Pathway Analysis Exemplified with Models of Dopamine Metabolism - - PowerPoint PPT Presentation
Pathway Analysis Exemplified with Models of Dopamine Metabolism Eberhard O Eberhard O. Voit it Department of Biomedical Engineering Georgia Institute of Technology and Emory University 2012 Winter School in Mathematical and Computational
2012 Winter School in Mathematical and Computational Biology
Advantages Steps of Generic Model Design Diagnostic Methods Methods of Analysis
Importance of the Pathway Specific Steps of Model Design Model Structure Results Implications for Diseases and Treatment
2
Simplified Central Dogma: Genes mRNA Protein Metabolites Response (Disease) Signaling Structure Other Functions (cell cycle, translation, ….) A whole lot can happen between gene expression and an organismic response! Also, metabolic pathways obey stoichiometric rules
Neurotransmitter Signals sent from one neuron (presynapse) to another (postsynapse) across a synapse. Human Brain: between 100 and 500 trillion synapses
psicopolis. com
Presynapse Postsynapse Synapse
5
Parkinson’ s Disease
Systemic disease Symptoms: resting tremor, rigidity, postural instability, loss of smell, … Diagnosis: experience based, subjective, no biomarker Etiology: environmental, genetic factors, and their interactions Pathogenesis: oxidative stress, mitochondrial dysfunction, protein misfolding, dopamine loss Pathology: early onset vs. later onset Treatment: mainly symptom relief, side effects, loss of effectiveness
6
Schizophrenia
Mental Disease Symptoms: abnormalities in perception or expression of reality Diagnosis: self-reported and/or psychiatric Etiology: environmental, genetic factors, recreational and prescription drugs, …, interactions Pathogenesis: Could be one or several disorders, increased dopamine activity Attention Deficit/Hyperactivity Disorder, Autism Drug Addiction
7
Macroscopic Level: Motor dysfunction, depression, mood, shaking, loss of smell, … Neuron loss Allostasis Microscopic Level: Genetic predisposition Electrophysiology and properties of membranes Enzyme kinetics Mechanisms of drug action Details of brain circuitry Mesoscopic Level: Function and malfunction in the presynapse Function and malfunction in the postsynapse Function and malfunction in circuitry
8
Typical situation in human disease: Not all metabolites and enzymes are known Not all regulatory signals are known Parameters are uncertain Concentrations are uncertain Flux rates are uncertain Q: Is there enough information to start constructing a model?
9
Type of Model Model Selection Model Design Model Analysis and Diagnosis Consistency, Robustness Validation of Dynamics Model Use and Applications Manipulation and Optimization Hypothesis Testing, Simulation, Discovery, Explanation Variables, Interactions Equations, Parameter Values Goals, Inputs, and Initial Exploration Data, Information Prior Knowledge Scope, Goals, Objective Scope, Goals, Objective Exploration of Possible Behaviors
11
Meth- Amphetamine Changes
Presynapse DA synthesis Vesicle dynamics DA recycling Postsynapse Incoming signals DARPP-32 AMPAR
Needs to be dynamic Could be discrete-time Choose continuous time; differential equations Although interesting spatial components, ignore space; at least initially Choose ordinary differential equations (ODEs) Alternative could be agent-based models (ABMs) Although stochastic effects, ignore them initially for simplicity ODEs much simpler than corresponding stochastic models
13
Biochemistry: Metabolite concentrations; enzymatic reactions *Postsynapse later
14
+
–
1 2 1 m n n n i i
inside
i i i i
Solution with Potential: “Biochemical Systems Theory” (BST)
n j f j k i ik
j i k
1 , /
, ,
Generic Strategy:
15
Example: 3,4-dihydroxyphenylacetaldehyde (DOPAL) in Synapse d DOPAL / dt = V+(Dopamine, MAO, SSAO, H2O2) – V -(DOPAL, ALDH) = Dopamineg1 MAOg2 SSAOg3 H2O2
g4 – DOPALh1 ALDHh2
m n i i i m n i i i
h m n h h i g m n g g i i
, 2 1 , 2 1
2 1 2 1
S-system Form :
+
–
+
–
ij ij i i
17
m n i i i m n i i i
h m n h h i g m n g g i i
, 2 1 , 2 1
2 1 2 1
S-system Form :
+
–
+
–
ij ij i i
Generalized Mass Action Form :
ijk
f j ik i
18
Steady-state equations of S-systems linear Recasting: Equivalence transformations of any ODE system into S-system format; function classification Interesting limit cycle / Hopf bifurcation analysis De novo creation of limit cycle oscillators Lie group analysis: Decoupling of systems Statistics: Recast S-system representation of distributions; Approximate S-distribution Facilitated optimization
19
Define Yi = log(Xi):
m n m n i i i i m n m n i i i i
, 2 2 1 1 , 2 2 1 1
S-system highly nonlinear, but steady-state equations linear.
