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A mathematical model of cell death in multiple sclerosis
Journal of Neuroscience Methods 201 (2011) 420–425
Contents lists available at ScienceDirect
Journal of Neuroscience Methods journal homepage: www.elsevier.com/locate/jneumeth
A mathematical model of cell death in multiple sclerosis Taylor M. Broome, Randolph A. Coleman ∗ Department of Chemistry Integrated Science Center, 540 Landrum Drive, The College of William and Mary, Williamsburg, VA 23187, USA
a r t i c l e
i n f o
Article history: Received 22 June 2011 Received in revised form 4 August 2011 Accepted 7 August 2011 Keywords: Multiple sclerosis Computational biology Neurodegenerative diseases Reactive oxygen species Reactive nitrogen species Apoptosis Permeability transition pore
a b s t r a c t This paper imparts a mathematical model of multiple sclerosis (MS) that was created using Biochemical Systems Theory (BST). This method uses mechanisms and initial values from the literature to create a mathematical model of a disease. The model can then be used to test potential drug therapies and to detect possible trigger points for the disease. The focus of this MS model is mainly the action of reactive oxygen and nitrogen species (RONS), the permeability transition pore (PTP), apoptotic factors, and the eventual cell death in the oligodendrocyte. Several treatment methods were applied based on current therapies; however, one treatment, the prevention of the PTP from opening, is completely experimental and showed positive results based on this model. BST is an effective means of studying MS and can be beneficial in testing new therapy ideas. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Multiple sclerosis (MS) is a neurodegenerative disorder characterized by demyelination. There have been many experiments to pinpoint a single cause of MS, but no such cause has been found, suggesting that the cause is a combination of several etiologies. Some of the proposed causes for the disorder are reactive oxygen and nitrogen species (RONS), an inflammatory response, excitotoxicity and ionic imbalance (Gonsette, 2008; Mao and Reddy, 2010). This study uses biochemical systems theory (BST) to create a model that details the interactions between these potential MS origins. The primary focus of this model is the death of the oligodendrocyte, the source of neuronal myelin, and some of its basic effects on the axon. BST was originally created by Savageau (1969) and expanded upon by Voit (2000) (Sass et al., 2009). The main purpose of BST is to provide a mathematical framework for a biochemical system. BST is useful in viewing the net effect of reactions through system equations, even when few experimental concentrations are actually known, which is the case with MS. In this study, BST was used to create a normal state, a diseased MS state, and treatment state. The treatment state was created by locating trigger points in the MS model that lead to the disease state, such as the generation of RONS, greatly weakening these processes mathematically, and comparing the resulting data to the diseased state. These MS trigger
∗ Corresponding author. Tel.: +1 757 221 2679; fax: +1 757 221 2715. E-mail address: [email protected] (R.A. Coleman). 0165-0270/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jneumeth.2011.08.008
points located using BST could lead the way to future therapeutic treatments for MS. 2. Methods This section details the cellular pathways presented in the MS model, as well as the process by which the model was mathematized. The modeled pathways were created using the program Cell Designer (Kitano et al., 2005), which allowed for a visual interpretation of the MS literature in the form of a model (Models 1 and 2, Appendix). PLAS, power law analysis and simulation (http://www.dqb.fc.ul.pt/docentes/aferreira/plas.html, link no longer available) was used to create a mathematical interpretation of the MS. See our lab’s earlier publications for more details (Sass et al., 2009; Yeager and Coleman, 2010). 2.1. Modeled cellular pathways 2.1.1. Reactive oxygen and nitrogen species formation Reactive oxygen and nitrogen species (RONS) are extremely detrimental to cellular processes and their formation, in excess, can lead to apoptosis. This model shows the formation and degradation of RONS in both an oligodendrocyte and a neuron. The formation of RONS begins with the secretion of nitric oxide synthase, either from astrocytes and macrophages in the inducible form (iNOS) or from the neuron itself (nNOS), to produce nitric oxide (NO) (van der Veen and Roberts, 1999; Mirshafiey and Mohsenzadegan, 2009; Trapp and Stys, 2009). Superoxide is formed either from electron transport chain mutations or secreted from macrophages (Parkinson
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Model 1. Activation of the inflammatory response and production of reactive oxygen and nitrogen species leading to cell death in the oligodendrocyte.
et al., 1997; Sayre et al., 2008). Superoxide and NO form peroxynitrite, which can then be converted into the less harmful H2 O2 by superoxide dismutase (SOD) (Smith et al., 1999; Sayre et al., 2008; Trapp and Stys, 2009). H2 O2 can either be converted to water via antioxidants, or the OH radical (Smith et al., 1999; Sayre et al., 2008). Peroxynitrite and OH radical are very harmful to the cell and in high concentrations lead to DNA, RNA, and mRNA damage, lipid peroxidation, and protein damage. 2.1.2. Ca2+ accumulation In a healthy neuron, Ca2+ concentrations are regulated by Ca2+ importation into the axoplasmic reticulum (AR) and Ca2+ being exported out of the cell. In MS conditions, Ca2+ is released from the AR via IP3 and Ry receptors, causing an accumulation of Ca2+ in the axon (Trapp and Stys, 2009). Ca2+ accumulation leads to nNOS production, which leads to RONS formation (Trapp and Stys, 2009). Demyelination causes reversal of the Ca2+ –Na+ exchanger, which
also results in a larger concentration of Ca2+ in the axon (Trapp and Stys, 2009). Moreover, Ca2+ triggers the activation of calpain, which then initiates caspase 12 and cathespin release, both of which lead to apoptosis (Das et al., 2008). Additionally, cytochrome C release from the mitochondria is exacerbated by excess Ca2+ . 2.1.3. Death complex formation and caspase activation One of the starting points for apoptosis is formation of a death complex. Death complex formation occurs when a death ligand (TNF-␣, Fas, TRAIL) binds to a death receptor (TNFR1, FasL, TRAILR1) (Kalman et al., 2007). Following this, several cofactors bind to the complex allowing it to activate caspase 8 and other apoptotic proteins (Ventimiglia et al., 2001; Kalman et al., 2007; Circu and Aw, 2010). Caspase 8, in addition to caspase 12 and caspase 9, activates other caspases, but does not lead directly to apoptosis like caspases 3 and 9 (Ghafourifar et al., 2008). The caspase cascade is a major precursor to apoptosis.
