Biopacemaker acceleration without increased synchronization by chronic exposure to phorbol myristate acetate

L'activité électrique du coeur est initiée par la génération spontanée de potentiels d'action venant des cellules pacemaker du noeud sinusal (SN). Toute dysfonction au niveau de cette région entraîne une instabilité électrique du coeur. La majorité des patients souffrant d'un noeud sinusal déficient nécessitent l'implantation chirurgicale d'un pacemaker électronique; cependant, les limitations de cette approche incitent à la recherche d'une alternative thérapeutique. La base moléculaire des courants ioniques jouant un rôle crucial dans l'activité du noeud sinusal sont de plus en plus connues. Une composante importante de l'activité des cellules pacemakers semble être le canal HCN, responsable du courant pacemaker If. Le facteur T-box 3 (Tbx3), un facteur de transcription conservé durant le processus de l'évolution, est nécessaire au développement du système de conduction cardiaque. De précédentes études ont démontré que dans différentes lignées cellulaires le Phorbol 12-myristate 13-acetate (PMA) active l'expression du gène codant Tbx3 via des réactions en cascade partant de la protéine kinase C (PKC). L'objectif principal de cette étude est de tester si le PMA peut augmenter la fréquence et la synchronisation de l'activité spontanée du pacemaker biologique en culture. Plus précisément, nous avons étudié les effets de l'exposition chronique au PMA sur l'expression du facteur de transcription Tbx3, sur HCN4 et l'activité spontanée chez des monocouches de culture de myocytes ventriculaires de rats néonataux (MVRN). Nos résultats démontrent que le PMA augmente significativement le facteur transcription de Tbx3 et l'expression ARNm de HCN4, favorisant ainsi l'augmentation du rythme et de la stabilité de l'activité autonome. De plus, une diminution significative de la vitesse de conduction a été relevée et est attribuée à la diminution du couplage intercellulaire. La diminution de la vitesse de conduction pourrait expliquer l'effet négatif du PMA sur la synchronisation de l'activité autonome du pacemaker biologique. Ces résultats ont été confirmés par un modèle mathématique multicellulaire suggérant que des fréquences et résistances intercellulaires plus élevée pourraient induire une activité plus stable et moins synchrone. Cette étude amène de nouvelles connaissances très importantes destinées à la production d'un pacemaker biologique efficient et robuste.

Molecular studies on a Dictyostelium homolog of the tafazzin gene, the cause of Barth syndrome in humans

Der eukaryotische Mikroorganismus Dictyostelium discoideum lebt als einzellige Amöbe solange ausreichende Nahrungsressourcen zur Verfügung stehen. Sobald Nahrungsmangel eintritt, entwickeln sich die Zellen von einem einzelligen zu einem mehrzelligen Zustand, der mit einem multizellulären Fruchtkörper abschließt. Dieser Prozess wird durch eine Reihe aufeinanderfolgender Signale organisiert, die eine differentielle Genexpression regulieren. Die Gene der Discoidin I Familie gehören zu den Ersten, die im Laufe des Wachstums-Differenzierungs-Übergangs (engl. GDT) aktiviert werden. Sie eignen sich daher vorzüglich als Marker für den Beginn der Entwicklung. Mit Hilfe einer REMI-Mutagenese und Discoidin I als molekularem Marker sind verschiedene Komponenten des Wachstums-Differenzierungs-Übergangs in unserer Arbeitsgruppe identifiziert worden (Zeng et al., 2000 A und B; Riemann und Nellen, persönliche Mitteilung). Mit demselben Ansatz wurde in der vorliegenden Arbeit eine REMI-Mutante identifiziert, die eine Fehl-Expression von Discoidin zeigte und einen axenischen Wachstumsdefekt bei 15 °C aufwies. Das Gen wurde als Homolog zum humanen Tafazzin-Gen identifiziert. Dieses Gen wurde zur Rekonstruktion des Phänotyps über homologe Rekombination erneut disruptiert, was wie erwartet zu dem zuerst beschriebenen Phänotyp führte. Folgerichtig ergab eine Überexpression des Gens in den Mutanten eine Komplementation des Phänotyps. Immunfluoreszenz-Experimente zeigten eine mitochondriale Lokalisation des Dictyostelium discoideum Taffazzin Proteins. Dass ein mitochondriales Protein in Zusammenhang mit dem Wachstums-Differenzierungs-Übergang steht, ist ein unerwarteter Befund, der aber als Hinweis darauf gewertet werden kann, dass Mitochondrien einen direkten Einfluss auf die entwicklungsspezifische Signaltransduktion ausüben. Die Taffazzin Disruptions-Mutante in Dictyostelium führte zu einem abnormalen Cardiolipin Metabolismus. Dieses Phospholipid ist ein charakteristischer Bestandteil der inneren Mitochondrienmembran und für die Funktion verschiedener Enzyme erforderlich. Unsere vorläufigen Analysen des Phospholipid-Gehalts zeigten Übereinstimmung mit Daten von Patienten mit Barth-Syndrom, einer humanen Erkrankung, bei der das Taffazzin-Gen Mutationen aufweist, und mit Hefe-Mutanten dieses Gens. Dies zeigt den Wert von Dictyostelium discoideum als einen weiteren Modelorganismus zur Untersuchung des Barth-Syndroms und zur Erprobung möglicher Therapieansätze.

