Incorporating spatial correlations into multispecies mean-field models

In biology, we frequently observe different species existing within the same environment. For example, there are many cell types in a tumour, or different animal species may occupy a given habitat. In modelling interactions between such species, we often make use of the mean field approximation, whereby spatial correlations between the locations of individuals are neglected. Whilst this approximation holds in certain situations, this is not always the case, and care must be taken to ensure the mean field approximation is only used in appropriate settings. In circumstances where the mean field approximation is unsuitable we need to include information on the spatial distributions of individuals, which is not a simple task. In this paper we provide a method that overcomes many of the failures of the mean field approximation for an on-lattice volume-excluding birth-death-movement process with multiple species. We explicitly take into account spatial information on the distribution of individuals by including partial differential equation descriptions of lattice site occupancy correlations. We demonstrate how to derive these equations for the multi-species case, and show results specific to a two-species problem. We compare averaged discrete results to both the mean field approximation and our improved method which incorporates spatial correlations. We note that the mean field approximation fails dramatically in some cases, predicting very different behaviour from that seen upon averaging multiple realisations of the discrete system. In contrast, our improved method provides excellent agreement with the averaged discrete behaviour in all cases, thus providing a more reliable modelling framework. Furthermore, our method is tractable as the resulting partial differential equations can be solved efficiently using standard numerical techniques.

Phenotypic changes associated with RNA interference silencing of chalcone synthase in apple (Malus × domestica)

We have identified in apple (Malus × domestica) three chalcone synthase (CHS) genes. In order to understand the functional redundancy of this gene family RNA interference knockout lines were generated where all three of these genes were down-regulated. These lines had no detectable anthocyanins and radically reduced concentrations of dihydrochalcones and flavonoids. Surprisingly, down-regulation of CHS also led to major changes in plant development, resulting in plants with shortened internode lengths, smaller leaves and a greatly reduced growth rate. Microscopic analysis revealed that these phenotypic changes extended down to the cellular level, with CHS-silenced lines showing aberrant cellular organisation in the leaves. Fruit collected from one CHS-silenced line was smaller than the 'Royal Gala' controls, lacked flavonoids in the skin and flesh and also had changes in cell morphology. Auxin transport experiments showed increased rates of auxin transport in a CHS-silenced line compared with the 'Royal Gala' control. As flavonoids are well known to be key modulators of auxin transport, we hypothesise that the removal of almost all flavonoids from the plant by CHS silencing creates a vastly altered environment for auxin transport to occur and results in the observed changes in growth and development.

Contribution of fibroblast and mast cell (afferent) and tumor (efferent) IL-6 effects within the tumor microenvironment

Hyperactive inflammatory responses following cancer initiation have led to cancer being described as a 'wound that never heals'. These inflammatory responses elicit signals via NFκB leading to IL-6 production, and IL-6 in turn has been shown to induce epithelial to mesenchymal transition in breast cancer cells in vitro, implicating a role for this cytokine in cancer cell invasion. We previously have shown that conditioned medium derived from cancer-associated fibroblasts induced an Epithelial to Mesenchymal transition (EMT) in PMC42-LA breast cancer cells and we have now identify IL-6 as present in this medium. We further show that IL-6 is expressed approximately 100 fold higher in a cancer-associated fibroblast line compared to normal fibroblasts. Comparison of mouse-specific (stroma) and human-specific (tumor) IL-6 mRNA expression from MCF-7, MDA MB 468 and MDA MB 231 xenografts also indicated the stroma rather than tumor as a significantly higher source of IL-6 expression. Mast cells (MCs) feature in inflammatory cancer-associated stroma, and activated MCs secrete IL-6. We observed a higher MC index (average number of mast cells per xenograft section/average tumor size) in MDA MB 468 compared to MDA MB 231 xenografts, where all MC were observed to be active (degranulating). This higher MC index correlated with greater mouse-specific IL-6 expression in the MDA MB 468 xenografts, implicating MC as an important source of stromal IL-6. Furthermore, immunohistochemistry on these xenografts for pSTAT3, which lies downstream of the IL-6 receptor indicated frequent correlations between pSTAT3 and mast cell positive cells. Analysis of publically available databases for IL-6 expression in patient tissue revealed higher IL-6 in laser capture microdissected stroma compared to adjacent tissue epithelium from patients with inflammatory breast cancer (IBC) and invasive non-inflammatory breast cancer (non-IBC) and we show that IL-6 expression was significantly higher in Basal versus Luminal molecular/phenotypic groupings of breast cancer cell lines. Finally, we discuss how afferent and efferent IL-6 pathways may participate in a positive feedback cycle to dictate tumor progression.