I I D D D
1 1
, 2 1 , 2 1
2 1 2 1
m n i i i m n i i i
h m n h h i g m n g g i i
20
Variables and processes directly from diagram; equations from BST Need to determine parameter values: , , g, h, initial values
Type of Model Model Selection Model Design Model Analysis and Diagnosis Consistency, Robustness Validation of Dynamics Model Use and Applications Manipulation and Optimization Hypothesis Testing, Simulation, Discovery, Explanation Variables, Interactions Equations, Parameter Values Goals, Inputs, and Initial Exploration Data, Information Prior Knowledge Scope, Goals, Objective Scope, Goals, Objective Exploration of Possible Behaviors
21
Issue: Have determined suitable functional form. How do I find the best parameter values? Parameter: A quantity in a function or set of equations that remains constant during a mathematical evaluation (“computational experiment”), but may vary from one experiment to the next. Parameter Estimation (Mathematics): The process of identifying values of parameters in a model that (typically) minimize the difference between the output of the model and corresponding data. Example: F(x) = m x + b
Bottom up: Find kinetic parameters for each enzyme (process) Convert information into numerical values of all parameters Merge all representations, hope for the best; refine Often, this method requires MANY iterations Top down Use time course data of many or all variables Apply an optimization algorithm to fit the model to data Data of this type are rare “Other”
23
24
Vi=Ri(Si, Mi)
p1, p2, p3, …
= fk(Xj, Vi) dXj dt
Voit, Drug Discovery Today, 2004
25 Voit, Drug Discovery Today, 2004
h g
X X X
' '
' '
h g
Y Y Y
'' ''
' ' ' '
h g
Z Z Z
Typical situation, especially in human (disease) systems: Not all metabolites and enzymes are known Not all regulatory signals are known Kinetic and regulatory characteristics are uncertain Concentrations are uncertain Flux rates are uncertain
26
Expert Opinion Ask question in a new fashion: Not: What is the concentration of DOPAC? What is the turnover rate of this step? But: Are concentrations of X and Y about the same? How do fluxes relate at this branch point? Defaults Kinetic orders in BST are within small ranges Restrict ranges based on experience with enzyme kinetics Diagnostics Massive sensitivity and robustness analysis
27
Biochemical Systems Theory (BST)
28
beta1_01 = a1_0 *J1 /(Xs1^h1_1_01 Xs10^h1_10_01 Xs50^h1_50_01 Xs2^h1_2_01 >> >> Xs3^h1_3_01 Xs14^h1_14_01 Xs30^h1_30_01) beta1_02 = a1_0 *J2 /(Xs1^h1_1_02 Xs52^h1_52_02 Xs2^h1_2_02) beta1_03 = a1_0 *J3 /(Xs1^h1_1_03 Xs52^h1_52_03 Xs2^h1_2_03) //to Dopaquinone # X52 beta1_04 = a1_0 *J4 /(Xs1^h1_1_04 Xs59^h1_59_04 Xs3^h1_3_04) //to Tyramine # X59 X1' = a1_0 - beta1_01 X1^h1_1_01 X10^h1_10_01 X50^h1_50_01 X2^h1_2_01 >> X3^h1_3_01 X14^h1_14_01 X30^h1_30_01 >> >>
>>
>>
//============================================================================== alpha10 = beta1_01 beta10 = beta1_01 //X10' = alpha10 X1^h1_1_01 X10^h1_10_01 X50^h1_50_01 X2^h1_2_01 X3^h1_3_01 >> X14^h1_14_01 X30^h1_30_01 >> >>
>> X3^h1_3_01 X14^h1_14_01 X30^h1_30_01 //============================================================================== h11_11 = 0.5 alpha11 = beta10 beta11 = (alpha11 Xs1^h1_1_01 Xs10^h1_10_01 Xs50^h1_50_01 Xs2^h1_2_01 >> Xs3^h1_3_01 Xs14^h1_14_01 Xs30^h1_30_01) /(Xs11^h11_11) X11' = alpha11 X1^h1_1_01 X10^h1_10_01 X50^h1_50_01 X2^h1_2_01 X3^h1_3_01 >> X14^h1_14_01 X30^h1_30_01 >> >>
//==============================================================================
Effects of changes in enzyme activities on metabolite concentrations
5 10 15 20 25 30 200 400 600 800 1000 t
Relative Change (% )
X2 X3 X32 X33 X24 X27 X4 X28 X30 X73 X77
a-
Dynamic responses of metabolite concentrations to a 30% decrease in tyrosine hydroxylase Sensitivity Analysis Simulation Analysis
30
Stability Analysis: Will a system, when slightly perturbed, return to its (previous) steady state? stable marginable stable unstable Interesting old theorem (Hartman & Grobman): Steady states of nonlinear systems can be assessed locally with methods of linear systems analysis
31
32
Bifurcation Analysis: A parameter is changed very slightly, but the system response is qualitatively different; threshold at 1 = 1
33
Type of Model Model Selection Model Design Model Analysis and Diagnosis Consistency, Robustness Validation of Dynamics Model Use and Applications Manipulation and Optimization Hypothesis Testing, Simulation, Discovery, Explanation Variables, Interactions Equations, Parameter Values Goals, Inputs, and Initial Exploration Data, Information Prior Knowledge Scope, Goals, Objective Scope, Goals, Objective Exploration of Possible Behaviors
Need to move from model design to validation: Does the model do things right? If so, use the model for new insights and predictions.
