Analysis of autophagy gene polymorphisms in Spanish patients with head and neck squamous cell carcinoma

Head and neck squamous cell carcinoma (HNSCC) is the sixth cancer on incidence worldwide. Tobacco and alcohol consumption are the most classical risk factors associated with its development. Autophagy process has a dual effect both in tumourigenesis and tumour suppressing activity. To investigate the importance of this pathway in HNSCC susceptibility, a risk factor matched case-control association study was performed with four candidate polymorphisms in autophagy genes (ATG2B, ATG5, ATG10, ATG16L1). We found an association between the variant in ATG10 rs1864183 and a higher susceptibility to develop laryngeal cancer, ATG2B rs3759601 and pharyngeal cancer and ATG16L1 rs2241880 and oral carcinoma. ATG5 rs2245214 SNP was not associated with any location. Overall, our results indicate the importance of the autophagy pathway in the susceptibility of head and neck squamous cell carcinoma and demonstrate the heterogeneity between its locations encompassed under a single terminology

Genetic Susceptibility in Head and Neck Squamous Cell Carcinoma in a Spanish Population

Despite classical environmental risk factors like tobacco, alcohol or viral infection, not all individuals develop head and neck cancer. Therefore, identification of the genetic susceptibility produced by single nucleotide polymorphisms (SNPs) is an important task. A total of 296 human papillomavirus negative head and neck cancer (HNC) patients (126 laryngeal, 100 pharyngeal and 70 oral cavity) were included in the study, involving 29 candidate SNPs in genes within important carcinogenic pathways (oncogenesis and tumour suppression, DNA repair, inflammation, oxidation and apoptosis). Genotyping was performed using TaqMan probes or restriction fragment length assays in peripheral blood DNA. In addition, 259 paired controls were also evaluated with the same risk factors for each specific location. Nine SNPs in DNA repair (ERCC1 rs11615, ERCC2 rs13181), inflammatory (IL2 rs2069762, IL6 rs1800795), oxidative (NFE2L2 rs13035806 and rs2706110) and apoptotic genes (TP53 rs1042522, MDM2 rs2279744, BCL2 rs2279115) were differently associated with HNSCC susceptibility by location. Some of these SNPs were not described before in this tumour type. In conclusion, we describe several SNPs associated with HNC in a Spanish population

