Stimulation of osteogenesis and angiogenesis of hBMSCs by delivering Si ions and functional drug from mesoporous silica nanospheres

Multifunctional bioactive materials with the ability to stimulate osteogenesis and angiogenesis of stem cells play an important role in the regeneration of bone defects. However, how to develop such biomaterials remains a significant challenge. In this study, we prepared mesoporous silica nanospheres (MSNs) with uniform sphere size (∼90 nm) and mesopores (∼2.7 nm), which could release silicon ions (Si) to stimulate the osteogenic differentiation of human bone marrow stromal cells (hBMSCs) via activating their ALP activity, bone-related gene and protein (OCN, RUNX2 and OPN) expression. Hypoxia-inducing therapeutic drug, dimethyloxaloylglycine (DMOG), was effectively loaded in the mesopores of MSNs (D-MSNs). The sustained release of DMOG from D-MSNs could stabilize HIF-1α and further stimulated the angiogenic differentiation of hBMSCs as indicated by the enhanced VEGF secretion and protein expression. Our study revealed that D-MSNs could combine the stimulatory effect on both osteogenic and angiogenic activity of hBMSCs. The potential mechanism of D-MSN-stimulated osteogenesis and angiogenesis was further elucidated by the supplementation of cell culture medium with pure Si ions and DMOG. Considering the easy handling characteristics of nanospheres, the prepared D-MSNs may be applied in the forms of injectable spheres for minimally invasive surgery, or MSNs/polymer composite scaffolds for bone defect repair. The concept of delivering both stimulatory ions and functional drugs may offer a new strategy to construct a multifunctional biomaterial system for bone tissue regeneration.

Dietary intake in Australian children aged 4–24 months: Consumption of meat and meat alternatives

Meat/meat alternatives (M/MA) are key sources of Fe, Zn and protein, but intake tends to be low in young children. Australian recommendations state that Fe-rich foods, including M/MA, should be the first complementary foods offered to infants. The present paper reports M/MA consumption of Australian infants and toddlers, compares intake with guidelines, and suggests strategies to enhance adherence to those guidelines. Mother–infant dyads recruited as part of the NOURISH and South Australian Infants Dietary Intake studies provided 3 d of intake data at three time points: Time 1 (T1) (n 482, mean age 5·5 (SD 1·1) months), Time 2 (T2) (n 600, mean age 14·0 (SD 1·2) months) and Time 3 (T3) (n 533, mean age 24 (SD 0·7) months). Of 170 infants consuming solids and aged greater than 6 months at T1, 50 (29 %) consumed beef, lamb, veal (BLV) or pork on at least one of 3 d. Commercial infant foods containing BLV or poultry were the most common form of M/MA consumed at T1, whilst by T2 BLV mixed dishes (including pasta bolognaise) became more popular and remained so at T3. The processed M/MA increased in popularity over time, led by pork (including ham). The present study shows that M/MA are not being eaten by Australian infants or toddlers regularly enough; or in adequate quantities to meet recommendations; and that the form in which these foods are eaten can lead to smaller M/MA serve sizes and greater Na intake. Parents should be encouraged to offer M/MA in a recognisable form, as one of the first complementary foods, in order to increase acceptance at a later age.