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Model 2. Death complex formation leads to the opening of the PTP, which releases cytochrome C and AIF from the mitochondrion, leading to apoptosome formation.
2.1.4. Release of apoptotic factors The permeability transition pore (PTP) controls whether or not certain substances exit the mitochondria and enter the cytoplasm. The PTP is controlled by the BID complex, which is made up of the cleaved BID protein and Bak, a transmembrane protein (Kalman et al., 2007). When caspase 8 is activated by the death complexes, it cleaves BID, allowing it to bind to Bak and form the BID complex. When the PTP is opened, it releases cytochrome c and apoptosis inducing factor (AIF) into the cytoplasm (Ventimiglia et al., 2001; Kalman et al., 2007; Circu and Aw, 2010). Cytochrome c binds with other proteins to form the apoptosome, which begins a caspase cascade; whereas AIF leads directly to apoptosis (Kalman et al., 2007).
2.2.1. Initial values The first step in mathematizing the MS model was assigning every species in the model an X-value and determining if the species was dependent or independent. For the most part if a species was affecting another species, but not itself being affected, it was labeled as independent. Each X was then given an initial concentration; these initial concentrations were based on relative terms, rather than absolute values. Where possible, the research literature was used to estimate initial concentrations and relative concentrations of each species. See our lab’s earlier publications for more details (Sass et al., 2009).
2.2. PLAS
2.2.2. Flux equations Each reaction in the model was assigned a J-value, which was used to identify the reaction, in addition to a rate constant, k. The X-value for each species used by the reaction is also incorporated into the flux equation. For example, peroxynitrite is formed (J34) by the combination of superoxide (X47) and NO (X46). The flux equation for this reaction would be J34 = k34 X47ˆg3447 X36ˆg3446, with k34, g3447, and g3446 as rate-determining constants; for the most part, the g-values are left as 1.00. Some reactions in the model are catalyzed or inhibited by certain species; this is shown by deriving the k value and multiplying it by the rate constants p for promoting and i for inhibiting. For example, H2 O2 formation (J33) is catalyzed by MnSOD (X51) and inhibited by NO (X46). The k equation would be k33 = 0.01 * (p3351 X51 + i3346 X46); the p-values are typically left as 1.00, while the i-values are left as −1.00. The k and k values vary based on the relative activity of the reaction.
Power law analysis and simulation (PLAS) is a program that uses mathematical equations to estimate projected concentrations and values over a time interval. In order to do this, each species and reaction in the MS model had to be converted into a mathematical variable or equation.
2.2.3. System equations To assess the interactions between the reactions, each dependent X-value is given a system equation. J-values that contribute to the X are added, and those the take away from the X are subtracted. The OH radical (X61) is formed from H2 O2 (J32), however, when
2.1.5. Inflammatory response While this model’s main focus is cellular neurodegeneration, the immune system also plays an important role in this process. Activated t-cells and macrophages produce proinflammatory cytokines, which activate other macrophages and astrocytes (Parkinson et al., 1997). The activated astrocytes produce iNOS, while the induced macrophages produce both iNOS and superoxide; both of which trigger an imbalance between RONS and antioxidants and contribute to the disease state (Parkinson et al., 1997; Sayre et al., 2008). Activated t-cells and macrophages also produce anti-inflammatory cytokines, however, the pro-inflammatory cytokines usually overwhelm this defense (Mirshafiey and Mohsenzadegan, 2009).
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Fig. 1. Increased levels of reactive oxygen and nitrogen species in the disease versus the baseline model.
Fig. 2. Lowered levels of reactive oxygen and nitrogen species in the treatment model versus disease model.
antioxidants are added H2 O2 is reformed from the OH radical (J31). So, the system equation would be X61 = J32 − J31.
(ODC) was the most increased by these rates (Fig. 3). The focus of this model was the death of the ODC, and as such there are more factors contributing to ODC death represented in the model. Axonal apoptosis was increased as well, due entirely to increased rates of theoretical mtDNA damage.
