1. Setting up an Initial CF Model
Eberhard O. Voit
September 1, 2011 1

2. FDA just released strategic plan (August 17, 2011)
Note:
FDA just released strategic plan (August 17, 2011)
“Advancing Regulatory Science at the FDA”
Priority area # 1:
Modernize Toxicology to Enhance Product Safety
· Evaluate and develop models better able to predict patient response.
· Identify improved biomarkers to monitor toxicity levels.
· Integrate computational tools to inform conclusions about preclinical data. 2

3. Toward a First CF Model: Complex System ― Overwhelming Task!
CF ultimately in inflammation problem >> are there inflammation models?
Hallmark: acute pulmonary exacerbations (APEs) 3

4. Vodovotz et al., 2009:
The role of alarm/danger signals in inflammation, distilled for mathematical modeling purposes. Solid arrows: induction; dashed lines: suppression. An initiating stimulus (e.g., a pathogen) stimulates both pro- and anti-inflammatory pathways. In the setting of infection, pro-inflammatory agents (e.g., TNF) cause tissue damage/dysfunction, which in turn stimulates further inflammation (e.g., through the release of “danger signals”). Anti-inflammatory agents (e.g., TGF-b1) both suppress inflammation and stimulate healing. 4

5. What does “cause inflammation” mean?
Adjustments needed
What does “cause inflammation” mean?
Is there a variable “inflammation”?
If so, is it measurable?
>> Use indicator: pro-inflammatory cytokines 5

6. How can inflammation” suppress pathogens?
Adjustments needed
How can inflammation” suppress pathogens?
>> Need a realistic, measurable mechanism 6

7. What does “cause damage” mean? Is there a damage indicator variable?
Adjustments needed
What does “cause damage” mean?
Is there a damage indicator variable?
>> Use healthy and diseased tissues 7

8. No spatial considerations …
Adjustments and
Decisions
No mucus
No neutrophils
One pathogen species
No spatial considerations …
>> need to make decisions on what to include and how 8

9. Anti-inflammatory Cytokines Pro-inflammatory Cytokines
Players
Healthy Tissue
Damaged Tissue
Mucus
Bacteria
Anti-inflammatory Cytokines
Pro-inflammatory Cytokines
Need to model the role of CF
>> Do I need to model the mutation? Missing transporter? 9

10. First Attempt Healthy Tissue P Pro-inflammatory Cytokines H B
Anti-inflammatory
Cytokines
Bacteria D A
Damaged
Tissue S
Scar
Tissue M
Mucous 10

11. First Attempt P A H D S B M 11

12. For the near future, this will be our reality!
Second Approach
Almost the same; clearer role of CF; cleaner handling of cells CF CF
Healthy
Cells
Damaged
Cells
Mucus M H D B A P
Bacteria
Anti-inflammatory
Cytokines
Pro-inflammatory
Cytokines
For the near future, this will be our reality! 12

13. Vi+ Vi– Xi complicated Choice of Dynamic Model Structure inside
outside
complicated
Solution with Potential:
“Biochemical Systems Theory”
(BST)

14. Advantages of BST Models
Prescribed model design: Rules for translating diagrams into equations; rules can be automated
Direct interpretability of parameters and other features
One-to-one relationship between parameters and model structure simplifies parameter estimation and model identification
Simplified steady-state computations (for S-systems), including
steady-state equations, stability, sensitivities, gains
Simplified optimization under steady-state conditions
Efficient numerical solutions and time-dependent sensitivities
Minimal bias of model choice and minimal model size; easy scalability

15. Mapping
Structure Parameters X 1 2 3 4
g41 = 0 X 1 2 3 4
g41 < 0

16. Generic: Rate constant x B^kinetic order x P^kinetic order CF CF
Healthy
Cells
Damaged
Cells
Mucus M H D B A P
Bacteria
Anti-inflammatory
Cytokines
Pro-inflammatory
Cytokines
Generic: Rate constant x B^kinetic order x P^kinetic order
PLAS: 1.5 B^.1 P^.1 16

17. Generic: Rate constant x A^kinetic order PLAS: 1.2 A^0.5 CF CF
Healthy
Cells
Damaged
Cells
Mucus M H D B A P
Bacteria
Anti-inflammatory
Cytokines
Pro-inflammatory
Cytokines
Generic: Rate constant x A^kinetic order
PLAS: 1.2 A^0.5
A' = 1.5 B^.1 P^ A^0.5 17

18. ? CF CF Healthy Cells Damaged Cells Mucus M H D B A P Bacteria
Anti-inflammatory
Cytokines
Pro-inflammatory
Cytokines ? 18

19. PLAS: P' = 125 B^.2 D^-.4 A^-.1 - 50 P^0.5 CF CF Healthy Cells Damaged
Mucus M H D B A P
Bacteria
Anti-inflammatory
Cytokines
Pro-inflammatory
Cytokines
PLAS: P' = 125 B^.2 D^-.4 A^ P^0.5 19

20. H' = 650 - 15 H^.5 P^.3 A^-.1 D' = 15 H^.5 P^.3 A^-.1 - 450 D^.2 CF CF
Healthy
Cells
Damaged
Cells
Mucus M H D B A P
Bacteria
Anti-inflammatory
Cytokines
Pro-inflammatory
Cytokines
H' = H^.5 P^.3 A^-.1
D' = 15 H^.5 P^.3 A^ D^.2 20