34
Compare model responses and results of heterozygotes, knock-outs, and inhibition studies
Qi et al., PLoS One, 3(6), e2444 (2008)
Correlation Coefficient: 0.919
2 4 6 8 10
1 2 3 4 5
Experimental Data Model Predictions
36
Significant two-site combinations
Glu ASB ALDH-e SOD TYR NO BH4 NADP+ MAO-e TH XO NADPH DCT ATP SAM GPx COM T Fe2+ GSH NAD+ PGHS NADH ACE GR AADC CAT ALDH PGG2
VMAT2 DAT MAO
Tyrosine Dynamics L-DOPA
TH
DA DOPAC HVA
Stimulus
Action potential
Presynapse
++ ++ ++ ++ ++ ++ ++ ++
DOPAC
Glial Cell
HVA
Capillary
COMT MAO COMT
Meth- Amphetamine Changes
Presynapse DA synthesis Vesicle dynamics DA recycling Postsynapse Incoming signals DARPP-32 AMPAR
In comparison to presynapse, proteins and signaling events more prominent than biochemical reactions
AMPA (-amino-3-hydroxyl-5-methyl-4-isoxazole-propionate)
41
Signaling function based on DARPP32 phosphorylation on four sites
Physiological signaling function Dopamine signals Glutamate signals Mixed signals Signal trains of different frequencies and amplitudes Natural design features Direct effect on medical or leisure drugs Long-term effects Adaptation Genomic alterations Changes in receptor types and densities
43
Example: Control Motifs Positive Feedback Loop Why is it there? How is it controlled? PP2A PKA D32-75P
Cost & Challenges:
number of individuals that do not relapse after 1 year
Koob GF et al. (2009) Nat Rev Drug Discov, 8, 500; Kauer JA, Malenka RC. Nat Rev Neurosci 2007, 8
Features of the Drug:
transduction and interpretation in the postsynapse
reinforcement and reward processing
form of learning and memory
accumbens (NAc)) is critical for neural adaptations that underlie addiction
45
DAT VMAT2 DA Tyrosine L-DOPA Dopamine (DA) DA quinone Cysteinyl DA DOPAL + H2O2 MAO TH AADC
+
HVA 3-MT DOPAC AD COMT
DOPA quinone
Presynapse
46
Postsynapse
47
Adapted from : Reynolds JN, W ickens JR. Neural Netw 2 0 0 2 , 1 5
Norm al dopam ine range
LTP LTD
Dopam ine depletion I nhibition
synthesis GLU signal > DA signal DA signal > GLU signal Dopamine concentration
Change in synaptic efficacy Striatum
Cortex DA GLU
49
Probably never! For long-term effects, we need to model gene expression and consequences, especially in the postsynapse. Need expanded, more detailed model (same principles, 100s of equations)
Pesticides perturb dopamine metabolism Specific (mechanistic) effects of pesticides on dopamine metabolism Alternative Computational Strategies: (1) Simulation; (2) Inverse Computation; (3) Monte Carlo Simulation (1) Simulation Use presynaptic model Alter processes (parameters) according to observed effects of pesticides Determine changes in metabolic profile Example: Ziram (organic zinc salt; used as a fungicide)
Tyrosine Dynamics L-DOPA
TH
DA DOPAL HVA
COMT MAO COMT
DOPAC
ALDH
Exocytosis, Endocytosis
52
Alternative Strategy 2: Inverse Computation “Inverse” means: Given a metabolite profile, can we infer mechanisms of pesticide action? Use S-system formulation Remember that steady-state equations are linear Consider impact of pesticides on steady-state concentrations Use linear algebra, pseudo-inverses, or optimization to “invert” system matrix*; identify changes in processes
Example: Observed effects of Paraquat TH-positive neurons:
~ -50% Tissue dopamine:
~ -50% HVA:
~ -50% DOPAC and 3-MT: 0% ~ -40% GSH: ~-45% GSSG: ~+60% GSH-PX:
SOD:
DAT mRNA:
DAT protein:
*Lee, Chen, Voit, Math. Biosc. 2010
53
Comparative Results of Inverse Computation (1): Paraquat Dieldrin Rotenone Flux through DAe Fluxes associated with DOPAC
Alternative Strategy 3: Monte Carlo Simulation Simulate model thousands of times with randomly varied parameter values Output: Distributions of model features of interest Scan for those consistent with clinical / experimental findings Identify likely affected kinetic parameters
Example: Effects on key parameters: No increases consistent With data Small values very unlikely; value probably within ~20%
Comparative Results of Monte Carlo Simulations: Pesticides have different mechanisms of action! Paraquat Dieldrin Rotenone Distributions of outcomes consistent with input data
development of new treatment options
57
Support from NSF (MCB), NIH (GM, NIEHS), DOE (BESC), Woodruff Foundation, University System of Georgia, Georgia Research Alliance
Gary Miller Zhen Qi Shinichi Kikuchi
58