2.2.4. Excel spreadsheets PLAS produces tables of data containing the concentrations of each X-value over a time interval. In order to better view the results, these tables were copied and pasted into excel spreadsheets; in this fashion tables for the baseline state, the disease state, and a treated state were produced. To compare the different states, analysis spreadsheets were formatted with the formula (Disease − Baseline)/Baseline for percent change from the baseline state, and (Treatment − Disease)/Disease for percent change from the disease state. The percent change values were created into graphs for a more visual interpretation of the data. 3. Results 3.1. Reactive oxygen and nitrogen species 3.1.1. Disease model Increased levels of reactive oxygen and nitrogen species were simulated in the disease model by increasing the rates of formation for peroxynitrite, hydrogen peroxide, and the hydroxy radical (Fig. 1). In addition, levels of nitric oxide were elevated by increasing the amount of inducible nitric oxide synthase (iNOS) released from macrophages and astrocytes (Model 1). Superoxide levels were elevated by increasing the mtDNA damage and thus electron transport chain mutations. 3.1.2. Treatment model The treatment model for reactive oxygen and nitrogen species was created by preventing the activation of pro-inflammatory cytokines by T-cells thereby mimicking a potential drug treatment. Activated pro-inflammatory cytokines activate macrophages and astrocytes, which secrete iNOS leading to nitric oxide production. NO production leads to the production of peroxynitrite and the hydroxy radical. Activated macrophages also increase the rate of conversion of oxygen to superoxide. Therefore, by preventing the activation of pro-inflammatory cytokines, NO and superoxide production is suppressed and thus all of their products (Fig. 2).
3.2.2. Treatment model The treatment model for apoptosis levels was created by preventing the activation of pro-inflammatory cytokines by T-cells. Activated pro-inflammatory cytokines activate macrophages and astrocytes, which secrete iNOS leading to nitric oxide production and increasing superoxide production. NO and superoxide production lead to the production of peroxynitrite and the hydroxyl radical, which damage DNA/RNA, proteins, and cause lipid peroxidation; these things lead to oligodendrocyte apoptosis in the disease model. Therefore, by preventing the activation of proinflammatory cytokines, NO production is suppressed and its products no longer cause oligodendrocyte death (Fig. 4). 3.3. Apoptotic factors 3.3.1. Disease model The disease model for increased apoptotic factors was made by increasing the rate at which Bid and Bak form a complex to open the permeability transition pore (PTP), which releases cytochrome C and AIF (Fig. 5; Model 2). Concentrations of the apoptosome complex were increased as a result of increased cytosolic cytochrome C and an increased rate of formation. Cytosolic calcium was elevated via increased glutamate due to a modeled excitotoxic state. 3.3.2. Treatment model The treatment model for the release of apoptotic factors was created by greatly lowering the rate of the opening of the PTP, in effect, closing the PTP. By preventing the PTP from opening, cytochrome
3.2. Apoptosis levels 3.2.1. Disease model The disease model for increased apoptosis was created by increasing theoretical levels of DNA/RNA damage, mtDNA damage, protein damage, and lipid peroxidation, which lead to apoptosis in the context of the model (Model 1). In addition, the rate of activation of caspases and the rate of release of apoptotic inducing factor (AIF) were increased. The rate of apoptosis of the oligodendrocyte
Fig. 3. Rate of oligodendrocyte and axon apoptosis elevated in the disease model versus the baseline model.
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Fig. 4. Rate of oligodendrocyte and axon apoptosis decreased in treatment model versus disease model.
Fig. 5. Increased levels of Ca2+ , cytochrome C, AIF, and the apoptosome complex in the disease versus baseline model.
Fig. 6. Lowered levels of cytochrome C, AIF, and the apoptosome in the treatment versus disease model.
C and AIF cannot be released from the mitochondria and these levels dramatically decrease (Fig. 6). Without cytosolic cytochrome C, apoptosome formation is decreased. Because the rate of apoptosome formation is held constant in the model in order to have only one therapeutic target (the PTP), the levels of apoptosome formation eventually rise. The decreased cytochrome C and AIF also contribute to the lowered rate of ODC apoptosis (Fig. 4). 4. Discussion 4.1. Disease model The results of the disease model when compared to the baseline model seem to mimic the results of actual MS and in most cases the experimental autoimmune encephalitis (EAE) that is the experimental model.
Fig. 1 shows greatly increased reactive oxygen and nitrogen species, with peroxynitrite being the most increased. Mitochondria naturally produce superoxide, H202, and the hydroxyl radical, but in MS, the mitochondria work excessively to counter depleted ATP (Ghafourifar et al., 2008). The overworked mitochondria produce excess ROS that cannot be quenched by normal levels of antioxidants. NO, which is found in higher levels in the spinal cord in EAE, is produced primarily by immune cells in MS and couples with superoxide in the mitochondria to produce peroxynitrite (Ghafourifar et al., 2008). Peroxynitrite is one of the most commonly studied free radicals and is considered the most destructive (Gonsette, 2008). Peroxynitrite has been found consistently in MS lesions and also plays a role in EAE (Gonsette, 2008), so it is promising that it is present in the disease model at the highest levels. The levels of ODC and axonal apoptosis (Fig. 3) are due to elevated hydroxyl radical and peroxynitrite. In the disease model of MS, the hydroxyl radical and peroxynitrite were shown activating the conversion of healthy DNA/RNA, lipids, proteins, and mtDNA into damaged forms (Sayre et al., 2008). These damaged forms compromise the cellular integrity and lead to apoptosis. The increased apoptotic factors (Fig. 5) were a result of the death receptor cascade as well as excitotoxicity in the disease model. The death ligand binds to the death receptor, activating caspase 8 (Kalman et al., 2007). Caspase 8 cleaves Bid into a form that binds to Bak to