Loss-of-Function Mutations in PTPN11 Cause Metachondromatosis, but Not Ollier Disease or Maffucci Syndrome.

Metachondromatosis (MC) is a rare, autosomal dominant, incompletely penetrant combined exostosis and enchondromatosis tumor syndrome. MC is clinically distinct from other multiple exostosis or multiple enchondromatosis syndromes and is unlinked to EXT1 and EXT2, the genes responsible for autosomal dominant multiple osteochondromas (MO). To identify a gene for MC, we performed linkage analysis with high-density SNP arrays in a single family, used a targeted array to capture exons and promoter sequences from the linked interval in 16 participants from 11 MC families, and sequenced the captured DNA using high-throughput parallel sequencing technologies. DNA capture and parallel sequencing identified heterozygous putative loss-of-function mutations in PTPN11 in 4 of the 11 families. Sanger sequence analysis of PTPN11 coding regions in a total of 17 MC families identified mutations in 10 of them (5 frameshift, 2 nonsense, and 3 splice-site mutations). Copy number analysis of sequencing reads from a second targeted capture that included the entire PTPN11 gene identified an additional family with a 15 kb deletion spanning exon 7 of PTPN11. Microdissected MC lesions from two patients with PTPN11 mutations demonstrated loss-of-heterozygosity for the wild-type allele. We next sequenced PTPN11 in DNA samples from 54 patients with the multiple enchondromatosis disorders Ollier disease or Maffucci syndrome, but found no coding sequence PTPN11 mutations. We conclude that heterozygous loss-of-function mutations in PTPN11 are a frequent cause of MC, that lesions in patients with MC appear to arise following a "second hit," that MC may be locus heterogeneous since 1 familial and 5 sporadically occurring cases lacked obvious disease-causing PTPN11 mutations, and that PTPN11 mutations are not a common cause of Ollier disease or Maffucci syndrome.

Current multiple myeloma treatment strategies with novel agents: a European perspective.

The treatment of multiple myeloma (MM) has undergone significant developments in recent years. The availability of the novel agents thalidomide, bortezomib, and lenalidomide has expanded treatment options and has improved the outcome of patients with MM. Following the introduction of these agents in the relapsed/refractory setting, they are also undergoing investigation in the initial treatment of MM. A number of phase III trials have demonstrated the efficacy of novel agent combinations in the transplant and nontransplant settings, and based on these results standard induction regimens are being challenged and replaced. In the transplant setting, a number of newer induction regimens are now available that have been shown to be superior to the vincristine, doxorubicin, and dexamethasone regimen. Similarly, in the front-line treatment of patients not eligible for transplantation, regimens incorporating novel agents have been found to be superior to the traditional melphalan plus prednisone regimen. Importantly, some of the novel agents appear to be active in patients with high-risk disease, such as adverse cytogenetic features, and certain comorbidities, such as renal impairment. This review presents an overview of the most recent data with these novel agents and summarizes European treatment practices incorporating the novel agents.

Heritability of left ventricular structure and function in Caucasian families.

AIMS: The aim of this study was to investigate the heritability as well as genetic and environmental correlations of left ventricular (LV) structural and functional traits in complex pedigrees of a Caucasian population. METHODS AND RESULTS: We randomly recruited 459 white European subjects from 52 families (50% women; mean age 45 years). LV structure was measured by M-mode and 2D echocardiography and LV function was measured by conventional Doppler and tissue Doppler imaging (TDI). Other measurements included blood pressure, anthropometric, and biochemical measurements. We estimated the heritability of LV traits while adjusting for covariables, including sex, age, body height and weight, systolic and diastolic blood pressures, and heart rate. With full adjustment, heritability of LV mass was 0.23 (P= 0.025). The TDI-derived mitral annular velocities Ea and Aa showed moderate heritability (h(2)= 0.36 and 0.53, respectively), whereas the mitral inflow A peak had weak heritability (h(2) = 0.25) and the E peak was not heritable (h(2) = 0.11). We partitioned the total phenotypic correlation when it reached significance, into a genetic and an environmental component. The genetic correlations were 0.61 between the E and Ea peaks and 0.90 between the A and Aa peaks. CONCLUSION: Our study demonstrated moderate heritability for LV mass as well as the mitral annular Ea and Aa peaks. We also found significant genetic correlations between the E and Ea peaks and between the A and Aa peaks. Our current findings support the ongoing research to map and detect genetic variants that contribute to the variation in LV mass and other LV structural and functional phenotypes.

