase in skin collagen with age and at an accelerated rate in diabetes. Their age-adjusted concentrations in skin collagen are correlated with the severity of diabetic complications. To determine the relative roles of increased glycation and/or oxidation in the accelerated formation of glycoxidation products in diabetes, we measured levels of amino acid oxidation products, distinct from glycoxidative modifications of amino acids, as independent indicators of oxidative stress and damage to collagen in aging and diabetes. We show that ortho-tyrosine and methionine sulfoxide are formed in concert with Nepsilon-(carboxymethyl)lysine and pentosidine during glycoxidation of collagen in vitro, and that they also increase with age in human skin collagen. The age-adjusted levels of these oxidized amino acids in collagen was the same in diabetic and nondiabetic subjects, arguing that diabetes per se does not cause an increase in oxidative stress or damage to extracellular matrix proteins. These results provide evidence for an age-dependent increase in oxidative damage to collagen and support previous conclusions that the increase in glycoxidation products in skin collagen in diabetes can be explained by the increase in glycemia alone, without invoking a generalized, diabetes-dependent increase in oxidative stress.

Age-dependent accumulation of N epsilon-(carboxymethyl)lysine and N epsilon-(carboxymethyl)hydroxylysine in human skin collagen

N epsilon-(Carboxymethyl)lysine (CML) is formed on oxidative cleavage of carbohydrate adducts to lysine residues in glycated proteins in vitro [Ahmed et al. (1988) J. Biol. Chem. 263, 8816-8821; Dunn et al. (1990) Biochemistry 29, 10964-10970]. We have shown that, in human lens proteins in vivo, the concentration of fructose-lysine (FL), the Amadori adduct of glucose to lysine, is constant with age, while the concentration of the oxidation product, CML, increases significantly with age [Dunn et al. (1989) Biochemistry 28, 9464-9468]. In this work we extend our studies to the analysis of human skin collagen. The extent of glycation of insoluble skin collagen was greater than that of lens proteins (4-6 mmol of FL/mol of lysine in collagen versus 1-2 mmol of FL/mol of lysine in lens proteins), consistent with the lower concentration of glucose in lens, compared to plasma. In contrast to lens, there was a slight but significant age-dependent increase in glycation of skin collagen, 33% between ages 20 and 80. As in lens protein, CML, present at only trace levels in neonatal collagen, increased significantly with age, although the amount of CML in collagen at 80 years of age, approximately 1.5 mmol of CML/mol of lysine, was less than that found in lens protein, approximately 7 mmol of CML/mol of lysine. The concentration of N epsilon-(carboxymethyl)hydroxylysine (CMhL), the product of oxidation of glycated hydroxylysine, also increased with age in collagen, in parallel with the increase in CML, from trace levels at infancy to approximately 5 mmol of CMhL/mol of hydroxylysine at age 80.(ABSTRACT TRUNCATED AT 250 WORDS)

Interaction of very-low-density lipoprotein isolated from type I (insulin-dependent) diabetic subjects with human monocyte-derived macrophages

Very-low-density lipoproteins (VLDL) (density less than 1.006 g/mL) were isolated from type I (insulin-dependent) diabetic patients in good to fair glycemic control and from age-, sex-, and race-matched, nondiabetic, control subjects. VLDL were incubated with human, monocyte-derived macrophages obtained from nondiabetic donors, and the rates of cellular cholesteryl ester synthesis and cholesterol accumulation were determined. VLDL isolated from diabetic patients stimulated significantly more cholesteryl ester synthesis than did VLDL isolated from control subjects (4.04 +/- 1.01 v 1.99 +/- 0.39 nmol 14C-cholesteryl oleate synthesized/mg cell protein/20 h; mean +/- SEM, P less than .05). The stimulation of cholesteryl ester synthesis in macrophages incubated with VLDL isolated from diabetic patients was paralleled by a significant increase in intracellular cholesteryl ester accumulation (P less than .05). The increase in cholesteryl ester synthesis and accumulation in macrophages were mediated by a significant increase in the receptor mediated, high affinity degradation (2.55 +/- 0.23 v 2.12 +/- 0.20 micrograms degraded/mg cell protein/20 h) and accumulation (283 +/- 35 v 242 +/- 33 ng/mg cell protein/20 h) of 125I-VLDL isolated from diabetic patients compared with VLDL from control subjects. To determine if changes in VLDL apoprotein composition were responsible for the observed changes in cellular rates of cholesteryl ester synthesis and accumulation, we also examined the apoprotein composition of the VLDL from both groups. There were no significant differences between the apoproteins B, E, and C content of VLDL from both groups. We also determined the chemical composition of VLDL isolated from both groups of subjects.(ABSTRACT TRUNCATED AT 250 WORDS)

