Kolmogorov’s Differential Equations and Positive Semigroups on First Moment Sequence Spaces

Spatially implicit metapopulation models with discrete patch-size structure and host-macroparasite models which distinguish hosts by their parasite loads lead to infinite systems of ordinary differential equations. In several papers, a this-related theory will be developed in sufficient generality to cover these applications. In this paper the linear foundations are laid. They are of own interest as they apply to continuous-time population growth processes (Markov chains). Conditions are derived that the solutions of an infinite linear system of differential equations, known as Kolmogorov’s differential equations, induce a C ₀-semigroup on an appropriate sequence space allowing for first moments. We derive estimates for the growth bound and the essential growth bound and study the asymptotic behavior. Our results will be illustrated for birth and death processes with immigration and catastrophes. An erratum to this article can be found at     

Allergen-specific B cell subset responses in cow’s milk allergy of late eczematous reactions in atopic dermatitis

B cells have regulatory functions in immune responses. Antigen-specific responses of B cell subsets by allergen stimulation ex vivo were examined in milk allergy of late eczematous reactions. Eight milk allergy subjects and 13 milk tolerant subjects were selected by DBPCFC. PBMCs were stimulated by casein ex vivo and stained for B cell subsets using monoclonal antibodies. CD19+ B cells unchanged from 8.7 ± 3.8% to 8.0 ± 5.1% (p = 0.504, n = 8) in the milk allergy group and decreased in the milk tolerant group from 8.5 ± 3.2% to 5.0 ± 1.6% (p = 0.001, n = 13). The fraction of apoptotic B cells in B cells significantly decreased 4.4 ± 3.1% to 1.3 ± 0.4% (p = 0.027, n = 4) in the allergy group and insignificantly increased from 2.8 ± 0.6% to 5.4 ± 2.6% (p = 0.059, n = 6) in the milk tolerant group. CD5+ regulatory B1 cell% in B cells decreased in milk allergy subjects from 36.2 ± 5.0% to 31.0 ± 5.7% (p = 0.010) and unchanged in milk tolerant subjects from 41.6 ± 10.2% to 43.8 ± 10.0% (p = 0.413). IL-10 producing CD19+CD5+ regulatory B cell% in CD19+CD5+ regulatory B cells significantly decreased from 24.9 ± 6.5% to 13.8 ± 5.6% (p = 0.002, n = 5) by casein stimulation in milk allergy group and unchanged from 44.8 ± 11.3% to 43.9 ± 10.0% (p = 0.297, n = 5) in the milk tolerant group. B cell subset responses to IL-4 and IL-5 were also similar in both groups. B cell subset changes seemed to have diagnostic value. Exact immunologic roles of regulatory CD5+ B1 cells need further investigation.     

Regional variation in adipogenesis and IGF regulatory proteins in the fetal baboon

Intrauterine growth rate is associated with body distribution in adulthood suggesting differential response of fetal fat depots to nutritional modifications. We hypothesize that there is regional differences in fetal adipogenesis, in part, due to depot-specific regulation of the availability of insulin growth factors. In near-term baboon fetuses (n = 3-5), the subcutaneous abdominal vs. omental preadipocytes had (1) more extensive lipid accumulation as assessed by BODIPY (lipid staining) to DAPI (nuclei) absorbance ratios (mean ± SEM; 0.51 ± 0.21, 0.35 ± 0.09, p < 0.05), (2) lower (p < 0.05) secretion of IGF-binding protein 4 (9.6 ± 1.2 vs. 17.4 ± 2.8 ng/ml) and its protease pregnancy associated plasma protein A (24.6 ± 1.9 vs. 39.1 ± 6.3 μIU/ml), (3) lower protein expression of IGF2 “clearance” receptor in cell lysate (0.28 ± 0.03 vs. 0.53 ± 0.02 OD U/mm², p < 0.05); all variables were intermediate in femoral preadipocytes. The regional variation of the adipogenesis and the IGF regulatory pathway set the stage for differential responsiveness of fat depots to external signals.     