21. Based on logistic growth: B’ = r B – r/K B^2 CF CF
Healthy
Cells
Damaged
Cells
Mucus M H D B A P
Bacteria
Anti-inflammatory
Cytokines
Pro-inflammatory
Cytokines
B' = 0.02 B^0.8 M^ B^1.2 P^0.5
Based on logistic growth: B’ = r B – r/K B^2
Generalized logistic growth: B’ = a B^g – b B^h 21

22. CF = 0 //normal = 0 (robust degradation);
Healthy
Cells
Damaged
Cells
Mucus M H D B A P
Bacteria
Anti-inflammatory
Cytokines
Pro-inflammatory
Cytokines
M' = B^.24 2^CF M^(2-1*CF)
CF = 0 //normal = 0 (robust degradation);
//disease = 1 (logistic growth) 22

23. PLAS file: http://enzymology.fc.ul.pt/software.htm
B' = 0.02 B^0.8 M^ B^1.2 P^.5
P' = 125 B^.2 D^-.4 A^ P^0.5
A' = 1.5 B^.1 P^ A^0.5
H' = VHD
D' = VHD D^.2
M' = B^.24 2^CF M^(2-1*CF)
VHD = 15 H^.5 P^.3 A^-.1
CF = 0
B = // set at steady state, but not very important
P =
A =
H =
D =
M =
t0 = 0
tf = 2000
hr= 1 23

24. Initial values not very critical (here)
B = 2, P = 2, A = 2, H = 1600, D = 10, M = 1 (separate lines in PLAS! 24

25. Set CF = 1 25

26. Set CF = 1; run longer 26

27. Set CF = 0 (healthy); start at st st; bacterial infections:
@ 100 B = 10; @ 500 B = 1000 B = 18 27

28. Set CF = 1 (diseased); start at st st; bacterial infections:
@ 100 B = 10; @ 500 B = 1000 B = 18 28

29. Same simulation; look at H (healthy cells / tissue)
>> looks like APEs! 29

30. Same simulation; look at H (healthy cells / tissue)
Suck out mucus (without M = 1.39) :
@ 400 M = 1.26
@ 400 M = 1.3
and
@ 1400 M = 1.3 30

31. Assume: control of B by P insufficient:
>>> P^0.1 instead of P^ 0.5 31

32. Assume: control of B by P insufficient: P^0.1
Intervene with 750 B = 3 B = 3
Previous
result (for
comparison) 32

33. Many scenarios possible: Frequency of infections
Anti-inflammatory drugs (one time; permanent)
Partial bacterial resistance
Bacteria with higher carrying capacity
Several bacterial species
Effects of parameter values 33

34. Cytokines need to be in balance; cytokine storms can be fatal
Life is complicated!
Cytokines need to be in balance; cytokine storms can be fatal 34

35. Cytokines interact in complicated ways
Life is complicated!
Cytokines interact in complicated ways 35

36. Cytokines affect numerous vital processes
Life is complicated!
Cytokines affect numerous vital processes 36

37. Bacteria really in dynamically changing metapopulations
Life is complicated!
Bacteria really in dynamically changing metapopulations
100 species? 1,000 species?
Dominant species changes with age of patient 37

38. Modeling Coexisting Bacterial Populations
Logistic growth: B’ = r B – r/K B^2
Generic: X’ = a X + b X X
Two species: X’ = aX X + bXX X X + bXY X Y
Y’ = aY Y + bYX Y X + bYY Y Y
Lotka-Volterra System :
Generalized LV –
Power-Law System: 38

39. Modeling Coexisting Bacterial Populations39

40. Modeling Coexisting Bacterial Populations
X1' = X X1^ X1 X3
X2' = X2^ X1 X X2^ X2 X3
X3' = X3^ X3^4
X1 = 0.1/3
X2 = 0.1/3
X3 = 0.1/3
tf = 0
tf = 2500
hr = 1 40

41. Modeling Coexisting Bacterial Populations in PLAS
X1' = X X1^ X1 X3
X2' = X2^ X1 X X2^ X2 X3
X3' = X3^ X3^4
X1 = 0.1/3
X2 = 0.1/3
X3 = 0.1/3
@ 1200 X1 = 0.1
@ 1200 X2 = 0.1 //antibiotics
@ 1200 X3 = 0.1
tf = 0
tf = 2500
hr = 1 41

42. Modeling Coexisting Bacterial Populations in PLAS
Same system and
settings, except:
@ 2500 X1 = 0.01
@ 2500 X2 = 0.05
@ 2500 X3 = 0
tf = 0
tf = 5000
hr = 1
“Normal” conditions: Steady state with B3 > B1 > B2
At t = 1,200, kill almost all bacteria (0.1 left each): Back to steady state
At t = 2,500, kill B3: Now B2 > B1 and total number of bacteria increased! 42

43. Very simple model; generic parameter values Some insights
Summary
Complex system
Very simple model; generic parameter values
Some insights
Tool for fast testing and exploration
Uncounted scenarios possible
Starting point for more and better things 43