open the PTP (Kalman et al., 2007). Cytochrome C and AIF are released from the mitochondria and cytochrome C goes onto form the apoptosome (Kalman et al., 2007). The PTP opening also results in the uncoupling of the ETC and the stopping of ATP synthesis (Kalman et al., 2007). The elevated levels of cytochrome C, AIF, and the apoptosome complex in the disease model signify a damaged and dying cell. The increased calcium ion in the disease model is a result of excitoxicity. Excitatory amino acids, primarily glutamate in MS, are coupled to ion channels and their dysfunction can lead to excess calcium ion and eventually apoptosis (Gonsette, 2008). In ODCs, NMDA receptors, when bound to glutamate, allow calcium ion into the cell (Trapp and Stys, 2009). In the axon, calcium can enter the via the Na+ /K+ exchanger or be released from the axoplasmic reticulum via IP3 receptors, which are activated by glutamate receptors on the surface of the axon (Trapp and Stys, 2009). These glutamate-related channels and receptors lead to increased intracellular calcium which has harmful effects. In the oligodendrocyte, calcium increases the release of cytochrome C from the mitochondria as well as activates calpain, which contributes to the caspase cascade (Das et al., 2008). In the axon, calcium activates a series of kinases, which eventually activate neuronal nitric oxide synthase (nNOS), which contributes to oxidative stress in the axon (Trapp and Stys, 2009). 4.2. Treatment model The results of the therapeutic treatments on the disease model reduced oligodendrocyte death and other intracellular toxins. Though this model suggests clinical treatment protocols for humans, it should also be applicable for studies using EAE mice with mitochondrial abnormalities. The mechanism of Figs. 2 and 4 involves preventing the activation of pro-inflammatory cytokines. This mechanism mimics the current treatment for MS, which typically involves suppression of the overzealous immune response characteristic of MS (Lim and Constantinescu, 2010). While this model highlights a treatment effect of decreased cytokine activation, the model did not present any compensatory activity in the model when pro-inflammatory cytokine levels were allowed to increase. The disease literature on which this model focused does not suggest any such compensatory action at this time. The PTP treatment (Fig. 6) was largely theoretical and the results showed a marked decrease in cytochrome C and AIF, which could prove ben-
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eficial to MS patients; however, the slight increase in the levels of apoptosome complex in this proposed treatment could prove detrimental. The elevated levels of apoptosome complex could be an actual increase or a mathematical anomaly. A 2007 study by Forte et al., studied the effects of knocking out cyclophilin D (CyPD), a gene that encodes a PTP regulator protein, in the neurons of mice (Fort et al., 2007). These knock-out mice were then subjected to EAE to simulate MS; the PTP resisted opening in the knock-out mice causing them to survive longer than controls. The CyPD knockout mice were also more resistant to reactive oxygen and nitrogen species. This model proposes that the PTPs of oligodendrocytes are also viable MS therapeutic targets. This potential treatment could be beneficial in human MS patients with further testing. 5. Conclusion Using BST to create a model of MS is a safe, cost-effective way to study potential therapeutic treatments for MS. Several possible disease mechanisms for MS are addressed in this MS model, such as oxidative stress, excitotoxicity, inflammation, death receptor cascades, caspase cascades, and apoptotic factors. The model not only provides a vehicle for visualizing these proposals, but it also emphasizes the interaction between the various biochemical species. The MS model supports some of the current treatments for MS and also suggests the PTP as a drug target for future research. This model can be used in the future to judge the efficacy of newly proposed treatments. Acknowledgements This work was supported by grants from the Howard Hughes Medical Institute, Undergraduate Biological Sciences Education Program, The College of William and Mary; The James Monroe Scholars Program, The College of William and Mary. The visual representations of modeled processes were created using CellDesigner 4.0.1., which can be found at http://www. celldesigner.org/. The models presented were constructed using the software program Power Law Analysis and Simulation (PLAS), developed by Antonio E.N. Ferreira, which upon beginning this work could be found at http://www.dqb.fc.ul.pt/docentes/aferreira/plas.html, a link which is currently inactive.
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Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.jneumeth.2011.08.008. References Circu ML, Aw TY. Reactive oxygen species, cellular redox systems, and apoptosis. Free Radic Biol Med 2010;48(March 15 (6)):749–62. Das A, Guyton MK, Butler JT, Ray SK, Banik NL. Activation of calpain and caspase pathways in demyelination and neurodegeneration in animal model of multiple sclerosis. CNS Neurol Disord Drug Targets 2008;7(June (3)):313–20. Forte M, Gold BG, Marracci G, Chaudhary P, Basso E, Johnsen D, et al. Cyclophilin D inactivation protects axons in experimental autoimmune encephalomyelitis, an animal model of multiple sclerosis. Proc Natl Acad Sci U S A 2007;104(May 1 (18)):7558–63. Ghafourifar P, Mousavizadeh K, Parihar MS, Nazarewicz RR, Parihar A, Zenebe WJ. Mitochondria in multiple sclerosis. Front Biosci 2008;13(January (1)):3116–26. Gonsette RE. Neurodegeneration in multiple sclerosis: The role of oxidative stress and excitotoxicity. J Neurol Sci 2008;274(November 15 (1–2)):48–53. Kalman B, Laitinen K, Komoly S. The involvement of mitochondria in the pathogenesis of multiple sclerosis. J Neuroimmunol 2007;188(August (1–2)):1–12. Kitano H, Funahashi A, Matsuoka Y, Oda K. Using process diagrams for the graphical representation of biological networks. Nat Biotechnol 2005;23(August (8)):961–6. Lim SY, Constantinescu CS. Current and future disease-modifying therapies in multiple sclerosis. International Journal of Clinical Practice 2010;64(April (5)):637–50. Mao P, Reddy PH. Is multiple sclerosis a mitochondrial disease? Biochim Biophys Acta Mol Basis Dis 2010;1802(January (1)):66–79. Mirshafiey A, Mohsenzadegan