Biofilmbildung bei Pflanzen-assoziierten Bakterien der Gattung Methylobacterium und molekulargenetisch-physiologische Charakterisierung eines neuen Marchantia-Isolats (Mtb. sp. JT1)

Bakterien existieren bevorzugt in Biofilmen. Das Zusammenleben in diesen Gemeinschaften bietet den einzelnen Mikroben einen wirksamen Schutz und ermöglicht die Ausbildung langfristiger, synergistischer Wechselwirkungen, die mit multizellulären Systemen verglichen werden können. Biofilme bestehen aus Mikrooganismen-Populationen, die sich an Grenzflächen ansammeln und typischerweise von einer Matrix aus extrazellulären polymeren Substanzen umgeben sind. Auch auf Pflanzen-Oberflächen bilden viele Bakterien Biofilme, um ihre Überlebenswahrscheinlichkeit zu erhöhen. In dieser Arbeit wurde die Biofilmbildung bei Pflanzen-assoziierten Bakterien der Gattung Methylobacterium (Mtb.) untersucht, wobei molekular- und mikrobiologische sowie mikroskopische Techniken eingesetzt wurden. Es zeigte sich, dass alle untersuchten Vertreter der Gattung Methylobacterium in unterschiedlichem Ausmaß Biofilme bilden. Die Ausprägung ist dabei Taxon (bzw. Isolat)-spezifisch und vor allem von der Stickstoff-Verfügbarkeit abhängig. Jedoch spielen auch andere Umweltfaktoren, wie die Versorgung der Zellen mit Phosphat und die Zelldichte, bei der Ausbildung der überzellulären Einheiten eine wichtige Rolle. Die Matrix der Biofilme wird meist durch ein fibrilläres Netzwerk gebildet. Dabei handelt es sich um Heteropolysaccharide, die von den Bakterien synthetisiert und sezerniert werden. Einige Isolate bilden zusätzlich zahlreiche Fimbrien (Auswüchse), durch die sie an andere Zellen oder Oberflächen binden können. Im zweiten Teil dieser Arbeit wurden mehrere neue Methylobacterium-Isolate physiologisch und molekulargenetisch charakterisiert (Nährstoffverwertung, DNA-Sequenzen verschiedener Gene, phylogenetische Analysen usw.). Im Vordergrund stand hierbei der von einer urtümlichen Landpflanze, dem Lebermoos (Marchantia polymorpha), isolierte Stamm Mtb. sp. JT1. Dabei zeigten sich deutliche Unterschiede in der Morphologie und Physiologie des Bakterienstamms JT1 und dem nahe verwandten Stamm 5b.2.20 zu den bereits beschriebenen Taxa der Gattung, so dass eine Spezies-Neubeschreibung erforderlich war. Als Artname wurde aufgrund der außergewöhnlichen Oberflächenstrukturen Mtb. fimbriae sp. nov. eingeführt. Auch andere Methylobakterien (unter anderem Isolat Mtb. sp. F3.2, isoliert vom Laubmoos Funaria hygrometrica) stellen wahrscheinlich Vertreter einer neue Spezies dar (Artname Mtb. funariae sp. nov.). Jedoch zeigen Mtb. fimbriae und Mtb. funariae nur geringe physiologische und morphologische Unterschiede und konnten auf Grundlage umfassender DNA-DNA-Hybridisierungs-Studien nicht eindeutig voneinander abgegrenzt werden.