Assessing the role of spatial correlations during collective cell spreading

Spreading cell fronts are essential features of development, repair and disease processes. Many mathematical models used to describe the motion of cell fronts, such as Fisher’s equation, invoke a mean–field assumption which implies that there is no spatial structure, such as cell clustering, present. Here, we examine the presence of spatial structure using a combination of in vitro circular barrier assays, discrete random walk simulations and pair correlation functions. In particular, we analyse discrete simulation data using pair correlation functions to show that spatial structure can form in a spreading population of cells either through sufficiently strong cell–to–cell adhesion or sufficiently rapid cell proliferation. We analyse images from a circular barrier assay describing the spreading of a population of MM127 melanoma cells using the same pair correlation functions. Our results indicate that the spreading melanoma cell populations remain very close to spatially uniform, suggesting that the strength of cell–to–cell adhesion and the rate of cell proliferation are both sufficiently small so as not to induce any spatial patterning in the spreading populations.

Genetic and phenotypic evidence supports evolutionary divergence of the American flamingo (Phoenicopterus ruber) population in the Galapagos islands

The Galapagos archipelago is characterized by a high degree of endemism across many taxa, linked to the archpelago's oceanic origin and distance from other colonizing land masses. A population of ~ 500 American Flamingos (Phoenicopterus ruber) resides in Galapagos, which is thought to share an historical origin with the American Flamingo currently found in the Caribbean region. Genetic and phenotypic parameters in American Flamingos from Galapagos and from the Caribbean were investigated. Microsatellite and microchondrial DNA markers data showed that the American Flamingo population in Galapagos differs genetically from that in the Caribbean. American Flamingos in Galapagos form a clade which differs by a single common nucleotide substitution from American Flamingos in the Caribbean. The genetic differentiation is also evident from nuclear DNA in that microsatellite data reveal a number of private alleles for the American Flamingo in Galapagos. Analysis of skeletal measurements showed that American Flamingos in Galapagos are smaller than those in the Caribbean primarily due to shorter tarsus length, and differences in body shape sexual dimorphism. American Flamingo eggs from Galapagos have smaller linear dimensions and volumes than those from the Caribbean. The findings are consistent with reproductive isolation of American Flamingo population in Galapagos.

JK1 (FAM134B) gene and colorectal cancer : a pilot study on the gene copy number alterations and correlations with clinicopathological parameters

AIMS The aims of the study are to characterize changes in JK-1 (FAM134B) at the DNA level in colorectal adenocarcinoma and adenoma and exploring the possible correlations with clinical and pathological features. METHOD JK-1 gene DNA copy number changes were studied in 211 colorectal carcinomas, 32 colorectal adenoma and 20 colorectal non-cancer colorectal tissue samples by real-time quantitative polymerase chain reaction. The results were correlated with clinical and pathological parameters. RESULTS Colorectal adenomas were more likely to be amplified than deleted with regard to JK-1 (FAM134B) DNA copy number change. The copy number level of JK-1 (FAM134B) DNA in colorectal adenocarcinomas was significantly lower in comparison to colorectal adenomas. Changes in JK-1 (FAM134B) DNA copy number were associated with histological subtypes, and cancer stage. Lower copy numbers were associated with higher tumor stage, lymph node stage and overall pathological stage of cancer. Conversely, higher DNA copy numbers were detected more often in the mucinous adenocarcinoma. CONCLUSIONS This is the first study showing significant correlations of the JK-1 (FAM134B) gene copy number alterations with clinical and pathological features in a large cohort of pre-invasive and invasive colorectal malignancies. The changes in DNA copy number associated with progression of colorectal malignancies reflect that JK-1 (FAM134B) gene could play a role in controlling some steps in development of the invasive phenotypes.