Characterization of protons accelerated from a 3 TW table-top laser system

[EN] We report on benchmark tests of a 3 TW/50 fs, table-top laser system specifically developed for proton acceleration with an intrinsic pump rate up to 100 Hz. In two series of single-shot measurements differing in pulse energy and contrast the successful operation of the diode pumped laser is demonstrated. Protons have been accelerated up to 1.6 MeV in interactions of laser pulses focused on aluminium and mylar foils between 0.8 and 25 mu m thickness. Their spectral distributions and maximum energies are consistent with former experiments under similar conditions. These results show the suitability of our system and provide a reference for studies of laser targets at high repetition rate and possible applications.This project has been funded by Centro para el Desarrollo Tecnologico Industrial (CDTI, Spain) within the INNPRONTA program, grant no. IPT-20111027, by EUROSTARS project E9113, and by the Spanish Ministry for Economy and Competitiveness within the Retos-Colaboracion 2015 initiative, ref. RTC-2015-3278-1.Bellido-Millán, PJ.; Lera, R.; Seimetz, M.; Ruiz-De La Cruz, A.; Torres Peiró, S.; Galán, M.; Mur, P.... (2017). Characterization of protons accelerated from a 3 TW table-top laser system. Journal of Instrumentation. 12:1-12. https://doi.org/10.1088/1748-0221/12/05/T05001S11212Daido, H., Nishiuchi, M., & Pirozhkov, A. S. (2012). Review of laser-driven ion sources and their applications. Reports on Progress in Physics, 75(5), 056401. doi:10.1088/0034-4885/75/5/056401Macchi, A., Borghesi, M., & Passoni, M. (2013). Ion acceleration by superintense laser-plasma interaction. Reviews of Modern Physics, 85(2), 751-793. doi:10.1103/revmodphys.85.751Ledingham, K., Bolton, P., Shikazono, N., & Ma, C.-M. (2014). Towards Laser Driven Hadron Cancer Radiotherapy: A Review of Progress. Applied Sciences, 4(3), 402-443. doi:10.3390/app4030402Kraft, S. D., Richter, C., Zeil, K., Baumann, M., Beyreuther, E., Bock, S., … Pawelke, J. (2010). Dose-dependent biological damage of tumour cells by laser-accelerated proton beams. New Journal of Physics, 12(8), 085003. doi:10.1088/1367-2630/12/8/085003Yogo, A., Sato, K., Nishikino, M., Mori, M., Teshima, T., Numasaki, H., … Daido, H. (2009). Application of laser-accelerated protons to the demonstration of DNA double-strand breaks in human cancer cells. Applied Physics Letters, 94(18), 181502. doi:10.1063/1.3126452Fritzler, S., Malka, V., Grillon, G., Rousseau, J. P., Burgy, F., Lefebvre, E., … Ledingham, K. W. D. (2003). Proton beams generated with high-intensity lasers: Applications to medical isotope production. Applied Physics Letters, 83(15), 3039-3041. doi:10.1063/1.1616661Kishimura, H., Morishita, H., Okano, Y. H., Okano, Y., Hironaka, Y., Kondo, K., … Nemoto, K. (2004). Enhanced generation of fast protons from a polymer-coated metal foil by a femtosecond intense laser field. Applied Physics Letters, 85(14), 2736-2738. doi:10.1063/1.1803915Nakamura, S., Iwashita, Y., Noda, A., Shirai, T., Tongu, H., Fukumi, A., … Wada, Y. (2006). Real-Time Optimization of Proton Production by Intense Short-Pulse Laser with Time-of-Flight Measurement. Japanese Journal of Applied Physics, 45(No. 34), L913-L916. doi:10.1143/jjap.45.l913Nishiuchi, M., Fukumi, A., Daido, H., Li, Z., Sagisaka, A., Ogura, K., … Nakamura, S. (2006). The laser proton acceleration in the strong charge separation regime. Physics Letters A, 357(4-5), 339-344. doi:10.1016/j.physleta.2006.04.053Yogo, A., Daido, H., Fukumi, A., Li, Z., Ogura, K., Sagisaka, A., … Itoh, A. (2007). Laser prepulse dependency of proton-energy distributions in ultraintense laser-foil interactions with an online time-of-flight technique. Physics of Plasmas, 14(4), 043104. doi:10.1063/1.2721066Robinson, A. P. L., Foster, P., Adams, D., Carroll, D. C., Dromey, B., Hawkes, S., … Neely, D. (2009). Spectral modification of laser-accelerated proton beams by self-generated magnetic fields. New Journal of Physics, 11(8), 083018. doi:10.1088/1367-2630/11/8/083018Nemoto, K., Maksimchuk, A., Banerjee, S., Flippo, K., Mourou, G., Umstadter, D., & Bychenkov, V. Y. (2001). Laser-triggered ion acceleration and table top isotope production. Applied Physics Letters, 78(5), 595-597. doi:10.1063/1.1343845Lee, K., Park, S. H., Cha, Y.-H., Lee, J. Y., Lee, Y. W., Yea, K.-H., & Jeong, Y. U. (2008). Generation of intense proton beams from plastic targets irradiated by an ultraintense laser pulse. Physical Review E, 78(5). doi:10.1103/physreve.78.056403Yogo, A., Daido, H., Bulanov, S. V., Nemoto, K., Oishi, Y., Nayuki, T., … Tajima, T. (2008). Laser ion acceleration via control of the near-critical density target. Physical Review E, 77(1). doi:10.1103/physreve.77.016401Lee, K., Lee, J. Y., Park, S. H., Cha, Y.