The empire of cancer: Gene patents and cancer voices

In his book, The Emperor of All Maladies, Siddhartha Mukherjee writes a history of cancer — "It is a chronicle of an ancient disease — once a clandestine, 'whispered-about' illness — that has metamorphosed into a lethal shape-shifting entity imbued with such penetrating metaphorical, medical, scientific, and political potency that cancer is often described as the defining plague of our generation." Increasingly, an important theme in the history of cancer is the role of law, particularly in the field of intellectual property law. It is striking that a number of contemporary policy debates over intellectual property and public health have concerned cancer research, diagnosis, and treatment. In the area of access to essential medicines, there has been much debate over Novartis’ patent application in respect of Glivec, a treatment for leukaemia. India’s Supreme Court held that the Swiss company’s patent application violated a safeguard provision in India’s patent law designed to stop evergreening. In the field of tobacco control, the Australian Government introduced plain packaging for tobacco products in order to address the health burdens associated with the tobacco epidemic. This regime was successfully defended in the High Court of Australia. In the area of intellectual property and biotechnology, there have been significant disputes over the Utah biotechnology company Myriad Genetics and its patents in respect of genetic testing for BRCA1 and BRCA2, which are related to breast cancer and ovarian cancer. The Federal Court of Australia handed down a decision on the validity of Myriad Genetics’ patent in respect of genetic testing for BRCA1 in February 2013. The Supreme Court of the United States heard a challenge to the validity of Myriad Genetics’ patents in this area in April 2013, and handed down a judgment in July 2013. Such disputes have involved tensions between intellectual property rights, and public health. This article focuses upon one of these important test cases involving intellectual property, public health, and cancer research. In June 2010, Cancer Voices Australia and Yvonne D’Arcy brought an action in the Federal Court of Australia against the validity of a BRCA1 patent — held by Myriad Genetics Inc, the Centre de Recherche du Chul, the Cancer Institute of Japan and Genetic Technologies Limited. Yvonne D’Arcy — a Brisbane woman who has had treatment for breast cancer — maintained: "I believe that what they are doing is morally and ethically corrupt and that big companies should not control any parts of the human body." She observed: "For my daughter, I've had her have [sic] mammograms, etc, because of me but I would still like her to be able to have the test to see if the mutation gene is in there from me." The applicants made the following arguments: "Genes and the information represented by human gene sequences are products of nature universally present in each individual, and the information content of a human gene sequence is fixed. Genetic variations or mutations are products of nature. The isolation of the BRCA1 gene mutation from the human body constitutes no more than a medical or scientific discovery of a naturally occurring phenomenon and does not give rise to a patentable invention." The applicants also argued that "the alleged invention is not a patentable invention in that, so far as claimed in claims 1–3, it is not a manner of manufacture within the meaning of s 6 of the Statute of Monopolies". The applicants suggested that "the alleged invention is a mere discovery". Moreover, the applicants contended that "the alleged invention of each of claims 1-3 is not a patentable invention because they are claims for biological processes for the generation of human beings". The applicants, though, later dropped the argument that the patent claims related to biological processes for the generation of human beings. In February 2013, Nicholas J of the Federal Court of Australia considered the case brought by Cancer Voices Australia and Yvonne D’Arcy against Myriad Genetics. The judge presented the issues in the case, as follows: "The issue that arises in this case is of considerable importance. It relates to the patentability of genes, or gene sequences, and the practice of 'gene patenting'. Briefly stated, the issue to be decided is whether under the Patents Act 1990 (Cth) a valid patent may be granted for a claim that covers naturally occurring nucleic acid — either deoxyribonucleic acid (DNA) or ribonucleic acid (RNA) — that has been 'isolated'". In this context, the word "isolated" implies that naturally occurring nucleic acid found in the cells of the human body, whether it be DNA or RNA, has been removed from the cellular environment in which it naturally exists and separated from other cellular components also found there. The genes found in the human body are made of nucleic acid. The particular gene with which the patent in suit is concerned (BRCA1) is a human breast and ovarian cancer disposing gene. Various mutations that may be present in this gene have been linked to various forms of cancer including breast cancer and ovarian cancer.' The judge held in this particular case that Myriad Genetics’ patent claims were a "manner of manufacture" under s 6 of the Statute of Monopolies and s 18(1)(a) of the Patents Act 1990 (Cth). The matter is currently under appeal in the Full Court of the Federal Court of Australia. This article interprets the dispute over Myriad Genetics in light of the scholarly work of Nobel Laureate Professor Joseph Stiglitz on inequality. Such work has significant explanatory power in the context of intellectual property and biotechnology. First, Stiglitz has contended that "societal inequality was a result not just of the laws of economics, but also of how we shape the economy — through politics, including through almost every aspect of our legal system". Stiglitz is concerned that "our intellectual property regime … contributes needlessly to the gravest form of inequality." He maintains: "The right to life should not be contingent on the ability to pay." Second, Stiglitz worries that "some of the most iniquitous aspects of inequality creation within our economic system are a result of 'rent-seeking': profits, and inequality, generated by manipulating social or political conditions to get a larger share of the economic pie, rather than increasing the size of that pie". He observes that "the most iniquitous aspect of this wealth appropriation arises when the wealth that goes to the top comes at the expense of the bottom." Third, Stiglitz comments: "When the legal regime governing intellectual property rights is designed poorly, it facilitates rent-seeking" and "the result is that there is actually less innovation and more inequality." He is concerned that intellectual property regimes "create monopoly rents that impede access to health both create inequality and hamper growth more generally." Finally, Stiglitz has recommended: "Government-financed research, foundations, and the prize system … are alternatives, with major advantages, and without the inequality-increasing disadvantages of the current intellectual property rights system.’" This article provides a critical analysis of the Australian litigation and debate surrounding Myriad Genetics’ patents in respect of genetic testing for BRCA1. First, it considers the ruling of Nicholas J in the Federal Court of Australia that Myriad Genetics’ patent was a manner of manufacture as it related to an artificially created state of affairs, and not mere products of nature. Second, it examines the policy debate over gene patents in Australia, and its relevance to the litigation involving Myriad Genetics. Third, it examines comparative law, and contrasts the ruling by Nicholas J in the Federal Court of Australia with developments in the United States, Canada, and the European Union. Fourth, this piece considers the reaction to the decision of Nicholas at first instance in Australia. Fifth, the article assesses the prospects of an appeal to the Full Federal Court of Australia over the Myriad Genetics’ patents. Finally, this article observes that, whatever happens in respect of litigation against Myriad Genetics, there remains controversy over Genetic Technologies Limited. The Melbourne firm has been aggressively licensing and enforcing its related patents on non-coding DNA and genomic mapping.