Glycosylation of low density lipoprotein in patients with type 1 (insulin-dependent) diabetes:correlations with other parameters of glycaemic control

Glycosylation of low density lipoproteins obtained from 16 patients with Type 1 (insulin-dependent) diabetes and from 16 age-, sex-, and race-matched controls, was determined. The diabetic patients were normolipaemic and were in good or fair glycaemic control. Eleven patients performed home blood glucose monitoring. Glycosylation of low density lipoproteins in the diabetic patients was significantly higher (p less than 0.001) than in the control subjects, and was significantly correlated with haemoglobin A1c, (p less than 0.01), glycosylation of plasma proteins, (p less than 0.001), and mean home blood glucose, (p less than 0.01). This study confirms that, in diabetic patients, increased glycosylation of low density lipoprotein occurs to an extent which correlates closely with other commonly used indices of glycaemic control.

Decay to equilibrium for jump processes with heavy tails

The case is made for a more careful analysis of the large time asymptotic of infinite particle systems in the thermodynamic limit beyond zero density. The insufficiency of current analysis even in the model case of free particles is demonstrated. Recent advances based on more sophisticated analytical tools like functions of mean variation and Hardy spaces are sketched.

Age-dependent changes in adenosine A(1) receptor distribution and density within the nucleus tractus solitarii of normotensive and hypertensive rats

This study shows the distribution and density of adenosine A1 receptor (A(1)R) within the nucleus tractus solitarii (NTS) of Wistar Kyoto (WKY) and spontaneously hypertensive rats (SHR) from birth to adulthood (1, 15, 30 and 90 days old). The NTS shows heterogeneous distribution of A(1)R in dorsomedial/dorsolateral, subpostremal and medial/intermediate subnuclei. A(1)R decrease from rostral to caudal within dorsomedial/dorsolateral subnucleus in 15-, 30- and 90-day-old WKY and SHR. A(1)R increase from rostral to caudal subpostremal subnucleus in 30- and 90-day-old WKY, and in 15-, 30- and 90-day-old SHR. Furthermore, A(1)Rs are increased in SHR as compared with WKY within dorsomedial/dorsolateral in 30- and 90-day-old and within subpostremal of 15-, 30- and 90-day-old rats. Finally, A(1)Rs increase from 1- to 30-day-old rats. Medial/intermediate did not show any changes in A(1)R from rostral to caudal levels, age or strain. In summary, our result highlights the importance of A1 adenosine system regarding the neural control of blood pressure and the development of hypertension.

Age-Dependent Acquisition of Protective Immunity to Malaria in Riverine Populations of the Amazon Basin of Brazil

Five community-based cross-sectional surveys of malaria morbidity and associated risk factors in remote riverine populations in northwestern Brazil showed average parasite rates of 4.2% (thick-smear microscopy) and 14.4% (polymerase chain reaction [PCR]) in the overall population, with a spleen rate of 13.9% among children 2-9 years of age. Plasmodium vivax was 2.8 times more prevalent than P. falciparum, with rare instances of P. malariae and mixed-species infections confirmed by PCR; 9.6% of asymptomatic subjects had parasitemias detected by PCR. Low-grade parasitemia detected by PCR only was a risk factor for anemia, after controlling for age and other covariates. Although clinical and subclinical infections occurred in all age groups, the risk of infection and disease decreased significantly with increasing age, after adjustment for several covariates in multilevel logistic regression models. These findings suggest that the continuous exposure to hypo- or mesoendemic malaria may induce significant anti-parasite and anti-disease immunity in native Amazonians.