1. Chapter 10. Mass Transport and Biochemical Interactions
BMOLE Biomolecular Engineering Engineering in the Life Sciences Era
BMOLE – Transport
Chapter 10. Mass Transport and Biochemical Interactions
Text Book: Transport Phenomena in Biological Systems
Authors: Truskey, Yuan, Katz
Focus on what is presented in class and problems…
Dr. Corey J. Bishop Assistant Professor of Biomedical Engineering Principal Investigator of the Pharmacoengineering Laboratory: pharmacoengineering.com Dwight Look College of Engineering Texas A&M University Emerging Technologies Building Room 5016 College Station, TX
Francis Crick and neuroscience? Why is E = mc2 and not ½ mc^2… Name all of the energy equations you know? Integral => 1/2
© Prof. Anthony Guiseppi-Elie; T: F:

2. Problems 10.5, 10.7, 10.8, 10.16 and a reaction scheme with Laplace PK and PD

3. Only part a
Problem 10.5

4. Only part a
Only part a
Problem 10.5 ?

5. Only part a
Problem 10.5 ?

6. Problem 10.5 ?
From the equilibrium relation for the enzyme-cofactor complex: ?

7. Only part a
Problem 10.5 ?
From the equilibrium relation for the enzyme-cofactor complex: ? ?

8. Only part a
Problem 10.5 ?
From the equilibrium relation for the enzyme-cofactor complex: ? ?
Then what is the enzyme-cofactor complex expression: CEC?

9. Only part a
Problem 10.5 ?
From the equilibrium relation for the enzyme-cofactor complex: ? ?
Then what is the enzyme-cofactor complex expression: CEC?
If CE is much much smaller than Kc then CEC=?

10. Only part a
Problem 10.5 ?
From the equilibrium relation for the enzyme-cofactor complex: ? ?
Then what is the enzyme-cofactor complex expression: CEC?
If CE is much much smaller than Kc then CEC=?

11. Only part a
Problem 10.5 ?
From the equilibrium relation for the enzyme-cofactor complex: ? ?
Then what is the enzyme-cofactor complex expression: CEC?
If CE is much much smaller than Kc then CEC=?

12. Only part a
Problem 10.5 ?
From the equilibrium relation for the enzyme-cofactor complex: ? ?
Then what is the enzyme-cofactor complex expression: CEC?
If CE is much much smaller than Kc then CEC=?

13. Only part a
Problem 10.5 ?
From the equilibrium relation for the enzyme-cofactor complex: ?
Quasi s.s. assumption ?
Then what is the enzyme-cofactor complex expression: CEC?
If CE is much much smaller than Kc then CEC=?

14. Only part a
Problem 10.5 ?
From the equilibrium relation for the enzyme-cofactor complex: ?
Quasi s.s. assumption ?
Then what is the enzyme-cofactor complex expression: CEC?
If CE is much much smaller than Kc then CEC=?

15. Problem 10.7

16. Problem 10.7
Since the lethal dose is much smaller than Km, it is likely
that toxin levels within the blood are less than the lethal dose.

17. Problem 10.7
Since the lethal dose is much smaller than Km, it is likely
that toxin levels within the blood are less than the lethal dose.
The reaction can be assumed to be first order.

18. Problem 10.7
Since the lethal dose is much smaller than Km, it is likely
that toxin levels within the blood are less than the lethal dose.
The reaction can be assumed to be first order.
Thiele modulus:
Figure Effectiveness factor as a function of the Thiele modulus. The dashed line represents the asymptotic value of ɳ ∼1/Փ for large values of Փ.
The Thiele modulus was developed by E.W. Thiele in his paper 'Relation between catalytic activity and size of particle' in 1939.[1] Thiele reasoned that with a large enough particle, the reaction rate is so rapid that diffusion forces are only able to carry product away from the surface of the catalyst particle. Therefore, only the surface of the catalyst would be experiencing any reaction. The Thiele Modulus was then developed to describe the relationship between diffusion and reaction rate in porous catalyst pellets with no mass transfer limitations. This value is generally used in determining the effectiveness factor for catalyst pellets.
The Thiele modulus is represented by different symbols in different texts, but is defined in Hill[2] as hT.
-Compliments of Wikipedia
Thiele modulus=> φ2 = diffusion time (L2/Deff)/reaction time (1/k)
η= effectiveness factor

