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2016, 13(5): 1043-1058. doi: 10.3934/mbe.2016029

Development of a computational model of glucose toxicity in the progression of diabetes mellitus

1. 

Department of Chemistry, University of Puerto Rico at Cayey, Cayey, PR 00736-9997, United States

2. 

Department of Natural Sciences, University of Puerto Rico at Cayey, Cayey, PR 00736-9997, United States, United States

3. 

Department of Mathematics - Physics, University of Puerto Rico at Cayey, Cayey, PR 00736-9997, United States

Received  October 2015 Revised  April 2016 Published  July 2016

Diabetes mellitus is a disease characterized by a range of metabolic complications involving an individual's blood glucose levels, and its main regulator, insulin. These complications can vary largely from person to person depending on their current biophysical state. Biomedical research day-by-day makes strides to impact the lives of patients of a variety of diseases, including diabetes. One large stride that is being made is the generation of techniques to assist physicians to ``personalize medicine''. From available physiological data, biological understanding of the system, and dimensional analysis, a differential equation-based mathematical model was built in a sequential matter, to be able to elucidate clearly how each parameter correlates to the patient's current physiological state. We developed a simple mathematical model that accurately simulates the dynamics between glucose, insulin, and pancreatic $\beta$-cells throughout disease progression with constraints to maintain biological relevance. The current framework is clearly capable of tracking the patient's current progress through the disease, dependent on factors such as latent insulin resistance or an attrite $\beta$-cell population. Further interests would be to develop tools that allow the direct and feasible testing of how effective a given plan of treatment would be at returning the patient to a desirable biophysical state.
Citation: Danilo T. Pérez-Rivera, Verónica L. Torres-Torres, Abraham E. Torres-Colón, Mayteé Cruz-Aponte. Development of a computational model of glucose toxicity in the progression of diabetes mellitus. Mathematical Biosciences & Engineering, 2016, 13 (5) : 1043-1058. doi: 10.3934/mbe.2016029
References:
[1]

Statistics about diabetes: American diabetes association, http://www.diabetes.org/diabetes-basics/statistics/,, Accessed: 2014-04-03., (): 2014.

[2]

V. Åberg, A. Thörne, A. Alvestrand and J. Nordenström, Combined hypertriglyceridemic and insulin-glucose clamps for the characterization of substrate oxidation and plasma elimination of a long-chain triglyceride emulsion in healthy men,, Metabolism, 61 (2012), 221.

[3]

J. M. Berg, J. L. Tymoczko and L. Stryer, Biochemistry,, 5th edition, (2002).

[4]

J. M. Berg, J. L. Tymoczko and L. Stryer, Glycogen breakdown and synthesis are reciprocally regulated,, in Biochemistry, (2002).

[5]

R. N. Bergman, L. S. Phillips and C. Cobelli, Physiologic evaluation of factors controlling glucose tolerance in man: Measurement of insulin sensitivity and beta-cell glucose sensitivity from the response to intravenous glucose,, Journal of Clinical Investigation, 68 (1981), 1456. doi: 10.1172/JCI110398.

[6]

M. J. Birnbaum, Turning down insulin signaling,, Journal of Clinical Investigation, 108 (2001), 655. doi: 10.1172/JCI200113714.

[7]

M. Bollen, S. Keppens and W. Stalmans, Specific features of glycogen metabolism in the liver,, Biochem. J, 15 (1998), 19. doi: 10.1042/bj3360019.

[8]

L. Bouwens and I. Rooman, Regulation of pancreatic beta-cell mass,, Physiological reviews, 85 (2005), 1255. doi: 10.1152/physrev.00025.2004.

[9]

A. E. Butler, J. Janson, S. Bonner-Weir, R. Ritzel, R. A. Rizza and P. C. Butler, $\beta$-cell deficit and increased $\beta$-cell apoptosis in humans with type 2 diabetes,, Diabetes, 52 (2003), 102.

[10]

M. R. Castro, Is hyperinsulinemia a form of diabetes?,, , (): 2014.

[11]

C. M. Elks, N. Mariappan, M. Haque, A. Guggilam, D. S. Majid and J. Francis, Chronic nf-$\kappa$b blockade reduces cytosolic and mitochondrial oxidative stress and attenuates renal injury and hypertension in shr,, American Journal of Physiology-Renal Physiology, 296 (2009).

[12]

M. Elks, Chronic perifusion of rat islets with palmitate suppresses glucose-stimulated insulin release.,, Endocrinology, 133 (1993), 208.

[13]

P. Felig and J. Wahren, Influence of endogenous insulin secretion on splanchnic glucose and amino acid metabolism in man,, Journal of Clinical Investigation, 50 (1971), 1702. doi: 10.1172/JCI106659.