-H., Lee, Y. W., Kim, K. N., & Jeong, Y. U. (2011). Dominant front-side acceleration of energetic proton beams from plastic targets irradiated by an ultraintense laser pulse. Physics of Plasmas, 18(1), 013101. doi:10.1063/1.3496058OKIHARA, S., SENTOKU, Y., SUEDA, K., SHIMIZU, S., SATO, F., MIYANAGA, N., … SAKABE, S. (2002). Energetic Proton Generation in a Thin Plastic Foil Irradiated by Intense Femtosecond Lasers. Journal of Nuclear Science and Technology, 39(1), 1-5. doi:10.1080/18811248.2002.9715150McKenna, P., Ledingham, K. W. D., Spencer, I., McCany, T., Singhal, R. P., Ziener, C., … Clark, E. L. (2002). Characterization of multiterawatt laser-solid interactions for proton acceleration. Review of Scientific Instruments, 73(12), 4176-4184. doi:10.1063/1.1516855Spencer, I., Ledingham, K. W. D., McKenna, P., McCanny, T., Singhal, R. P., Foster, P. S., … Davies, J. R. (2003). Experimental study of proton emission from 60-fs, 200-mJ high-repetition-rate tabletop-laser pulses interacting with solid targets. Physical Review E, 67(4). doi:10.1103/physreve.67.046402Kaluza, M., Schreiber, J., Santala, M. I. K., Tsakiris, G. D., Eidmann, K., Meyer-ter-Vehn, J., & Witte, K. J. (2004). Influence of the Laser Prepulse on Proton Acceleration in Thin-Foil Experiments. Physical Review Letters, 93(4). doi:10.1103/physrevlett.93.045003Ceccotti, T., Lévy, A., Popescu, H., Réau, F., D’Oliveira, P., Monot, P., … Martin, P. (2007). Proton Acceleration with High-Intensity Ultrahigh-Contrast Laser Pulses. Physical Review Letters, 99(18). doi:10.1103/physrevlett.99.185002Neely, D., Foster, P., Robinson, A., Lindau, F., Lundh, O., Persson, A., … McKenna, P. (2006). Enhanced proton beams from ultrathin targets driven by high contrast laser pulses. Applied Physics Letters, 89(2), 021502. doi:10.1063/1.2220011Steinke, S., Henig, A., Schnürer, M., Sokollik, T., Nickles, P. V., Jung, D., … Habs, D. (2010). Efficient ion acceleration by collective laser-driven electron dynamics with ultra-thin foil targets. Laser and Particle Beams, 28(1), 215-221. doi:10.1017/s0263034610000157Strickland, D., & Mourou, G. (1985). Compression of amplified chirped optical pulses. Optics Communications, 56(3), 219-221. doi:10.1016/0030-4018(85)90120-8Yogo, A., Kondo, K., Mori, M., Kiriyama, H., Ogura, K., Shimomura, T., … Bolton, P. R. (2014). Insertable pulse cleaning module with a saturable absorber pair and a compensating amplifier for high-intensity ultrashort-pulse lasers. Optics Express, 22(2), 2060. doi:10.1364/oe.22.002060Trisorio, A., Grabielle, S., Divall, M., Forget, N., & Hauri, C. P. (2012). Self-referenced spectral interferometry for ultrashort infrared pulse characterization. Optics Letters, 37(14), 2892. doi:10.1364/ol.37.002892Seimetz, M., Bellido, P., Soriano, A., Garcia Lopez, J., Jimenez-Ramos, M. C., Fernandez, B., … Benlloch, J. M. (2015). Calibration and Performance Tests of Detectors for Laser-Accelerated Protons. IEEE Transactions on Nuclear Science, 62(6), 3216-3224. doi:10.1109/tns.2015.2480682Nürnberg, F., Schollmeier, M., Brambrink, E., Blažević, A., Carroll, D. C., Flippo, K., … Roth, M. (2009). Radiochromic film imaging spectroscopy of laser-accelerated proton beams. Review of Scientific Instruments, 80(3), 033301. doi:10.1063/1.3086424Oishi, Y., Nayuki, T., Fujii, T., Takizawa, Y., Wang, X., Yamazaki, T., … Andreev, A. A. (2005). Dependence on laser intensity and pulse duration in proton acceleration by irradiation of ultrashort laser pulses on a Cu foil target. Physics of Plasmas, 12(7), 073102. doi:10.1063/1.1943436Nishiuchi, M., Daito, I., Ikegami, M., Daido, H., Mori, M., Orimo, S., … Yoshiyuki, T. (2009). Focusing and spectral enhancement of a repetition-rated, laser-driven, divergent multi-MeV proton beam using permanent quadrupole magnets. Applied Physics Letters, 94(6), 061107. doi:10.1063/1.3078291Antici, P., Fuchs, J., d’ Humières, E., Lefebvre, E., Borghesi, M., Brambrink, E., … Pépin, H. (2007). Energetic protons generated by ultrahigh contrast laser pulses interacting with ultrathin targets. Physics of Plasmas, 14(3), 030701. doi:10.1063/1.2480610Green, J. S., Carroll, D. C., Brenner, C., Dromey, B., Foster, P. S., Kar, S., … Zepf, M. (2010). Enhanced proton flux in the MeV range by defocused laser irradiation. New Journal of Physics, 12(8), 085012. doi:10.1088/1367-2630/12/8/085012Zeil, K., Kraft, S. D., Bock, S., Bussmann, M., Cowan, T. E., Kluge, T., … Schramm, U. (2010). The scaling of proton energies in ultrashort pulse laser plasma acceleration. New Journal of Physics, 12(4), 045015. doi:10.1088/1367-2630/12/4/045015Nishiuchi, M., Daido, H., Yogo, A., Orimo, S., Ogura, K., Ma, J., … Azuma, H. (2008). Efficient production of a collimated MeV proton beam from a polyimide target driven by an intense femtosecond laser pulse. Physics of Plasmas, 15(5), 053104. doi:10.1063/1.2928161Macchi, A., Sgattoni, A., Sinigardi, S., Borghesi, M., & Passoni, M. (2013). Advanced strategies for ion acceleration using high-power lasers. Plasma Physics and Controlled Fusion, 55(12), 124020. doi:10.1088/0741-3335/55/12/124020Fuchs, J., Antici, P., d’ Humières, E., Lefebvre, E., Borghesi, M., Brambrink, E., … Audebert, P. (2005). Laser-driven proton scaling laws and new paths towards energy increase. Nature Physics, 2(1), 48-54. doi:10.1038/nphys199Schwoerer, H., Pfotenhauer, S., Jäckel, O., Amthor, K.-U., Liesfeld, B., Ziegler, W., … Esirkepov, T. (2006). Laser-plasma acceleration of quasi-monoenergetic protons from microstructured targets. Nature, 439(7075), 445-448. doi:10.1038/nature04492Margarone, D., Klimo, O., Kim, I. J., Prokůpek, J., Limpouch, J., Jeong, T. M., … Korn, G. (2012). Laser-Driven Proton Acceleration Enhancement by Nanostructured Foils. Physical Review Letters, 109(23). doi:10.1103/physrevlett.109.234801Flippo, K. A., d’ Humières, E., Gaillard, S. A., Rassuchine, J., Gautier, D. C., Schollmeier, M., … Hegelich, B. M. (2008). Increased efficiency of short-pulse laser-generated proton beams from novel flat-top cone targets. Physics of Plasmas, 15(5), 056709. doi:10.1063/1.291812

