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Lipin family members (lipin 1, 2 and 3) are bi-functional proteins that dephosphorylate PA (phosphatidic acid) to produce DAG (diacylglycerol) and act in the nucleus to regulate gene expression. Although other components of the triacylglycerol synthesis pathway can form oligomeric complexes, it is unknown whether lipin proteins also exist as oligomers. In the present study, using various approaches, we revealed that lipin 1 formed stable homo-oligomers with itself and hetero-oligomers with lipin 2/3. Both the N- and C-terminal regions of lipin 1 mediate its oligomerization in a head-to-head/tail-to-tail manner. We also show that lipin 1 subcellular localization can be influenced through oligomerization, and the individual lipin 1 monomers in the oligomer function independently in catalysing dephosphorylation of PA. The present study provides evidence that lipin proteins function as oligomeric complexes and that the three mammalian lipin isoforms can form combinatorial units.
Lipin proteins are a novel family of Mg2+-dependent PAPs [PA (phosphatidic acid) phosphatases], which catalyse the dephosphorylation of PA into DAG (diacylglycerol) [1]. They are evolutionarily conserved and show similar primary organization [2]. Lipin proteins consist of a N-terminal domain (N-LIP) and a C-terminal domain (C-LIP), with the latter containing a conserved DXDXT motif that is required for the catalytic activity [1–3]. Distinct from fungi, nematodes and insects that only express one lipin isoform, mammals express three lipin isoforms named lipin 1, 2 and 3 [2]. In addition, three lipin 1 protein isoforms are produced by alternative mRNA splicing [4–6]. Mice lacking lipin 1 have a reduction in adipose tissue mass and are insulin-resistant [7]. Targeted overexpression of lipin 1 in mouse adipose tissue results in obesity, yet the mice maintain insulin sensitivity [8]. In humans, point mutations in the LPIN2 gene encoding lipin 2 cause Majeed syndrome [9], an autoinflammatory disorder, which may result from ablation of the PAP activity of the enzyme [10].
The lipin proteins primarily localize to the cytosol and are found in both the soluble and cytosolic membrane compartments, but can also be found in the nucleus [2,3,5,11]. Biochemical studies of PAP activities conducted prior to the identification of the gene encoding lipin 1 led to the hypothesis that this enzymatic activity transiently associates with membranes to dephosphorylate PA (reviewed in [12]). Subsequent work has suggested that phosphorylation controls lipin 1 movement between cellular compartments [3,11]. The yeast lipin Pah1p has been reported to associate with the promoters of genes involved in phospholipid biosynthesis [13]. In mammalian cells, lipin 1 can positively or negatively regulate gene expression via interaction with transcription factors, such as PPARα (peroxisome-proliferator-activated receptor α) and NFATc4 (nuclear factor of activated T-cells c4), as well as transcriptional co-regulators such as PGC-1α (PPARγ co-activator 1α) and HDACs (histone deacetylases) [14,15]. The PAP catalytic activity of lipin 1 appears to be separate from its activity in the regulation of transcription.
In the course of studies designed to identify lipin-1-interacting proteins by immunoprecipitation of epitope-tagged lipin isoforms we made the surprising discovery that lipin 1 can self-associate. The present study was conducted to investigate potential interactions between lipin isoforms. We show that lipin 1 forms stable homo-oligomers and hetero-oligomers with lipin 2 and lipin 3, suggesting that the function of these enzymes may be linked in a previously unappreciated manner.
DAG (1-2-dioleoyl-sn-glycerol dioleoyl) and PA (1,2-dioleoyl-sn-glycero-3-phosphate) were purchased from Avanti Polar Lipids. NEM (N-ethylmaleimide) was purchased from Sigma. λPPase (λ-phosphatase) was purchased from New England Biolabs.
V5-tagged lipin 1a, lipin 1b, lipin 2 and lipin 3 expression vectors were gifts from Dr Karen Reue (University of California, Los Angeles, CA, U.S.A.) [16]. HA (haemagglutinin)–lipin 1a, HA–lipin 1b (G84R), HA–lipin 1b (Lmut), HA–lipin 1b (D712E), GST (glutathione transferase)–lipin 1b (1–641) and GST–lipin 1b (642–924) have been described previously [14]. To construct V5–lipin 1b (N1, 1–171), V5–lipin 1b (N2, 1–641), V5–lipin 1b (C1, 121–924) and V5–lipin 1b (C2, 469–924), corresponding cDNA fragments were PCR-amplified from mouse lipin 1b and ligated into the pcDNA 3.1 D/V5-His-TOPO vector (Invitrogen). V5–LPP3 (lipid phosphate phosphatase 3) has been described previously [17]. EYFP [enhanced YFP (yellow fluorescent protein); Venus] and ECFP [enhanced CFP (cyan fluorescent protein); Cerulean]-tagged lipin 1b constructs were constructed by subcloning full-length lipin 1b upstream of the fluorescent tags. Both Cerulean and Venus contained the monomeric A206K mutation. CAAX–lipin 1b was generated by PCR using the reverse primer 5′-GAGCGGCCGCCTATGAGAGCACGCACTTGCATGACATGCACTGACGGTCCTCTGGCTGCTTAGCTGAGGCTGAATGC-3′. This removed the endogenous stop codon from lipin 1 and added the amino acid sequence KQPEDRQCMSCKCVLS*, with the Ras-derived CAAX box at the C-terminus underlined. All of the clones were confirmed by DNA sequencing. Adenoviral constructs expressing HA-tagged lipin 1 and 2 have been described previously [14,18].
Anti-lipin 1 (LAb1 and LAb2) and anti-lipin 2 polyclonal antibodies have been described previously [4,18]. The following antibodies were obtained commercially: anti-GAPDH (glyceraldehyde-3-phosphate dehydrogenase; Abcam), anti-V5 (Invitrogen), anti-HA (Santa Cruz Biotechnology), anti-lipin 1 (Santa Cruz Biotechnology; C-15), anti-V5–agarose (Sigma), anti-HA–agarose (Sigma), Alexa Fluor® 488-, Alexa Fluor® 555- and Alexa Fluor® 568-conjugated anti-IgG antibodies (Invitrogen), HRP (horseradish peroxidase)-conjugated anti-IgG antibodies (Pierce) and AP (alkaline phosphatase)-conjugated anti-IgG antibodies (Sigma).
Cell culture and transfection
COS-7 (A.T.C.C.), HEK-293T [HEK (human embryonic kidney)-293 cells expressing the large T-antigen of SV40 (simian virus 40); American Type Culture Collection] and HEK-293A (Invitrogen) cells were maintained in DMEM (Dulbecco's modified Eagle's medium) supplemented with 10% FBS (fetal bovine serum; Invitrogen) and antibiotics (penicillin/streptomycin). Cell transfections were performed with Lipofectamine™ 2000 (Invitrogen). 3T3-L1 cells were differentiated and maintained as described previously [3].
Generation of lipin baculovirus
Recombinant baculoviruses for expression of lipin 1b with an N-terminal tandem His6 and HA tag were generated using the Bac-to-Bac baculovirus expression system (Invitrogen) according to the manufacturer's protocol. Viral stocks were obtained by transfection of Sf9 insect cells cultured in Grace's insect medium with recombinant bacmids.
Purification of recombinant lipin protein
Recombinant lipin 1b protein tagged with both HA and His6 was extracted from a soluble fraction obtained from lysates of Sf9 cells that were infected with the recombinant lipin 1b baculovirus and cultured for 48 h post-infection. Lipin protein was purified with the Ni-NTA (Ni2+-nitrilotriacetate) purification system (Invitrogen). Briefly, pelleted cells were suspended in lysis buffer [50 mM sodium phosphate and 0.5 M NaCl (pH 8.0)] and disrupted by three freeze–thaw cycles using liquid nitrogen and a 37 °C water bath. After centrifugation at 16000 g for 15 min, the supernatant was collected and mixed with the Ni-NTA resin for 1 h at 4 °C with gentle agitation. The resin was allowed to settle under gravity, and washed with 8 ml of washing buffer [50 mM sodium phosphate, 0.5 M NaCl and 0.02 M imidazole (pH 8.0)] five times. Purified lipin protein was eluted with 6 ml of elution buffer [50 mM sodium phosphate, 0.5 M NaCl and 0.25 M imidazole (pH 8.0)]. The eluates were combined and concentrated to approx. 100 μl using Millipore Amicon ultra-4 centrifugal filter units.
Immunoprecipitations and immunoblotting
Cells were lysed by brief sonication in lysis buffer [50 mM Tris/HCl (pH 7.5), 250 mM NaCl, 1 mM EDTA, 1 mM EGTA, 0.5% Triton X-100, 10% glycerol and Complete™ Protease Inhibitor Cocktail (Roche Diagnostics)]. Lysates were subjected to immunoprecipitation with anti-V5– or anti-HA–agarose. Immune complexes were washed five times with lysis buffer and subjected to immunoblotting with proper antibodies. Immunoblotting analysis was performed as described previously [3,19]. 3T3-L1 cells were homogenized with glass/Teflon in buffer A [50 mM 2-glycerophosphate, 50 mM NaCl, 1 mM EDTA, 1 mM EGTA, 10 mM sodium phosphate (pH 7.4) and 10 mM Triton X-100] supplemented with protease inhibitors (1 mM PMSF, 10 μg/ml leupeptin, 10 μg/ml aprotinin, 10 μg/ml pepstatin and 0.25 μM microcystin) and cleared by centrifugation at 16000 g for 10 min. [3]. Lysates were subjected to immunoprecipitation using non-immune IgG, LAb2 [4] or anti-lipin 2 antibodies [18].
