American Institute of Mathematical Sciences

Advanced
2013, 2013(special): 825-835. doi: 10.3934/proc.2013.2013.825

Foam cell formation in atherosclerosis: HDL and macrophage reverse cholesterol transport

Shuai Zhang 1, , L.R. Ritter 2, and  A.I. Ibragimov 3,

1. 

Southern Polytechnic State University, Marietta, GA 30060, United States
2. 

Southern Polytechnic State University, Marietta, GA 30060-2896
3. 

Texas Tech University, Lubbock, TX 79409, United States

Received  September 2012 Revised  December 2012 Published  November 2013

Macrophage derived foam cells are a major constituent of the fatty deposits characterizing the disease atherosclerosis. Foam cells are formed when certain immune cells (macrophages) take on oxidized low density lipoproteins through failed phagocytosis. High density lipoproteins (HDL) are known to have a number of anti-atherogenic effects. One of these stems from their ability to remove excess cellular cholesterol for processing in the liver---a process called reverse cholesterol transport (RCT). HDL perform macrophage RCT by binding to forming foam cells and removing excess lipids by efflux transporters.
    We propose a model of foam cell formation accounting for macrophage RCT. This model is presented as a system of non-linear ordinary differential equations. Motivated by experimental observations regarding time scales for oxidation of lipids and MRCT, we impose a quasi-steady state assumption and analyze the resulting systems of equations. We focus on the existence and stability of equilibrium solutions as determined by the governing parameters with the results interpreted in terms of their potential bio-medical implications.
Keywords: stability analysis, steady state., Atherosclerosis modeling.
Mathematics Subject Classification: Primary: 92B05, 92C50; Secondary: 34D2.
Citation: Shuai Zhang, L.R. Ritter, A.I. Ibragimov. Foam cell formation in atherosclerosis: HDL and macrophage reverse cholesterol transport. Conference Publications, 2013, 2013 (special) : 825-835. doi: 10.3934/proc.2013.2013.825
References:
[1]

T. Bjornheden, A. Babiy, G. Bondjers, G., and O. Wiklund, Accumulation of lipoprotein fractions and subfractions in the arterial wall, determined in an in vitro perfusion system, Atherosclerosis, 123 (1996), 43-560.

[2]

C. A. Cobbold, J. A. Sherratt, and S. J. R. Maxwell, Lipoprotein oxidation and its significance for atherosclerosis: a mathematical approach, Bull. Math. Biol., 64 (2002), 65-95.

[3]

M. A. Creager, M. A. and Braunwald, E. eds., "Atlas of Vascular Disease," $2^{nd}$ edition, Current Medicine, Inc. (2003)

[4]

A. Daugherty, and D. L. Rateri, Pathogenesis of atherosclerotic lesions, Cardiol. Rev., 1 (1993), 157-166.

[5]

J. Fan, and T. Watanabe, Inflammatory reactions in the pathogenesis of atherosclerosis, JAT, 10(2) (2003), 63-71.

[6]

R. Franssen, A. W. M. Schimmel, S. I. van Leuven, S. C. S. Wolfkamp, E. S.G. Stroes, and G. M. Dallinga-Thie, In vivo inflammation does not impair ABCA1-mediated cholesterol efflux capacity of HDL, Cholesterol, 2012 (2012), 1-8.

[7]

J. L. Goldstein, Y. K. Ho, S. K. Basu, and M. S. Brown, Binding site on macrophages that mediates uptake and degradation of acetylated low density lipoproteins, producing massive cholesterol deposition, Proc. Natl. Acad. Sci. USA, 76 (1977), 333-337

[8]

J. Hubbard and B. West, "Differential Equations: A Dynamical Systems Approach," Springer-Verlag, New York, (1991)

[9]

A. I. Ibragimov, C. J. McNeal, L. R. Ritter, and J. R. Walton, A mathematical model of atherogenesis as an inflammatory response, Math. Med. and Biol., 22 (2005), 305-333

[10]

A. I. Ibragimov, C. J. McNeal, L. R. Ritter, and J. R. Walton, Stability analysis of a model of atherogenesis: An energy estimate approach, J. of Comp. and Math. Meth. in Med., 9(2) (2008), 121-142

[11]

A. I. Ibragimov, L. R. Ritter, and J. R Walton, Stability analysis of a reaction-diffusion system modeling atherogenesis, SIAM J. Appl. Math., 70(7) (2010), 2150-2185

[12]

K. U. Ingold, V. W. Bowry, R. Stocker, and C. Walling, Autoxidation and antioxidation by $\alpha$-tocopherol and ubiquinol in homogeneous solution and in aqueous dispersions of lipids: unrecognized consequences of lipid particle size as exemplified by oxidation of human low density lipoprotein, Proc. Natl. Acad. Sci. USA, 90 (1993), 45-49.