Ionic metallomesogens derived from silver(I) bis-amine complexes: Structure and mesogenic behavior

Complexes [Ag(NH₂R)₂]X, (X = NO₃, R = -C₆H₄-C_nH_2n+1-p, -C₆H₄-O-C_nH_2n+1-p, -CH₂-C₆H₄-O-C_nH_2n+1-p, n = 6, 8, 10, 12, 14; X = BF₄, R = -CH₂-C₆H₄-O-C_nH_2n+1-p, n = 6, 8, 10, 12, 14; X = OAc, R = -CH₂-C₆H₄-O-C₁₀H₂₁-p; X = CF₃SO₃, R = -CH₂-C₆H₄-O-C₁₀H₂₁-p) have been prepared. They all show S_A mesophases corresponding to two kinds of structures, already present in the solid state. The alkylaniline and alkoxyaniline derivatives adopt a bilayered structure where the cation has an extended centrosymmetric conformation. The benzylamine derivatives contain U-shaped cations giving rise to a bilayered structure which allows microsegregation of the organic part of the molecule from the inorganic Ag?(anion) part. Some degree of interdigitation of the terminal chains is observed for all the complexes with aryl containing ligands.     

A controlled water-table depth system to study the influence of fine-scale differences in water regime for plant growth

A method was developed to maintain water-table depths at a constant level in outdoor mesocosms. The system included a water treatment reservoir, where tap water was microbially deoxygenated and denitrified; an adjustable-level control chamber that set desired water-table depths and plant growing mesocosms.The soil water status was evaluated by constant monitoring using tensiometers, pressure transducers and dipwells. The robustness of the system was tested by inducing sudden incidents of flooding and drainage. The system was able to revert to the original set water-table depths within 5 and 10 min, respectively. It also reliably sustained consistent water-table depths throughout the growing season without the need for maintenance.As an example, the method was used to grow plants at five set water-table depths: 50, 150, 250, 350, and 450 mm below ground surface. Two wet grassland species Festuca pratensis (meadow fescue), and Carex nigra (common sedge) were grown and dry biomass production recorded. Results showed differences in growth response between the two species to subjected water-table depths. In monoculture, F. pratensis production followed the order 50 = 150 = 350 > 250 = 450 mm (p < 0.001), while for C. nigra it was 150 = 250 > 50 = 350 = 450 mm (p < 0.001). In mixture, F. pratensis did not show a significant trend (p < 0.06), whereas C. nigra showed 50 = 150 > 250 > 350 = 450 mm (p < 0.001).The ease of the system to establish constant and/or dynamic water-table depths and its reliability outdoors renders it useful for a wide variety of studies involving plant growth.     

The use of PIB-PET as a dual pathological and functional biomarker in AD

Amyloid imaging with positron emission tomography (PET) is presently used in Alzheimer's disease (AD) research. In this study we investigated the possibility to use early frames (ePIB) of the PIB scans as a rough index of CBF by comparing normalised early PIB values with cerebral glucose metabolism (rCMRglc). PIB-PET and FDG-PET were performed in 37 AD patients, 21 subjects with mild cognitive impairment (MCI) and 6 healthy controls (HC). The patients were divided based on their PIB retention (amyloid load) as either PIB positive (PIB+) or PIB negative (PIB−). Data of the unidirectional influx K₁ from a subset of the subjects including 7 AD patients and 3 HC was used for correlative analysis. Data was analysed using regions of interest (ROI) analysis. A strong, positive correlation was observed across brain regions between K₁ and ePIB (r = 0.70; p ≤ 0.001). The ePIB values were significantly lower in the posterior cingulate (p ≤ 0.001) and the parietal cortices (p = 0.002) in PIB+ subjects compared to PIB−, although the group difference were stronger for rCMRglc in cortical areas (p ≤ 0.001). Strong positive correlations between ePIB and rCMRglc were observed in all cortical regions analysed, especially in the posterior cingulate and parietal cortices (p ≤ 0.001). A single dynamic PIB-PET scan may provide information about pathological and functional changes (amyloidosis and impaired blood flow). This might be important for diagnosis of AD, enrichment of patients in clinical trials and evaluation of treatment effects. This article is part of a Special Issue entitled: Imaging Brain Aging and Neurodegenerative disease.     