The prion-like RNA-processing protein HNRPDL forms inherently toxic amyloid-like inclusion bodies in bacteria

BACKGROUND: The formation of protein inclusions is connected to the onset of many human diseases. Human RNA binding proteins containing intrinsically disordered regions with an amino acid composition resembling those of yeast prion domains, like TDP-43 or FUS, are being found to aggregate in different neurodegenerative disorders. The structure of the intracellular inclusions formed by these proteins is still unclear and whether these deposits have an amyloid nature or not is a matter of debate. Recently, the aggregation of TDP-43 has been modelled in bacteria, showing that TDP-43 inclusion bodies (IBs) are amorphous but intrinsically neurotoxic. This observation raises the question of whether it is indeed the lack of an ordered structure in these human prion-like protein aggregates the underlying cause of their toxicity in different pathological states. RESULTS: Here we characterize the IBs formed by the human prion-like RNA-processing protein HNRPDL. HNRPDL is linked to the development of limb-girdle muscular dystrophy 1G and shares domain architecture with TDP-43. We show that HNRPDL IBs display characteristic amyloid hallmarks, since these aggregates bind to amyloid dyes in vitro and inside the cell, they are enriched in intermolecular β-sheet conformation and contain inner amyloid-like fibrillar structure. In addition, despite their ordered structure, HNRPDL IBs are highly neurotoxic. CONCLUSIONS: Our results suggest that at least some of the disorders caused by the aggregation of human prion-like proteins would rely on the formation of classical amyloid assemblies rather than being caused by amorphous aggregates. They also illustrate the power of microbial cell factories to model amyloid aggregation. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12934-015-0284-7) contains supplementary material, which is available to authorized users