M. TGF-beta as a promising option in the treatment of multiple sclerosis. Neuropharmacology 2009;56(May–June (6–7)):929–36. Parkinson JF, Mitrovic B, Merrill JE. The role of nitric oxide in multiple sclerosis. J Mol Med 1997;75(March (3)):174–86. Sass MB, Lorenz AN, Green RL, Coleman RA. A pragmatic approach to biochemical systems theory applied to an alpha-synuclein-based model of parkinson’s disease. J Neurosci Methods 2009;178(April 15 (2)):366–77. Savageau MA. Bicohemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation. J Theor Biol 1969;25:370–9. Sayre LM, Perry G, Smith MA. Oxidative stress and neurotoxicity. Chem Res Toxicol 2008;21(January (1)):172–88. Smith KJ, Kapoor R, Felts PA. Demyelination: the role of reactive oxygen and nitrogen species. Brain Pathol 1999;9(January (1)):69–92. Trapp BD, Stys PK. Virtual hypoxia and chronic necrosis of demyelinated axons in multiple sclerosis. Lancet Neurol 2009;8(March (3)):280–91. van der Veen RC, Roberts LJ. Contrasting roles for nitric oxide and peroxynitrite in the peroxidation of myelin lipids. J Neuroimmunol 1999;95(March 1 (1–2)):1–7. Ventimiglia R, Lau LF, Kinloch RA, Hopkins A, Karran EH, Petalidis LP, et al. Role of caspases in neuronal apoptosis. Drug Dev Res 2001;52(April (4)):515–33. Voit EO. Computation analysis of biochemical systems: a practical guide for biochemists and molecular biologists. New York: Cambridge University Press; 2000. Yeager MP, Coleman RA. In silico evidence for glutathione- and iron-related pathogeneses in parkinson’s disease. J Neurosci Methods 2010;188(4/30 (1)):151–64.
Contents lists available at ScienceDirect
Journal of Neuroscience Methods journal homepage: www.elsevier.com/locate/jneumeth
A mathematical model of cell death in multiple sclerosis Taylor M. Broome, Randolph A. Coleman ∗ Department of Chemistry Integrated Science Center, 540 Landrum Drive, The College of William and Mary, Williamsburg, VA 23187, USA
a r t i c l e
i n f o
Article history: Received 22 June 2011 Received in revised form 4 August 2011 Accepted 7 August 2011 Keywords: Multiple sclerosis Computational biology Neurodegenerative diseases Reactive oxygen species Reactive nitrogen species Apoptosis Permeability transition pore
a b s t r a c t This paper imparts a mathematical model of multiple sclerosis (MS) that was created using Biochemical Systems Theory (BST). This method uses mechanisms and initial values from the literature to create a mathematical model of a disease. The model can then be used to test potential drug therapies and to detect possible trigger points for the disease. The focus of this MS model is mainly the action of reactive oxygen and nitrogen species (RONS), the permeability transition pore (PTP), apoptotic factors, and the eventual cell death in the oligodendrocyte. Several treatment methods were applied based on current therapies; however, one treatment, the prevention of the PTP from opening, is completely experimental and showed positive results based on this model. BST is an effective means of studying MS and can be beneficial in testing new therapy ideas. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Multiple sclerosis (MS) is a neurodegenerative disorder characterized by demyelination. There have been many experiments to pinpoint a single cause of MS, but no such cause has been found, suggesting that the cause is a combination of several etiologies. Some of the proposed causes for the disorder are reactive oxygen and nitrogen species (RONS), an inflammatory response, excitotoxicity and ionic imbalance (Gonsette, 2008; Mao and Reddy, 2010). This study uses biochemical systems theory (BST) to create a model that details the interactions between these potential MS origins. The primary focus of this model is the death of the oligodendrocyte, the source of neuronal myelin, and some of its basic effects on the axon. BST was originally created by Savageau (1969) and expanded upon by Voit (2000) (Sass et al., 2009). The main purpose of BST is to provide a mathematical framework for a biochemical system. BST is useful in viewing the net effect of reactions through system equations, even when few experimental concentrations are actually known, which is the case with MS. In this study, BST was used to create a normal state, a diseased MS state, and treatment state. The treatment state was created by locating trigger points in the MS model that lead to the disease state, such as the generation of RONS, greatly weakening these processes mathematically, and comparing the resulting data to the diseased state. These MS trigger
∗ Corresponding author. Tel.: +1 757 221 2679; fax: +1 757 221 2715. E-mail address: [email protected] (R.A. Coleman). 0165-0270/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jneumeth.2011.08.008
points located using BST could lead the way to future therapeutic treatments for MS. 2. Methods This section details the cellular pathways presented in the MS model, as well as the process by which the model was mathematized. The modeled pathways were created using the program Cell Designer (Kitano et al., 2005), which allowed for a visual interpretation of the MS literature in the form of a model (Models 1 and 2, Appendix). PLAS, power law analysis and simulation (http://www.dqb.fc.ul.pt/docentes/aferreira/plas.html, link no longer available) was used to create a mathematical interpretation of the MS. See our lab’s earlier publications for more details (Sass et al., 2009; Yeager and Coleman, 2010). 2.1. Modeled cellular pathways 2.1.1. Reactive oxygen and nitrogen species formation Reactive oxygen and nitrogen species (RONS) are extremely detrimental to cellular processes and their formation, in excess, can lead to apoptosis. This model shows the formation and degradation of RONS in both an oligodendrocyte and a neuron. The formation of RONS begins with the secretion of nitric oxide synthase, either from astrocytes and macrophages in the inducible form (iNOS) or from the neuron itself (nNOS), to produce nitric oxide (NO) (van der Veen and Roberts, 1999; Mirshafiey and Mohsenzadegan, 2009; Trapp and Stys, 2009). Superoxide is formed either from electron transport chain mutations or secreted from macrophages (Parkinson
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Model 1. Activation of the inflammatory response and production of reactive oxygen and nitrogen species leading to cell death in the oligodendrocyte.