19. Problem 10.7
Since the lethal dose is much smaller than Km, it is likely
that toxin levels within the blood are less than the lethal dose.
The reaction can be assumed to be first order.
Thiele modulus:
The Thiele modulus was developed by E.W. Thiele in his paper 'Relation between catalytic activity and size of particle' in 1939.[1] Thiele reasoned that with a large enough particle, the reaction rate is so rapid that diffusion forces are only able to carry product away from the surface of the catalyst particle. Therefore, only the surface of the catalyst would be experiencing any reaction. The Thiele Modulus was then developed to describe the relationship between diffusion and reaction rate in porous catalyst pellets with no mass transfer limitations. This value is generally used in determining the effectiveness factor for catalyst pellets.
The Thiele modulus is represented by different symbols in different texts, but is defined in Hill[2] as hT.
-Compliments of Wikipedia
Thiele modulus=> φ2 = diffusion time (L2/Deff)/reaction time (1/k)
Reaction limited
η= effectiveness factor
Diffusion
limited

20. Problem 10.7
Since the lethal dose is much smaller than Km, it is likely
that toxin levels within the blood are less than the lethal dose.
The reaction can be assumed to be first order.
Thiele modulus:
The Thiele modulus was developed by E.W. Thiele in his paper 'Relation between catalytic activity and size of particle' in 1939.[1] Thiele reasoned that with a large enough particle, the reaction rate is so rapid that diffusion forces are only able to carry product away from the surface of the catalyst particle. Therefore, only the surface of the catalyst would be experiencing any reaction. The Thiele Modulus was then developed to describe the relationship between diffusion and reaction rate in porous catalyst pellets with no mass transfer limitations. This value is generally used in determining the effectiveness factor for catalyst pellets.
The Thiele modulus is represented by different symbols in different texts, but is defined in Hill[2] as hT.
-Compliments of Wikipedia
Thiele modulus=> φ2 = diffusion time (L2/Deff)/reaction time (1/k)
Reaction limited
η= effectiveness factor
Diffusion
limited

21. Problem 10.7
Since the lethal dose is much smaller than Km, it is likely
that toxin levels within the blood are less than the lethal dose.
The reaction can be assumed to be first order.
Thiele modulus:
The Thiele modulus was developed by E.W. Thiele in his paper 'Relation between catalytic activity and size of particle' in 1939.[1] Thiele reasoned that with a large enough particle, the reaction rate is so rapid that diffusion forces are only able to carry product away from the surface of the catalyst particle. Therefore, only the surface of the catalyst would be experiencing any reaction. The Thiele Modulus was then developed to describe the relationship between diffusion and reaction rate in porous catalyst pellets with no mass transfer limitations. This value is generally used in determining the effectiveness factor for catalyst pellets.
The Thiele modulus is represented by different symbols in different texts, but is defined in Hill[2] as hT.
-Compliments of Wikipedia
Thiele modulus=> φ2 = diffusion time (L2/Deff)/reaction time (1/k)
Reaction limited
η= effectiveness factor
Diffusion
limited

22. Problem 10.7
Since the lethal dose is much smaller than Km, it is likely
that toxin levels within the blood are less than the lethal dose.
The reaction can be assumed to be first order.
Thiele modulus:
The Thiele modulus was developed by E.W. Thiele in his paper 'Relation between catalytic activity and size of particle' in 1939.[1] Thiele reasoned that with a large enough particle, the reaction rate is so rapid that diffusion forces are only able to carry product away from the surface of the catalyst particle. Therefore, only the surface of the catalyst would be experiencing any reaction. The Thiele Modulus was then developed to describe the relationship between diffusion and reaction rate in porous catalyst pellets with no mass transfer limitations. This value is generally used in determining the effectiveness factor for catalyst pellets.
The Thiele modulus is represented by different symbols in different texts, but is defined in Hill[2] as hT.
-Compliments of Wikipedia
Why 1/3?
Remember ZP?
L=1/3 diam.
Thiele modulus=> φ2 = diffusion time (L2/Deff)/reaction time (1/k)
Reaction limited
η= effectiveness factor
Diffusion
limited

23. Problem 10.7
Since the lethal dose is much smaller than Km, it is likely
that toxin levels within the blood are less than the lethal dose.
The reaction can be assumed to be first order.
Thiele modulus:
The Thiele modulus was developed by E.W. Thiele in his paper 'Relation between catalytic activity and size of particle' in 1939.[1] Thiele reasoned that with a large enough particle, the reaction rate is so rapid that diffusion forces are only able to carry product away from the surface of the catalyst particle. Therefore, only the surface of the catalyst would be experiencing any reaction. The Thiele Modulus was then developed to describe the relationship between diffusion and reaction rate in porous catalyst pellets with no mass transfer limitations. This value is generally used in determining the effectiveness factor for catalyst pellets.
The Thiele modulus is represented by different symbols in different texts, but is defined in Hill[2] as hT.
-Compliments of Wikipedia
Why 1/3?
Remember ZP?
L=1/3 diam.
Thiele modulus=> φ2 = diffusion time (L2/Deff)/reaction time (1/k)
Reaction limited
η= effectiveness factor
What does that mean
Km increases? If Km
increases, does this tend
to be more reaction- or diffusion-Limited?
Diffusion
limited
Why do you want it reaction-limited and not diffusion-limited?