Nuclear organisation and epigenetic regulation of gene expression in Dictyostelium discoideum

A series of vectors for the over-expression of tagged proteins in Dictyostelium were designed, constructed and tested. These vectors allow the addition of an N- or C-terminal tag (GFP, RFP, 3xFLAG, 3xHA, 6xMYC and TAP) with an optimized polylinker sequence and no additional amino acid residues at the N or C terminus. Different selectable markers (Blasticidin and gentamicin) are available as well as an extra chromosomal version; these allow copy number and thus expression level to be controlled, as well as allowing for more options with regard to complementation, co- and super-transformation. Finally, the vectors share standardized cloning sites, allowing a gene of interest to be easily transfered between the different versions of the vectors as experimental requirements evolve. The organisation and dynamics of the Dictyostelium nucleus during the cell cycle was investigated. The centromeric histone H3 (CenH3) variant serves to target the kinetochore to the centromeres and thus ensures correct chromosome segregation during mitosis and meiosis. A number of Dictyostelium histone H3-domain containing proteins as GFP-tagged fusions were expressed and it was found that one of them functions as CenH3 in this species. Like CenH3 from some other species, Dictyostelium CenH3 has an extended N-terminal domain with no similarity to any other known proteins. The targeting domain, comprising α-helix 2 and loop 1 of the histone fold is required for targeting CenH3 to centromeres. Compared to the targeting domain of other known and putative CenH3 species, Dictyostelium CenH3 has a shorter loop 1 region. The localisation of a variety of histone modifications and histone modifying enzymes was examined. Using fluorescence in situ hybridisation (FISH) and CenH3 chromatin-immunoprecipitation (ChIP) it was shown that the six telocentric centromeres contain all of the DIRS-1 and most of the DDT-A and skipper transposons. During interphase the centromeres remain attached to the centrosome resulting in a single CenH3 cluster which also contains the putative histone H3K9 methyltransferase SuvA, H3K9me3 and HP1 (heterochromatin protein 1). Except for the centromere cluster and a number of small foci at the nuclear periphery opposite the centromeres, the rest of the nucleus is largely devoid of transposons and heterochromatin associated histone modifications. At least some of the small foci correspond to the distal telomeres, suggesting that the chromosomes are organised in a Rabl-like manner. It was found that in contrast to metazoans, loading of CenH3 onto Dictyostelium centromeres occurs in late G2 phase. Transformation of Dictyostelium with vectors carrying the G418 resistance cassette typically results in the vector integrating into the genome in one or a few tandem arrays of approximately a hundred copies. In contrast, plasmids containing a Blasticidin resistance cassette integrate as single or a few copies. The behaviour of transgenes in the nucleus was examined by FISH, and it was found that low copy transgenes show apparently random distribution within the nucleus, while transgenes with more than approximately 10 copies cluster at or immediately adjacent to the centromeres in interphase cells regardless of the actual integration site along the chromosome. During mitosis the transgenes show centromere-like behaviour, and ChIP experiments show that transgenes contain the heterochromatin marker H3K9me2 and the centromeric histone variant H3v1. This clustering, and centromere-like behaviour was not observed on extrachromosomal transgenes, nor on a line where the transgene had integrated into the extrachromosomal rDNA palindrome. This suggests that it is the repetitive nature of the transgenes that causes the centromere-like behaviour. A Dictyostelium homolog of DET1, a protein largely restricted to multicellular eukaryotes where it has a role in developmental regulation was identified. As in other species Dictyostelium DET1 is nuclear localised. In ChIP experiments DET1 was found to bind the promoters of a number of developmentally regulated loci. In contrast to other species where it is an essential protein, loss of DET1 is not lethal in Dictyostelium, although viability is greatly reduced. Loss of DET1 results in delayed and abnormal development with enlarged aggregation territories. Mutant slugs displayed apparent cell type patterning with a bias towards pre-stalk cell types.

Campanian crustacean burrow system from Israel with brood and nursery chambers representing communal organization

Phosphorite-filled crustacean burrows associated with a Campanian-age omission surface in the north-western Negev are described. The phosphatic burrow casts weather out displaying scratches (bioglyphs) and two types of local swellings (chambers), which are flattened normal to the course of the burrow. The more abundant chamber type is a flattened spheroid (diameter 45-50 mm) or a flattened, highly prolate ellipsoid of larger dimensions, with bioglyphs. The other type is a flattened spheroid (diameter 45 mm), gently rounded on the upper side and flat on the base. Rings of elevations on the cast (representing moats) form interconnected circlets, each capped by about eight rounded hemispherical tubercles (4 x 4 mm) (pits on original), the whole forming a discrete network. The first type of chamber may have hosted the young (nursery chamber) and/or stored food. The second type of cast replicates a chamber with a pitted floor, which may have formed a brood chamber for 60-70 spherical eggs, each about 3 mm in diameter. Brood chambers in crustacean burrow systems were previously suspected, but only at burrow terminations. The interpreted K-type breeding strategy, brood care and associated functions require a high degree of social organization, none of which has been observed in extant crustaceans, but all occur within social insects.