[14]

J. E. Gerich, The genetic basis of type 2 diabetes mellitus: Impaired insulin secretion versus impaired insulin sensitivity,, Endocrine reviews, 19 (1998), 491.

[15]

S. Gremlich, C. Bonny, G. Waeber and B. Thorens, Fatty acids decrease idx-1 expression in rat pancreatic islets and reduce glut2, glucokinase, insulin, and somatostatin levels,, Journal of Biological Chemistry, 272 (1997), 30261. doi: 10.1074/jbc.272.48.30261.

[16]

M. J. Haller, M. A. Atkinson and D. Schatz, Type 1 diabetes mellitus: Etiology, presentation, and management,, Pediatric Clinics of North America, 52 (2005), 1553. doi: 10.1016/j.pcl.2005.07.006.

[17]

M.-T. Huang and R. L. Veech, Role of the direct and indirect pathways for glycogen synthesis in rat liver in the postprandial state,, Journal of Clinical Investigation, 81 (1988), 872. doi: 10.1172/JCI113397.

[18]

R. Lupi and S. Del Prato, $\beta$-cell apoptosis in type 2 diabetes: Quantitative and functional consequences,, Diabetes & metabolism, 34 (2008).

[19]

A. Makroglou, J. Li and Y. Kuang, Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: An overview,, Applied numerical mathematics, 56 (2006), 559. doi: 10.1016/j.apnum.2005.04.023.

[20]

T. M. Mason, T. Goh, V. Tchipashvili, H. Sandhu, N. Gupta, G. F. Lewis and A. Giacca, Prolonged elevation of plasma free fatty acids desensitizes the insulin secretory response to glucose in vivo in rats,, Diabetes, 48 (1999), 524. doi: 10.2337/diabetes.48.3.524.

[21]

D. Mellitus, Diagnosis and classification of diabetes mellitus,, Diabetes care, 28 (2005).

[22]

S. Y. Morris, How insulin and glucagon work,, , (): 2014.

[23]

R. Murray, D. Bender, K. M. Botham, P. J. Kennelly, V. Rodwell and P. A. Weil, Harpers Illustrated Biochemistry 29/E,, McGraw Hill Professional, (2012).

[24]

J. M. Olefsky, Pathogenesis of insulin resistance and hyperglycemia in non-insulin-dependent diabetes mellitus,, The American Journal of Medicine, 79 (1985), 1. doi: 10.1016/S0002-9343(85)80001-2.

[25]

G. Paolisso, A. Gambardella, L. Amato, R. Tortoriello, A. d'Amore, M. Varricchio and F. d'Onofrio, Opposite effects of short-and long-term fatty acid infusion on insulin secretion in healthy subjects,, Diabetologia, 38 (1995), 1295. doi: 10.1007/BF00401761.

[26]

K. F. Petersen and G. I. Shulman, Etiology of insulin resistance,, The American journal of medicine, 119 (2006). doi: 10.1016/j.amjmed.2006.01.009.

[27]

V. Poitout and R. P. Robertson, Minireview: secondary $\beta$-cell failure in type 2 diabetes?a convergence of glucotoxicity and lipotoxicity,, Endocrinology, 143 (2002), 339.

[28]

K. Polonsky, B. Given, L. Hirsch, E. Shapiro, H. Tillil, C. Beebe, J. Galloway, B. Frank, T. Karrison and E. Van Cauter, Quantitative study of insulin secretion and clearance in normal and obese subjects,, Journal of Clinical Investigation, 81 (1988), 435. doi: 10.1172/JCI113338.

[29]

G. M. Reaven, Role of insulin resistance in human disease,, Role of Insulin Resistance in Human Disease, 1 (1992), 91. doi: 10.1007/978-94-011-2700-4_10.

[30]

J. Reece, L. A. Urry, N. Meyers, M. L. Cain, S. A. Wasserman, P. V. Minorsky, R. B. Jackson and B. N. Cooke, Campbell Biology,, Pearson Higher Education AU, (2011).

[31]

R. P. Robertson, J. Harmon, P. O. Tran, Y. Tanaka and H. Takahashi, Glucose toxicity in $\beta$-cells: Type 2 diabetes, good radicals gone bad, and the glutathione connection,, Diabetes, 52 (2003), 581.

[32]

R. P. Robertson, J. Harmon, P. O. T. Tran and V. Poitout, $\beta$-cell glucose toxicity, lipotoxicity, and chronic oxidative stress in type 2 diabetes,, Diabetes, 53 (2004).