24. Problem 10.8

25. Problem 10.8 BBB Blood brain barrier:
Active drug vs pro-drug’s active metabolite or function as a reagent + X =>active agent
Pro-drug might be permeable to BBB whereas the active agent might not be…

26. Problem 10.8
i.e., NuvaRing
Patrick Kiser
Anti-HIV and Contraceptive

27. Problem 10.8 “Long” means don’t worry about the ends R Λ L
Dissolution Rate = Ro
Ke = rate of metabolism (km would be more conventional)
Anti-HIV and Contraceptive

28. Problem 10.8 “Long” means don’t worry about the ends R Λ L
Dissolution Rate = Ro
Ke = rate of metabolism (km would be more conventional)
Anti-HIV and Contraceptive

29. Problem 10.8 “Long” means don’t worry about the ends R Λ L
Dissolution Rate = Ro
Ke = rate of metabolism (km would be more conventional)
1st order rate constant means what?
Anti-HIV and Contraceptive

30. Problem 10.8 “Long” means don’t worry about the ends R Λ L
Dissolution Rate = Ro
Ke = rate of metabolism (km would be more conventional)
1st order rate constant means what?
Is this diffusion-limited?
Anti-HIV and Contraceptive

31. Problem 10.8 “Long” means don’t worry about the ends R Λ L
Dissolution Rate = Ro
Ke = rate of metabolism (km would be more conventional)
1st order rate constant means what?
Is this diffusion-limited? What would that mean?
Anti-HIV and Contraceptive

32. Problem 10.8 “Long” means don’t worry about the ends R Λ L
Dissolution Rate = Ro
Ke = rate of metabolism (km would be more conventional)
1st order rate constant means what?
Is this diffusion-limited? What would that mean?
Is being diffusion-limited desirable in this application?
Anti-HIV and Contraceptive

33. Problem 10.8 “Long” means don’t worry about the ends R Λ L
Dissolution Rate = Ro
Ke = rate of metabolism (km would be more conventional)
1st order rate constant means what?
Is this diffusion-limited? What would that mean?
Is being diffusion-limited desirable in this application?
Do you want what to be delivered to be controlled by diffusion or control diffusion by your
drug delivery system?
Anti-HIV and Contraceptive

34. Problem 10.8 “Long” means don’t worry about the ends R Λ L
Dissolution Rate = Ro
Ke = rate of metabolism (km would be more conventional)
1st order rate constant means what?
Is this diffusion-limited? What would that mean?
Is being diffusion-limited desirable in this application?
Do you want what to be delivered to be controlled by diffusion or control diffusion by your
drug delivery system? What happens in time?
Anti-HIV and Contraceptive

35. Problem 10.8 “Long” means don’t worry about the ends R Λ L
Dissolution Rate = Ro
Ke = rate of metabolism (km would be more conventional)
1st order rate constant means what?
Is this diffusion-limited? What would that mean?
Is being diffusion-limited desirable in this application?
Do you want what to be delivered to be controlled by diffusion or control diffusion by your
drug delivery system? What happens in time? Will this always be reaction-limited in time?
Anti-HIV and Contraceptive

36. Problem 10.8 “Long” means don’t worry about the ends R Λ L
Dissolution Rate = Ro
Ke = rate of metabolism (km would be more conventional)
1st order rate constant means what?
Is this diffusion-limited? What would that mean?
Is being diffusion-limited desirable in this application?
Do you want what to be delivered to be controlled by diffusion or control diffusion by your
drug delivery system? What happens in time? Will this always be reaction-limited in time?
Anti-HIV and Contraceptive

37. Problem 10.8 “Long” means don’t worry about the ends R Λ L
Dissolution Rate = Ro
Ke = rate of metabolism (km would be more conventional)
1st order rate constant means what?
Is this diffusion-limited? What would that mean?
Is being diffusion-limited desirable in this application?
Do you want what to be delivered to be controlled by diffusion or control diffusion by your
drug delivery system? What happens in time? Will this always be reaction-limited in time?
Anti-HIV and Contraceptive
Anti-cancer: Nerve growth factor: 14.92
Anti-cancer: Nerve growth factor: 0.067
η>3 =diffusion-limited (may see diff. values in lit.)

38. Problem 10.16

39. Only part a
Problem 10.16
Conservation relation:

40. How do you find the max
size from this?

42. There is one other… invL(1/[(s-a)(s-b)])= eat-ebt ------------------
a-b