Expression profile of endothelin 1 and its receptor endothelin receptor A in papillary thyroid carcinoma and their correlations with clinicopathologic characteristics

The endothelin axis is a group of signaling molecules and their receptors that have been implicated in vascularization of cancers, with their expression being observed to change in different cancer types. In this research, we examined the expression of endothelin 1 and endothelin receptor A at the protein and messenger RNA (mRNA) levels in 123 papillary thyroid carcinomas and 40 matched lymph nodes with metastatic papillary thyroid carcinomas. We found altered endothelin axis mRNA expression in several clinicopathologic parameters with increased endothelin 1 expression in thyroid papillary carcinoma showing stromal calcification, cancers in men, and primary cancers with lymph node metastases. Increased endothelin receptor A mRNA expression was noted in the larger cancers. There is a significant correlation between expression of endothelin receptor A and endothelin 1 in papillary thyroid carcinoma. Both endothelin receptor A and endothelin 1 mRNA expressions were significantly higher in metastatic carcinoma in the lymph node than in primary thyroid cancer. The metastatic carcinoma in the lymph node had increased expression compared with matched primary thyroid carcinoma. Expressions of endothelin 1 and endothelin receptor A were also documented as being high at the protein level. Our results indicate that in thyroid cancer, endothelin 1 and endothelin receptor A are associated with growth in advanced stages and lymph node metastases, likely through known angiogenic linkages. Targeting the endothelin axis may be useful in planning angiogenesis therapy for thyroid cancer.

Correlations and volatility spillovers across commodity and stock markets: Linking energies, food, and gold

This paper employs a VAR-GARCH model to investigate the return links and volatility transmission between the S&P 500 and commodity price indices for energy, food, gold and beverages over the turbulent period from 2000 to 2011. Understanding the price behavior of commodity prices and the volatility transmission mechanism between these markets and the stock exchanges are crucial for each participant, including governments, traders, portfolio managers, consumers, and producers. For return and volatility spillover, the results show significant transmission among the S&P 500 and commodity markets. The past shocks and volatility of the S&P 500 strongly influenced the oil and gold markets. This study finds that the highest conditional correlations are between the S&P 500 and gold index and the S&P 500 and WTI index. We also analyze the optimal weights and hedge ratios for commodities/S&P 500 portfolio holdings using the estimates for each index. Overall, our findings illustrate several important implications for portfolio hedgers for making optimal portfolio allocations, engaging in risk management and forecasting future volatility in equity and commodity markets. © 2013 Elsevier B.V.

Modeling conditional correlations of asset returns : a smooth transition approach

In this paper we propose a new multivariate GARCH model with time-varying conditional correlation structure. The time-varying conditional correlations change smoothly between two extreme states of constant correlations according to a predetermined or exogenous transition variable. An LM–test is derived to test the constancy of correlations and LM- and Wald tests to test the hypothesis of partially constant correlations. Analytical expressions for the test statistics and the required derivatives are provided to make computations feasible. An empirical example based on daily return series of five frequently traded stocks in the S&P 500 stock index completes the paper.

Heritability of head motion during resting state functional MRI in 462 healthy twins

Head motion (HM) is a critical confounding factor in functional MRI. Here we investigate whether HM during resting state functional MRI (RS-fMRI) is influenced by genetic factors in a sample of 462 twins (65% fema≤ 101 MZ (monozygotic) and 130 DZ (dizygotic) twin pairs; mean age: 21 (SD=3.16), range 16-29). Heritability estimates for three HM components-mean translation (MT), maximum translation (MAXT) and mean rotation (MR)-ranged from 37 to 51%. We detected a significant common genetic influence on HM variability, with about two-thirds (genetic correlations range 0.76-1.00) of the variance shared between MR, MT and MAXT. A composite metric (HM-PC1), which aggregated these three, was also moderately heritable (h2=42%). Using a sub-sample (N=35) of the twins we confirmed that mean and maximum translational and rotational motions were consistent "traits" over repeated scans (r=0.53-0.59); reliability was even higher for the composite metric (r=0.66). In addition, phenotypic and cross-trait cross-twin correlations between HM and resting state functional connectivities (RS-FCs) with Brodmann areas (BA) 44 and 45, in which RS-FCs were found to be moderately heritable (BA44: h2-=0.23 (sd=0.041), BA45: h2-=0.26 (sd=0.061)), indicated that HM might not represent a major bias in genetic studies using FCs. Even so, the HM effect on FC was not completely eliminated after regression. HM may be a valuable endophenotype whose relationship with brain disorders remains to be elucidated.

