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The Treatment of Bipolar Disorder: Modeling Lithiums Effect on - - PowerPoint PPT Presentation
The Treatment of Bipolar Disorder: Modeling Lithiums Effect on - - PowerPoint PPT Presentation
The Treatment of Bipolar Disorder: Modeling Lithiums Effect on Neuronal Bursting Rosa Rossi-Goldthorpe Bowdoin College January 27th, 2019 NCUWM 2019 The Biology The Model and the Math Lithium in the Model Lithium Treatment Table of
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Bipolar Disorder
- Mental illness characterized by “unusual shifts in
mood, energy, activity levels, and the ability to carry
- ut day-to-day tasks” (NIMH)
- Extreme mood “episodes” tend to be between two
extreme mood-states: mania and depression (NIMH)
- The transition between extreme moods is not cyclical;
both internal and environmental stressors can trigger a mood swing
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The Biology The Model and the Math Lithium in the Model Lithium Treatment
Lithium as a Mood Stabilizer
- Lithium is the most commonly prescribed drug for
bipolar disorder, the only widely used mood-stabilizer
- Newer mood stabilizers are not typically as effective
(Thies-Flechtner, 1996)
- Competing hypotheses about biological mechanism
- f bipolar and how lithium corrects it
- Lithium treatment tailored to individual
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Proposed Mechanism
Potential Genetic Mechanism Gene Mutation High IP3 Excess Ca2+ High NT Release
Gene mutation associated with high risk of bipolar disorder causes elevated Ca2+ levels(Psychiatric Genomics Consortium, 2011)
Proposed Lithium Mechanism Lithium Inhibits IP3R action Lowers Ca2+ Decrease NT
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Neurons and Neurotransmitters (NT)
Neurons:
- Type of cell in the nervous system
- Carries information throughout the nervous system by
chemical and electrical signals (NINDS)
- Electrical impulse to chemical signal to electrical
impulse
Neurotransmitters:
- Chemical messengers that transmit information to a
neuron
- Norepinephrine implicated in euphoria/grandiosity,
defining characteristics of mania (Goodwin, 1974)
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Action Potentials (AP)
- APs are electrical impulses caused by membrane
depolarization (Bear, 84)
- Arrival of AP in terminal triggers release of NT(Bear,
122)
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Model Hypothesis
- Burst-frequency determines amount of NT released
(Wilkins, 232)
Assume high NT release causes mania. And lithium treat- ment works by lowering intracellular calcium which lowers burst frequency. This decreases NT release which stabi- lizes mood. Lithium Lowers Ca2+ Decrease burst freq. Decrease NT ?
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Morris-Lecar Model
dV dt = 1 C
5
(I − gcaM∞(V − Vca) − gkW(V − Vk) − gl(V − Vl))
6
dW dt = φ(W∞ − W) τW M∞(V) = 1 2
5
1 + tanh
3V − V1
V2
46
W∞(V) = 1 2
5
1 + tanh
3V − V3
V4
46
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Bursting in 2-D ML Model
What is a“burst”?
- “a rapid cluster of action potentials followed by a brief
pause” (Bear, 106)
- 2-D model, every action potential represents a burst
(Williams, 2013)
1
1Hayashi, 2016. Orange by Rosa 12 / 38
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Nernst Equation for Calcium
ICa = gCaM∞(V − VCa) Reversal potential is the membrane voltage at electochemical equilibrium (Bear, 68) VCa = RT 2F ln
3[Ca2+]out
[Ca2+]in
4
So, if intracellular Ca2+ concentration, [Ca2+]in, increases, the VCa would decrease
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Lithium Addition to Morris-Lecar Model
How does the addition of lithium change the model? Lithium Lowers Ca2+ Decrease burst freq. Decrease NT ? If bipolar disorder is caused by abnormal intracellular lev- els of calcium, where intracellular calcium is elevated, we would expect the reversal potential of calcium, VCa, to be lower than the average value.
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Lithium Addition to Morris-Lecar Model
How does the addition of lithium change the model? Lithium Lowers Ca2+ Decrease burst freq. Decrease NT ? Increase VCa ? If bipolar disorder is caused by abnormal intracellular lev- els of calcium, where intracellular calcium is elevated, we would expect the reversal potential of calcium, VCa, to be lower than the average value.
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Bifurcations
Using Vca as the bifurcation parameter
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Bifurcations
Emergence of Limit Cycles, VCa = 85.6 T ≈ 73.85; f ≈ .0135, for stable LC
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Frequency of Limit Cycle
20 40 60 80 100 120 140 160 180 200 0.011 0.0115 0.012 0.0125 0.013 0.0135 0.014 0.0145 0.015
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Response Function for Lithium to Vca
Vca = α tanh(.003(L(t) − 1000)) + β; α and β are scaling factors to account for physiological differences
200 400 600 800 1000 1200 1400 1600 1800 2000 60 70 80 90 100 110 120 130
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Lithium Concentration in Bloodstream
Differential equation for exponential decay: dL dt = −αL L(0) = L0 α = ln(2) 36 Solution Flow: φt(L0) = L0e−αt Ln = φτ(Ln−1) + κ
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Equilibrium for Lithium Concentration
FDA has the standard lithium dosage at 300 mg every 8 hours (τ = 8, κ = 300):
2 4 6 8 10 12 108 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 L* t *
Where (L∗) and when (t∗) does L stabilize?