[33]

R. P. Robertson, L. K. Olson and H.-J. Zhang, Differentiating glucose toxicity from glucose desensitization: a new message from the insulin gene,, Diabetes, 43 (1994), 1085.

[34]

S. Robin, Expected blood glucose after a high carb meal,, , (): 2014.

[35]

J. Ruhl, How blood sugar control works-and how it stops working,, , (): 2014.

[36]

Y. SAKO and V. E. GRILL, A 48-hour lipid infusion in the rat time-dependently inhibits glucose-induced insulin secretion and b cell oxidation through a process likely coupled to fatty acid oxidation*,, Endocrinology, 127 (1990), 1580. doi: 10.1210/endo-127-4-1580.

[37]

G. Scheiner, Strike the spike ii." diabetes self-managment,, , (): 2014.

[38]

O. Shaham, R. Wei, T. J. Wang, C. Ricciardi, G. D. Lewis, R. S. Vasan, S. A. Carr, R. Thadhani, R. E. Gerszten and V. K. Mootha, Metabolic profiling of the human response to a glucose challenge reveals distinct axes of insulin sensitivity,, Molecular Systems Biology, 4 (2008). doi: 10.1038/msb.2008.50.

[39]

M. C. Stoppler, Hyperglycemia: Facts on symptom, signs and treatment,, , (): 2014.

[40]

M. Stumvoll, A. Mitrakou, W. Pimenta, T. Jenssen, H. Yki-Järvinen, T. Van Haeften, W. Renn and J. Gerich, Use of the oral glucose tolerance test to assess insulin release and insulin sensitivity,, Diabetes care, 23 (2000), 295. doi: 10.2337/diacare.23.3.295.

[41]

O. Tanner, Intensive versus conventional glucose control in critically ill patients,, Journal of the Intensive Care Society, 10 (2009), 216. doi: 10.1177/175114370901000314.

[42]

B. Topp, K. Promislow, G. Devries, R. M. Miura and D. T FINEGOOD, A model of $\beta$-cell mass, insulin, and glucose kinetics: Pathways to diabetes,, Journal of Theoretical Biology, 206 (2000), 605.

[43]

Y.-F. Wang, M. Khan and H. A. van den Berg, Interaction of fast and slow dynamics in endocrine control systems with an application to $\beta$-cell dynamics,, Mathematical biosciences, 235 (2012), 8. doi: 10.1016/j.mbs.2011.10.003.

[44]

G. C. Weir and S. Bonner-Weir, Five stages of evolving beta-cell dysfunction during progression to diabetes,, Diabetes, 53 (2004). doi: 10.2337/diabetes.53.suppl_3.S16.

[45]

L. Wu, W. Nicholson, S. M. Knobel, R. J. Steffner, J. M. May, D. W. Piston and A. C. Powers, Oxidative stress is a mediator of glucose toxicity in insulin-secreting pancreatic islet cell lines,, Journal of Biological Chemistry, 279 (2004), 12126. doi: 10.1074/jbc.M307097200.

[46]

Y.-P. Zhou and V. E. Grill, Long-term exposure of rat pancreatic islets to fatty acids inhibits glucose-induced insulin secretion and biosynthesis through a glucose fatty acid cycle,, Journal of Clinical Investigation, 93 (1994), 870. doi: 10.1172/JCI117042.

show all references

References:
[1]

Statistics about diabetes: American diabetes association, http://www.diabetes.org/diabetes-basics/statistics/,, Accessed: 2014-04-03., (): 2014.

[2]

V. Åberg, A. Thörne, A. Alvestrand and J. Nordenström, Combined hypertriglyceridemic and insulin-glucose clamps for the characterization of substrate oxidation and plasma elimination of a long-chain triglyceride emulsion in healthy men,, Metabolism, 61 (2012), 221.

[3]

J. M. Berg, J. L. Tymoczko and L. Stryer, Biochemistry,, 5th edition, (2002).

[4]

J. M. Berg, J. L. Tymoczko and L. Stryer, Glycogen breakdown and synthesis are reciprocally regulated,, in Biochemistry, (2002).

[5]

R. N. Bergman, L. S. Phillips and C. Cobelli, Physiologic evaluation of factors controlling glucose tolerance in man: Measurement of insulin sensitivity and beta-cell glucose sensitivity from the response to intravenous glucose,, Journal of Clinical Investigation, 68 (1981), 1456. doi: 10.1172/JCI110398.

[6]

M. J. Birnbaum, Turning down insulin signaling,, Journal of Clinical Investigation, 108 (2001), 655. doi: 10.1172/JCI200113714.

