Abstract
Protein degradation by the proteasome is one of the key steps in cell biology and in immune biology. For degradation a mathematical model can be based on a binomial distribution, where the wanted cleavage probabilities are characterized by a minimization problem. The proposed method analyzes the singular values of the Jacobian, thus giving a significant parameter reduction. The computation time is 50 fold reduced compared to the unreduced model, which in practice means hours instead of days for a run. The implementation is based on MATLAB.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alt, W.: Nichtlineare Optimierung. Vieweg, Braunschweig (2002)
Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A. and Sorensen, D.: LAPACK User’s Guide, Third Edition. SIAM, Philadelphia (1999)
Bock, R. K., Krischer, W.: The Data Analysis BriefBook. Springer, New York (1998)
Golub, G. H., van Loan, C. F.: Matrix Computations. The Johns Hopkins University Press, Baltimore London (1996)
Hadeler, K.P., Kuttler, C., Nussbaum, A. K.: Cleaving proteins for the immune system. Mathematical Biosciences, 188, 63–79 (2004)
Higham, D. J.: Nine ways to implement the binomial method for option valuation in MATLAB. SIAM Review, 44, 661–677 (2002)
Kuttler, C., Nussbaum, A. K., Dick, T. P., Rammensee, H.-G., Schild, H., Hadeler, K.-P.: An algorithm for the prediction of proteasomal cleavages. J. Mol. Biol., 298, 417–429 (2000)
MATLAB 6 R13 Documentation: MATLAB functions and Optimization Toolbox, (2003)
Müller, J., Schönfisch, B., Nussbaum, A. K.: Modeling Proteasomal Protein Degradation, Preprint GSF PP02-033 (2002)
Nussbaum, A. K., Dick, T. P., Keilholz, W., Schirle, M., Stevanovic, S., Dietz, K., Heinemeyer, W., Groll, M., Wolf, D. H., Huber, R., Rammensee, H.-G., Schild, H.: Cleavage motifs of the yeast 20S proteasome ß subunits deduced from digests of enolase. Proc. Natl. Acad. Sci. USA, 95, 12504–12509 (1998)
Spellucci, P.: Numerische Verfahren der nichtlinearen Optimierung. Birkhäuser, Berlin (1993)
Tenzer S, Stoltze L, Schönfisch B, Dengjel J, Müller M, Stevanovic S, Rammensee HG, Schild H.: Quantitative analysis of prion-protein degradation by constitutive and immuno-20S proteasomes indicates differences correlated with disease susceptibility. J Immunol., 172(2), 1083–1091 (2004)
Toes, R. E. M., Nussbaum, A. K., Degermann, S., Schirle, M., Emmerich, N., Kraft, M., Laplace, C., Zwinderman, A., Dick, T., Müller, J., Schönfisch, B., Schmid, C., Fehling, H.-J., Stevanovic, S., Rammensee, H.-G., Schild, H.: Discrete cleavage motifs of constitutive and immunoproteasomes revealed by quantitative analysis of cleavage products. J. Exp. Med., 194, 1–12 (2001)
van Loan C. F.: Introduction to scientific computing. MATLAB Curriculum Series, New Jersey (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Stolte, T., Rentrop, P. (2008). A Singular Value Based Probability Algorithm for Protein Cleavage. In: Breitner, M.H., Denk, G., Rentrop, P. (eds) From Nano to Space. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74238-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-74238-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74237-1
Online ISBN: 978-3-540-74238-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)