Selfish genetic elements favor the evolution of a distinction between soma and germline

Many multicellular organisms have evolved a dedicated germline. This can benefit the whole organism, but its advantages to genetic parasites have not been explored. Here I model the evolutionary success of a selfish element, such as a transposable element or endosymbiont, which is capable of creating or strengthening a germline-soma distinction in a primitively multicellular host, and find that it will always benefit the element to do so. Genes causing germline sequestration can therefore spread in a population even if germline sequestration is maladaptive for the host organism. Costly selfish elements are expected to survive only in sexual populations, so sexual species may experience an additional push toward germline-soma distinction, and hence toward cell differentiation and multicellularity.

Genesis and expansion of metazoan transcription factor gene classes

We know little about the genomic events that led to the advent of a multicellular grade of organization in animals, one of the most dramatic transitions in evolution. Metazoan multicellularity is correlated with the evolution of embryogenesis, which presumably was underpinned by a gene regulatory network reliant on the differential activation of signaling pathways and transcription factors. Many transcription factor genes that play critical roles in bilaterian development largely appear to have evolved before the divergence of cnidarian and bilaterian lineages. In contrast, sponges seem to have a more limited suite of transcription factors, suggesting that the developmental regulatory gene repertoire changed markedly during early metazoan evolution. Using whole- genome information from the sponge Amphimedon queenslandica, a range of eumetazoans, and the choanoflagellate Monosiga brevicollis, we investigate the genesis and expansion of homeobox, Sox, T- box, and Fox transcription factor genes. Comparative analyses reveal that novel transcription factor domains ( such as Paired, POU, and T- box) arose very early in metazoan evolution, prior to the separation of extant metazoan phyla but after the divergence of choanoflagellate and metazoan lineages. Phylogenetic analyses indicate that transcription factor classes then gradually expanded at the base of Metazoa before the bilaterian radiation, with each class following a different evolutionary trajectory. Based on the limited number of transcription factors in the Amphimedon genome, we infer that the genome of the metazoan last common ancestor included fewer gene members in each class than are present in extant eumetazoans. Transcription factor orthologues present in sponge, cnidarian, and bilaterian genomes may represent part of the core metazoan regulatory network underlying the origin of animal development and multicellularity.

Modelling the formation of necrotic regions in avascular tumours

The mechanisms underlying the formation of necrotic regions within avascular tumours are not well understood. In this paper, we examine the relative roles of nutrient deprivation and of cell death, from both the proliferating phase of the cell cycle via apoptosis and from the quiescent phase via necrosis, in changing the structure within multicellular tumour spheroids and particularly the accumulation of dead cell material in the centre. A mathematical model is presented and studied that accounts for nutrient diffusion, changes in cell cycling rates, the two different routes to cell death as well as active motion of cells and passive motion of the dead cell material. In studying the accumulation of dead cell matter we do not distinguish between the route by which each was formed. The resulting mathematical model is examined for a number of scenarios. Results show that in many cases the size of the necrotic core is closely correlated with low levels in nutrient concentration. However, in certain cases, particularly where the rate of necrosis is large, the resulting necrotic core can lead to regions of non-negligible nutrient concentration-dependent upon the mode of cell death.

An unusual choanoflagellate protein released by hedgehog autocatalytic processing

Hedgehog proteins are important cell-cell signalling proteins utilized during the development of multicellular animals. Members of the hedgehog gene family have not been detected outside the Metazoa, raising unanswered questions about their evolutionary origin. Here we report a highly unusual hedgehog-related gene from a choanoflagellate, a close unicellular relative of the animals. The deduced C-terminal domain, Hoglet-C, is homologous to the autocatalytic domain of Hedgehog proteins and is predicted to function in autocatalytic cleavage of the precursor peptide. In contrast, the N-terminal Hoglet-N peptide has no similarity to the signalling peptide of Hedgehog (Hh-N). Instead, Hoglet-N is deduced to be a secreted protein with an enormous threonine-rich domain of unprecedented size and purity (over 200 threonine residues) and two polysaccharide-binding domains. Structural modelling reveals that these domains have a novel combination of features found in cellulose-binding domains (CBD) of types IIa and IIb, and are expected to bind cellulose. We propose that the two CBD domains enable Hoglet-N to bind to plant matter, tethering an amorphous nucleophilic anchor, facilitating transient adhesion of the choanoflagellate cell. Since HhC and Hoglet-C are homologous, but Hh-N and Hoglet-N are not, we argue that metazoan hedgehog genes evolved by fusion of two distinct genes.