et al., 1997; Sayre et al., 2008). Superoxide and NO form peroxynitrite, which can then be converted into the less harmful H2 O2 by superoxide dismutase (SOD) (Smith et al., 1999; Sayre et al., 2008; Trapp and Stys, 2009). H2 O2 can either be converted to water via antioxidants, or the OH radical (Smith et al., 1999; Sayre et al., 2008). Peroxynitrite and OH radical are very harmful to the cell and in high concentrations lead to DNA, RNA, and mRNA damage, lipid peroxidation, and protein damage. 2.1.2. Ca2+ accumulation In a healthy neuron, Ca2+ concentrations are regulated by Ca2+ importation into the axoplasmic reticulum (AR) and Ca2+ being exported out of the cell. In MS conditions, Ca2+ is released from the AR via IP3 and Ry receptors, causing an accumulation of Ca2+ in the axon (Trapp and Stys, 2009). Ca2+ accumulation leads to nNOS production, which leads to RONS formation (Trapp and Stys, 2009). Demyelination causes reversal of the Ca2+ –Na+ exchanger, which
also results in a larger concentration of Ca2+ in the axon (Trapp and Stys, 2009). Moreover, Ca2+ triggers the activation of calpain, which then initiates caspase 12 and cathespin release, both of which lead to apoptosis (Das et al., 2008). Additionally, cytochrome C release from the mitochondria is exacerbated by excess Ca2+ . 2.1.3. Death complex formation and caspase activation One of the starting points for apoptosis is formation of a death complex. Death complex formation occurs when a death ligand (TNF-␣, Fas, TRAIL) binds to a death receptor (TNFR1, FasL, TRAILR1) (Kalman et al., 2007). Following this, several cofactors bind to the complex allowing it to activate caspase 8 and other apoptotic proteins (Ventimiglia et al., 2001; Kalman et al., 2007; Circu and Aw, 2010). Caspase 8, in addition to caspase 12 and caspase 9, activates other caspases, but does not lead directly to apoptosis like caspases 3 and 9 (Ghafourifar et al., 2008). The caspase cascade is a major precursor to apoptosis.
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Model 2. Death complex formation leads to the opening of the PTP, which releases cytochrome C and AIF from the mitochondrion, leading to apoptosome formation.
2.1.4. Release of apoptotic factors The permeability transition pore (PTP) controls whether or not certain substances exit the mitochondria and enter the cytoplasm. The PTP is controlled by the BID complex, which is made up of the cleaved BID protein and Bak, a transmembrane protein (Kalman et al., 2007). When caspase 8 is activated by the death complexes, it cleaves BID, allowing it to bind to Bak and form the BID complex. When the PTP is opened, it releases cytochrome c and apoptosis inducing factor (AIF) into the cytoplasm (Ventimiglia et al., 2001; Kalman et al., 2007; Circu and Aw, 2010). Cytochrome c binds with other proteins to form the apoptosome, which begins a caspase cascade; whereas AIF leads directly to apoptosis (Kalman et al., 2007).
2.2.1. Initial values The first step in mathematizing the MS model was assigning every species in the model an X-value and determining if the species was dependent or independent. For the most part if a species was affecting another species, but not itself being affected, it was labeled as independent. Each X was then given an initial concentration; these initial concentrations were based on relative terms, rather than absolute values. Where possible, the research literature was used to estimate initial concentrations and relative concentrations of each species. See our lab’s earlier publications for more details (Sass et al., 2009).
2.2. PLAS
2.2.2. Flux equations Each reaction in the model was assigned a J-value, which was used to identify the reaction, in addition to a rate constant, k. The X-value for each species used by the reaction is also incorporated into the flux equation. For example, peroxynitrite is formed (J34) by the combination of superoxide (X47) and NO (X46). The flux equation for this reaction would be J34 = k34 X47ˆg3447 X36ˆg3446, with k34, g3447, and g3446 as rate-determining constants; for the most part, the g-values are left as 1.00. Some reactions in the model are catalyzed or inhibited by certain species; this is shown by deriving the k value and multiplying it by the rate constants p for promoting and i for inhibiting. For example, H2 O2 formation (J33) is catalyzed by MnSOD (X51) and inhibited by NO (X46). The k equation would be k33 = 0.01 * (p3351 X51 + i3346 X46); the p-values are typically left as 1.00, while the i-values are left as −1.00. The k and k values vary based on the relative activity of the reaction.
Power law analysis and simulation (PLAS) is a program that uses mathematical equations to estimate projected concentrations and values over a time interval. In order to do this, each species and reaction in the MS model had to be converted into a mathematical variable or equation.