[13]

I. Jailal, G. L. Vega, S. M. and Grundy, Physologic levels of ascorbate inhibit the oxidative modification of low density lipoprotein, Atherosclerosis, 82 (1990), 185-191.

[14]

W. Khovidhunkit, M. S. Kim, R. A. Memon, J. K. Shigenaga, A. H. Moser, K. R. Feingold, and C. Grunfeld, Effects of infection and inflammation on lipid and lipoprotein metabolism: mechanisms and consequences to the host, Journal of Lipid Research, 45(7) (2004), 1169-1196

[15]

P. Libby, P. M. Ridker, and A. Maseri, Inflammation and atherosclerosis, Circulation, 105(9) (2002), 11351143.

[16]

L. B. Neilsen, Transfer of low density lipoprotein into the arterial wall and risk of atherosclerosis, Atherosclerosis, 123 (1996), 1-15.

[17]

J. Neuzil, S. R. Thomas, and R. Stocker, Requirement for, promotion, or inhibition by $\alpha$-tocopherol of radical-induced initiation of plasma lipoprotein lipid peroxidation, Free Radic. Biol. Med., 22 (1997), 57-71

[18]

J. E. Packer, T. F. Slater, and R. L. Willson, Direct observation of a free radical interaction between vitamin E and vitamin C, Nature, 278 (1979), 737-738

[19]

E. A. Podrez, E. Poliakov, Z. Shen, R. Zhang, Y. Deng, M. Sun, P. J. Finton, L. Shan, B. Gugiu, P. L. Fox, H. F. Hoff, R. G. Salomon, and S. L. Hazen, Identification of a novel family of oxidized phospholipids that serve as ligands for the macrophage scavenger receptor CD36, J. Biol. Chem., 277 (2002), 38503-38516

[20]

Russell Ross, Cell biology of atherosclerosis, Annu. Rev. Physiol., 57 (1995), 791-804.

[21]

Russell Ross, Atherosclerosis-An inflammatory disease, N. Engl. J. Med., 340(2) (1999), 115-126

[22]

D. c. Schwenke, and T. E. Carew, Initiation of atherosclerotic lesions in cholesterol fed rabbits. II Selective retention of LDL vs. Selective increases in LDL permeability in susceptible sites of arteries, Arteriosclerosis, 9 (1989), 908-918

[23]

H. C. Stary, B. Chandler, S. Glagov, J. R. Guyton, W. Insull Jr., M. E. Rosenfeld, S. A. Schaffer, C. J. Schwartz, W. D. Wagner, and R. W. Wissler, A definition of initial, fatty streak, and intermediate lesions of atherosclerosis: a report from the Committee on Vascular Lesions of the Council on Arteriosclerosis, American Heart Association. Special report., Arterioscler. Thromb., 14 (1994), 840-856

[24]

D. Steinberg, Atherogenesis in perspective: hypercholesterolemia and inflammation as partners in crime, Nat. Med., 8 (2002), 1211-1217

[25]

A. R. Tall, Plasma high density lipoproteins: metabolism and relationship to atherogenesis, J. Clin. Invest., 86 (1990), 379-384

[26]

N. Wang, D. Lan, W. Chen, F. Matsuura, and A. Tall, ATP-binding cassette transporters G1 and G4 mediate cellular cholesterol efflux to high-density lipoproteins, Proc. Natl. Acad. Sci. USA, 101(26) (2004), 9774-9779

show all references

References:
[1]

T. Bjornheden, A. Babiy, G. Bondjers, G., and O. Wiklund, Accumulation of lipoprotein fractions and subfractions in the arterial wall, determined in an in vitro perfusion system, Atherosclerosis, 123 (1996), 43-560.

[2]

C. A. Cobbold, J. A. Sherratt, and S. J. R. Maxwell, Lipoprotein oxidation and its significance for atherosclerosis: a mathematical approach, Bull. Math. Biol., 64 (2002), 65-95.

[3]

M. A. Creager, M. A. and Braunwald, E. eds., "Atlas of Vascular Disease," $2^{nd}$ edition, Current Medicine, Inc. (2003)

[4]

A. Daugherty, and D. L. Rateri, Pathogenesis of atherosclerotic lesions, Cardiol. Rev., 1 (1993), 157-166.

[5]

J. Fan, and T. Watanabe, Inflammatory reactions in the pathogenesis of atherosclerosis, JAT, 10(2) (2003), 63-71.

[6]

R. Franssen, A. W. M. Schimmel, S. I. van Leuven, S. C. S. Wolfkamp, E. S.G. Stroes, and G. M. Dallinga-Thie, In vivo inflammation does not impair ABCA1-mediated cholesterol efflux capacity of HDL, Cholesterol, 2012 (2012), 1-8.