Abnormal Lung Function and Risk for Heart Failure in the Elderly: The Health, Aging, and Body Composition Study

Background: Chronic obstructive pulmonary disease (COPD) has been associated with increased risk for heart failure (HF). The impact of subclinical abnormal spirometric findings on HF risk among older adults without history of COPD is not well elucidated. Methods: We evaluated 2125 participants (age 73.6±2.9 years; 50.5% men; 62.3% white; 45.6/9.4% past/current smokers; body mass index [BMI] 27.2±4.6 kg/m2) without prevalent COPD or HF who underwent baseline spirometry in the Health ABC Study. Abnormal lung function was defined either as forced vital capacity (FVC) below lower limit of normal (LLN) or forced expiratory volume in 1st sec (FEV1) to FVC ratio below LLN. Results: On follow-up (median, 9.4 years), 68 of 350 (19.4%) participants with abnormal lung function developed HF, as compared to 172 of 1775 (9.7%) participants with normal lung function (hazard ratio [HR], 2.31; 95% confidence interval [CI], 1.74 -3.06; P<.001). This increased risk persisted after adjusting for all other independent predictors of HF in the Health ABC Study, BMI, incident coronary events, and several inflammatory markers (HR, 1.82; 95% CI, 1.30 -2.54; P<.001), and remained constant over time. Baseline FVC and FEV1 had a linear association with HF risk (Figure). In adjusted models, HF risk increased by 21% (95% CI, 10 -36%) per 10% decrease in FVC and 18% (95% CI, 10 -28%) per 10% decrease in FEV1 (both P<.001); this association persisted among participants with normal lung function at baseline. Findings were consistent across sex, race, and smoking status. Conclusions: Subclinical abnormal spirometric findings are prevalent among older adults and are independently associated with risk for incident HF.

Protection of pancreatic beta-cells by high density lipoproteins

SUMMARYThe incidence of type 2 diabetes (T2D) is increasing worldwide and is linked to the enhancement of obesity. The principal cause of T2D development is insulin resistance, which lead to the increase of insulin production by the pancreatic beta-cells. In a pathological environment, namely dyslipidaemia, hyperglycaemia and inflammation, beta-cell compensation will fail in more vulnerable cells and diabetes will occur. High Density Lipoproteins (HDLs), commonly named "good cholesterol" are known to be atheroprotective. Low levels of HDLs are associated with increased prevalence of cardiovascular disease but are also an independent risk factor for the development of T2D. HDLs were demonstrated to protect pancreatic beta-cells against several stresses. However the molecular mechanisms of the protection are unknown and the objectives of this work were to try to elucidate the way how HDLs protect. The first approach was a broad screening of genes regulated by the stress and HDLs. A microarray analysis was performed on beta-cells stressed by serum deprivation and rescued by HDLs. Among the genes regulated, we focused on 4E-BP1, a cap-dependent translational inhibitor. In addition, HDLs were also found to protect against several other stresses.Endoplasmic reticulum (ER) stress is a mechanism that may play a role in the onset of T2D. The unfolded protein response (UPR) is a physiological process that aims at maintaining ER homeostasis in conditions where the protein folding and secretion is perturbed. Specific signalling pathways are involved in the increase of folding, export and degradation capacity of the ER. However, in case where the stress is prolonged, this mechanism turns to be pathological, by inducing cell death effector pathways, leading to beta-cell apoptosis. In our study, we discovered that HDLs were protective against ER stress induced by drugs and physiological stresses such as saturated free fatty acids. HDLs protected beta-cells by promoting ER homeostasis via the improvement of the folding and trafficking od proteins from the ER to the Golgi apparatus.Altogether our results suggest that HDLs are important for beta-cell function and survival, by protecting them from several stresses and acting on ER homeostasis. This suggests that attempt in keeping normal HDLs levels or function in patients is crucial to lessen the development of T2D.RÉSUMÉL'incidence du diabète de type 2 est en constante augmentation et est fortement liée à l'accroissement du taux d'obésité. La cause principale du diabète de type 2 est la résistance à l'insuline, qui entraîne une surproduction d'insuline par les cellules bêta pancréatiques. Dans un environnement pathologique associé à l'obésité (dyslipidémie, hyperglycémie et inflammation), les cellules bêta les plus vulnérables ne sont plus capables de compenser en augmentant leur production d'insuline, dysfonctionnent, ce qui conduit à leur mort par apoptose. Les lipoprotéines de hautes densités (HDLs), communément appelées (( bon cholestérol », sont connues pour leurs propriétés protectrices contre l'athérosclérose. Des niveaux bas de HDLs sanguins sont associés au risque de développer un diabète de type 2. Les HDLs ont également montré des propriétés protectrices contre divers stresses dans la cellule bêta. Cependant, les mécanismes de protection restent encore inconnus et l'objectif de ce travail a été d'investiguer les mécanismes moléculaires de protection des HDLs. La première approche choisie a été une étude du profil d'expression génique par puce à ADN afin d'identifier les gènes régulés par le stress et les HDLs. Parmi les gènes régulés, notre intérêt s'est porté sur 4E-BP1, un inhibiteur de la traduction coiffe- dépendante, dont l'induction par le stress était corrélée avec une augmentation de l'apoptose. Suite à cette étude, les HDLs ont également montrés un rôle protecteur contre d'autres stresses. Il s'agit particulièrement du stress du réticulum endoplasmique (RE), qui est un mécanisme qui semble jouer un rôle clé dans le développement du diabète. L'UPR (« Unfolded Protein Response ») est un processus physiologique tendant à maintenir l'homéostasie du réticulum endoplasmique, organelle prépondérante pour la fonction des cellules sécrétrices, notamment lorsqu'elle est soumise à des conditions extrêmes telles que des perturbations de la conformation tertiaire des protéines ou de la sécrétion. Dans ces cas, des voies de signalisation moléculaires sont activées, ce qui mène à l'exportation des protéines mal repliées, à leur dégradation et à l'augmentation de l'expression de chaperonnes capables d'améliorer le repliement des protéines mal formées. Toutefois, en cas de stress persistant, ce mécanisme de protection s'avère être pathologique. En induisant des voies de signalisation effectrices de l'apoptose, il conduit finalement au développement du diabète. Dans cette étude, nous avons démontré que les HDLs étaient capables de protéger la cellule bêta contre le stress du RE induits par des inhibiteurs (thapsigargine, tunicamycine) ou des stresses physiologiques tels que les acides gras libres. Les HDLs ont la capacité d'améliorer l'homéostasie du RE, notamment en favorisant le repliement et le transfert des protéines du RE à l'appareil de Golgi.En résumé, ces données suggèrent que les HDLs sont bénéfiques pour la survie des cellules bêta soumises à des stresses impliqués dans le développement du diabète, notamment en restaurant l'homéostasie du RE. Ces résultats conduisent à soutenir que le maintien des taux de cholestérol joue un rôle important dans la limitation de l'incidence du diabète.

Phenotype and function of protective T cell immune responses in HIV.

PURPOSE OF REVIEW: Definition of T cell immune correlates in HIV infection remains a lofty goal towards our understanding of the HIV-specific immune response. This review will focus upon recent developments and controversies in our understanding of protective T cell responses against HIV. RECENT FINDINGS: It has become clear that multiple functions and phenotypic markers of T cells must be assessed to accurately characterize the complexity of CD4 and CD8 T cell responses. While evidence indicates that a hallmark of protective immune responses in HIV infection is the presence of 'polyfunctional' T cell responses, a disconnect remains between the function and phenotype of effective HIV-specific T cells. Moreover, there may be inherent differences in the ability of specific human leukocyte antigen class I families to promote CD8 T cell effector versus polyfunctional responses. It remains to be determined how polyfunctional responses arise in HIV infection, which functions are important for control, and whether surface phenotype markers provide an indication of protective capacity. SUMMARY: Polyfunctional and phenotypic assessment of T cell responses have clearly advanced our understanding of HIV specific immune responses. Critical questions remain, however, especially whether polyfunctional T cell responses control, or are controlled by, HIV replication.

Intrinsically photosensitive retinal ganglion cells: classification, function and clinical implications.

PURPOSE OF REVIEW: The discovery of a new class of intrinsically photosensitive retinal ganglion cells (ipRGCs) revealed their superior role for various nonvisual biological functions, including the pupil light reflex, and circadian photoentrainment. RECENT FINDINGS: Recent works have identified and characterized several anatomically and functionally distinct ipRGC subtypes and have added strong new evidence for the accessory role of ipRGCs in the visual system in humans. SUMMARY: This review summarizes current concepts related to ipRGC morphology, central connections and behavioural functions and highlights recent studies having clinical relevance to ipRGCs. Clinical implications of the melanopsin system are widespread, particularly as related to chronobiology.

Characterization of PHO1 and PHO1;H1 gene function in Arabidopsis thaliana

Summary Phosphorus is one of the major macronutrients required for plant growth and development. Plant roots acquire phosphorus as inorganic phosphate (Pi), which is further distributed to the shoot, via the transpiration stream and root pressure, where Pi is imported again into cells. PHO1 in Arabidopsis has been identified as a protein involved in the loading of Pi into the root xylem. PHO1 does not have any homology to described Pi transporters including the Pht1 family of H+/ Pi cotransporters. PHO1 bears two domains, SPX and EXS domains, previously identified in Saccharomyces cerevisiae proteins involved in Pi transport and/or sensing, or in sorting proteins to endomembranes. Phylogenetic analysis of the PHO1 gene family revealed the presence of three clusters, with PHO1 and PHO1;H1 forming one cluster. The biological significance behind this cluster was demonstrated by the complementation of the pho1 mutant with only PHO1 and PHO1;H1, of all the PHO1 family members, when expressed under the PHO1 promoter. PHO1 has been shown to be expressed mostly in the root vascular cylinder and at low level in the shoot. PHO1;H1 had a different expression pattern, being expressed in both root and shoot vascular cylinder to the same level, with the levels in leaves increasing with the leaf maturity, suggesting additional role of PHO1;H1 in the Pi mobilization in leaves. In order to further explore the role of PHO1, Pi dynamics was studied on plants expressing PHO1 at different levels compared to the wild type: PHO1 overexpressors, PHO1 underexpressors and the pho1 mutant. Overexpression of the PHO1 protein in the shoot vascular tissue was shown to lead to increased Pi efflux out of the leaf cells and Pi accumulation in the shoot xylem apoplast compared to wild type, confirming the hypothesized role of PHO1 in xylem loading with Pi. The overexpression of PHO1 in the shoot was responsible far both changed Pi dynamic and stunted growth of PHO1 overexpressors, as shown by grafting experiments between wild type and PHO1 overexpressor. We found a ca. 2 fold decrease of shoot phosphorus and a 5-10 fold decrease in vacuolar Pi content in the PHO1 underexpressors and the pho1 null mutant compared to wild type, consistent with the role of PHO1 in the transfer of Pi from the root to the shoot. Shoot Pi deficiency results in a poor growth of the pho1 mutant. Grafting experiments between pho1 and wild type confirmed that both Pi deficiency and stunt growth of the pho1 mutant were dependent on the pho1 root, further supporting the importance of PHO1 in the root xylem loading with Pi. The pho1 mutant and the PHO1 underexpressors accumulated 8-15 fold more Pi in the root relative to wild type. In contrast to the pho1 mutant, the growth of PHO1 underexpressors was not impaired by the low shoat Pi content. This finding suggests that either PHO1 protein or root Pi concentration is important in Pi signaling and development of Pi deficiency symptoms leading to reduced growth. Résumé Le phosphore est l'un des nutriments essentiels à la croissance et au développement des plantes. Les racines absorbent le phosphore sous forme de phosphate inorganique (Pi) qui est dirigé, par la transpiration et la pression de la racine, vers les feuilles où le phosphate est acquis par les cellules. La protéine PHO1 a été démontrée indispensable au chargement du Pi dans le xylème des racines d'Arabidopsis. PHO1 ne démontre pas d'homologie aux transporteurs de Pi connus, incluant la famille Pht1 de cotransporteurs H+/Pi qui ont comme fonction le transport du phosphate à l'intérieur de la cellule. PHO1 contient deux domaines, SPX et EXS, aussi présents dans des protéines de Saccharomyces cerevisiae impliquées dans le transport ou la perception du phosphate, ou dans la localisation des protéines vers différentes membranes. Le génome d'Arabidopsis contient onze gènes homologues à PHO1. Neuf de ces homologues sont répartis en trois groupes. PHO1 et PHO1;H1 forment un de ces groupes. Nos travaux ont démontré que seuls PHO1;H1 et PHO1, sous contrôle du promoteur PHO1, peuvent complémenter le mutant pho1. PHO1 est exprimé principalement dans le cylindre vasculaire de la racine et faiblement dans la partie aérienne. Le degré d'expression de PHO1;H1 est similaire dans le cylindre vasculaire de la racine et des feuilles. Ceci suggère que PHO1;H1 est aussi impliqué dans la mobilisation du Pi dans les feuilles, en plus de son rôle dans le transfert du Pi dans le xylème des racines. Afin de mieux explorer le rôle de PHO1, la dynamique du phosphate a été observée dans trois lignées de plantes transgéniques: un sur-expresseur de PHO1, un sous-expresseur de PHO1 et le mutant pho1. La sur-expression de PHO1 dans le tissue vasculaire des feuilles a provoqué l'efflux du Pi vers l'espace apoplastic du xylème, ce qui confirme le rôle de PHO1 dans le chargement du Pi dans le xylème. La sur-expressìon de PHO1 dans la rosette est responsable d'un changement de la dynamique du Pi et de la diminution de la croissance, ce qui fut démontré par une expérience de greffe de la rosette du sur-expresseur de PHO1 sur les racines du sauvage. On a observé pour le sous-expresseur de PHO1 et le mutant pho1 une diminution du phosphore d'environ 2 fais au niveau des feuilles, et une diminution de 5-10 fois du Pi dans les vacuoles des feuilles, par rapport au sauvage. Ceci confirme le rôle proposé de PHO1 dans le transfert du Pi des racines aux feuilles. La carence de Pi chez pho1 implique une diminution de la taille de la rosette. Pour expliquer ce phénotype une autre expérience de greffe démontra que la cause de ce changement provenait des racines. Ceci renforce l'hypothèse de l'importance du rôle de PHO1 dans le xylème de la racine pour le chargement du Pi. Le mutant phot et le sous-expresseur de PHO1 accumulent 8-15 fois plus de Pi dans leurs racines comparé au sauvage. Cependant, contrairement au phot mutant, le sous-expresseur de PHO1 avait une croissance comparable au sauvage malgré le niveau bas du Pi dans les feuilles. Ceci suggère que la taille de la rosette lors d'une carence en Pi chez Arabidopsis serait la conséquence d'un changement de concentration de Pi dans les racines ou d'une influence de la protéine PHO1.

Between Equity and Differentiation: An Analytical Schema of the Social Function of Education

The educational sphere has an internal function relatively agreed by social scientists. Nonetheless, the contribution that educational systems provide to the society (i.e., their social function) does not have the same degree of consensus. Taking into consideration such theoretical precedent, the current article raises an analytical schema to grasp the social function of education considering a sociological perspective. Starting from the assumption that there is an intrinsic relationship between the internal and social functions of social systems, we suggest there are particular stratification determinants modifying the internal pedagogical function of education, which impact on its social function by creating simultaneous conditions of equity and differentiation. Throughout the paper this social function is considered a paradoxical mechanism. We highlight how this paradoxical dynamic is deployed in different structural levels of the educational sphere. Additionally, we discuss eventual consequences of this paradoxical social function for the inclusion possibilities that educational systems offer to individuals.

Angiotensin-converting enzyme inhibition improves vascular function in rheumatoid arthritis.

BACKGROUND: The excess in cardiovascular risk in patients with rheumatoid arthritis provides a strong rationale for early therapeutical interventions. In view of the similarities between atherosclerosis and rheumatoid arthritis and the proven benefit of angiotensin-converting enzyme inhibitors in atherosclerotic vascular disease, it was the aim of the present study to delineate the impact of ramipril on endothelial function as well as on markers of inflammation and oxidative stress in patients with rheumatoid arthritis. METHODS AND RESULTS: Eleven patients with rheumatoid arthritis were included in this randomized, double-blind, crossover study to receive ramipril in an uptitration design (2.5 to 10 mg) for 8 weeks followed by placebo, or vice versa, on top of standard antiinflammatory therapy. Endothelial function assessed by flow-mediated dilation of the brachial artery, markers of inflammation and oxidative stress, and disease activity were investigated at baseline and after each treatment period. Endothelial function assessed by flow-mediated dilation increased from 2.85+/-1.49% to 4.00+/-1.81% (P=0.017) after 8 weeks of therapy with ramipril but did not change with placebo (from 2.85+/-1.49% to 2.84+/-2.47%; P=0.88). Although systolic blood pressure and heart rate remained unaltered, diastolic blood pressure decreased slightly from 78+/-7 to 74+/-6 mm Hg (P=0.03). Tumor necrosis factor-alpha showed a significant inverse correlation with flow-mediated dilation (r=-0.408, P=0.02), and CD40 significantly decreased after ramipril therapy (P=0.049). CONCLUSIONS: Angiotensin-converting enzyme inhibition with 10 mg/d ramipril for 8 weeks on top of current antiinflammatory treatment markedly improved endothelial function in patients with rheumatoid arthritis. This finding suggests that angiotensin-converting enzyme inhibition may provide a novel strategy to prevent cardiovascular events in these patients.

Spin and density longitudinal response of quantum dots in the time-dependent local-spin-density approximation

The longitudinal dipole response of a quantum dot has been calculated in the far-infrared regime using local-spin-density-functional theory. We have studied the coupling between the collective spin and density modes as a function of the magnetic field. We have found that the spin dipole mode and single-particle excitations have a sizable overlap, and that the magnetoplasmon modes can be excited by the dipole spin operator if the dot is spin polarized. The frequency of the dipole spin edge mode presents an oscillation which is clearly filling factor (v) related. We have found that the spin dipole mode is especially soft for even-n values. Results for selected numbers of electrons and confining potentials are discussed.

Density-functional calculations of magnetoplasmons in quantum rings

We have studied the structure and dipole charge-density response of nanorings as a function of the magnetic field using local-spin-density-functional theory. Two small rings consisting of 12 and 22 electrons confined by a positively charged background are used to represent the cases of narrow and wide rings. The results are qualitatively compared with experimental data existing on microrings and on antidots. A smaller ring containing five electrons is also analyzed to allow for a closer comparison with a recent experiment on a two-electron quantum ring.

Vertically coupled quantum dots in the local spin-density functional theory

We have investigated the structure of double quantum dots vertically coupled at zero magnetic field within local-spin-density functional theory. The dots are identical and have a finite width, and the whole system is axially symmetric. We first discuss the effect of thickness on the addition spectrum of one single dot. Next we describe the structure of coupled dots as a function of the interdot distance for different electron numbers. Addition spectra, Hund's rule, and molecular-type configurations are discussed. It is shown that self-interaction corrections to the density-functional results do not play a very important role in the calculated addition spectra

Multipole modes and spin features in the Raman spectrum of nanoscopic quantum rings

We present a systematic study of ground state and spectroscopic properties of many-electron nanoscopic quantum rings. Addition energies at zero magnetic field (B) and electrochemical potentials as a function of B are given for a ring hosting up to 24 electrons. We find discontinuities in the excitation energies of multipole spin and charge density modes, and a coupling between the charge and spin density responses that allow to identify the formation of ferromagnetic ground states in narrow magnetic field regions. These effects can be observed in Raman experiments, and are related to the fractional Aharonov-Bohm oscillations of the energy and of the persistent current in the ring

Method to estimate soil macroporosity and microporosity based on sand content and bulk density

Macroporosity is often used in the determination of soil compaction. Reduced macroporosity can lead to poor drainage, low root aeration and soil degradation. The aim of this study was to develop and test different models to estimate macro and microporosity efficiently, using multiple regression. Ten soils were selected within a large range of textures: sand (Sa) 0.07-0.84; silt 0.03-0.24; clay 0.13-0.78 kg kg-1 and subjected to three compaction levels (three bulk densities, BD). Two models with similar accuracy were selected, with a mean error of about 0.02 m³ m-3 (2 %). The model y = a + b.BD + c.Sa, named model 2, was selected for its simplicity to estimate Macro (Ma), Micro (Mi) or total porosity (TP): Ma = 0.693 - 0.465 BD + 0.212 Sa; Mi = 0.337 + 0.120 BD - 0.294 Sa; TP = 1.030 - 0.345 BD 0.082 Sa; porosity values were expressed in m³ m-3; BD in kg dm-3; and Sa in kg kg-1. The model was tested with 76 datum set of several other authors. An error of about 0.04 m³ m-3 (4 %) was observed. Simulations of variations in BD as a function of Sa are presented for Ma = 0 and Ma = 0.10 (10 %). The macroporosity equation was remodeled to obtain other compaction indexes: a) to simulate maximum bulk density (MBD) as a function of Sa (Equation 11), in agreement with literature data; b) to simulate relative bulk density (RBD) as a function of BD and Sa (Equation 13); c) another model to simulate RBD as a function of Ma and Sa (Equation 16), confirming the independence of this variable in relation to Sa for a fixed value of macroporosity and, also, proving the hypothesis of Hakansson & Lipiec that RBD = 0.87 corresponds approximately to 10 % macroporosity (Ma = 0.10 m³ m-3).