2.2.3. System equations To assess the interactions between the reactions, each dependent X-value is given a system equation. J-values that contribute to the X are added, and those the take away from the X are subtracted. The OH radical (X61) is formed from H2 O2 (J32), however, when
2.1.5. Inflammatory response While this model’s main focus is cellular neurodegeneration, the immune system also plays an important role in this process. Activated t-cells and macrophages produce proinflammatory cytokines, which activate other macrophages and astrocytes (Parkinson et al., 1997). The activated astrocytes produce iNOS, while the induced macrophages produce both iNOS and superoxide; both of which trigger an imbalance between RONS and antioxidants and contribute to the disease state (Parkinson et al., 1997; Sayre et al., 2008). Activated t-cells and macrophages also produce anti-inflammatory cytokines, however, the pro-inflammatory cytokines usually overwhelm this defense (Mirshafiey and Mohsenzadegan, 2009).
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Fig. 1. Increased levels of reactive oxygen and nitrogen species in the disease versus the baseline model.
Fig. 2. Lowered levels of reactive oxygen and nitrogen species in the treatment model versus disease model.
antioxidants are added H2 O2 is reformed from the OH radical (J31). So, the system equation would be X61 = J32 − J31.
(ODC) was the most increased by these rates (Fig. 3). The focus of this model was the death of the ODC, and as such there are more factors contributing to ODC death represented in the model. Axonal apoptosis was increased as well, due entirely to increased rates of theoretical mtDNA damage.
2.2.4. Excel spreadsheets PLAS produces tables of data containing the concentrations of each X-value over a time interval. In order to better view the results, these tables were copied and pasted into excel spreadsheets; in this fashion tables for the baseline state, the disease state, and a treated state were produced. To compare the different states, analysis spreadsheets were formatted with the formula (Disease − Baseline)/Baseline for percent change from the baseline state, and (Treatment − Disease)/Disease for percent change from the disease state. The percent change values were created into graphs for a more visual interpretation of the data. 3. Results 3.1. Reactive oxygen and nitrogen species 3.1.1. Disease model Increased levels of reactive oxygen and nitrogen species were simulated in the disease model by increasing the rates of formation for peroxynitrite, hydrogen peroxide, and the hydroxy radical (Fig. 1). In addition, levels of nitric oxide were elevated by increasing the amount of inducible nitric oxide synthase (iNOS) released from macrophages and astrocytes (Model 1). Superoxide levels were elevated by increasing the mtDNA damage and thus electron transport chain mutations. 3.1.2. Treatment model The treatment model for reactive oxygen and nitrogen species was created by preventing the activation of pro-inflammatory cytokines by T-cells thereby mimicking a potential drug treatment. Activated pro-inflammatory cytokines activate macrophages and astrocytes, which secrete iNOS leading to nitric oxide production. NO production leads to the production of peroxynitrite and the hydroxy radical. Activated macrophages also increase the rate of conversion of oxygen to superoxide. Therefore, by preventing the activation of pro-inflammatory cytokines, NO and superoxide production is suppressed and thus all of their products (Fig. 2).
3.2.2. Treatment model The treatment model for apoptosis levels was created by preventing the activation of pro-inflammatory cytokines by T-cells. Activated pro-inflammatory cytokines activate macrophages and astrocytes, which secrete iNOS leading to nitric oxide production and increasing superoxide production. NO and superoxide production lead to the production of peroxynitrite and the hydroxyl radical, which damage DNA/RNA, proteins, and cause lipid peroxidation; these things lead to oligodendrocyte apoptosis in the disease model. Therefore, by preventing the activation of proinflammatory cytokines, NO production is suppressed and its products no longer cause oligodendrocyte death (Fig. 4). 3.3. Apoptotic factors 3.3.1. Disease model The disease model for increased apoptotic factors was made by increasing the rate at which Bid and Bak form a complex to open the permeability transition pore (PTP), which releases cytochrome C and AIF (Fig. 5; Model 2). Concentrations of the apoptosome complex were increased as a result of increased cytosolic cytochrome C and an increased rate of formation. Cytosolic calcium was elevated via increased glutamate due to a modeled excitotoxic state. 3.3.2. Treatment model The treatment model for the release of apoptotic factors was created by greatly lowering the rate of the opening of the PTP, in effect, closing the PTP. By preventing the PTP from opening, cytochrome
3.2. Apoptosis levels 3.2.1. Disease model The disease model for increased apoptosis was created by increasing theoretical levels of DNA/RNA damage, mtDNA damage, protein damage, and lipid peroxidation, which lead to apoptosis in the context of the model (Model 1). In addition, the rate of activation of caspases and the rate of release of apoptotic inducing factor (AIF) were increased. The rate of apoptosis of the oligodendrocyte
Fig. 3. Rate of oligodendrocyte and axon apoptosis elevated in the disease model versus the baseline model.
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Fig. 4. Rate of oligodendrocyte and axon apoptosis decreased in treatment model versus disease model.
Fig. 5. Increased levels of Ca2+ , cytochrome C, AIF, and the apoptosome complex in the disease versus baseline model.
Fig. 6. Lowered levels of cytochrome C, AIF, and the apoptosome in the treatment versus disease model.
C and AIF cannot be released from the mitochondria and these levels dramatically decrease (Fig. 6). Without cytosolic cytochrome C, apoptosome formation is decreased. Because the rate of apoptosome formation is held constant in the model in order to have only one therapeutic target (the PTP), the levels of apoptosome formation eventually rise. The decreased cytochrome C and AIF also contribute to the lowered rate of ODC apoptosis (Fig. 4). 4. Discussion 4.1. Disease model The results of the disease model when compared to the baseline model seem to mimic the results of actual MS and in most cases the experimental autoimmune encephalitis (EAE) that is the experimental model.
