Biological Applications of Transport Phenomena

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Biological Applications of Transport Phenomena

• E. N. Lightfoot and K. A. Duca

Topics Modeling physiological systems and
biomedical devices Suggesting transport related
aspects of species evolution
and organism development Concepts Emergence Univ
ersality Robustness Self organization Approach
converting mysteries to puzzles
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Emergence
Basic Definitions
and self organization
Termite Mound
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Slime Mold Cycle
Onset of starvation
camp
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2. Universality

• Definition understanding system behavior does
  not require accurate component models
• Justification
• utility of time constants and
  asymptotic approximations
• widespread model insensitivity
• Extension (?) effectiveness of approximate
  objective functions

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2. Universality
CSTR PFR
Pulse Response
Net response to an exponentially decaying
input
t/t0
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Robustness

• Evolutionary experience
• Bases
• Quasi-species
• Weak regulatory linkages
• Separation of time constants
• Time constant rations near unity
• Utilization of environment (tr/rxn)

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Separation of Time Constants

• Hemodialysis
• Pharmacokinetics
• Compartmental modeling
• Glycolysis
• Gene Expression

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Pharmacokinetic Approximations
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Test of Creatinine Modeling
Metabolic buildup Days Dialysis
Hours Organ residence time
Minutes Blood circulation time 1 Minute
Concentration
Time (days)
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Glycolysis
HK
PFK
PK
2NADH
2NAD
2 (Lactic acid)
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Lecture 22, p. 2Gene Expression in a Bacterial
Cell
Effective radius ca. 1 micron (10-6 m)
DNA distributed throughout cell
Protein diffusion hindered by
intracellular elements
.
.
.
Gene to be expressed
Promoter molecule
Ratio of intra-cellular to water
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Time Constant Summary
Randomization time Boundary-layer
transients Diffusion controlled reaction time
Gene
BL
Protein
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Empirical modification
Must use an effective gene site greater than
actual.
The promoter binds weakly to all of chromosome
and Samples a finite length !
This is really a foraging problem as discussed
elsewhere
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Dispersion Models
Levy walk
Brownian diffusion
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Typical Predicted Levy Flight Behavior
Here
mean free path
mean number of flights between successive targets

mean flight distance
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Foraging of Deer
Free
Fenced
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Foraging of bumble bees
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Near Equality of Time Constants

• Diffusion and reaction
• Swimming and flying
• Mass and heat transport in the micro-circulation

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Catalyst Effectiveness Factors
Porous catalyst pellet
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Effectiveness Factors
0th
1st
2cd
Hinshelwood, most biological kinetics in this
intermediate region
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Control of IntermediatesThe Pyruvate
Dehydrogenase Complex
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Electron Transport Chain
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Dealing with Unfavorable Intermediates
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Optimizing Granule Size
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Flying and Flipping
The Strouhal Number
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Vortex Shedding
0.31 1.25 1.89
3.78
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Cerebral Oxygen Supply
Oxygenation Supply to Grey Matter
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Classification of Blood Vessels
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Mass and Heat Transfer in Blood Vessels
0.0148
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PulmonaryOrganization
Cat Pulmonary Tree
Alveoli
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Oxygenation in Gills

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Mouse Pulmonary Branching
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Accurate Prediction of Mass Transfer Rates
Keeping Salmonids Happy
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Steelhead Data
Torr
nMols/s x 10-3
Oxygen Tension vs. Metabolic Rate
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Adult salmonid oxygenation is thermodynamically
limited
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Oxygenation of Embryos
water flow
capsule (shell)
boundary layer
Embryo
Mixing by embryo and by its internal circulation
Hypothesis Embryo oxygenation is limited by mass
transfer across an external boundary layer and
and diffusion through the egg capsule or shell.
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Comparison of Behavior
t
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Glucose Tolerance Test
Excess Blood Glucose mg/dl
Diabetic
Normal
Time, minutes
Time
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Glucose Dynamics
sedentary
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Breakfast Glucose Balance

• Intake
• Normal blood concentration
• Normal post-prandial BG mass
• Fraction of intake per meal in normal blood
• Typical post-prandial diabetic load
• Excess to remove from blood

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Glucose Transport to Muscle
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GlucoseMetabolisminMuscle
Exercise
Exercise Recruits Glucose Transporter GLUT4
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The rule
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Acknowledgement

• Amanda my sympathetic ear