An application of graphical numerical accelerators in simulations of ion-transport through biological membranes
Warsaw University of Life Sciences WULS-SGGW,
Nowoursynowska St. 159, 02-787 Warsaw, Poland
E-mail: adam_gorecki@sggw.pl
Received:
(Received: 27 October 2012; revised: 20 February 2013; accepted: 21 February 2013; published online: 28 February 2013)
DOI: 10.12921/cmst.2013.19.01.33-46
OAI: oai:lib.psnc.pl:427
Abstract:
The modeling of ion-transport through biological membranes is important for understanding many life processes. The transmembrane potential and ion concentrations in the stationary state can be measured in in-vivo experiments. They can also be simulated within membrane models. Here we consider a basic model of ion transport that describes the time evolution of ion concentrations and potentials through a set of nonlinear ordinary differential equations. To reduce the computation time I have developed an application for simulation of the ion-flows through a membrane starting from an ensemble of initial conditions, optimized for a Graphical Processing Unit (GPU). The application has been designed for the CUDA (Compute Unified Device Architecture) technology. It is written in CUDA C programming language and runs on NVIDIA TESLA family of numerical accelerators. The calculation speed can be increased almost 1000 times compared with a sequential program running on the Central Processing Unit (CPU) of a typical PC.
Key words:
biological membranes, CUDA, differential equations integration, electrochemistry, TESLA
References:
[1] L. Stryer, Biochemistry. W. H. Freeman, StateplaceNew York, 1981.
[2] D. C. Gadsby, P. Vergani, L. Csanády, The ABC protein turned chloride channel whose failure causes cystic fibrosis. Nature 7083, 477–83 (2006).
[3] I. Scheffer, S. Berkovic, Generalized epilepsy with febrile seizures plus. A genetic disorder with heterogeneous clinical phenotypes. Brain 120, 479–90 (1997).
[4] S. A. Goldstein, C. Miller, Mechanism of charybdotoxin block of a voltage gated K+ channel. Biophysical Journal 65, 1613–1619 (1993).
[5] S. Candia, M. L. Garcia, R. Latorre, Mode of action of iberiotoxin, a potent blocker of the large conductance Ca(2+)- activated K+ channel.Biophysical Journal 63, 583–590 (1992).
[6] R. Toczylowska-Maminska, K. Dolowy, Ion transporting proteins of human bronchial epithelium. Journal of Cellular Biochemistry 113, 426-432 (2012).
[7] C. V. Falkenberg, E. Jakobsson, A Biophysical Model for Integration of Electrical, Osmotic, and pH Regulation in the Human Bronchial Epithelium. Biophysical Journal 98,1476–1485 (2010).
[8] Y. Sohma, M. A. Gray, Y. Imai, B. E. Argent, HCO3-
Transport in a Mathematical Model of the Pancreatic Ductal Epithelium. Journal of Membrane Biology 176,77–100 (2000).
[9] S. H. Wright, Generation of resting membrane potential.Advances in Physiology Education 28, 139-142 (2004).
[10] NVIDIA corporation, 2012. CUDA C Programming Guide Available from: http://developer.NVIDIA.com/ NVIDIA-gpu-computing-documentation Accesed: Jul 11, 2012
[11] W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, chapter 16.1 in Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, 1993.
The modeling of ion-transport through biological membranes is important for understanding many life processes. The transmembrane potential and ion concentrations in the stationary state can be measured in in-vivo experiments. They can also be simulated within membrane models. Here we consider a basic model of ion transport that describes the time evolution of ion concentrations and potentials through a set of nonlinear ordinary differential equations. To reduce the computation time I have developed an application for simulation of the ion-flows through a membrane starting from an ensemble of initial conditions, optimized for a Graphical Processing Unit (GPU). The application has been designed for the CUDA (Compute Unified Device Architecture) technology. It is written in CUDA C programming language and runs on NVIDIA TESLA family of numerical accelerators. The calculation speed can be increased almost 1000 times compared with a sequential program running on the Central Processing Unit (CPU) of a typical PC.
Key words:
biological membranes, CUDA, differential equations integration, electrochemistry, TESLA
References:
[1] L. Stryer, Biochemistry. W. H. Freeman, StateplaceNew York, 1981.
[2] D. C. Gadsby, P. Vergani, L. Csanády, The ABC protein turned chloride channel whose failure causes cystic fibrosis. Nature 7083, 477–83 (2006).
[3] I. Scheffer, S. Berkovic, Generalized epilepsy with febrile seizures plus. A genetic disorder with heterogeneous clinical phenotypes. Brain 120, 479–90 (1997).
[4] S. A. Goldstein, C. Miller, Mechanism of charybdotoxin block of a voltage gated K+ channel. Biophysical Journal 65, 1613–1619 (1993).
[5] S. Candia, M. L. Garcia, R. Latorre, Mode of action of iberiotoxin, a potent blocker of the large conductance Ca(2+)- activated K+ channel.Biophysical Journal 63, 583–590 (1992).
[6] R. Toczylowska-Maminska, K. Dolowy, Ion transporting proteins of human bronchial epithelium. Journal of Cellular Biochemistry 113, 426-432 (2012).
[7] C. V. Falkenberg, E. Jakobsson, A Biophysical Model for Integration of Electrical, Osmotic, and pH Regulation in the Human Bronchial Epithelium. Biophysical Journal 98,1476–1485 (2010).
[8] Y. Sohma, M. A. Gray, Y. Imai, B. E. Argent, HCO3-
Transport in a Mathematical Model of the Pancreatic Ductal Epithelium. Journal of Membrane Biology 176,77–100 (2000).
[9] S. H. Wright, Generation of resting membrane potential.Advances in Physiology Education 28, 139-142 (2004).
[10] NVIDIA corporation, 2012. CUDA C Programming Guide Available from: http://developer.NVIDIA.com/ NVIDIA-gpu-computing-documentation Accesed: Jul 11, 2012
[11] W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, chapter 16.1 in Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, 1993.