Fig. 1 shows greatly increased reactive oxygen and nitrogen species, with peroxynitrite being the most increased. Mitochondria naturally produce superoxide, H202, and the hydroxyl radical, but in MS, the mitochondria work excessively to counter depleted ATP (Ghafourifar et al., 2008). The overworked mitochondria produce excess ROS that cannot be quenched by normal levels of antioxidants. NO, which is found in higher levels in the spinal cord in EAE, is produced primarily by immune cells in MS and couples with superoxide in the mitochondria to produce peroxynitrite (Ghafourifar et al., 2008). Peroxynitrite is one of the most commonly studied free radicals and is considered the most destructive (Gonsette, 2008). Peroxynitrite has been found consistently in MS lesions and also plays a role in EAE (Gonsette, 2008), so it is promising that it is present in the disease model at the highest levels. The levels of ODC and axonal apoptosis (Fig. 3) are due to elevated hydroxyl radical and peroxynitrite. In the disease model of MS, the hydroxyl radical and peroxynitrite were shown activating the conversion of healthy DNA/RNA, lipids, proteins, and mtDNA into damaged forms (Sayre et al., 2008). These damaged forms compromise the cellular integrity and lead to apoptosis. The increased apoptotic factors (Fig. 5) were a result of the death receptor cascade as well as excitotoxicity in the disease model. The death ligand binds to the death receptor, activating caspase 8 (Kalman et al., 2007). Caspase 8 cleaves Bid into a form that binds to Bak to open the PTP (Kalman et al., 2007). Cytochrome C and AIF are released from the mitochondria and cytochrome C goes onto form the apoptosome (Kalman et al., 2007). The PTP opening also results in the uncoupling of the ETC and the stopping of ATP synthesis (Kalman et al., 2007). The elevated levels of cytochrome C, AIF, and the apoptosome complex in the disease model signify a damaged and dying cell. The increased calcium ion in the disease model is a result of excitoxicity. Excitatory amino acids, primarily glutamate in MS, are coupled to ion channels and their dysfunction can lead to excess calcium ion and eventually apoptosis (Gonsette, 2008). In ODCs, NMDA receptors, when bound to glutamate, allow calcium ion into the cell (Trapp and Stys, 2009). In the axon, calcium can enter the via the Na+ /K+ exchanger or be released from the axoplasmic reticulum via IP3 receptors, which are activated by glutamate receptors on the surface of the axon (Trapp and Stys, 2009). These glutamate-related channels and receptors lead to increased intracellular calcium which has harmful effects. In the oligodendrocyte, calcium increases the release of cytochrome C from the mitochondria as well as activates calpain, which contributes to the caspase cascade (Das et al., 2008). In the axon, calcium activates a series of kinases, which eventually activate neuronal nitric oxide synthase (nNOS), which contributes to oxidative stress in the axon (Trapp and Stys, 2009). 4.2. Treatment model The results of the therapeutic treatments on the disease model reduced oligodendrocyte death and other intracellular toxins. Though this model suggests clinical treatment protocols for humans, it should also be applicable for studies using EAE mice with mitochondrial abnormalities. The mechanism of Figs. 2 and 4 involves preventing the activation of pro-inflammatory cytokines. This mechanism mimics the current treatment for MS, which typically involves suppression of the overzealous immune response characteristic of MS (Lim and Constantinescu, 2010). While this model highlights a treatment effect of decreased cytokine activation, the model did not present any compensatory activity in the model when pro-inflammatory cytokine levels were allowed to increase. The disease literature on which this model focused does not suggest any such compensatory action at this time. The PTP treatment (Fig. 6) was largely theoretical and the results showed a marked decrease in cytochrome C and AIF, which could prove ben-
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eficial to MS patients; however, the slight increase in the levels of apoptosome complex in this proposed treatment could prove detrimental. The elevated levels of apoptosome complex could be an actual increase or a mathematical anomaly. A 2007 study by Forte et al., studied the effects of knocking out cyclophilin D (CyPD), a gene that encodes a PTP regulator protein, in the neurons of mice (Fort et al., 2007). These knock-out mice were then subjected to EAE to simulate MS; the PTP resisted opening in the knock-out mice causing them to survive longer than controls. The CyPD knockout mice were also more resistant to reactive oxygen and nitrogen species. This model proposes that the PTPs of oligodendrocytes are also viable MS therapeutic targets. This potential treatment could be beneficial in human MS patients with further testing. 5. Conclusion Using BST to create a model of MS is a safe, cost-effective way to study potential therapeutic treatments for MS. Several possible disease mechanisms for MS are addressed in this MS model, such as oxidative stress, excitotoxicity, inflammation, death receptor cascades, caspase cascades, and apoptotic factors. The model not only provides a vehicle for visualizing these proposals, but it also emphasizes the interaction between the various biochemical species. The MS model supports some of the current treatments for MS and also suggests the PTP as a drug target for future research. This model can be used in the future to judge the efficacy of newly proposed treatments. Acknowledgements This work was supported by grants from the Howard Hughes Medical Institute, Undergraduate Biological Sciences Education Program, The College of William and Mary; The James Monroe Scholars Program, The College of William and Mary. The visual representations of modeled processes were created using CellDesigner 4.0.1., which can be found at http://www. celldesigner.org/. The models presented were constructed using the software program Power Law Analysis and Simulation (PLAS), developed by Antonio E.N. Ferreira, which upon beginning this work could be found at http://www.dqb.fc.ul.pt/docentes/aferreira/plas.html, a link which is currently inactive.
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