Hydroponic isotope labeling of entire plants (HILEP) for quantitative plant proteomics

Quantitative analysis by mass spectrometry (MS) is a major challenge in proteomics as the correlation between analyte concentration and signal intensity is often poor due to varying ionisation efficiencies in the presence of molecular competitors. However, relative quantitation methods that utilise differential stable isotope labelling and mass spectrometric detection are available. Many drawbacks inherent to chemical labelling methods (ICAT, iTRAQ) can be overcome by metabolic labelling with amino acids containing stable isotopes (e.g. 13C and/or 15N) in methods such as Stable Isotope Labelling with Amino acids in Cell culture (SILAC). SILAC has also been used for labelling of proteins in plant cell cultures (1) but is not suitable for whole plant labelling. Plants are usually autotrophic (fixing carbon from atmospheric CO2) and, thus, labelling with carbon isotopes becomes impractical. In addition, SILAC is expensive. Recently, Arabidopsis cell cultures were labelled with 15N in a medium containing nitrate as sole nitrogen source. This was shown to be suitable for quantifying proteins and nitrogen-containing metabolites from this cell culture (2,3). Labelling whole plants, however, offers the advantage of studying quantitatively the response to stimulation or disease of a whole multicellular organism or multi-organism systems at the molecular level. Furthermore, plant metabolism enables the use of inexpensive labelling media without introducing additional stress to the organism. And finally, hydroponics is ideal to undertake metabolic labelling under extremely well-controlled conditions. We demonstrate the suitability of metabolic 15N hydroponic isotope labelling of entire plants (HILEP) for relative quantitative proteomic analysis by mass spectrometry. To evaluate this methodology, Arabidopsis plants were grown hydroponically in 14N and 15N media and subjected to oxidative stress.

Integrated cytokine and metabolic analysis of pathological responses to parasite exposure in rodents

Parasitic infections cause a myriad of responses in their mammalian hosts, on immune as well as on metabolic level. A multiplex panel of cytokines and metabolites derived from four parasite-rodent models, namely, Plasmodium berghei-mouse, Trypanosoma brucei brucei-mouse, Schistosoma mansoni-mouse, and Fasciola hepatica-rat were statistically coanalyzed. 1H NMR spectroscopy and multivariate statistical analysis were used to characterize the urine and plasma metabolite profiles in infected and noninfected animals. Each parasite generated a unique metabolic signature in the host. Plasma cytokine concentrations were obtained using the ‘Meso Scale Discovery’ multi cytokine assay platform. Multivariate data integration methods were subsequently used to elucidate the component of the metabolic signature which is associated with inflammation and to determine specific metabolic correlates with parasite-induced changes in plasma cytokine levels. For example, the relative levels of acetyl glycoproteins extracted from the plasma metabolite profile in the P. berghei-infected mice were statistically correlated with IFN-γ, whereas the same cytokine was anticorrelated with glucose levels. Both the metabolic and the cytokine data showed a similar spatial distribution in principal component analysis scores plots constructed for the combined murine data, with samples from all infected animals clustering according to the parasite species and whereby the protozoan infections (P. berghei and T. b. brucei) grouped separately from the helminth infection (S. mansoni). For S. mansoni, the main infection-responsive cytokines were IL-4 and IL-5, which covaried with lactate, choline, and D-3-hydroxybutyrate. This study demonstrates that the inherently differential immune response to single and multicellular parasites not only manifests in the cytokine expression, but also consequently imprints on the metabolic signature, and calls for in-depth analysis to further explore direct links between immune features and biochemical pathways.

Evolution of immune systems: specificity and autoreactivity

Multicellularity evolved well before 600 million years ago, and all multicellular animals have evolved since then with the need to protect against pathogens. There is no reason to expect their immune systems to be any less sophisticated than ours. The vertebrate system, based on rearranging immunoglobulin-superfamily domains, appears to have evolved partly as a result of chance insertion of RAG genes by horizontal transfer. Remarkably sophisticated systems for expansion of immunological repertoire have evolved in parallel in many groups of organisms. Vaccination of invertebrates against commercially important pathogens has been empirically successful, and suggests that the definition of an adaptive and innate immune system should no longer depend on the presence of memory and specificity, since these terms are hard to define in themselves. The evolution of randomly-created immunological repertoire also carries with it the potential for generating autoreactive specificities and consequent autoimmune damage.While invertebrates may use systems analogous to ours to control autoreactive specificities, they may have evolved alternative mechanisms which operate either at the level of individuals-within-populations rather than cells-within-individuals, by linking self-reactive specificities to regulatory pathways and non-self-reactive to effector pathways.

Nuclear Factor-kappaB controls the reaggregation of 3D neurosphere cultures in vitro

The approach of reaggregation involves the regeneration and self-renewal of histotypical 3D spheres from isolated tissue kept in suspension culture. Reaggregated spheres can be used as tumour, genetic, biohybrid and neurosphere models. In addition the functional superiority of 3D aggregates over conventional 2D cultures developed the use of neurospheres for brain engineering of CNS diseases. Thus 3D aggregate cultures created enormous interest in mechanisms that regulate the formation of multicellular aggregates in vitro. Here we analyzed mechanisms guiding the development of 3D neurosphere cultures. Adult neural stem cells can be cultured as self-adherent clusters, called neurospheres. Neurospheres are characterised as heterogeneous clusters containing unequal stem cell sub-types. Tumour necrosis factor-alpha (TNF-alpha is one of the crucial inflammatory cytokines with multiple actions on several cell types. TNF-alpha strongly activates the canonical Nuclear Factor Kappa-B (NF- kappaB) pathway. In order to investigate further functions of TNF in neural stem cells (NSCs) we tested the hypothesis that TNF is able to modulate the motility and/or migratory behaviour of SVZ derived adult neural stem cells. We observed a significantly faster sphere formation in TNF treated cultures than in untreated controls. The very fast aggregation of isolated NSCs (<2h) is a commonly observed phenomenon, though the mechanisms of 3D neurosphere formation remain largely unclear. Here we demonstrate for the first time, increased aggregation and enhanced motility of isolated NSCs in response to the TNF-stimulus. Moreover, this phenomenon is largely dependent on activated transcription factor NF-kappaB. Both, the pharmacological blockade of NF-kappaB pathway by pyrrolidine dithiocarbamate (PDTC) or Bay11-7082 and genetic blockade by expression of a transdominant-negative super-repressor IkappaB-AA1 led to decreased aggregation.

Rayleigh scattering by hexagonal ice crystals and the interpretation of dual-polarisation radar measurements

Dual-polarisation radar measurements provide valuable information about the shapes and orientations of atmospheric ice particles. For quantitative interpretation of these data in the Rayleigh regime, common practice is to approximate the true ice crystal shape with that of a spheroid. Calculations using the discrete dipole approximation for a wide range of crystal aspect ratios demonstrate that approximating hexagonal plates as spheroids leads to significant errors in the predicted differential reflectivity, by as much as 1.5 dB. An empirical modification of the shape factors in Gans's spheroid theory was made using the numerical data. The resulting simple expressions, like Gans's theory, can be applied to crystals in any desired orientation, illuminated by an arbitrarily polarised wave, but are much more accurate for hexagonal particles. Calculations of the scattering from more complex branched and dendritic crystals indicate that these may be accurately modelled using the new expression, but with a reduced permittivity dependent on the volume of ice relative to an enclosing hexagonal prism.

Equation for the microwave backscatter cross section of aggregate snowflakes using the self-similar Rayleigh–Gans approximation

In this paper an equation is derived for the mean backscatter cross section of an ensemble of snowflakes at centimeter and millimeter wavelengths. It uses the Rayleigh–Gans approximation, which has previously been found to be applicable at these wavelengths due to the low density of snow aggregates. Although the internal structure of an individual snowflake is random and unpredictable, the authors find from simulations of the aggregation process that their structure is “self-similar” and can be described by a power law. This enables an analytic expression to be derived for the backscatter cross section of an ensemble of particles as a function of their maximum dimension in the direction of propagation of the radiation, the volume of ice they contain, a variable describing their mean shape, and two variables describing the shape of the power spectrum. The exponent of the power law is found to be −. In the case of 1-cm snowflakes observed by a 3.2-mm-wavelength radar, the backscatter is 40–100 times larger than that of a homogeneous ice–air spheroid with the same mass, size, and aspect ratio.