Effects of Echinaforce treatment on ex vivo-stimulated blood cells

The herb Echinacea purpurea, also called purple coneflower, is regarded as an immune modulator. This study examined changes in cytokine production in blood samples from 30 volunteers before and during 8-day oral administration with an ethanolic extract of fresh Echinacea purpurea (Echinaforce^®). Daily blood samples were ex vivo stimulated by LPS/SEB or Zymosan and analysed for a series of cytokines and haematological and metabolic parameters. Treatment reduced the proinflammatory mediators TNF-α and IL-1β by up to 24% (p < 0.05) and increased anti-inflammatory IL-10 levels by 13% (p < 0.05) in comparison to baseline. This demonstrated a substantial overall anti-inflammatory effect of Echinaforce^® for the whole group (n = 28). Chemokines MCP-1 and IL-8 were upregulated by 15% in samples from subjects treated with Echinaforce^® (p < 0.05). An analysis of a subgroup of volunteers who showed low pre-treatment levels of the cytokines MCP-1, IL-8, IL-10 or IFN-γ (n = 8) showed significant stimulation of these factors upon Echinaforce^® treatment (30-49% increases; p < 0.05), whereas the levels in subjects with higher pre-treatment levels remained unaffected. We chose the term “adapted immune-modulation” to describe this observation. Volunteers who reported high stress levels (n = 7) and more than 2 colds per year experienced a significant transient increase in IFN-γ upon Echinaforce^® treatment (>50%). Subjects with low cortisol levels (n = 11) showed significant down-regulation of the acute-phase proteins IL1-β, IL-6, IL-12 and TNF-α by Echinaforce^® (range, 13-25%), while subjects with higher cortisol levels showed no such down-regulation. This is the first ex vivo study to demonstrate adapted immune-modulation by an Echinacea preparation. While Echinaforce^® did not affect leukocyte counts, we speculate that the underlying therapeutic mechanism is based on differential multi-level modulation of the responses of the different types of leukocytes. Echinaforce^® thus regulates the production of chemokines and cytokines according to current immune status, such as responsiveness to exogenous stimuli, susceptibility to viral infection and exposure to stress.     

Neurohormonal and cytokine fluctuations following transcatheter closure for an atrial septal defect

Introduction

Inflammation and neurohormonal activation are considered to be involved in the development of earlier and/or later complications in congenital heart disease patients, even after a successful repair of the lesion. It is not yet clarified what is the role of the therapeutic interventions in the occurrence of such a response and how it could be associated with possible postoperative complications.

Aim

We sought to assess the inflammatory and neurohormonal response to transcatheter closure of secundum type atrial septal defects (ASD) over a six-month follow-up period. We also evaluated the association between the respective markers and catheterization data as well as echocardiographic measurements.

Methods

Plasma concentrations of interleukin-6 (IL-6), tumor necrosis factor-alpha (TNF-α), interleukin-10 (IL-10), N-terminal-proatrial natriuretic peptide (NT-proANP) and N-terminal-probrain natriuretic peptide (NT-proBNP) were assessed and echocardiographic measurements were performed in twenty-eight patients with atrial septal defect prior to, and at the first, second and sixth months post transcatheter closure. Thirty-three age-matched healthy volunteers were also enrolled.