[7]

M. Bollen, S. Keppens and W. Stalmans, Specific features of glycogen metabolism in the liver,, Biochem. J, 15 (1998), 19. doi: 10.1042/bj3360019.

[8]

L. Bouwens and I. Rooman, Regulation of pancreatic beta-cell mass,, Physiological reviews, 85 (2005), 1255. doi: 10.1152/physrev.00025.2004.

[9]

A. E. Butler, J. Janson, S. Bonner-Weir, R. Ritzel, R. A. Rizza and P. C. Butler, $\beta$-cell deficit and increased $\beta$-cell apoptosis in humans with type 2 diabetes,, Diabetes, 52 (2003), 102.

[10]

M. R. Castro, Is hyperinsulinemia a form of diabetes?,, , (): 2014.

[11]

C. M. Elks, N. Mariappan, M. Haque, A. Guggilam, D. S. Majid and J. Francis, Chronic nf-$\kappa$b blockade reduces cytosolic and mitochondrial oxidative stress and attenuates renal injury and hypertension in shr,, American Journal of Physiology-Renal Physiology, 296 (2009).

[12]

M. Elks, Chronic perifusion of rat islets with palmitate suppresses glucose-stimulated insulin release.,, Endocrinology, 133 (1993), 208.

[13]

P. Felig and J. Wahren, Influence of endogenous insulin secretion on splanchnic glucose and amino acid metabolism in man,, Journal of Clinical Investigation, 50 (1971), 1702. doi: 10.1172/JCI106659.

[14]

J. E. Gerich, The genetic basis of type 2 diabetes mellitus: Impaired insulin secretion versus impaired insulin sensitivity,, Endocrine reviews, 19 (1998), 491.

[15]

S. Gremlich, C. Bonny, G. Waeber and B. Thorens, Fatty acids decrease idx-1 expression in rat pancreatic islets and reduce glut2, glucokinase, insulin, and somatostatin levels,, Journal of Biological Chemistry, 272 (1997), 30261. doi: 10.1074/jbc.272.48.30261.

[16]

M. J. Haller, M. A. Atkinson and D. Schatz, Type 1 diabetes mellitus: Etiology, presentation, and management,, Pediatric Clinics of North America, 52 (2005), 1553. doi: 10.1016/j.pcl.2005.07.006.

[17]

M.-T. Huang and R. L. Veech, Role of the direct and indirect pathways for glycogen synthesis in rat liver in the postprandial state,, Journal of Clinical Investigation, 81 (1988), 872. doi: 10.1172/JCI113397.

[18]

R. Lupi and S. Del Prato, $\beta$-cell apoptosis in type 2 diabetes: Quantitative and functional consequences,, Diabetes & metabolism, 34 (2008).

[19]

A. Makroglou, J. Li and Y. Kuang, Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: An overview,, Applied numerical mathematics, 56 (2006), 559. doi: 10.1016/j.apnum.2005.04.023.

[20]

T. M. Mason, T. Goh, V. Tchipashvili, H. Sandhu, N. Gupta, G. F. Lewis and A. Giacca, Prolonged elevation of plasma free fatty acids desensitizes the insulin secretory response to glucose in vivo in rats,, Diabetes, 48 (1999), 524. doi: 10.2337/diabetes.48.3.524.

[21]

D. Mellitus, Diagnosis and classification of diabetes mellitus,, Diabetes care, 28 (2005).

[22]

S. Y. Morris, How insulin and glucagon work,, , (): 2014.

[23]

R. Murray, D. Bender, K. M. Botham, P. J. Kennelly, V. Rodwell and P. A. Weil, Harpers Illustrated Biochemistry 29/E,, McGraw Hill Professional, (2012).

[24]

J. M. Olefsky, Pathogenesis of insulin resistance and hyperglycemia in non-insulin-dependent diabetes mellitus,, The American Journal of Medicine, 79 (1985), 1. doi: 10.1016/S0002-9343(85)80001-2.

[25]

G. Paolisso, A. Gambardella, L. Amato, R. Tortoriello, A. d'Amore, M. Varricchio and F. d'Onofrio, Opposite effects of short-and long-term fatty acid infusion on insulin secretion in healthy subjects,, Diabetologia, 38 (1995), 1295. doi: 10.1007/BF00401761.

[26]

K. F. Petersen and G. I. Shulman, Etiology of insulin resistance,, The American journal of medicine, 119 (2006). doi: 10.1016/j.amjmed.2006.01.009.

[27]

V. Poitout and R. P. Robertson, Minireview: secondary $\beta$-cell failure in type 2 diabetes?a convergence of glucotoxicity and lipotoxicity,, Endocrinology, 143 (2002), 339.