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Equilibrium for Lithium Concentration
FDA has the standard lithium dosage at 300 mg every 8 hours (τ = 8, κ = 300): L∗ ≈ 2097.1 mg t∗ ≈ 13 days
2 4 6 8 10 12 108 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 L* t *
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Numerical Simulations
First 36 hours of Lithium, 5 doses
2 4 6 8 10 12 14 16 18 107 200 400 600 800 1000 1200 1400
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Numerical Simulations
100 200 300 400 500 600 700 800 900 1000
t
- 40
- 30
- 20
- 10
10 20
V 25 / 38
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Numerical Simulations
2 4 6 8 10 12 14 16 18 107 200 400 600 800 1000 1200 1400
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Numerical Simulations
100 200 300 400 500 600 700 800 900 1000
t
- 40
- 30
- 20
- 10
10 20
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Numerical Simulations
2 4 6 8 10 12 14 16 18 107 200 400 600 800 1000 1200 1400
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Numerical Simulations
100 200 300 400 500 600 700 800 900 1000 t
- 50
- 40
- 30
- 20
- 10
10 20 30 40 V
- 50
- 40
- 30
- 20
- 10
10 20 30 40 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
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Numerical Simulations
16 days of Lithium treatment
2 4 6 8 10 12 14 108 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
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Numerical Simulations
- 50
- 40
- 30
- 20
- 10
10 20 30 40 50 0.1 0.2 0.3 0.4 0.5 0.6 100 200 300 400 500 600 700 800 900 1000 t
- 50
- 40
- 30
- 20
- 10
10 20 30 40 50 V
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Frequency Plots
90 100 110 120 130 140 150 160 170 0.009 0.01 0.011 0.012 0.013 0.014 0.015 90 100 110 120 130 140 150 160 170 0.009 0.01 0.011 0.012 0.013 0.014 0.015
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Mood Quantification
90 100 110 120 130 140 150 160 170 0.009 0.01 0.011 0.012 0.013 0.014 0.015
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Mania
Lithium equilibrium
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Conclusion
- Model lithium decreases the burst frequency in the
physiological ‘typical’ range by increasing the calcium reversal potential
- This decreases the amount of neurotransmitter
released by the neuron, reducing symptoms of mania
Lithium Lowers Ca2+ Decrease burst freq. Decrease NT X Increase VCa X
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Future Work
- Sensitivity analysis of parameters
- Determining an ‘optimal’ dosage for stability
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References
- Bear, Mark F., Barry W. Connors, and Michael A. Paradiso. Neuroscience: Exploring the Brain. 4th ed.
Philadelphia: Wolters Kluwer, 2016.
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Calcium Ion Concentration in Platelets and Lymphocytes of Bipolar Patients.” American Journal of Psychiatry 149, no. 1 (1992): 118-20. doi:10.1176/ajp.149.1.118.
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Research 4, no. 3-4 (2004): 227-31. doi:10.1016/j.cnr.2004.09.014.
- FDA. Lithium Prescription Label. PDF. Federal Drug Administration, October 2016.
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Enzyme Inhibitors, and Studies of Central Dopamine Turnover.” Advances in Biochemical Psychopharmacology 12 (1974): 261-79. https://www.ncbi.nlm.nih.gov/pubmed/4608958.
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References
- National Institute of Mental Health. ”Bipolar Disorder.” NIMH. April 2016.
https://www.nimh.nih.gov/health/topics/bipolar-disorder/index.shtml.
- National Institute of Neurological Disorders and Stroke. ”Brain Basics: The Life and Death of a Neuron.”
- NIH. November 2018.
https://www.ninds.nih.gov/Disorders/Patient-Caregiver-Education/life-and-death-neuron.
- Psychiatric GWAS Consortium Bipolar Disorder Working Group. ”Large-scale Genome-wide Association
Analysis of Bipolar Disorder Identifies a New Susceptibility Locus near ODZ4.” Nature Genetics 43 (September 2011): 977-83. https://www.nature.com/articles/ng.943.
- Thies-Flechtner, K., B. Muller-Oerlinghausen, W. Seibert, A. Walther, and W. Greil. ”Effect of Prophylactic
Treatment on Suicide Risk in Patients with Major Affective Disorders.” Pharmacopsychiatry 29, no. 03 (1996): 103-07. doi:10.1055/s-2007-979553.
- Williams, Alex H., Molly A. Kwiatkowski, Adam L. Mortimer, Eve Marder, Mary Lou Zeeman, and Patsy S.
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Experimental and Computational Analysis.” Journal of Neurophysiology 109, no. 10 (2013): 2451-465. doi:10.1152/jn.01010.2012.
- Wilkins, Robert. Oxford Handbook of Medical Sciences. Oxford: Oxford Univ. Press, 2011.
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Acknowledgments
Thank you to Mary Lou Zeeman for being the best advisor ever (even across the ocean), to the members of the Resilience group of the Mathematical Climate Research Network, and to Professor Levy and Professor Chong for their help on the project. This project was funded by NSF grant CCS-1521672, NSF grant DMS-1722578 and the Grua/O’Connell Research Fellowship.
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