Shaping development through mechanical strain: The transcriptional basis of diet-induced phenotypic plasticity in a cichlid fish

Adaptive phenotypic plasticity, the ability of an organism to change its phenotype to match local environments, is increasingly recognized for its contribution to evolution. However, few empirical studies have explored the molecular basis of plastic traits. The East African cichlid fish Astatoreochromis alluaudi displays adaptive phenotypic plasticity in its pharyngeal jaw apparatus, a structure that is widely seen as an evolutionary key innovation that has contributed to the remarkable diversity of cichlid fishes. It has previously been shown that in response to different diets, the pharyngeal jaws change their size, shape and dentition: hard diets induce an adaptive robust molariform tooth phenotype with short jaws and strong internal bone structures, while soft diets induce a gracile papilliform tooth phenotype with elongated jaws and slender internal bone structures. To gain insight into the molecular underpinnings of these adaptations and enable future investigations of the role that phenotypic plasticity plays during the formation of adaptive radiations, the transcriptomes of the two divergent jaw phenotypes were examined. Our study identified a total of 187 genes whose expression differs in response to hard and soft diets, including immediate early genes, extracellular matrix genes and inflammatory factors. Transcriptome results are interpreted in light of expression of candidate genesmarkers for tooth size and shape, bone cells and mechanically sensitive pathways. This study opens up new avenues of research at new levels of biological organization into the roles of phenotypic plasticity during speciation and radiation of cichlid fishes.

The IFITM5 mutation c.-14C > T results in an elongated transcript expressed in human bone; And causes varying phenotypic severity of osteogenesis imperfecta type V

Background The genetic mutation resulting in osteogenesis imperfecta (OI) type V was recently characterised as a single point mutation (c.-14C > T) in the 5' untranslated region (UTR) of IFITM5, a gene encoding a transmembrane protein with expression restricted to skeletal tissue. This mutation creates an alternative start codon and has been shown in a eukaryotic cell line to result in a longer variant of IFITM5, but its expression has not previously been demonstrated in bone from a patient with OI type V. Methods Sanger sequencing of the IFITM5 5' UTR was performed in our cohort of subjects with a clinical diagnosis of OI type V. Clinical data was collated from referring clinicians. RNA was extracted from a bone sample from one patient and Sanger sequenced to determine expression of wild-type and mutant IFITM5. Results: All nine subjects with OI type V were heterozygous for the c.-14C > T IFITM5 mutation. Clinically, there was heterogeneity in phenotype, particularly in the manifestation of bone fragility amongst subjects. Both wild-type and mutant IFITM5 mRNA transcripts were present in bone. Conclusions The c.-14C > T IFITM5 mutation does not result in an RNA-null allele but is expressed in bone. Individuals with identical mutations in IFITM5 have highly variable phenotypic expression, even within the same family.

Evolution of a ~2.7 Ga large igneous province: A volcanological, geochemical and geochronological study of the Agnew Greenstone Belt, and new regional correlations for the Kalgoorlie Terrane (Yilgarn Craton, Western Australia)

The thick package of ~2.7 Ga mafic and ultramafic lavas and intrusions preserved among the Neoarchean of the Kalgoorlie Terrene in Western Australia provides valuable insight into geological processes controlling the most prodigious episode of growth and preservation of juvenile continental crust in Earth’s history. Limited exposure of these rocks results in uncertainty about their age, physical and chemical characteristics, and stratigraphic relationships. This in turn prevents confident correlation of regional occurrences of mafic and ultramafic successions (both intrusive and extrusive) and hinders the interpretation of tectonic setting and magmatic evolution. A recent stratigraphic drilling program of the Neoarchean stratigraphy of the Agnew Greenstone Belt in Western Australia has provided continuous exposures through a c. 7 km thick sequence of mafic and ultramafic units. In this study, we present a volcanological, lithogeochemical and chronological study of the Agnew Greenstone Belt, and provide the first pre-2690 Ma regional correlation across the Kalgoorlie Terrane. The Agnew Greenstone Belt records ~30 m.y. of episodic ultramafic-mafic magmatism that includes two cycles, each defined by a komatiite that is overlain by units that become more evolved and contaminated with time. The sequence is divided into nine conformable packages, each consisting of stacked subaqueous lava flows and comagmatic intrusions, as well as two sills without associated extrusions. Lavas, with the exception of intercalations between two units, form a layer-cake stratigraphy and were likely erupted from a system of fissures tapping the same magma source. The komatiites are not contaminated by continental crust ([La/Sm]PM ~0.7) and are of the Al-undepleted Munro-type. Crustal contamination is evident in many units (Songvang Basalt, Never Can Tell Basalt, Redeemer Basalt, and Turrett Dolerite), as judged by [La/Sm]>1, negative Nb and Ti anomalies, and geochemical mixing trends towards felsic contaminants. Crystal fractionation was also significant, with early olivine and chromite (Mg#>65) followed by plagioclase and clinopyroxene removal (Mg<65), and in the most evolved case, titanomagnetite accumulation. Three new TIMS dates on granophyric zones of mafic sills and one ICP-MS date from an interflow felsic tuff are presented and used for regional stratigraphic correlation. Cycle I magmatism began at ~2720 Ma and ended ~2705 Ma, whereas cycle II began ~2705 Ma and ended at 2690.7±1.2 Ma. Regional correlations indicate the western Kalgoorlie Terrane consists of a remarkably similar stratigraphy that can be recognised at Agnew, Ora Banda and Coolgardie, whereas the eastern part of the terrane (e.g., Kambalda Domain) does not include cycle I, but correlates well with cycle II. This research supports an autochthonous model of greenstone formation, in which one large igneous province, represented by two complete cycles, is constructed on sialic crust. New stratigraphic correlations for the Kalgoorlie Terrane indicate that many units can be traced over distances >100 km, which has implications for exploration targeting for stratigraphically hosted ultramafic Ni and VMS deposits.

Conformation-activity correlations for chemotactic tripeptide analogs incorporating dialkyl residues with linear and cyclic alkyl sidechains at position 2

Five stereochemically constrained analogs of the chemotactic tripeptide incorporating 1-aminocycloalkane-1-carboxylic acid (Ac(n)c) and alpha,alpha-dialkylglycines (Deg, diethylglycine; Dpg, n,n-dipropylglycine and Dbg, n,n-dibutylglycine) at position 2 have been synthesized. NMR studies of peptides For-Met-Xxx-Phe-OMe (Xxx = Ac(7)c, I; Ac(8)c, II; Deg, III; Dpg, IV and Dbg, V; For, formyl) establish that peptides with cycloalkyl residues, I and II, adopt folded beta-turn conformations in CDCl3 and (CD3)(2)SO. In contrast, analogs with linear alkyl sidechains, III-V, favour fully extended (C-5) conformations in solution. Peptides I-V exhibit high activity in inducing beta-glucosaminidase release from rabbit neutrophils, with ED(50) values ranging from 1.4-8.0 x 10(-11)M. In human neutrophils the Dxg peptides III-V have ED(50) values ranging from 2.3 x 10(-8) to 5.9 x 10(-10) M, with the activity order being V > IV > III. While peptides I-IV are less active than the parent. For-Met-Leu-Phe-OH, in stimulating histamine release from human basophils, the Dbg peptide V is appreciably more potent, suggesting its potential utility as a probe for formyl peptide receptors.