Immunofluorescence microscopy
Immunofluorescence staining was performed as described previously [20]. In brief, cells were fixed with 4% paraformaldehyde in PBS for 30 min. Following fixation, cells were treated with 0.2% Triton X-100 in PBS for 5 min. After blocking with 10% FBS in PBS for 20 min, cells were incubated for 1 h with primary antibody, followed by washing in PBS and incubation for 1 h with the relevant secondary antibody. Nuclei were stained with Hoechst 33342 (Invitrogen) or DAPI (4′,6-diamidino-2-phenylindole; Vector Laboratories). Pictures of cells were taken with a laser-scanning confocal microscope (Olympus FV500, Tokyo, Japan) or a Zeiss Axiovert 200 fluorescence microscope. Images were pseudo-colorized and merged with ImageJ or Adobe Photoshop.
FRET (Förster resonance energy transfer) imaging
COS-7 cells on coverslips in six-well plates were transfected with 6 μg of plasmids. At 48 h after transfection, cells were fixed at room temperature (25 °C) in 4% (w/v) paraformaldehyde for 15 min. The system used for spectral imaging was a Zeiss Axiovert 200 M epifluorescence motorized microscope coupled to a Zeiss 510 confocal-multiphoton imaging system at the W.M. Keck Center for Cellular Imaging (University of Virginia, Charlottesville, VA, U.S.A.). Details of imaging and the computational analysis used to separate DSBT (donor spectral bleed-through) and ASBT (acceptor spectral bleed-through) from the signal acquired during excitation of the FRET channel have been published previously [21]. Briefly, reference spectra for untagged, monomeric Cerulean or Venus fluorescent proteins were subtracted from cells expressing both lipin–Venus and lipin–Cerulean fusion proteins using linear unmixing and the algorithm described previously [21–23]. All FLIM (fluorescence lifetime imaging microscopy) imaging was performed on live HEK-293T cells that were transfected 36–48 h previously with 3 μg of lipin 1b–Cerulean, or lipin 1b–Cerulean+lipin 1b–Venus. FLIM data were acquired using a multiphoton system consisting of a Nikon TE300 epifluorescence microscope coupled to a Bio-Rad Radiance 2100 confocal and multiphoton system. A 10 W Verdi tunable (700–1000 nm) pulsed Ti:sapphire laser tuned to 820 nm was used for two-photon excitation of the Cerulean fluorophore at 13 ns pulse intervals. Photons were collected using a PMT (photomultiplier tube) over a period of 120 s for each measurement. Data collection and analysis were performed using SPCImage software (Becker and Hickl), as well as ImageJ.
GST pull-down
The GST pull-down experiment was performed as described previously [24], with major modifications. In brief, HEK-293A cells transiently expressing various V5-tagged lipin 1b fragments were lysed in ice-cold lysis buffer [50 mM Tris/HCl (pH 7.5), 250 mM NaCl, 1 mM EDTA, 1 mM EGTA, 0.5% Triton X-100, 10% glycerol and Complete™ Protease Inhibitor Cocktail]. Samples were briefly sonicated and centrifuged at 16000 g at 4 °C for 30 min. The supernatant was incubated with anti-V5–agarose at 4 °C overnight. The beads were extensively washed with lysis buffer, and the recombinant lipin peptide was eluted by incubation with 70 μl of V5 peptide (100 μg/ml) in lysis buffer at 4 °C for 1 h. After brief centrifugation, the supernatants were mixed with GST, GST–lipin 1b-(1–641) or GST–lipin 1b-(642–924) prebound to glutathione–Sepharose beads in 1 ml of binding buffer [50 mM Tris/HCl (pH 7.5), 250 mM NaCl, 1 mM EDTA, 1 mM EGTA, 0.5% Triton X-100, 10% glycerol and Complete™ Protease Inhibitor Cocktail], and incubated with rotation for 4 h at 4 °C. The beads were washed four times with 1 ml of binding buffer, separated by SDS/PAGE (4–12% gradient gels) and analysed by immunoblotting.
PAP activity assay
For the PAP activity assay, 10 cm plates of HEK-293T cells were transfected (using Lipofectamine™ 2000) with 0.5 μg of Myc–lipin 1b, and 0.25, 0.5 or 1.0 μg of HA–lipin 1b (D712E) plasmids. At 48 h after transfection, cells were homogenized in glass/Teflon at 1000 rev./min in 1 ml of buffer A. Immunoprecipitations were performed as described previously [3] and divided into separate aliquots for electrophoresis and PAP activity measurement. PAP activity was determined by measurement of soluble [32P]Pi release from [32P]PA using substrates presented in Triton X-100/PA mixed micelles as described previously [18].
Gel-filtration chromatography of 3T3-L1 adipocyte extracts
3T3-L1 adipocytes were homogenized by glass/Teflon in a minimal volume of TES buffer [255 mM sucrose, 1 mM EDTA, 0.1 mM DTT (dithiothreitol) and 1 mM Tris/HCl (pH 7.4)] supplemented with protease inhibitors. Extracts were centrifuged at 16000 g for 10 min and the resulting supernatants subjected to centrifugation at 53000 rev./min (in a Ti-90 rotor) for 60 min at 10 °C. The soluble fraction was filtered through a 0.45 μm cellulose acetate syringe filter, and 400 μl representing 1.0–1.6 mg of total protein was loaded on a Superose 6 10/300 GL column equilibrated with buffer A. The sample was eluted at a flow rate of 0.1 ml/min and 1 ml fractions were collected. The columns were calibrated with molecular mass standards obtained from GE Healthcare/Pharmacia. PAP activity measurements were performed on 40 μl aliquots for 20 min at 37 °C. In some cases samples were pre-incubated in 10 mM Triton X-100 or 1% fatty-acid-free BSA for 15 min at room temperature with continuous mixing before loading on to the column.
Gel-filtration chromatography of recombinant lipin 1b protein
Concentrated protein (50 μl) representing approx. 10 μg of purified lipin 1b was analysed by gel-filtration chromatography on a Superose 6 10/300 GL column. The flow rate used in the separation was 0.5 ml/min with PBS (pH 7.4). The columns were calibrated with molecular mass standards obtained from GE Healthcare/Pharmacia. After 14 min, 30 fractions of 0.5 ml of each were collected. PAP activity measurements of gel-filtration fractions of recombinant lipin 1 were performed essentially as described previously [16]. Briefly, 65 μl of column eluates were assayed for times up to 60 min (<20% substrate hydrolysis) at 30 °C in 100 μl volumes of reaction buffer [50 mM Tris/HCl (pH 7.4), 1 mM MgCl2, 2 mM Triton X-100, 2 mg/ml fatty-acid-free BSA and 0.1 mM PA (with ~20 000 d.p.m. of 32P-labelled PA made by phosphorylation of DAG with bacterial DAG kinase)] for the release of soluble [32P]Pi from Triton X-100/[32P]PA mixed micelles.
BN-PAGE (blue-native PAGE)
HEK-293A cells cultured in 35 mm plates were transfected with pcDNA3 (vector), lipin 1b–V5 or lipin 1b–V5 (D712E). At 36 h later, cells were lysed in 100 μl of lysis buffer [50 mM Tris/HCl (pH 7.5), 50 mM NaCl, 1% digitonin and Complete™ Protease Inhibitor Cocktail]. Following centrifugation, 15 μl of samples were loaded on to NativePAGE™ Novex Bis-Tris Gel sytem (Invitrogen) and transferred on to a PVDF membrane, according to the manufacturer's protocol. The proteins on the membrane were fixed with 8% acetic acid and probed with an anti-V5 antibody and HRP-coupled secondary antibody.
Lipin proteins self-associate in mammalian cells
COS-7 cells were transiently transfected with plasmid constructs encoding N-terminally HA-tagged lipin 1b, with or without C-terminally V5-tagged lipin 1a, 1b, 2 or 3 respectively. At 36 h later, the cells were homogenized in stringent lysis buffer (0.5% Triton X-100 and 250 mM NaCl) and epitope-tagged proteins were precipitated with anti-V5–agarose. As shown in Figure 1(A), HA–lipin 1b was co-immunoprecipitated with all of the V5-tagged lipin isoforms. In a reciprocal co-immunoprecipitation experiment, HA-tagged lipin 1a or lipin 1b also associated with lipin 1b–V5 (Figure 1B). As reported previously [16], the V5-tagged lipin 2 was expressed at lower levels than V5-tagged lipin 1 or 3 (Figure 1A). However, despite decreased expression, V5-tagged lipin 2 still co-immunoprecipitated lipin 1 at levels proportionate to its expression. Next, since LPP family proteins are also PAPs and have been reported to form homo- or hetero-oligomers [25], we examined the possible interaction between lipin 1b and LPP3, a representative LPP. As shown in Figure 1(C), HA–lipin 1b did not co-immunoprecipitate with V5-tagged LPP3, arguing that lipin 1 associates with itself and other lipin isoforms, but not with LPPs. In the subsequent experiment we found that endogenous lipin 2 was immunoprecipitated with anti-lipin 1 antibodies from the lysates of differentiated 3T3-L1 cells. This indicates that the lipin–lipin associations are not a result of ectopic expression of the proteins (Figure 1D). Whereas we failed to detect lipin 1 in anti-lipin 2 immunoprecipitates from 3T3-L1 lysates, this could be explained by the possibility that association with lipin 1 might prevent the accessibility of the lipin 2 epitope to the anti-lipin 2 antibody. Finally, immunoprecipitation of adenovirally delivered HA-tagged lipin 1 or lipin 2 in 3T3-L1 adipocytes revealed that endogenous lipin 1 and 2 were able to interact with recombinant lipin 1 and 2 (Figure 1E). Taken together, these co-immunoprecipitation experiments reveal that lipin proteins can form homo- or hetero-oligomers in vivo.