[7]

J. L. Goldstein, Y. K. Ho, S. K. Basu, and M. S. Brown, Binding site on macrophages that mediates uptake and degradation of acetylated low density lipoproteins, producing massive cholesterol deposition, Proc. Natl. Acad. Sci. USA, 76 (1977), 333-337

[8]

J. Hubbard and B. West, "Differential Equations: A Dynamical Systems Approach," Springer-Verlag, New York, (1991)

[9]

A. I. Ibragimov, C. J. McNeal, L. R. Ritter, and J. R. Walton, A mathematical model of atherogenesis as an inflammatory response, Math. Med. and Biol., 22 (2005), 305-333

[10]

A. I. Ibragimov, C. J. McNeal, L. R. Ritter, and J. R. Walton, Stability analysis of a model of atherogenesis: An energy estimate approach, J. of Comp. and Math. Meth. in Med., 9(2) (2008), 121-142

[11]

A. I. Ibragimov, L. R. Ritter, and J. R Walton, Stability analysis of a reaction-diffusion system modeling atherogenesis, SIAM J. Appl. Math., 70(7) (2010), 2150-2185

[12]

K. U. Ingold, V. W. Bowry, R. Stocker, and C. Walling, Autoxidation and antioxidation by $\alpha$-tocopherol and ubiquinol in homogeneous solution and in aqueous dispersions of lipids: unrecognized consequences of lipid particle size as exemplified by oxidation of human low density lipoprotein, Proc. Natl. Acad. Sci. USA, 90 (1993), 45-49.

[13]

I. Jailal, G. L. Vega, S. M. and Grundy, Physologic levels of ascorbate inhibit the oxidative modification of low density lipoprotein, Atherosclerosis, 82 (1990), 185-191.

[14]

W. Khovidhunkit, M. S. Kim, R. A. Memon, J. K. Shigenaga, A. H. Moser, K. R. Feingold, and C. Grunfeld, Effects of infection and inflammation on lipid and lipoprotein metabolism: mechanisms and consequences to the host, Journal of Lipid Research, 45(7) (2004), 1169-1196

[15]

P. Libby, P. M. Ridker, and A. Maseri, Inflammation and atherosclerosis, Circulation, 105(9) (2002), 11351143.

[16]

L. B. Neilsen, Transfer of low density lipoprotein into the arterial wall and risk of atherosclerosis, Atherosclerosis, 123 (1996), 1-15.

[17]

J. Neuzil, S. R. Thomas, and R. Stocker, Requirement for, promotion, or inhibition by $\alpha$-tocopherol of radical-induced initiation of plasma lipoprotein lipid peroxidation, Free Radic. Biol. Med., 22 (1997), 57-71

[18]

J. E. Packer, T. F. Slater, and R. L. Willson, Direct observation of a free radical interaction between vitamin E and vitamin C, Nature, 278 (1979), 737-738

[19]

E. A. Podrez, E. Poliakov, Z. Shen, R. Zhang, Y. Deng, M. Sun, P. J. Finton, L. Shan, B. Gugiu, P. L. Fox, H. F. Hoff, R. G. Salomon, and S. L. Hazen, Identification of a novel family of oxidized phospholipids that serve as ligands for the macrophage scavenger receptor CD36, J. Biol. Chem., 277 (2002), 38503-38516

[20]

Russell Ross, Cell biology of atherosclerosis, Annu. Rev. Physiol., 57 (1995), 791-804.

[21]

Russell Ross, Atherosclerosis-An inflammatory disease, N. Engl. J. Med., 340(2) (1999), 115-126

[22]

D. c. Schwenke, and T. E. Carew, Initiation of atherosclerotic lesions in cholesterol fed rabbits. II Selective retention of LDL vs. Selective increases in LDL permeability in susceptible sites of arteries, Arteriosclerosis, 9 (1989), 908-918

[23]

H. C. Stary, B. Chandler, S. Glagov, J. R. Guyton, W. Insull Jr., M. E. Rosenfeld, S. A. Schaffer, C. J. Schwartz, W. D. Wagner, and R. W. Wissler, A definition of initial, fatty streak, and intermediate lesions of atherosclerosis: a report from the Committee on Vascular Lesions of the Council on Arteriosclerosis, American Heart Association. Special report., Arterioscler. Thromb., 14 (1994), 840-856

[24]

D. Steinberg, Atherogenesis in perspective: hypercholesterolemia and inflammation as partners in crime, Nat. Med., 8 (2002), 1211-1217

[25]

A. R. Tall, Plasma high density lipoproteins: metabolism and relationship to atherogenesis, J. Clin. Invest., 86 (1990), 379-384

[26]

N. Wang, D. Lan, W. Chen, F. Matsuura, and A. Tall, ATP-binding cassette transporters G1 and G4 mediate cellular cholesterol efflux to high-density lipoproteins, Proc. Natl. Acad. Sci. USA, 101(26) (2004), 9774-9779

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