[28]

K. Polonsky, B. Given, L. Hirsch, E. Shapiro, H. Tillil, C. Beebe, J. Galloway, B. Frank, T. Karrison and E. Van Cauter, Quantitative study of insulin secretion and clearance in normal and obese subjects,, Journal of Clinical Investigation, 81 (1988), 435. doi: 10.1172/JCI113338.

[29]

G. M. Reaven, Role of insulin resistance in human disease,, Role of Insulin Resistance in Human Disease, 1 (1992), 91. doi: 10.1007/978-94-011-2700-4_10.

[30]

J. Reece, L. A. Urry, N. Meyers, M. L. Cain, S. A. Wasserman, P. V. Minorsky, R. B. Jackson and B. N. Cooke, Campbell Biology,, Pearson Higher Education AU, (2011).

[31]

R. P. Robertson, J. Harmon, P. O. Tran, Y. Tanaka and H. Takahashi, Glucose toxicity in $\beta$-cells: Type 2 diabetes, good radicals gone bad, and the glutathione connection,, Diabetes, 52 (2003), 581.

[32]

R. P. Robertson, J. Harmon, P. O. T. Tran and V. Poitout, $\beta$-cell glucose toxicity, lipotoxicity, and chronic oxidative stress in type 2 diabetes,, Diabetes, 53 (2004).

[33]

R. P. Robertson, L. K. Olson and H.-J. Zhang, Differentiating glucose toxicity from glucose desensitization: a new message from the insulin gene,, Diabetes, 43 (1994), 1085.

[34]

S. Robin, Expected blood glucose after a high carb meal,, , (): 2014.

[35]

J. Ruhl, How blood sugar control works-and how it stops working,, , (): 2014.

[36]

Y. SAKO and V. E. GRILL, A 48-hour lipid infusion in the rat time-dependently inhibits glucose-induced insulin secretion and b cell oxidation through a process likely coupled to fatty acid oxidation*,, Endocrinology, 127 (1990), 1580. doi: 10.1210/endo-127-4-1580.

[37]

G. Scheiner, Strike the spike ii." diabetes self-managment,, , (): 2014.

[38]

O. Shaham, R. Wei, T. J. Wang, C. Ricciardi, G. D. Lewis, R. S. Vasan, S. A. Carr, R. Thadhani, R. E. Gerszten and V. K. Mootha, Metabolic profiling of the human response to a glucose challenge reveals distinct axes of insulin sensitivity,, Molecular Systems Biology, 4 (2008). doi: 10.1038/msb.2008.50.

[39]

M. C. Stoppler, Hyperglycemia: Facts on symptom, signs and treatment,, , (): 2014.

[40]

M. Stumvoll, A. Mitrakou, W. Pimenta, T. Jenssen, H. Yki-Järvinen, T. Van Haeften, W. Renn and J. Gerich, Use of the oral glucose tolerance test to assess insulin release and insulin sensitivity,, Diabetes care, 23 (2000), 295. doi: 10.2337/diacare.23.3.295.

[41]

O. Tanner, Intensive versus conventional glucose control in critically ill patients,, Journal of the Intensive Care Society, 10 (2009), 216. doi: 10.1177/175114370901000314.

[42]

B. Topp, K. Promislow, G. Devries, R. M. Miura and D. T FINEGOOD, A model of $\beta$-cell mass, insulin, and glucose kinetics: Pathways to diabetes,, Journal of Theoretical Biology, 206 (2000), 605.

[43]

Y.-F. Wang, M. Khan and H. A. van den Berg, Interaction of fast and slow dynamics in endocrine control systems with an application to $\beta$-cell dynamics,, Mathematical biosciences, 235 (2012), 8. doi: 10.1016/j.mbs.2011.10.003.

[44]

G. C. Weir and S. Bonner-Weir, Five stages of evolving beta-cell dysfunction during progression to diabetes,, Diabetes, 53 (2004). doi: 10.2337/diabetes.53.suppl_3.S16.

[45]

L. Wu, W. Nicholson, S. M. Knobel, R. J. Steffner, J. M. May, D. W. Piston and A. C. Powers, Oxidative stress is a mediator of glucose toxicity in insulin-secreting pancreatic islet cell lines,, Journal of Biological Chemistry, 279 (2004), 12126. doi: 10.1074/jbc.M307097200.

[46]

Y.-P. Zhou and V. E. Grill, Long-term exposure of rat pancreatic islets to fatty acids inhibits glucose-induced insulin secretion and biosynthesis through a glucose fatty acid cycle,, Journal of Clinical Investigation, 93 (1994), 870. doi: 10.1172/JCI117042.

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