Populations of models, experimental designs and coverage of parameter space by Latin Hypercube and Orthogonal Sampling

In this paper we have used simulations to make a conjecture about the coverage of a t-dimensional subspace of a d-dimensional parameter space of size n when performing k trials of Latin Hypercube sampling. This takes the form P(k,n,d,t) = 1 - e^(-k/n^(t-1)). We suggest that this coverage formula is independent of d and this allows us to make connections between building Populations of Models and Experimental Designs. We also show that Orthogonal sampling is superior to Latin Hypercube sampling in terms of allowing a more uniform coverage of the t-dimensional subspace at the sub-block size level. These ideas have particular relevance when attempting to perform uncertainty quantification and sensitivity analyses.

Monoclonal antibody screening of a phage-displayed random peptide library reveals mimotopes of chemokine receptor CCR5: Implications for the tertiary structure of the receptor and for an n-terminal binding site for HIV-1 gp120

The chemokine receptor CCR5 contains seven transmembrane-spanning domains. It binds chemokines and acts as co-receptor for macrophage (m)-tropic (or R5) strains of HIV-1. Monoclonal antibodies (mAb) to CCR5, 3A9 and 5C7, were used for biopanning a nonapeptide cysteine (C)-constrained phage-displayed random peptide library to ascertain contact residues and define tertiary structures of possible epitopes on CCR5. Reactivity of antibodies with phagotopes was established by enzyme-linked immunosorbent assay (ELISA). mAb 3A9 identified a phagotope C-HASIYDFGS-C (3A9/1), and 5C7 most frequently identified C-PHWLRDLRV-C (5C7/1). Corresponding peptides were synthesized. Phagotopes and synthetic peptides reacted in ELISA with corresponding antibodies and synthetic peptides inhibited antibody binding to the phagotopes. Reactivity by immunofluorescence of 3A9 with CCR5 was strongly inhibited by the corresponding peptide. Both mAb 3A9 and 5C7 reacted similarly with phagotopes and the corresponding peptide selected by the alternative mAb. The sequences of peptide inserts of phagotopes could be aligned as mimotopes of the sequence of CCR5. For phage 3A9/1, the motif SIYD aligned to residues at the N terminus and FG to residues on the first extracellular loop; for 5C7/1, residues at the N terminus, first extracellular loop, and possibly the third extracellular loop could be aligned and so would contribute to the mimotope. The synthetic peptides corresponding to the isolated phagotopes showed a CD4-dependent reactivity with gp120 of a primary, m-tropic HIV-1 isolate. Thus reactivity of antibodies raised to CCR5 against phage-displayed peptides defined mimotopes that reflect binding sites for these antibodies and reveal a part of the gp120 binding sites on CCR5.