Effect of viral storm in patients admitted to intensive care units with severe COVID-19 in Spain: a multicentre, prospective, cohort study

Background: The contribution of the virus to the pathogenesis of severe COVID-19 is still unclear. We aimed to evaluate associations between viral RNA load in plasma and host response, complications, and deaths in critically ill patients with COVID-19. Methods: We did a prospective cohort study across 23 hospitals in Spain. We included patients aged 18 years or older with laboratory-confirmed SARS-CoV-2 infection who were admitted to an intensive care unit between March 16, 2020, and Feb 27, 2021. RNA of the SARS-CoV-2 nucleocapsid region 1 (N1) was quantified in plasma samples collected from patients in the first 48 h following admission, using digital PCR. Patients were grouped on the basis of N1 quantity: VIR-N1-Zero ([removed]2747 N1 copies per mL). The primary outcome was all-cause death within 90 days after admission. We evaluated odds ratios (ORs) for the primary outcome between groups using a logistic regression analysis. Findings: 1068 patients met the inclusion criteria, of whom 117 had insufficient plasma samples and 115 had key information missing. 836 patients were included in the analysis, of whom 403 (48%) were in the VIR-N1-Low group, 283 (34%) were in the VIR-N1-Storm group, and 150 (18%) were in the VIR-N1-Zero group. Overall, patients in the VIR-N1-Storm group had the most severe disease: 266 (94%) of 283 patients received invasive mechanical ventilation (IMV), 116 (41%) developed acute kidney injury, 180 (65%) had secondary infections, and 148 (52%) died within 90 days. Patients in the VIR-N1-Zero group had the least severe disease: 81 (54%) of 150 received IMV, 34 (23%) developed acute kidney injury, 47 (32%) had secondary infections, and 26 (17%) died within 90 days (OR for death 0·30, 95% CI 0·16–0·55; p<0·0001, compared with the VIR-N1-Storm group). 106 (26%) of 403 patients in the VIR-N1-Low group died within 90 days (OR for death 0·39, 95% CI 0·26–0·57; p[removed]11 página

Implementación del método del caso en docencia virtual para asignaturas prácticas y teóricas del Grado en Química y del Grado en Ingeniería Química de la Facultad de Ciencias Químicas

Memoria ID-0073. Ayudas de la Universidad de Salamanca para la innovación docente, curso 2014-2015

Role of age and comorbidities in mortality of patients with infective endocarditis

[Purpose]: The aim of this study was to analyse the characteristics of patients with IE in three groups of age and to assess the ability of age and the Charlson Comorbidity Index (CCI) to predict mortality. [Methods]: Prospective cohort study of all patients with IE included in the GAMES Spanish database between 2008 and 2015.Patients were stratified into three age groups:<65 years,65 to 80 years,and ≥ 80 years.The area under the receiver-operating characteristic (AUROC) curve was calculated to quantify the diagnostic accuracy of the CCI to predict mortality risk. [Results]: A total of 3120 patients with IE (1327 < 65 years;1291 65-80 years;502 ≥ 80 years) were enrolled.Fever and heart failure were the most common presentations of IE, with no differences among age groups.Patients ≥80 years who underwent surgery were significantly lower compared with other age groups (14.3%,65 years; 20.5%,65-79 years; 31.3%,≥80 years). In-hospital mortality was lower in the <65-year group (20.3%,<65 years;30.1%,65-79 years;34.7%,≥80 years;p < 0.001) as well as 1-year mortality (3.2%, <65 years; 5.5%, 65-80 years;7.6%,≥80 years; p = 0.003).Independent predictors of mortality were age ≥ 80 years (hazard ratio [HR]:2.78;95% confidence interval [CI]:2.32–3.34), CCI ≥ 3 (HR:1.62; 95% CI:1.39–1.88),and non-performed surgery (HR:1.64;95% CI:11.16–1.58).When the three age groups were compared,the AUROC curve for CCI was significantly larger for patients aged <65 years(p < 0.001) for both in-hospital and 1-year mortality. [Conclusion]: There were no differences in the clinical presentation of IE between the groups. Age ≥ 80 years, high comorbidity (measured by CCI),and non-performance of surgery were independent predictors of mortality in patients with IE.CCI could help to identify those patients with IE and surgical indication who present a lower risk of in-hospital and 1-year mortality after surgery, especially in the <65-year group