Lipin 1 co-immunoprecipitates with itself and lipin 2 and 3, but not LPP3
Lipin 1 forms stable oligomers
Next, we examined the biochemical properties of lipin oligomers by identifying experimental conditions that would allow us to reversibly assemble and disassemble these complexes in vitro. Co-ordination of Mg2+ in the active site is necessary for the PAP activity of lipin 1 [1]. However, lipin oligomerization was observed in the presence of both EDTA and EGTA indicating that these associations are divalent-cation-independent. PAP activity of lipin 1 is dependent on NEM-sensitive cysteine residues [16,26]. However, as shown in Figure 1(F), washing immunoprecipitates with a buffer containing either oxidants NEM or H2O2, or the reducing agent DTT, did not affect lipin 1b self-association (Figure 1F, lanes 6,7 and 8). This suggests that lipin 1 oligomerization is redox-insensitive, and does not involve formation of intermolecular disulfide bonds. Lipin 1 is a phosphoprotein, and phosphorylation of lipin 1 may play a regulatory role in mediated oligomerization. However, we found that lipin 1 oligomerization appears to be independent of its phosphorylation status, because incubation of the immunoprecipitates with λPPase, which effectively dephosphorylated the protein as indicated by altered mobility on SDS/PAGE (Figure 1F), did not impair the lipin–lipin interaction (Figure 1F, lane 9). Finally, the interaction between V5–lipin 1b and HA–lipin 1b was resistant to a high concentration of salt (2 M NaCl) and moderate concentration (2 M) of urea (Figure 1F, lanes 5 and 10), suggesting that lipin 1 oligomers are stable even at increased ionic strength or in the presence of a denaturant.
Mapping the domains of lipin 1 in mediating oligomerization
We next investigated the regions of lipin 1 that are necessary for self-association. A series of N- or C-terminally truncated variants of lipin 1b with a C-terminal V5 tag was constructed and co-expressed with HA–lipin 1b in COS-7 cells. The interactions between the full-length and the truncated mutants of lipin 1b were determined by co-immunoprecipitation. As shown in Figures 2(A) and 2(B), full-length lipin 1b interacted with all of the N- and C-terminal fragments of lipin 1b employed, suggesting that the N-terminal (amino acids 1–171) and C-terminal (amino acids 469–924) regions of lipin 1b simultaneously mediate lipin 1 oligomerization. Using dimerization, the simplest organization form of lipin 1, as an example, there are two possible models for lipin–lipin association: (i) 'head-to-head/tail-to-tail', and (ii) 'head-to-tail/tail-to-head'. To test these two possibilities, glutathione–Sepharose-bound GST–lipin 1b-(1–641) or lipin 1b-(642–924) from bacteria was incubated with V5–lipin 1b-(1–171) or V5–lipin 1b-(469–924) immunopurified from HEK-293A cells, and interacting proteins were evaluated by immunoblotting with anti-V5 antibody. As shown in Figure 2(C), the N-terminal part of lipin 1b only interacted with the N-terminus, whereas the C-terminal part preferred to associate with the C-terminus. Our results thus suggest a model that lipin 1 oligomerizes through 'head-to-head/tail-to-tail' interactions.
Mapping the lipin 1b domains in mediating its oligomerization
Co-localization of lipin family members in cells
Lipins exhibit variable subcellular localization patterns. As shown in Figure 3(A), except for lipin 2 which is mainly excluded from nucleus, other lipin isoforms including lipin 1a, 1b and 3 are targeted to both cytosol and nucleus in the COS-7 cells. Co-expression of HA-tagged lipin 1b with individual V5-tagged lipin isoforms revealed substantial co-localization (as shown by yellow immunofluorescence in the merged panels of Figure 3B). Lipin 1 also showed a co-localization with lipin 2 outside of the nucleus (Figure 3B). Co-localization of these lipin isoforms is consistent with their ability to self-associate as revealed by the experiments shown in Figure 1.
Co-localization of lipin 1 and lipin 1, 2 and 3 in cells
Demonstration of intermolecular interactions between lipin monomers in cells by FRET
The results shown in Figure 3 indicate that lipin isoforms are co-localized in cells, but provide no information about the proximity of these proteins. To address this issue, lipin 1 was tagged at the C-terminus with either Venus fluorescent protein or Cerulean fluorescent protein, and energy transfer from the donor (Cerulean–lipin 1) to the acceptor (Venus–lipin 1) was determined by spectral imaging. Venus–lipin 1 and Cerulean–lipin 1 showed extensive co-localization, as expected from the immunofluorescence imaging results (Figure 4A). In the event of close opposition of the fluorescent tags, such as occurs upon interaction of the tagged proteins, energy from the donor molecule can be transferred to the acceptor molecule by a process termed FRET. Because FRET is dependent on proximity, fluorophores must be within ~1–10 nm of each other for energy transfer to occur, a distance that also typically occurs during protein–protein interaction. Excitation at 458 nm in cells where Venus–lipin 1 and Cerulean–lipin 1 were co-expressed led to an increase in emission at 540 nm when compared with either alone (Figure 4B). To quantify the amount of energy transferred by excitation of the donor to emission of the acceptor requires subtraction of the contaminating DSBT and ASBT. For example, excitation of either Cerulean or Cerulean–lipin 1 alone at 458 nm gives a peak emission at 500 nm; however, DSBT can be seen in the emission at 540 nm in double-labelled cells (Figure 4B). Whereas excitation of YFP or Venus–lipin 1 at 514 nm gives a peak emission at 540 nm, excitation at 458 nm also leads to ASBT emission at 540 nm, albeit at a reduced level compared with excitation at 514 nm. In order to subtract DSBT and ASBT from the actual FRET signal, linear unmixing was used to remove the DSBT from the FRET channel, and a computer algorithm was employed to identify and remove contaminating ASBT from the FRET signal [21,22]. The resulting values, termed PFRET (processed FRET) showed that the efficiency of energy transferred from the donor to the acceptor (E%) was 21.7% [±4.66 (S.D., n = 5)] which is similar in magnitude to the energy transfer efficiency observed for a number of other well-characterized protein–protein interactions such as CFP- and YFP-tagged C/EBPα (CCAAT/enhancer-binding protein α) homodimers at 23% [±5% (S.D.)] [21]. That the energy transfer E% values are not dependent on acceptor concentration is shown in Figure 4(C), where the calculated E% values from a single cell are plotted against the acceptor intensity (intensity/pixels). Non-specific transfer of energy (E%) that is dependent on acceptor intensity gives a correlation coefficient approaching 1, whereas the correlation coefficient of the fluorescently tagged lipin 1 protein(s) in this representative example was −0.284, showing that the calculated E% was independent of acceptor concentration. Taken together, these results indicate that the association between lipin isoforms observed using biochemical approaches in cell lysates reflects close interactions between these proteins in live cells.
FRET analysis of fluorescent-tagged lipin 1
As a second measure of FRET we employed FLIM to measure changes in fluorescence decay of the donor in the presence of an acceptor. We measured the lifetime of the donor, Cerulean–lipin 1b, with and without the acceptor, Venus–lipin 1b, in live HEK-293T cells. In order to do so, the fluorophores were excited by a single laser pulse at 820 nm and the photons released during the return of the fluorophore to the ground state from the excited state were captured and displayed as data points. SPCImage software generated a fitted curve based on these data that verified an exponential decay of the fluorophore. Figure 4(D) compares the fluorescence decay of Cerulean–lipin 1 alone with Cerulean–lipin 1 plus Venus–lipin 1. In this example the presence of Venus–lipin 1 decreases the slope of the decay curve of Cerulean–lipin 1. Quantification of multiple cells reveals that this is significant with the average decay time of Cerulean–lipin 1 decreasing from 2.226 ns [±0.05 (S.D., n = 14)] to 2.101 ns [±0.09 (S.D., n = 16, P<0.00001)] in the presence of Venus–lipin 1, providing additional support for the Venus and Cerulean fluorophores being in close enough apposition for energy to be transferred from the donor to the acceptor.
Forced relocalization of lipin 1 in cells
Subcellular fractionation studies indicate that lipin 1 translocates between the cytosol and the endoplasmic reticulum/microsomal membranes in a dynamic manner dependent on its phosphorylation state and fatty acid availability [3,27]. However, when visualized by immunofluorescence, intracytosolic changes in lipin 1 localization are subtle (results not shown). Therefore to test the hypothesis that lipin self-association could lead to redistribution of lipin isoforms in cells, we determined whether co-expression of a plasma-membrane-targeted lipin 1b variant (see below) could redirect cytosolic lipin 1b to the plasma membrane through oligomerization. We employed a Myc-tagged lipin 1, which is localized diffusely in transfected COS-7 cells, with undetectable plasma membrane staining (Figure 5, upper panels). In addition, we developed a plasma-membrane-targeted lipin 1b (lipin 1b–CAAX) construct which, upon overexpression, showed clear plasma membrane localization in addition to the whole-cell distribution (Figure 5, middle panels). The plasma-membrane-targeted lipin 1b was obtained by fusing a CAAX-box motif to the C-terminal tail of lipin 1b, to direct prenylation of lipin 1 [28]. Co-transfection of both constructs resulted in the easily observable relocalization of Myc–lipin 1 to the plasma membrane. A portion of the images are shown at a larger size at the bottom. Similar results were seen with lipin 2 co-transfected with lipin 1–CAAX (results not shown). These results demonstrate that oligomerization between lipin isoforms can direct intracellular localization.