Pilot study: Effect of age on visual acuity with defocus and astigmatism

PURPOSE: To investigate how distance visual acuity in the presence of defocus and astigmatism is affected by age and whether aberration properties of young and older eyes can explain any differences. METHODS: Participants were 12 young adults (mean [±SD] age, 23 [±2] years) and 10 older adults (mean [±SD] age, 57 [±4] years). Cyclopleged right eyes were used with 4-mm effective pupil sizes. Thirteen blur conditions were used by adding five spherical lens conditions (-1.00 diopters [D], -0.50 D, plano/0.00 D, +0.50 D, and +1.00 D) and adding two cross-cylindrical lenses (+0.50 DS/-1.00 DC and +1.00 D/-2.00 DC, or 0.50 D and 1.00 D astigmatism) at four negative cylinder axes (45, 90, 135, and 180 degrees). Targets were single lines of high-contrast letters based on the Bailey-Lovie chart. Successively smaller lines were read until a participant could no longer read any of the letters correctly. Aberrations were measured with a COAS-HD Hartmann-Shack aberrometer. RESULTS: There were no significant differences between the two age groups. We estimated that 70 to 80 participants per group would be needed to show significant effects of the trend of greater visual acuity loss for the young group. Visual acuity loss for astigmatism was twice that for defocus of the same magnitude of blur strength (0.33 logMAR [logarithm of the minimum angle of resolution]/D compared with 0.18 logMAR/D), contrary to the geometric prediction of similar loss. CONCLUSIONS: Any age-related differences in visual acuity in the presence of defocus and astigmatism were swamped by interparticipant variation.

Vitamin D deficiency in patients with malignancy in Brisbane

PURPOSE: This study aims to investigate the prevalence and factors predictive of vitamin D deficiency in patients with malignancy in Brisbane, Australia (latitude 27° S). METHODS: This is a prospective cross-sectional study measuring serum levels of 25-hydroxyvitamin D (25-OHD) in 100 subjects with non-haematological cancer at least 18 years of age not taking vitamin D supplements attending a day oncology unit and oncology/palliative care inpatient ward in Brisbane, Australia. RESULTS: Thirty-seven per cent of outpatient and 49 % of inpatient subjects respectively were vitamin D deficient. Functional status was predictive of low vitamin D levels. CONCLUSION: There was a high prevalence of vitamin D deficiency in patients with cancer in Brisbane, Australia.

Polymorphisms in a desaturase 2 ortholog associate with cuticular hydrocarbon and male mating success variation in a natural population of Drosophila serrata

Elucidating the nature of genetic variation underlying both sexually selected traits and the fitness components of sexual selection is essential to understanding the broader consequences of sexual selection as an evolutionary process. To date, there have been relatively few attempts to connect the genetic variance in sexually selected traits with segregating DNA sequence polymorphisms. We set out to address this in a well-characterized sexual selection system - the cuticular hydrocarbons (CHCs) of Drosophila serrata - using an indirect association study design that allowed simultaneous estimation of the genetic variance in CHCs, sexual fitness and single nucleotide polymorphism (SNP) effects in an outbred population. We cloned and sequenced an ortholog of the D. melanogaster desaturase 2 gene, previously shown to affect CHC biosynthesis in D. melanogaster, and associated 36 SNPs with minor allele frequencies > 0.02 with variance in CHCs and sexual fitness. Three SNPs had significant multivariate associations with CHC phenotype (q-value < 0.05). At these loci, minor alleles had multivariate effects on CHCs that were weakly associated with the multivariate direction of sexual selection operating on these traits. Two of these SNPs had pleiotropic associations with male mating success, suggesting these variants may underlie responses to sexual selection due to this locus. There were 15 significant male mating success associations (q-value < 0.1), and interestingly, we detected a nonrandom pattern in the relationship between allele frequency and direction of effect on male mating success. The minor-frequency allele usually reduced male mating success, suggesting a positive association between male mating success and total fitness at this locus.

Simulating the dissipation of two herbicides using micro paddy lysimeters

A set of packed micro paddy lysimeters, placed in a greenhouse, was used to simulate the dissipation of two herbicides, simetryn and thiobencarb, in a controlled environment. Data from a field monitoring study in 2003, including the soil condition and water balances, were used in the simulation. The herbicides were applied and monitored over a period of 21 d. The water balances under two water management scenarios, intermittent irrigation management (AI) and continuous irrigation management (CI), were simulated. In the AI scenario, the pattern of herbicide dissipation in the surface water of the field were simulated, following the first-order kinetics. In the CI scenario, similarity was observed in most lysimeter and field concentrations, but there were differences in some data points. Dissipation curves of both herbicides in the surface water of the two simulated scenarios were not significantly different (P > 0.05) from the field data except for intercept of the thiobencarb curve in the CI scenario. The distribution of simetryn and thiobencarb in the soil profile after simulation were also similar to the field data. The highest concentrations of both herbicides were found on the topsoil layer at 0-2.5 cm depth. Only a small amount of herbicides moved down to the deeper soil layers. Micro paddy lysimeters are thus a good alternative for the dissipation study of pesticides in the paddy environment.

Fate and transport of bensulfuron-methyl and imazosulfuron in paddy fields: Experiments and model simulation

Experiments were conducted to determine the fate of bensulfuron-methyl (BSM) and imazosulfuron (IMS) under paddy conditions. Initially, laboratory experiments were conducted and the photolysis half-lives of the two herbicides were found to be much shorter than their hydrolysis half-lives in aqueous solutions. In the aerobic water–soil system, dissipation followed first-order kinetics with water half-lives of 9.1 and 11.0 days and soil half-lives of 12.4 and 18.5 days (first phase) and 35.0 and 44.1 days (second phase) for bensulfuron-methyl and imazosulfuron, respectively. However, the anaerobic soil half-lives were only 12.7 and 9.8 days for BSM and IMS, respectively. The values of K d were determined to be 16.0 and 13.8 for BSM and IMS, respectively. Subsequent field measurements for the two herbicides revealed that dissipation of both herbicides in paddy water involved biphasic first-order kinetics, with the dissipation rates in the first phase being much faster than those in the second phase. The dissipation of bensulfuron-methyl and imazosulfuron in the paddy surface soil were also followed biphasic first-order kinetics. These results were then used as input parameters for the PCPF-1 model to simulate the fate and transport of BSM and IMS in the paddy environment (water and 1-cm surface soil layer). The measured and simulated values agreed well and the mass balance error during the simulation period was −1.2 and 2.8% of applied pesticide, respectively, for BSM and IMS.

Serum vitamin D levels are lower in Australian children and adolescents with type 1 diabetes than in children without diabetes

Vitamin D is synthesised in the skin through the action of UVB radiation (sunlight), and 25-hydroxy vitamin D (25OHD) measured in serum as a marker of vitamin D status. Several studies, mostly conducted in high latitudes, have shown an association between type 1 diabetes mellitus (T1DM) and low serum 25OHD. We conducted a case-control study to determine whether, in a sub-tropical environment with abundant sunlight (latitude 27.5°S), children with T1DM have lower serum vitamin D than children without diabetes. Fifty-six children with T1DM (14 newly diagnosed) and 46 unrelated control children participated in the study. Serum 25OHD, 1,25-dihydroxy vitamin D (1,25(OH)2D) and selected biochemical indices were measured. Vitamin D receptor (VDR) polymorphisms Taq1, Fok1, and Apa1 were genotyped. Fitzpatrick skin classification, self-reported daily hours of outdoor exposure, and mean UV index over the 35d prior to blood collection were recorded. Serum 25OHD was lower in children with T1DM (n=56) than in controls (n=46) [mean (95%CI)=78.7 (71.8-85.6) nmol/L vs. 91.4 (83.5-98.7) nmol/L, p=0.02]. T1DM children had lower self-reported outdoor exposure and mean UV exposure, but no significant difference in distribution of VDR polymorphisms. 25OHD remained lower in children with T1DM after covariate adjustment. Children newly diagnosed with T1DM had lower 1,25(OH)2D [median (IQR)=89 (68-122) pmol/L] than controls [121 (108-159) pmol/L, p=0.03], or children with established diabetes [137 (113-153) pmol/L, p=0.01]. Children with T1DM have lower 25OHD than controls, even in an environment of abundant sunlight. Whether low vitamin D is a risk factor or consequence of T1DM is unknown. © 2012 John Wiley & Sons A/S.

Enhancement of nonvolatile polarization and pyroelectric sensitivity in lithium tantalate (LT)/poly(vinylidene fluoride) (PVDF) nanocomposite

We report the ferroelectric and pyroelectric properties of the composite films of lithium tantalate (LT) nanoparticle in poly(vinylidene fluoride) PVDF matrix at different volume fractions of LT (f(LT) = 0.047, 0.09 and 0.17). For an applied electric field of 150 kV cm(-1) the nonvolatile polarization of the composite was observed to increase from 0.014 mu C cm(-2) at f(LT) = 0 to 2.06 mu C cm(-2) at f(LT) = 0.17. For f(LT) = 0.17, the composite films exhibit a saturated ferroelectric hysteresis loop with a remanent polarization (2P(r) = 4.13 mu C cm(-2)). Compared with pure poled PVDF the composite films also showed a factor of about five enhancement in the pyroelectric coefficient at f(LT) = 0.17. When used in energy detection mode the pyroelectric voltage sensitivity of the composite films was found to increase from 3.93 to 18.5 VJ(-1) with an increase in f(LT) from 0.0 to 0.17.

Magnetization, magnetotransport and electron magnetic resonance studies of nanoparticles and nanowires of Pr0.5Sr0.5MnO3

In this paper, we present the preparation and characterization of nanoparticles and nanowires of Pr0.5Sr0.5MnO3 (PSMO). The main results of this investigation are as follows: (a) a comparison with the properties of the bulk material shows that the ferromagnetic (FM) transition at 270 K remains unaffected but the anti-ferromagnetic (AFM) transition at TN = 150 K disappears in the nanoparticles, (b) the size induced ground state magnetic phase (below 150 K) is predominantly FM, coexisting with a residual AFM phase, and (c) the temperature dependence of magnetic anisotropy shows complex behaviour, being higher in the nanoparticles at high temperatures and lower at moderately lower temperatures in comparison with the bulk. The results obtained from the extensive magnetization, magnetotransport and electron magnetic resonance studies made on various samples are presented and discussed in detail.

Influence of lanthanum doping on the dielectric, ferroelectric and relaxor behaviour of barium bismuth titanate ceramics

Barium lanthanum bismuth titanate (Ba1−(3/2)xLaxBi4Ti4O15, x = 0–0.4) ceramics were fabricated using the powders synthesized via the solid-state reaction route. X-ray powder diffraction analysis confirmed the above compositions to be monophasic and belonged to the m = 4 member of the Aurivillius family of oxides. The effect of the partial presence of La3+ on Ba2+ sites on the microstructure, dielectric and relaxor behaviour of BaBi4Ti4O15 (BBT) ceramics was investigated. For the compositions pertaining to x ≤ 0.1, the dielectric constant at both room temperature and in the vicinity of the temperature of the dielectric maximum (Tm) of the parent phase (BBT) increased significantly with an increase in x while Tm remained almost constant. Tm shifted towards lower temperatures accompanied by a decrease in the magnitude of the dielectric maximum (εm) with an increase in the lanthanum content (0.1 < x ≤ 0.4). The dielectric relaxation was modelled using the Vogel–Fulcher relation and a decrease in the activation energy for frequency dispersion with increasing x was observed. The frequency dispersion of Tm was found to decrease with an increase in lanthanum doping, and for compositions corresponding to x ≥ 0.3, Tm was frequency independent. Well-developed P(polarization)–E(electric field) hysteresis loops were observed at 150 °C for all the samples and the remanent polarization (2Pr) was improved from 6.3 µC cm−2 for pure BBT to 13.4 µC cm−2 for Ba0.7La0.2Bi4Ti4O15 ceramics. Dc conductivities and associated activation energies were evaluated using impedance spectroscopy.

On the cubicity of bipartite graphs

A unit cube in k-dimension (or a k-cube) is defined as the Cartesian product R-1 x R-2 x ... x R-k, where each R-i is a closed interval on the real line of the form [a(j), a(i), + 1]. The cubicity of G, denoted as cub(G), is the minimum k such that G is the intersection graph of a collection of k-cubes. Many NP-complete graph problems can be solved efficiently or have good approximation ratios in graphs of low cubicity. In most of these cases the first step is to get a low dimensional cube representation of the given graph. It is known that for graph G, cub(G) <= left perpendicular2n/3right perpendicular. Recently it has been shown that for a graph G, cub(G) >= 4(Delta + 1) In n, where n and Delta are the number of vertices and maximum degree of G, respectively. In this paper, we show that for a bipartite graph G = (A boolean OR B, E) with |A| = n(1), |B| = n2, n(1) <= n(2), and Delta' = min {Delta(A),Delta(B)}, where Delta(A) = max(a is an element of A)d(a) and Delta(B) = max(b is an element of B) d(b), d(a) and d(b) being the degree of a and b in G, respectively , cub(G) <= 2(Delta' + 2) bar left rightln n(2)bar left arrow. We also give an efficient randomized algorithm to construct the cube representation of G in 3 (Delta' + 2) bar right arrowIn n(2)bar left arrow dimension. The reader may note that in general Delta' can be much smaller than Delta.