Results

IL-6 plasma levels, although higher preoperatively, [physical logarithm (ln) IL-6: 3.37 ± 0.66 vs 2.92 ± 0.44 pg/ml, p = 0.015], reached control levels postoperatively, at the end of the third month, whereas TNF-α and IL-10 were not influenced by the procedure. NT-proANP levels were elevated preoperatively compared to the control group (ln NT-proANP 3.78 ± 0.572 vs 3.48 ± 0.30, p = 0.031), with a further significant increase during the 1st month (ln NT-proANP 3.78 ± 0.572 vs 4.2 ± 0.42, p = 0.006), following the pattern of the left atrial volume enlargement, and remained high even 6 months after the procedure .On the other hand, the initially normal concentrations of NT-proBNP, after a transient significant increase during the first month postoperatively (ln NT-proBNP 3.56 ± 0.94 vs 4.58 ± 0.91, p < 0.0001) returned to the controls’ levels at the end of the third month. Preoperative concentrations of NT-proANP positively correlated with NT-proBNP concentrations and pulmonary to systemic flow ratio (Qp/Qs).

Conclusions

Transcatheter closure could improve, on a mid- term basis, the inflammatory process but natriuretic peptides’ secretion continues in parallel with left atrial volume increase. Further follow up is required to determine the long-term progress of the inflammatory and neurohormonal response to the procedure.     

A geometric principle may guide self-assembly of fullerene cages from clathrin triskelia and from carbon atoms

Clathrin triskelia and carbon atoms alike self-assemble into a limited selection of fullerene cages (with n three connected vertices, 3n/2 edges, 12 pentagonal faces, and (n−20)/2 hexagonal faces). We show that a geometric constraint—exclusion of head-to-tail dihedral angle discrepancies (DADs)—explains this limited selection as well as successful assembly into such closed cages in the first place. An edge running from a pentagon to a hexagon has a DAD, since the dihedral angles about the edge broaden from its pentagon (tail) end to its hexagon (head) end. Of the 21 configurations of a central face and surrounding faces, six have such DAD vectors arranged head-to-tail. Of the 5770 mathematically possible fullerene cages for n ≤ 60, excluding those with any of the six configurations leaves just 15 cages plus buckminsterfullerene (n = 60), among them the known clathrin cages. Of the 216,739 mathematically possible cages for 60 < n ≤ 84, just the 50 that obey the isolated-pentagon rule, among them known carbon cages, pass. The absence of likely fullerenes for some n (30,34,46,48,52-58,62-68) explains the abundance of certain cages, including buckminsterfullerene. These principles also suggest a “probable roads” path to self-assembly in place of pentagon-road and fullerene-road hypotheses.     

Characterisation of allergen-specific responses of IL-10-producing regulatory B cells (Br1) in Cow Milk Allergy

CD19+CD5+ regulatory B cells regulate immune responses by producing IL-10. IL-10-producing regulatory B cell (Br1) responses by allergen stimulation were investigated in human food allergy. Six milk allergy patients and eight milk-tolerant subjects were selected according to DBPCFC. PBMCs were stimulated by casein in vitro and stained for intracellular IL-10 and apoptosis. In response to allergen stimulation, Br1 decreased from 26.2 ± 18.3 to 15.5 ± 8.9% (p = 0.031, n = 6) in the milk allergy group and increased from 15.4 ± 9.0 to 23.7 ± 11.2% (p = 0.023, n = 8) in the milk-tolerant group. Apoptotic non-IL-10-producing regulatory B cells increased from 21.8 ± 9.3 to 38.0 ± 16.1% (p = 0.031, n = 6) in the milk allergy group and unchanged from 28.8 ± 13.8 to 28.0 ± 15.0% (p = 0.844, n = 8) in the milk-tolerant group. Br1 may be involved in the immune tolerance of food allergies by producing IL-10 and simultaneously undergoing apoptosis in humans. The exact roles for Br1 in immune tolerance needs to be further investigated.     

Overexpression of apolipoprotein-B improves cardiac function and increases survival in mice with myocardial infarction

Background

The heart produces apolipoprotein-B containing lipoproteins (apoB) whose function is not well understood. The aim of this study was to evaluate importance of myocardial apoB for cardiac function, structure and survival in myocardial infarction (MI) and heart failure (HF).

Methods and results

MI was induced in mice (n = 137) and myocardial apoB content was measured at 30 min, 3, 6, 24, 48, 120 h and 8 weeks post-MI. Transgenic mice overexpressing apoB (n = 27) and genetically matched controls (n = 27) were used to study the effects of myocardial apoB on cardiac function, remodeling, arrhythmias and survival after MI. Echocardiography was performed at rest and stress conditions at baseline, 2, 4 and 6 week post-MI and cumulative survival rate was registered. The myocardial apoB content increased both in the injured and the remote myocardium (p < 0.05) in response to ischemic injury. ApoB mice had 2-fold higher survival rate (p < 0.05) and better systolic function (p < 0.05) post-MI.

Conclusion

Overexpression of apoB in the heart increases survival and improves cardiac function after acute MI. Myocardial apoB may be an important cardioprotective system in settings such as myocardial ischemia and HF.     

Human plasma phospholipid transfer protein specific activity is correlated with HDL size: Implications for lipoprotein physiology

To gain further insights into the relationship between plasma phospholipid transfer protein (PLTP) and lipoprotein particles, PLTP mass and phospholipid transfer activity were measured, and their associations with the level and size of lipoprotein particles examined in 39 healthy adult subjects. No bivariate correlation was observed between PLTP activity and mass. PLTP activity was positively associated with cholesterol, triglyceride, apo B and VLDL particle level (r_s = 0.40–0.56, p ≤ 0.01) while PLTP mass was positively associated with HDL-C, large HDL particles, and mean LDL and HDL particle sizes (r_s = 0.44–0.52, p < 0.01). Importantly, plasma PLTP specific activity (SA) was significantly associated with specific lipoprotein classes, positively with VLDL, IDL, and small LDL particles (r_s = 0.42–0.62, p ≤ 0.01) and inversely with large LDL, large HDL, and mean LDL and HDL particle size (r_s = − 0.42 to − 0.70, p ≤ 0.01). After controlling for triglyceride levels, the correlation between PLTP mass or SA and HDL size remained significant. In linear models, HDL size explained 45% of the variability of plasma PLTP SA while triglyceride explained 34% of the PLTP activity. Thus, in healthy adults a significant relationship exists between HDL size and plasma PLTP SA (r_s = − 0.70), implying that HDL particle size may modulate PLTP SA in the vascular compartment.     

Association of the Ser326Cys polymorphism in the OGG1 gene with type 2 DM

The association of the Ser326Cys polymorphism of the 8-oxoguanine glycosylase 1 (OGG1) gene with type 2 diabetes was examined using a Japanese population (n (M/W): 4585 (2085/2500); age: 62.6 ± 10.9 years). HbA1c levels and frequency of diabetic subjects were significantly higher in subjects with genotypes with Cys allele than in those without (p = 0.032 and 0.037, respectively). Multiple logistic regression analysis showed that genotypes with Cys allele were significantly associated with diabetes (OR: 1.32, p = 0.0289). In subjects whose glucose tolerance was classified by FPG and 2-h PG (n = 1.634), the association was more substantial (genotypes with Cys allele vs. without, OR: 1.70, p = 0.0059; genotypes Cys/Cys vs. Ser/Ser, OR: 2.19, p = 0.0008). In subjects with genotype Ser/Ser, the insulin secretion index, HOMA-β, increased in the subjects with glucose intolerance and decreased in the subjects with diabetes, while, in subjects with genotypes Ser/Cys + Cys/Cys, HOMA-β decreased as the glucose tolerance progressed (p for trend = 0.010).     

Butane-2,3-dionethiosemicarbazone: an oxime with antioxidant properties

Oximes are compounds generally used to reverse the acetylcholinesterase (AChE) inhibition caused by organophosphates (OPs). The aim of this study was to examine the capacity of the butane-2,3-dionethiosemicarbazone oxime to scavenge different forms of reactive species (RS) in vitro, as well as counteract their formation. The potential antioxidant and toxic activity of the oxime was assayed both in vitro and ex vivo. The obtained results indicate a significant hydrogen peroxide (H₂O₂), nitric oxide (NO) and 1,1-diphenyl-2-picrylhydrazyl (DPPH) radical scavenging activity at 0.275, 0.5 and 5 μM of oxime, respectively (p ≤ 0.05). The oxime exhibited a powerful inhibitory effect on dihydroxybenzoate formation (25 μM) (p ≤ 0.05) and also decreased deoxyribose degradation induced by Fe²⁺ and via Fenton reaction (0.44 and 0.66 mM, respectively) (p ≤ 0.05). The oxime showed a significant inhibitory effect on σ-phenantroline reaction with Fe²⁺ (0.4 mM) suggesting a possible interaction between the oxime and iron. A significant decrease in the basal and pro-oxidant-induced lipid peroxidation in brain, liver, and kidney of mice was observed both in vitro and ex vivo (p ≤ 0.05). In addition, in our ex vivo experiments the oxime did not depict any significant changes in thiol levels of liver, kidney and brain as well as did not modify the δ-aminolevulinate dehydratase (δ-ALA-D) activity in these tissues. Taken together our results indicate an in vitro and ex vivo antioxidant activity of the oxime possibly due to its scavenging activity toward different RS and a significant iron interaction.     

Development of an all-in-one technology for glycan profiling targeting formalin-embedded tissue sections

An ultra-sensitive method for glycan analysis targeting small tissue sections (1.5 mm in diameter) is described as an application of a recently-established lectin microarray technology. The developed system achieved a high level of detection of a tissue section consisting of approximately 500 cells for differential profiling, where both N- and O-glycans attached to a pool of glycoproteins are subjected to multiplex analysis with 43 lectins. By using an optimized protocol for differential glycan analysis, sections of adenocarcinoma (n = 28) and normal epithelia (n = 12) of the colon were analyzed in an all-in-one manner. As a result, Wisteria floribunda agglutinin (WFA) was found to clearly differentiate cancerous from normal epithelia with P < 0.0001. The obtained results correlated well with the subsequent histochemical study using biotinylated WFA. Thus, the developed technology proved to be valid for expanding the lectin microarray applications to tissue-based glycomics, and hence, should accelerate a discovery phase of glycan-related biomarkers.     

Salt consumption-dependent association of the GNB3 gene polymorphism with type 2 DM

The associations of the C825T polymorphism (rs5443) of the G-protein β3 subunit (GNB3) gene and eight adjacent single nucleotide polymorphisms (SNPs) with diabetes were examined using a Japanese population (n (M/W): 2956 (1335/1621); age: 63.0 ± 10.2 years). Fasting plasma glucose (FPG) levels were significantly associated with the C825T polymorphism and two flanking SNPs (rs2301339 and rs5446) (p = 0.002, 0.001, and 0.008, respectively). A case-control association study of the C825T polymorphism with diabetes using multiple logistic regression analysis showed a significant association of the genotypes TT + TC with an odds ratio of 0.62 (p = 0.008) independent of age, gender, and BMI. The effects of salt consumption on the association were then examined (n = 1635). The FPG levels were significantly associated with the C825T polymorphism only in subjects with low salt consumption (<12.44 g/day) (p = 0.002). A case-control association study also showed a significant association with diabetes only in subjects with low salt consumption (p = 0.006).     

Ghrelin inhibited serotonin release from hippocampal slices

Ghrelin (Ghr) is a peptide produced peripherally and centrally. It participates in the modulation of different biological processes. In our laboratory we have shown that (a) Ghr administration, either intracerebroventricular or directly into the hippocampus enhanced memory consolidation in a step down test in rats (b) the effect of Ghr upon memory decreases in animals pretreated with a serotonin (5-HT) reuptake inhibitor, Fluoxetine, suggesting that Ghr effects in the hippocampus could be related to the availability of 5-HT. It has been demonstrated that Ghr inhibits 5-HT release from rat hypothalamic synaptosomes. Taking in mint these evidences, we studied the release of radioactive 5-HT to the superfusion medium from hippocampal slices treated with two doses of Ghr (0.3 and 3 nm/μl). Ghr inhibited significantly the 5-HT release in relation to those superfused with artificial cerebrospinal fluid (ACSF) (H = 9.48, df = 2, p ≤ 0.05). In another set of experiments, Ghr was infused into the CA1 area of hippocampus of the rats immediately after training in the step down test and the 5-HT release from slices was studied 24 h after Ghr injection showing that in this condition also the 5-HT release was inhibited (H = 11.72, df = 1, p ≤ 0.05). In conclusion, results provide additional evidence about the neurobiological bases of Ghr action in hippocampus.     

Macrophage-conditioned medium inhibits differentiation-induced Rb phosphorylation in 3T3-L1 preadipocytes

This study examines the mechanisms underlying the anti-adipogenic effect of macrophage-secreted products. 3T3-L1 preadipocytes were induced to differentiate over 8 days in medium conditioned by murine J774 macrophages (MacCM). The inhibitory effect on lipid accumulation and expression of adipogenic markers was diminished when addition of MacCM was delayed to day 2 of differentiation. Clonal expansion, an early event required for 3T3-L1 adipogenesis, was reduced in the presence of MacCM (89%; n = 3; p < 0.001), and BrdU incorporation was impaired by 55% (n = 3; p < 0.01). Activation of ERK1/2 was not affected by MacCM, and neither was the expression of p27^kip1, a cyclin-dependent kinase inhibitor. However, phosphorylation of the retinoblastoma protein (Rb), required for cell cycle progression, was impaired by MacCM (94% inhibition; n = 3; p < 0.01). Differentiation-dependent expression, nuclear localization, and DNA binding ability of C/EBPβ were not inhibited by MacCM. Alterations in cell cycle-associated proteins may be important with respect to the anti-adipogenic action of MacCM.     

A Derivative Matching Approach to Moment Closure for the Stochastic Logistic Model

Continuous-time birth-death Markov processes serve as useful models in population biology. When the birth-death rates are nonlinear, the time evolution of the first n order moments of the population is not closed, in the sense that it depends on moments of order higher than n. For analysis purposes, the time evolution of the first n order moments is often made to be closed by approximating these higher order moments as a nonlinear function of moments up to order n, which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model. We obtain the moment closure function by first assuming a certain separable form for it, and then matching time derivatives of the exact (not closed) moment equations with that of the approximate (closed) equations for some initial time and set of initial conditions. The separable structure ensures that the steady-state solutions for the approximate equations are unique, real and positive, while the derivative matching guarantees a good approximation, at least locally in time. Explicit formulas to construct these moment closure functions for arbitrary order of truncation n are provided with higher values of n leading to better approximations of the actual moment dynamics. A host of other moment closure functions previously proposed in the literature are also investigated. Among these we show that only the ones that achieve derivative matching provide a close approximation to the exact solution. Moreover, we improve the accuracy of several previously proposed moment closure functions by forcing derivative matching.     

Amplitude variability and extracellular low-pass filtering of neuronal spikes

The influence of neural morphology and passive electrical parameters on the width and amplitude of extracellular spikes is investigated by combined analytical and numerical investigations of idealized and anatomically reconstructed pyramidal and stellate neuron models. The main results are: 1), All models yield a low-pass filtering effect, that is, a spike-width increase with increasing distance from soma. 2), A neuron's extracellular spike amplitude is seen to be approximately proportional to the sum of the dendritic cross-sectional areas of all dendritic branches connected to the soma. Thus, neurons with many, thick dendrites connected to soma will produce large amplitude spikes, and therefore have the largest radius of visibility. 3), The spike shape and amplitude are found to be dependent on the membrane capacitance and axial resistivity, but not on the membrane resistivity. 4), The spike-amplitude decay with distance r is found to depend on dendritic morphology, and is decaying as 1/rⁿ with 1 ≤ n ≤ 2 close to soma and n ≥ 2 far away.