Forced plasma membrane targeting of lipin 1 via a CAAX domain can recruit soluble lipin 1 to the plasma membrane
Estimation of the native size of endogenous and recombinantly expressed lipin 1
Taken together, the results presented indicate that lipin proteins can self-associate to form oligomeric complexes that can be isolated biochemically and visualized by fluorescence imaging. The NEM-sensitive PAP activity (a hallmark feature of the lipin enzymes) of rat liver cytosol was reported to elute with a molecular mass of 540 kDa during gel-filtration chromatography [29]. Because 3T3-L1 adipocytes express high levels of lipin 1 protein, we analysed soluble fractions of these cells by Superose 6 gel-filtration chromatography to determine the size of native lipin 1. As detected by Western blotting, lipin 1 and lipin 2 were eluted from the column with a molecular mass of 500–600 kDa; the same size observed for the majority of the PAP activity (Figures 6A and 6B). Although the predicted molecular mass of the lipin 1, 2 and 3 polypeptides is ~90–100 kDa, on SDS/PAGE these proteins migrate aberrantly with an apparent molecular mass of ~140–150 kDa. In the case of lipin 1, phosphorylation accounts for part, but not all, of the unexpected decrease in mobility on SDS/PAGE [3]. Gel filtration measures the hydrodynamic radius of a molecule, not the molecular mass, and the tertiary structure of lipin molecules could partially account for the discrepancy in its elution from the column. Alternatively, unidentified post-translational modifications other than phosphorylation could produce changes in lipin migration on SDS/PAGE and elution by size-exclusion chromatography. Indeed, a proportion of lipin 1 has been recently reported to be SUMOylated, a covalent modification of ~17 kDa [30]. Nevertheless, it is highly unlikely that post-translational modification or the shape of individual lipin molecules would change the elution profile from a molecular mass of 100 kDa to a molecular mass of 500–600 kDa. Based purely on the predicted molecular mass of lipin 1, tetramerization of lipin 1 would produce an molecular mass of approx. 400 kDa if the lipin tetramer adopted a mostly spherical shape. Therefore a combination of oligomerization, probably tetramerization, molecular shape and possibly post-translational modifications probably account for size of lipin 1, as measured by size-exclusion chromatography. Addition of 10 mM Triton X-100 to cytosolic extracts before loading on to the column caused a partial shift in the lipin 1 elution profile consistent with the addition of the predicted molecular mass of a Triton X-100 micelle, whereas treatment of extracts with 1% BSA was without effect (Figure 6A and results not shown).
Lipin 1 exists as an oligomer in 3T3-L1 adipocytes
We also examined the molecular mass of recombinant lipin 1 that was expressed in insect cells and purified by metal-ion-affinity chromatography. Similar to our observations with endogenously expressed lipin 1 in 3T3-L1 cells, purified lipin 1 eluted as a discrete peak of molecular mass ~600 kDa, coincident with the elution pattern of PAP activity from the column (Figures 7A and 7B). Isolation of mono/di/tetrameric lipin 1 would allow functional studies to determine whether the different oligomeric forms of lipin 1 display differing enzymatic activities. In an attempt to obtain fractions containing lipin 1 species with molecular masses that are consistent with those of a monomer or dimer we employed a Superdex 200 column to increase the resolution of recombinant lipin eluting at a molecular mass of 50–500 kDa (results not shown). However, recombinant lipin appears to be largely, if not exclusively, tetrameric and so we were unable to address the question of oligomer effects on PAP activity.
Recombinant lipin 1 forms dimers and tetramers
As an alternative method to gel-filtration chromatography, extracts from HEK-293A cells expressing V5-tagged lipin 1b were subjected to BN-PAGE in an attempt to preserve the native molecular structure. As shown in Figure 7(C), immunoblotting with an anti-V5 antibody clearly showed that native non-denatured lipin 1b existed in two forms with a molecular mass slightly more than 2- and 4-fold that of the predicted lipin 1b–V5 monomer (compared with the molecular mass with SDS/PAGE in Figure 1A). Like gel filtration, native PAGE measures hydrodynamic radius, and the more the divergence from a spherical shape the larger the molecule or molecular complex will appear by these chromatographic methods. These experiments suggest that both endogenous and recombinant lipin 1 exists primarily as tetrameric complexes both in cells and when purified in vitro. Although more detailed analyses will be required to rule out the presence of other non-lipin proteins in these complexes, our determination of the molecular mass of recombinant lipin 1 by gel-filtration chromatography and by non-denaturing electrophoresis argue that the major lipin 1 species is a tetramer.
The relationship between oligomerization and the catalytic activity of lipin 1
Clearly lipin 1 variants with altered self-association would be valuable reagents to probe the regulation and biological importance of this interaction. We therefore examined the self-association of a series of previously described lipin 1 mutants with defects in enzymatic activity of phosphorylation. As shown in Figure 8, lipin 1b (G84R), a natural mutation that results in a mouse fatty liver dystrophy phenotype and reduces lipin enzymatic activity [2,3], lipin 1b (D712E), a catalytic site mutation that eliminates PAP activity [3], and the coactivator-deficient mutant lipin 1b (Lmut) [14], retained the ability to associate with V5–lipin 1b. Similar results were obtained with other single (or double)-site lipin 1 mutants we generated (e.g. SUMOylation-deficient lipin 1 mutant [30], lipin phosphorylation site mutants and others), which are predicted to be deficient in various post-translational modifications (results not shown). Taken together with the results shown in Figures 1(F) and 2, these findings suggest that lipin 1 oligomers are stable and difficult to disrupt by single (or double) amino acid mutations. This could result from a 'double security' mechanism for oligomerization that utilizes both N- and C-terminal interactions. Our results also indicate that the loss-of-function phenotypes associated with the synthetic and naturally occurring lipin 1 mutations noted above do not result from defects in self-association.
Co-immunoprecipitation between lipin 1b and various lipin 1b mutants
We next determined how the lipin 1 monomers function as PAP enzymes in the context of oligomers. Since our findings suggest that lipin 1 self-associates in a 'head-to-head/tail-to-tail' orientation, we postulated that the PAP activity might require two functional catalytic sites in physical proximity to function. To test this we co-expressed catalytically deficient HA-tagged lipin 1b (D712E) with Myc-tagged lipin 1b in HEK-293T cells. The PAP activity in lysates of Myc-tagged lipin 1b-transfected cells was unaffected by increasing amounts of the HA-tagged D712E lipin 1b mutant (results not shown), demonstrating that PAP-null lipin 1 does not act in a dominant manner to inhibit the PAP activity of its oligomeric partner(s). We also verified that the measured PAP activity came from HA–lipin1b-D712E/myc–lipin 1b oligomers by immunoprecipitation (Figure 9A). Although tetrameric combinations preclude a simple 1:1 stoichiometry within each lipin 1 oligomer at equimolar amounts, the selective use of epitope tags suggests that there will be at least one mutant or wild-type lipin 1b within each immunoprecipitated oligomer. We speculated that if a catalytically inactive monomer of lipin 1b negatively interferes with the PAP activity of its wild-type lipin 1b oligomeric partner, then HA–lipin 1 (D712E) immune complexes would not contain detectable PAP activity. In fact, we detected a linear increase in the PAP activity contained in HA–lipin 1 (D712E) immune complexes with the increasing amount of transfected wild-type lipin 1b (Figure 9B). As a control, immunoprecipitated HA–lipin 1b (D712E) itself showed no detectable PAP activity and anti-HA antibodies did not immunoprecipitate catalytically active Myc-tagged lipin 1b (Figure 9B). These observations suggest that lipin 1 monomers function independently in catalysing dephosphorylation of PA (Figure 9C).
Individual lipin 1b monomers in oligomers dephosphorylate PA independently
In the present study, we demonstrate that lipin proteins self-associate and appear to exist predominately as stable homo- and hetero-dimers/tetramers in vitro and in vivo. Our evidence for this includes observations from co-immunoprecipitation studies in which both overexpressed and endogenous lipin 1 robustly interacts with itself and other lipin isoforms. Gel-filtration and native protein electrophoresis suggests that both native and recombinant lipin 1 exists as a dimer and tetramer with little if any monomeric protein present. The three lipin isoforms are extensively co-localized in transfected cells, and the spatial distance between lipin monomers is close enough to allow for efficient FRET. Mutational studies combined with co-immunoprecipitation and in vitro GST-pull-down experiments support a model in which lipin monomers self-associate in a 'head-to-head/tail-to-tail' orientation. Catalytically inactive lipin 1 (D712E) mutant was able to efficiently pull down PAP activity when co-expressed with wild-type lipin 1 in cells, indicating that the active sites of individual lipin 1 monomers operate independently in the oligomer.
Our observations raise the interesting possibility that oligomerization plays an important role in lipin 1 function. It is conceivable that the lipin 1 oligomers may be more stable or trafficked differentially to the appropriate cellular locale. Alternatively, oligomerization could directly affect some of the functions of lipin 1. For example, oligomerization could facilitate the ability of lipin 1 to function as an adapter protein to regulate gene transcription. Lipin 1 is predicted to simultaneously bind PPARα, PGC-1α and p300 [14]. In this model, it is feasible that the dimerization/tetramerization of lipin 1 allows it to interact with each component of the transcriptional machinery to exert its 'scaffold' functions. The observation that lipin 1, lipin 2 and lipin 3 all can interact with PPARα ([14] and H. B. Kim and T. E. Harris, unpublished work) suggests a possibility that they could be recruited to the gene promoter and activate transcription in a hetero-oligomeric form, perhaps in specific physiological contexts.
Our results also indicate that the catalytic activity of lipin 1 oligomerization is not necessary for its oligomerization. This conclusion is supported by several observations, including: (i) lipin 1 oligomerization does not require Mg2+; (ii) NEM, a thiol-targeting agent that abrogates the PAP activity of lipin 1, has no effect on oligomerization; (iii) enzymatically inactive lipin 1 mutants can still form oligomers; and (iv) wild-type lipin 1 and enzymatically inactive lipin 1 function independently in oligomers.
In lower organisms, such as yeast and worms, there is only one lipin isoform [2]. The present study suggests that in higher organisms that express more than one lipin isoform hetero-oligomerization could produce lipin complexes with unique functions. For example, mammalian lipin 2 and 3 show a lower Vmax for catalytic activity compared with lipin 1 [16]. Given that each lipin monomer functions independently as a phosphatase within the oligomeric complex, hetero-oligomers containing lipin 1 would be predicted to have a higher PAP activity than lipin 2 or 3 homo-oligomers. In liver, lipin 2 is expressed at much higher levels than lipin 1 [18]. However, lipin 1 is robustly induced by stimuli that increase hepatic PAP activity (e.g. fasting and glucocorticoids; [14]), which probably serves to increase lipin 1 content or proportion in hetero-oligomers. In addition, lipin 2 demonstrates a different intracellular localization when compared with lipin 1, and may be enriched in the nuclear envelope [31], where the lipin phosphatase Dullard/NET56 is localized [32,33]. Thus hetero-oligomerization between lipin 2 and lipin 1 in the tissues where they are both expressed (such as liver and adipocytes) could allow a lipin-2-mediated recruitment of lipin 1 on to the nuclear envelope in order to obtain a high level of PAP activity at the nuclear periphery. As expression of the lipin isoforms approach parity, it seems reasonable to conclude that there will be a great likelihood of forming heterodimers with resulting changes in specific activity as well as subcellular localization.
Homo-oligomerization may be related to substrate-induced lipin 1 activation. Allosterically activated enzymes are frequently multisubunit protein complexes. For example, ACAT1 (acyl-coA:cholesterol acyltransferase 1) is thought to have separate dimerization domains in the N- and C-termini, similar to what we have observed with lipin 1 [34]. In a mixed micelle assay system, purified ACAT1 exhibits allosteric activation by its substrate, cholesterol [35]. Purified Pah1p, the yeast lipin homologue, shows positive co-operative kinetics in its activation by its substrate PA, indicative of two PA-binding sites and suggestive of allosteric activation [36,37], although it remains to be demonstrated that Pah1p forms oligomers. Mammalian lipin 1 also shows positive co-operative kinetics with PA, although it is unclear whether this is due to co-operative interaction between lipin and its substrate or allosteric activation of lipin enzymatic activity by the substrate [6,16]. Interestingly, the inhibition of rat lipin 1 by acyl-CoAs and fatty acids has been described as occurring through a negative allosteric interaction [38]. Whereas the lipin 1 monomers function independently in dephosphorylating PA within the oligomeric complex, it is possible that full lipin catalytic activity, particularly with regard to substrate co-operativity, requires oligomerization. To definitively determine whether lipin 1 oligomerization regulates allosteric activation by substrate will require identification of lipin mutants that fail to oligomerize and/or the isolation and characterization of lipin monomers. Unfortunately our efforts to generate such mutants and to isolate monomeric lipin 1 have been unsuccessful, so further work will be required to test these interesting possibilities.
The last two enzymatic reactions in triacylglycerol synthesis are lipin-mediated dephosphorylation of PA to generate DAG, followed by the acylation of DAG to form triacylglycerol (reviewed in [39]). There are two DAG acyltransferases, DGAT1 and DGAT2. DGAT1 is structurally similar to ACAT1, whereas DGAT2 is unrelated [40]. Interestingly, DGAT1 also forms homo- and hetero-oligomers [41]. Although allosteric activation of DGAT1 by DAG or acyl-CoAs has not been shown, an N-terminal fragment of DGAT1 can bind to acyl-CoAs in a co-operative fashion suggestive of allosteric activation [42,43]. Like lipin family members, dimerization of DGAT1 is not required for enzymatic activity, as heterodimerization with a truncated and inactive isoform of DGAT1 did not eliminate catalytic activity of the full-length form [41]. It is curious that the two proteins that catalyse the final two steps in triacylglycerol synthesis, lipin 1 and DGAT1, both form homo- and hetero-oligomers. Future questions should address whether oligomerization of these enzymes has any functional role in channelling lipid intermediates towards esterification.
In summary, the present study reveals for the first time that lipins can form homo- and hetero-oligomers and suggests that the three mammalian lipin isoforms are tightly linked with each other and serve as an integrated unit.
acyl-coA:cholesterol acyltransferase 1
acceptor spectral bleed-through
blue-native PAGE
cyan fluorescent protein
lipin C-terminal domain
DAG acetyltransferase
donor spectral bleed-through
fetal bovine serum
fluorescence lifetime imaging microscopy
Förster resonance energy transfer
glutathione transferase
human embryonic kidney
HEK-293 cells expressing the large T-antigen of SV40 (simian virus 40)
horseradish peroxidase
lipid phosphate phosphatase
- Ni-NTA
lipin N-terminal domain
phosphatidic acid
PA phosphatase
processed FRET
- PGC-1α
peroxisome-proliferator-activated receptor γ co-activator 1α
- λPPase
- PPARα
peroxisome-proliferator-activated receptor α
yellow fluorescent protein
Guanghui Liu, Jing Qu, Anne Carmack, Hyun Bae Kim, Chang Chen, Hongmei Ren and Thurl Harris performed the experiments. Guanghui Liu, Andrew Morris and Thurl Harris conceived and designed the experiments. Guanghui Liu, Chang Chen, Andrew Morris, Brian Finck and Thurl Harris analysed the data and wrote the paper. All of the contributing authors critically reviewed the manuscript.
We thank Dr Larry Gerace (The Scripps Research Institute, La Jolla, CA, U.S.A.) and Dr Karen Reue (University of Calfornia, Los Angeles, CA, U.S.A.) for kindly providing reagents used in the present study. We also thank Dr Ammasi Periasamy and Dr Yuansheng Sun (Unversity of Virginia, Charlottesville, VA, U.S.A.) for valuable assistance in acquiring and interpreting FRET and FLIM data.
This work was supported by the National Basic Research Program of China [grant number 2006CB911001 (to C.C.)]; the National Institutes of Health [grant numbers R01-DK078187 (to B.F.), R01-GM50388]; and the National Center for Research Resources [grant number P20RR021954 (to A.M.)]. T.E.H. is supported by the National Institutes of Health [grant number R01-DK052753]. H.R. is an American Heart Association Postdoctoral Research Fellow.
Author notes
These author contributed equally to the present work.
Present address: Gene expression laboratory, The Salk Institute for Biological Studies, La Jolla, CA, USA


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Global Frozen Food Market Growth, Trend, and Forecast 2017-2022: Competition From Really Large Companies and Huge Budgets - Research and Markets
07 Jun, 2017, 17:24 BST
DUBLIN, June 7, 2017 /PRNewswire/ --
Research and Markets has announced the addition of the "Global Frozen Food Market - Growth, Trend, and Forecast (2017 - 2022)" report to their offering.
There has been a remarkable expansion in frozen food product categories, owing to the considerable growth in freezer space in modern retail markets. Busy lifestyles and increasing demand for convenience food are among the major driving factors of the global frozen food market. When a food product (regional/staple/seasonal) is frozen and preserved, it is easily available, anywhere & anytime. This easy availability has influenced the purchasing patterns of consumers, placing frozen foods among the products on their list of daily consumables. The market has few limitations like the price of a frozen product is much higher when compared to its fresh form due to its high production cost. There are limitations in monitoring accurate freezing temperature and maintaining the frozen product intact. The global frozen food market is vast, and there are excellent opportunities to explore this market, especially, in developing countries.
The global frozen food market is segmented based on four key factors. By type, it is differentiated as ready-to-eat (thaw & serve), ready-to-cook and ready-to-drink. The product segmentation covers various frozen food categories of fruits & vegetables, meat, fish, ready meals, beverages, snacks, etc. The market is also segmented by the major freezing technologies, such as IQF (Individual Quick Freezing), blast freezing, etc.
Japan leads the Asian countries, regarding frozen food consumption, with 7.82 million tons, in 2010. Ready meals are the most expensive among the frozen food product categories, and thus, account for the largest market share of 40%, regarding revenue. Frozen pizza is the fastest-growing segment in the frozen ready meals segment.
Competitive Environment
Increased consumption of frozen foods is influencing companies to produce sustainable and durable food products. Leading companies in the global food & beverages industry are investing in the growth of the global frozen foods market. As per estimates, the contribution of the top four companies, such as Nestle and H.J. Heinz, in the global frozen foods market is approximately 19%, collectively.
Other key companies include
- ConAgra Foods Inc.
- Maple Leaf Foods Inc.
- General Mills
Key Topics Covered:
1.1 Research Methodology
1.2 Market Definition
1.3 Report Description
2. Market Overview
2.1 Market Trends
3. Market Dynamics
3.1 Drivers
3.1.1 Increase in Demand for Convenience Food Products
3.1.2 Availability of Staple, Seasonal and Regional Food Irrespective of Time and Place
3.1.3 Finest Preservation Technique
3.2 Restraints
3.2.1 Competition From Really Large Companies and Huge Budgets
3.2.2 Health and Sensory (Taste and Texture) Concerns
3.3 Opportunities
3.3.1 Increase in Novel Frozen Food Product Portfolio
3.3.2 Lower Penetration & High Exploration Market
3.4 Porter's Five Forces Analysis
4. Segmentation
4.1 By Type
4.1.1 Ready-To-Eat
4.1.2 Ready-To-Cook
4.1.3 Ready-To-Drink
4.1.4 Others
4.2 By Application
4.2.1 Frozen Fruits & Vegetables
4.2.2 Frozen Meat & Fish
4.2.3 Frozen-Cooked Ready Meals
4.2.4 Frozen Beverages
4.2.5 Frozen Snacks
4.2.6 Others
4.3 By Freezing Technique
4.3.1 IQF- Individual Quick Freezing
4.3.2 Blast Freezing
4.3.3 Belt Freezing
4.3.4 Others
4.4 By Geography
5. Competitive Landscape
5.1 Most Adopted Market Strategies
5.2 Most Active Companies
5.3 Market Share Analysis
6. Company Profiles
6.1 Nestle
6.2 Uniliver Plc
6.3 Mc Cain foods
6.4 Iceland Foods Ltd.
6.5 Amy's Kitchen, Inc.
6.6 Conagra Foods, Inc.
6.7 Kraft Food, Inc.
6.8 Ajinomoto Co., Inc.
6.9 Pinnacle Foods Inc.
6.10 General Mills, Inc.
6.11 H. J. Heinz Company.
6.12 Mother Dairy Fruit & Vegetable Pvt. Ltd.
6.13 Tyson Foods, Inc.
6.14 General Mills Inc.
6.15 The Schwan Food Company
6.16 Quirch Foods Company
6.17 Rich Products Corporation
7. Appendix
For more information about this report visit http://www.researchandmarkets.com/research/txnrhx/global_frozen
Media Contact:
Research and Markets
Laura Wood, Senior Manager
For E.S.T Office Hours Call +1-917-300-0470
For U.S./CAN Toll Free Call +1-800-526-8630
For GMT Office Hours Call +353-1-416-8900
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Fax (outside U.S.): +353-1-481-1716
Related Links
SOURCE Research and Markets


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Great Britain's Rachel Atherton won the women's downhill final at the mountain bike World Championships in Switzerland to claim the title for a fifth time.
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Fans Will Not Be Happy About This Male R&B Singer Calling Out Beyoncé, SZA And Cardi B
"Stop using that f**king pain to make it OK to say some bullsh** on your record and get nominated for a Grammy..."
Ciara got candid about her split from Future and the soul-searching journey that lead her to love. The R&B songstress sat down with the Pinkett-Smith ladies for their latest episode of The Red Table Talk, where she delved into the emotional healing and reflection that helped her gain some new beauty marks in the process. Although it did a number on her, she credits that moment for putting her on the path to finding the love of her life.
Here are some takeaways from the enlightening 25-minute conversation:
"It was a combination of everything because none of it was ideal," Ciara began before delving into the final straw that led to her calling it quits on the relationship. "I remember one time I was working out on an elliptical machine and I was just not sure about do I stay or what direction do I go? What's the right thing to do? It's easy to do this but is the easy thing the right thing?"
Ciara called off her engagement to Future three months after giving birth to their son, Future Zahir, in 2014.
Although she was afraid of being a single mother, she ultimately took control of the situation by traveling all over of the world with her son to bond with her newborn, while finding the strength to love herself again.
"When I was thinking about my son, I know what I want to feel. I know the kind of love that I want for us and I think it's important to understand that too, because sometimes we give people on Earth more power than they should have."
Despite that fear that came with the choice, the course of action was the right one for what she envisioned for her personal affairs and love life, which was based on the example her parents' set.
"I grew up with my mom and dad being together, the idea of it being, 'Mommy and Daddy made baby,' then all of a sudden you're living your life in front of the world. That adds a whole 'nother layer," she explained of her hesitation to end things with a child in the mix. "'I feel like I'm failing right now. Other people, they're gonna roast me. Here they come in the comment section. I'm about to get fried."
She continued: "The one thing I fear in life is really wasting my life. I really fear that 'cause you realize that time does not stop and it will be the worst scenario to stay in a situation that it's just not healthy, it's not going to get any better. I realized that I have to start making different decisions."
"My dad's love is what saved me in all my situations. I would think of him in the right moment," she said, crediting her father for teaching her how to approach dating. "I've always had the same goal of wanting to be loved a certain way, but I was just looking in the wrong direction."
"When Russ came into our lives, Future was two months old. It was different," Ciara admitted. "I had never had that feeling in my life. It was calm."
Even though her and Russell initially met as friends, CiCi felt an instant connection with him after a conversation among her, her dad and Russ where they talked about their views on life and marriage. She also recounted how her sports beau instantly took to baby Future and how he has gone above and beyond to show the two how much he cares for them everyday.
"That consistency is so crucial. Whenever he would think of me, he would think of my son and to love me is to love my son. It's a different level of love."
Watch the full interview below.
(Photos from left: Prince Williams/Wireimage, Sean Zanni/Patrick McMullan via Getty Images)
"Stop using that f**king pain to make it OK to say some bullsh** on your record and get nominated for a Grammy..."
Here are all the artists who posted tributes to the late R&B singer.


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National Register of Historic Places
Restoration of Lake Park Bridge Deemed Feasible
A barricaded historic pedestrian bridge in Milwaukee's Lake Park can be restored, according to a new report by a structural engineering firm with expertise in repairing historic bridges. Read more
The Changing Face of the Oriental Theatre
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text: 11Apr2019 335 Jeddah Comments A group of Indian expatriates, who were working in Kuwait and came for Umrah – mini pilgrimage, lost their passports in holy city of Makkah and are desperately trying to go back to Kuwait to resume their jobs. It is believed that passports were lost at hotel apparently due to act of negligence of the hotel, according to stranded pilgrims. A group of 43 Indians, including women and children, arrived through a bus in Saudi Arabia from Kuwait for a week to spend in holy cities of Makkah and Madina. A large group of NRIs hailing from Kerala, followed by Uttar Pradesh and Telangana besides other States. To their shock, all visiting pilgrims came to know about loss of their passports only on Tuesday afternoon when the tour operator told them to be ready to visit Jeddah for applying passports. "We were simply shocked to know that our passports were lost only when the hotel informed us yesterday to be prepared to travel to Jeddah for applying duplicate passports at Indian consulate", Basheer Abubacker Razq, one of the standard pilgrims has told media. He added that "We believe that our passports were lost or misplaced at the hotel where we were staying." A group of pilgrims, guided by a prominent Malayali community leader KTA Muneer, approached Indian consulate here for applying duplicate passports. They the consul general Md. Noor Rahman Sheikh and consul Sahil Sharma to narrate their version. Source: Read more Share this post Comments


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Since leaving the Love Island villa with Ellie Brown on his arm, millionaire Charlie Brake has found his love life has become a rollercoaster ride.
After the public split from his Casa Amor lover, Charlie has become the most eligible bachelor in town and just days ago, was pictured on a date with television presenter, Ferne McCann.
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Chyna, 23, had split earlier in the year from Jordan Davies , her fellow rep on Ibiza Weekender and onlookers have told The Sun, that she was openly kissing 23-year-old Charlie during a night out.
Posting on Instagram on Thursday morning, Chyna was not shy about her antics, captioning a photo of herself with, "Right back on my worst behaviour last night."
This behaviour seems to be from when she hooked up with Charlie, with whom an eyewitness said they were chatting for while, "before they started snogging."
According to this eye witness, the pair were not holding back and "couldn't keep their hands off each other" and were not bothered about "who could see them kissing."
It has been a turbulent couple of months for Charlie after his fiery relationship with Ellie Brown finally came to an end in September.
He was then seen holding hands with former Towie star Ferne McCann, as they walked down the street during a date.
It would seem that this romance was snuffed out before it could blossom and Charlie has moved on in quick fashion before the longing for another date with Ferne took hold.
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|Exosomes and Exosomal miRNA in Respiratory Diseases
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My knowledge of QM is very limited, but I think that the wave function collapses to a 'particle' when measured - at least for particles like the photon. A very small, collapsed, wave could be mistaken for a point particle? It would seem neat and tidy if all particle types had similar behaviour in this regard (string theory comes to mind). But probably we have to stick with uncollapsed waves from what you are saying. They could still be centred on a discrete grid point though. — Devans99
I think that our theories use continuous variables as an excellent approximation for a reality that is discrete on such a fine level that it appears continuous to us (and thus continuous theories give results very close to reality). So continuous calculus gives good results but does not reflect the micro nature of reality correctly. This seems to be how classical physics works - the classical approximation of (what we now know to be) discrete matter are good enough because discreteness of matter only manifests its effects in the micro world. — Devans99
So, I'll try to change my style of writing: go straight to the answer of only one specific question and keep the post short and focused on one question at a time. — Mephist
The Italian paper is about a formalization of real numbers in Coq:
"We have formalized and used our axioms inside the Logical Framework Coq" (from the first page).
That's why I was speaking about Coq — Mephist
Ok. Question: How can any model of the reals built on constructive principles be Cauchy complete?
— fishfry
Answer: because Cauchy completeness is assumed as an axiom of the theory (this is not a model of the reals because real numbers are described axiomatically). You can argue about the consistency of the theory, but you cannot argue about Cauchy completeness. Cauchy completeness is assumed as an hypothesis. — Mephist
Let me rephrase the question: "If a sequence is Cauchy in ZFC, is it Cauchy in intuitionist math?"
This question is too vague to have an yes/no answer:
"a sequence is Cauchy in ZFC" we know what it means.
"a sequence is Cauchy in intuitionist math" I don't know what you mean.
The adjective "intuitionist" is a property of a logic. You should say of what theory of real numbers (formulated in that logic) you are referring to. — Mephist
I can try to interpret it as "a sequence is Cauchy in the theory of real numbers of the Italian paper". — Mephist
Answer: If you take a Cauchy sequence in ZFC, you have a set of sets such that... (a proposition about that set of sets). Not all sets of sets that are expressible in the language of ZFC have a corresponding term of type R (the type of real numbers) in the language used in the theory of the Italian paper. So, you cannot really compare them. — Mephist
Put it in another way: which logic do you want to use to compare the two sequences? The first one is expressed in first order logic, the other one in Coq (If you don't want to speak about Coq, please choose another concrete intuitionistic logic and model of real numbers. There are too many of them to be able to speak in general). — Mephist
The definition of real numbers in the Italian paper is on the third page. The last axiom of that definition is this one:
Is that what we are speaking about? ( finally I learned how to write symbols :-) ) — Mephist
[ I don't want to address too many points because I'll go off the road again. So, I'll wait for an answer about these ones for the moment ] — Mephist
The constructive reals are Dedekind complete but not Cauchy complete
— fishfry
Hmm.. I am sorry that I have always to disagree with what you say, — Mephist
The simplest topology that corresponds to Euclidean geometry is that of flat, infinite space. So by Occam's razor, we can conclude that in the absence of evidence to the contrary, the universe appears infinite. — Mark Dennis
in the absence of evidence to the contrary — Mark Dennis
But this necessarily leaves out all those Cauchy sequences whose convergence rates are not so constrained; and the limits of those sequences can not be Italian-Cauchy reals. But they are standard reals (being the limits of Cauchy sequences). So what the constructivists call Cauchy complete can not be actual Cauchy completeness. I am pretty sure about this. If the constructivists don't care, all fine and well. A lot of smart people are constructivists these days so I'm sure the fault is my own. But the Italian definition of a Cauchy sequence omits a lot of more slowly converging sequences unless I am mistaken (I haven't fully gotten to the bottom of this yet). — fishfry
Because in ZFC you can define non computable functions by using the axiom of choice, that is not available in constructive mathematics. — Mephist
This would destroy the foundation of modern probability theory and everything that sits above it (statistical mechanics, quantum field theory, sociology, the state lottery, etc.) — fishfry
The constructive reals are Dedekind complete but not Cauchy complete
— fishfry
Hmm.. I am sorry that I have always to disagree with what you say, but in my opinion this is not exactly what that paper says :sad: — Mephist
Let's read the abstract: "It is consistent with constructive set theory (...) that the Cauchy reals (...) are not Cauchy complete".
That is exactly equivalent to say this: "It is not possible to prove with constructive set theory (...) that it is not true that the Cauchy reals (...) are not Cauchy complete.": — Mephist
To say that a proposition is consistent with a theory means that it's not possible to prove that the proposition is false in that theory. It doesn't mean that it's possible to prove that the proposition is true. — Mephist
In fact, the proposition "Cauchy reals (...) are not Cauchy complete" cannot be proved with the constructive set theory that he considers. — Mephist
How do I know? Because the axioms of IZF_Ref (the constructive set theory that the paper is speaking about) are provable in ZFC, and the rules of IZF_Ref are the same rules of ZFC without Excluded Middle (here is a good reference for the axioms: https://plato.stanford.edu/entries/set-theory-constructive/axioms-CZF-IZF.html).
Then, all theorems that are provable in IZF_Ref are provable even in ZFC: just use ZFC axioms to prove IZF_Ref axioms, and then apply the same rules as the original theorem (ZFC has all rules of IZF_Ref, then it can be done). — Mephist
So, if "Cauchy reals (...) are not Cauchy complete" were provable in IZF_Ref, it would be provable even in ZFC. But, as we know, in ZFC this is provably false. — Mephist
In fact, some models of IZF_Ref are not Cauchy complete (the two models that he considers) and some other models of IZF_Ref (the standard ZFC reals) are Cauchy complete. — Mephist
And so, here is a confession: I don't even know what Dedekind completeness is
— fishfry
Dedekind completeness is simpler than Cauchy completeness to formulate in set theory, but practically impossible to use in analysis. — Mephist
Basically, this is the thing: if you build "Dedekind cuts" of rational numbers you obtain the real numbers (this is not part of the theorem, but the definition of real numbers in ZFC), — Mephist
but if you build "Dedekind cuts" of real numbers you obtain again the same real numbers. — Mephist
The same thing hapens with Cauchy: taking limits of rationals you obtain reals but taking limits of reals you obtain again reals (the set is closed under the operation of taking limits and forming Dedekind cuts).
A Dedekind cut is simply the partition of an ordered set in two non empty sets that respects the order relation (any element of the first set is smaller than any element of the second set). — Mephist
and then start to attempt to grok what it means to be Dedekind complete but not Cauchy complete in an intuitionist setting (whatever that means!)
— fishfry
OK. In my opinion, intuitively it means that they can be the same thing as standard ZFC reals, but can even be something very different. — Mephist
Simply there are more possible "forms" for the object called "set of real numbers". — Mephist
And there is even another problem with the definition of convergent Cauchy sequences defined in this article: they are not the sequences of rational numbers (as the standard definition) but sequences of pairs made of a real number plus a function (from page 2: "So a real is taken to be an equivalence class of pairs <X, f>, where X is a Cauchy sequence and f a modulus of convergence). — Mephist
* Finally I just want to say that with all the back and forth, and I do note that we both tend to the wordy side, this current post of mine represents my latest thinking about everything; and all prior comments are null and void.
— fishfry
OK, I'll not look at you previous posts any more :wink: — Mephist
Constructivism is not about the rejection or acceptance of actual infinity, but it's about choosing computable functions as a fundamental logic concept (that is implemented the rules of logic), as opposed to the more abstract idea of functions that is implied by the classical axiom of choice.
I believe you responded this to someone else's post but it brings up a question.
You talk about computable functions. Every time I drill down, constructivism turns out to be about computability. But the constructivists seem to regard the computable reals as somewhat different than the constructive reals. One article referred to the constructive reals as the "realization" of the computable reals. Or the other way 'round? Either way the point is that computability is not exactly the same as constructivity. I'd like to understand this.
The other minor point is that you jumped from computability to the axiom of choice, but as I pointed out in my previous post there's an intermediate step. ZF is already noncomputable, even before we get to ZFC. — Mephist
What part of probability theory is inconsistent with the negation of axiom of choice? — Mephist
* ZF. We have statements of existence of sets we can't compute. The powerset axiom for example is very powerful. Cantor's theorem is a theorem of ZF so that the powerset of the naturals must be uncountable; yet there are only countably many Turing machines. So most of the subsets of the naturals are noncomputable sets. No axiom of choice is needed for ZF-noncomputability. — fishfry
Although in ZF we can enumerate the Turing machines, no such enumeration can be computable! That's because a computable enumeration of TMs would effectively solve the Halting problem, which Turing showed can't be done. — fishfry
We know nothing about the elements of this set. Is 1/2 in it? We don't know, only that it contains exactly one rational (proof by reader). — fishfry
So to sum up, the next thing past computability is ZF, which already gives you sets that are arguably not computable (depending on who's arguing). Then AC gives you sets that are not only noncomputable, but beyond even the reach of ZF. — fishfry
You talk about computable functions. Every time I drill down, constructivism turns out to be about computability. But the constructivists seem to regard the computable reals as somewhat different than the constructive reals. — Mephist
Wait I think you said that wrong. It's not a sequence of pairs (rational number, modulus function). Rather it's a pair (entire sequence, single modulus function). It's the sequence, plus the function that inputs epsilon and outputs a suitable N. — fishfry
Ah ... you are saying that the standard reals are a model of C. That is a very enticing remark. I'll spend some time on this. That's a clue for me to hang some understanding on. — fishfry
I don't know...Isn't that just because the constructive reals can't see all those ZF-Cauchy sequences that it's leaving out? This MUST be the case. Isn't it? — fishfry
You talk about computable functions. Every time I drill down, constructivism turns out to be about computability. But the constructivists seem to regard the computable reals as somewhat different than the constructive reals. — Mephist
If you take as sets the sets of finite segments, all sets have a measure and Kolmogorov axioms work perfectly well: zero-length segments will have zero measure and non zero segments will have a non zero measure. Where is the contradiction? — Mephist
Power Set in ZF:
Power Set in Coq:
Inductive Power_set (A:Ensemble U) : Ensemble (Ensemble U) :=
Definition_of_Power_set : — Mephist
Although in ZF we can enumerate the Turing machines, no such enumeration can be computable! That's because a computable enumeration of TMs would effectively solve the Halting problem, which Turing showed can't be done.
— fishfry
Are you sure about this? I think turing machines are simply strings that can be enumerated as integers. This is not the same thing as solving the halting problem. — Mephist
The sets that you say are not computable, but computable in ZF, are the ones that in type theory are called Inductive types, and correspond to initial algebras in category theory. — Mephist
The simplest example is the set of natural numbers. You say the set of natural numbers is not computable. — Mephist
It's not so simple: an inductive set is not a function, and the recursor on this inductive set is a computable function, because the recursion is done counting down to zero. — Mephist
And there are even co-recursive sets, that correspond to co-initial algebras in category theory (not sure if the name is correct). Co-inductive functions are not required to terminate, but only to consume data at every step. However, you never get an infinite loop because there are restrictions on how co-inductive functions can be used. So, it's not so easy to define what is "computable" from the point of view of a constructive type theory. — Mephist
There are too many points, and I have the impression that this discussion doesn't make sense if we don't agree on the definitions of the worlds. So, let me start from the most ambiguous one: what do you mean by "computable reals"? How do you "compute" a number that is not representable as a fraction? I'll wait for this answer before going ahead with the other points, because I really don't know what are the "computable reals". — Mephist
But I have to tell you that in my opinion the road that you've chosen to learn about constructive mathematics is the most difficult that you could choose. — Mephist
In my opinion ZFC, or ZF, makes sense only in first order logic (of course!), and intuitionistic logic makes the most sense in the context of type theory. But of course you can choose whatever random combination of axioms and rules, and find their implications, but I doubt that in this way you can discover something meaningful about what the "real" real numbers are... — Mephist
Consider this question: why modules don't have a base? Is it because they can't see all those inverse functions of multiplication that vector spaces see? Well, yes! But does it mean that modules are vector spaces when you close your eyes to not the inverse of multiplication? — Mephist
Real numbers are a concrete unique object, because there is only one model of real numbers. — Mephist
Basically, the point is that building proofs in intuitionistic logic is equivalent (it's really the same thing) to building computable functions: there is a one-to one correspondence between intuitionistic proofs and terms of lambda calculus (sorry, lambda calculus again...). This is really a very simple and practical thing, but I don't know why all explanations that I am able to find on the web are extremely abstract and complicated! — Mephist
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Bigg Boss 12's Sreesanth is a doting father to his two little kids Saanvika and Suryashree. Sreesanth is absolutely in awe of his little babies and loves to be with them all the time.
Recently, Sreesanth's wife Bhuvneshwari Kumari shared a throwback video on her social media handle wherein her daughter Saanvika is seen sitting in a bucket full of water and splashing water. The little baby is seen having a blast.
Sreesanth has been extremely attached to his family members especially to the ladies of his life. Sreesanth in a conversation with TimesofIndia.com stated that he had missed his daughter the most during his Bigg Boss 12 stint.
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Let's splash some 💦 #throwback #memories #watersplash #happiness #sreesaanvika
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On the occasion of the family week in the BB12 house, Bhuvaneshwari and kids had entered the house and Sreesanth had become extremely emotional. He hugged his babies especially his little girl tightly after seeing her after a really long time and took them to meet his housemates. Sreesanth's daughter had then walked up to Dipika Kakar and planted a kiss on her cheek and cutely addressed her 'Dipika Bua.'


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text: Arizona's Alamo Tony Mandile - October 04, 2010 It's time to remember the other Alamo -- Alamo Lake in central Arizona. Bass are back after years of devastating drought. (April 2008) By Tony Mandile This is the typical size for most largemouth bass in Arizona's Alamo Lake. Bruce Fritz hooked this one on a watermelon-colored Yum Craw Papi. Photo by Tony Mandile.In 1836, a garrison of about 200 Americans, including Jim Bowie and Davy Crockett, died fighting to free Texas from the control of Mexico. The site of the 13-day battle with General Antonio López de Santa Anna's Mexican army was a Spanish mission -- the now-famous landmark known as the Alamo in San Antonio.Since that bloody encounter occurred, the phrase "Remember the Alamo" has become as prominent in history as "I shall return," uttered by Gen. Douglas MacArthur during World War II. But repeat, "Remember the Alamo" to an Arizona angler, and if he was around during the 1970s, you'll likely get a much different reaction. That's when Alamo Lake, located in the west-central part of the state, furnished some of the state's best bass fishing. Its fertile waters consistently produced 10-fish catches weighing 35 pounds, and bigger bass between 6 and 10 pounds were common. Those days disappeared with the arrival of a long drought that affected many of the state's fisheries. But recent reports suggest it might again be time to remember the Alamo. Rory Aikens is a public information officer for the Arizona Game and Fish Department. He often fishes Alamo and said fishing at the lake has improved dramatically, especially if you're after numbers rather than size."Most will be in the 3/4- to 1 1/2-pound range," he said. "But I always seem to hook one or two larger fish on every trip." AGREEMENT HELPS REBIRTHTSituated in the Bill Williams River Valley where the Big Sandy and Santa Maria rivers come together, Alamo Lake was originally designed as a flood-control project by the Bureau of Reclamation. The dam was completed in 1968. When filled to the spillway crest, the lake would cover more than 17,000 acres with a maximum depth of 80 feet. Over the last two decades, except for one or two years of above-average moisture, the surface area has been a lot less than that. When the winter run-off is normal, the lake's surface area averages between 8,000 and 9,000 acres. This up-and-down pattern of water level led to an agreement between various agencies to keep the lake filled to where it is more favorable to both fish and wildlife in the area. The joint effort between the AGFD, Arizona State Parks, the U.S. Fish & Wildlife Service and the Corps of Engineers -- which controls the dam -- has helped the fishing by maintaining a higher water level during the spring months when the largemouth bass spawn. In 1968, the AGFD stocked Alamo with the northern strain of largemouth bass. But the fishing declined in the 1980s. The fisheries folks put into effect a slot limit that mandated the release of any bass between 12 and 16 inches long. The rule worked well for a few years. Then along came a couple of those excellent above-moisture years. Huge spawns of bass took place. Coupled with other factors such as lower water levels in subsequent years, the overpopulation of fish began producing dire consequences. The forage base declined, and the effects quickly showed up in the form of stunted bass.Consequently, the AGFD adjusted the slot size, making it 13 to 16 inches. Unlike the old slot rule, this one allows fisherman to keep one fish that falls within the slot, with a total daily limit of six bass that can also include those under or over the slot limit. In other words, the daily bag now allows for six fish of any size, as long as only one measures between 13 and 16 inches. For the total daily bag, any combination of smaller or larger fish, with no slot fish, is also legal.The possession limit is 12, with the same criteria as if it were two separate daily limits.PRIME HABITATAlamo contains plenty of prime habitat. There are huge stands of underwater brush, steep and rocky shorelines, large downed trees, flat weedy shallows and long sloping points. All of them harbor fish. Much of the lake's upper end comprises big shallow flats and numerous fishy-looking coves. Brush patches dot the flats and a few of the coves, such as Date Creek and Kaiser washes. The main lake has everything from large coves and long sloping points to deep-water areas. This mixture provides good shallow-water fishing with surface lures or spinnerbaits in the morning and evening -- and during the warmer parts of the day, deep fishing off the points or steep banks with crankbaits or plastics.During the winter months and right up to the spawn, which normally begins in March and often runs into April, rocky shorelines near the dam can also be good. Especially productive in these areas are crankbaits or plastic worms and jigs in dark colors. For many anglers, the early spring months are the best times to catch bass. Because Alamo is a low-elevation desert lake, the spawn usually begins several weeks before other warm-water fisheries in central Arizona. Once the major winter weather disappears, the air and water temperatures could both climb quickly. During late February or early March, it's common to hit a low in the 40s at night and then have the temperature climb into the mid-80s or above during the day. When that happens, the water also warms quickly, and the fish get very active.TACKLEJim Warnecke once ran a store at Alamo. Now he usually fishes water from 10 to 20 feet deep before the fish go into their spawning ritual. "While living at the lake, I kept a daily log of my fishing activity," he said recently, "and crankbaits dominate the list for the bass I caught." Warnecke said a No. 5 Shad Rap in crawdad colors accounted for many of the larger bass he landed. Although he fishes the coves occasionally, Warnecke does most of his cranking on the outside points. He'll normally run over an area with his graph to see what kind of fish are holding where. If he finds a decent concentration of bass, he'll move off to the deeper water parallel to the point itself and throw his crankbait across the point.Jim Weller is another Alamo regular. "It really doesn't matter what crankbait I use as long as it runs at the right depth."But color is also very important, he said. Either a crawdad pattern or one with black and chartreuse always seems to catch the most fish, he said.The bass also feed heavily on Alamo's huge bluegill population, so he sometimes throws a Punkin Seed with good success. In water from 10 to 15 feet deep, his choices are a Bagley DKB, Deep Vee R, Fat Rap, or a Cordell Spot. Buzzbaits can also be productive at this time of year. The bass tend to move in and out of the shallows during the day, he said. "So when I get on the lake, I often throw a buzzbait right up against the banks in the larger coves, especially in areas where the brush sticks out of the water. Get Your Fish On. Plan your next fishing and boating adventure here.


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This course will equip you with adequate skills and knowledge to effectively manage a project. It will prepare you for Certified Associate in Project Management (CAPM) Exam and help you understand and practice the test pattern and key areas/sections.
This course focuses mostly on opting a broad approach for technological projects and it will enhance your skills and knowledge level about project management. It will teach you about a set of tools, techniques and strategies that can be of great use to you as a project manager.
This course will prepare you in-depth in the process of claiming your Certified Associate in Project Management CAPM qualification. This qualification is based on your profession and knowledge of preeminent global standards and best practices within organizations.
This is an Associate In Project Management training offered by Laurels Training Institute. You will be trained by richly experienced and highly qualified teachers by using comprehensive study materials. The curriculum is designed by following the books authored by subject experts.