The evolution of the ventilatory ratio is a prognostic factor in mechanically ventilated COVID-19 ARDS patients

Background: Mortality due to COVID-19 is high, especially in patients requiring mechanical ventilation. The purpose of the study is to investigate associations between mortality and variables measured during the first three days of mechanical ventilation in patients with COVID-19 intubated at ICU admission. Methods: Multicenter, observational, cohort study includes consecutive patients with COVID-19 admitted to 44 Spanish ICUs between February 25 and July 31, 2020, who required intubation at ICU admission and mechanical ventilation for more than three days. We collected demographic and clinical data prior to admission; information about clinical evolution at days 1 and 3 of mechanical ventilation; and outcomes. Results: Of the 2,095 patients with COVID-19 admitted to the ICU, 1,118 (53.3%) were intubated at day 1 and remained under mechanical ventilation at day three. From days 1 to 3, PaO2/FiO2 increased from 115.6 [80.0-171.2] to 180.0 [135.4-227.9] mmHg and the ventilatory ratio from 1.73 [1.33-2.25] to 1.96 [1.61-2.40]. In-hospital mortality was 38.7%. A higher increase between ICU admission and day 3 in the ventilatory ratio (OR 1.04 [CI 1.01-1.07], p = 0.030) and creatinine levels (OR 1.05 [CI 1.01-1.09], p = 0.005) and a lower increase in platelet counts (OR 0.96 [CI 0.93-1.00], p = 0.037) were independently associated with a higher risk of death. No association between mortality and the PaO2/FiO2 variation was observed (OR 0.99 [CI 0.95 to 1.02], p = 0.47). Conclusions: Higher ventilatory ratio and its increase at day 3 is associated with mortality in patients with COVID-19 receiving mechanical ventilation at ICU admission. No association was found in the PaO2/FiO2 variation

Clonal chromosomal mosaicism and loss of chromosome Y in elderly men increase vulnerability for SARS-CoV-2

The pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, COVID-19) had an estimated overall case fatality ratio of 1.38% (pre-vaccination), being 53% higher in males and increasing exponentially with age. Among 9578 individuals diagnosed with COVID-19 in the SCOURGE study, we found 133 cases (1.42%) with detectable clonal mosaicism for chromosome alterations (mCA) and 226 males (5.08%) with acquired loss of chromosome Y (LOY). Individuals with clonal mosaic events (mCA and/or LOY) showed a 54% increase in the risk of COVID-19 lethality. LOY is associated with transcriptomic biomarkers of immune dysfunction, pro-coagulation activity and cardiovascular risk. Interferon-induced genes involved in the initial immune response to SARS-CoV-2 are also down-regulated in LOY. Thus, mCA and LOY underlie at least part of the sex-biased severity and mortality of COVID-19 in aging patients. Given its potential therapeutic and prognostic relevance, evaluation of clonal mosaicism should be implemented as biomarker of COVID-19 severity in elderly people. Among 9578 individuals diagnosed with COVID-19 in the SCOURGE study, individuals with clonal mosaic events (clonal mosaicism for chromosome alterations and/or loss of chromosome Y) showed an increased risk of COVID-19 lethality

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis