Tissue Turnover and Growth

Turnover assessed via source switching experiments

Fitting exponentialsDescribe growth of critter as:

k = ln(Mt/M0)/twhere k is specific growth rate constant, t is time, Mt is mass at time, M0 is starting mass.

Model isotope incorporation during growth and turnover as:d/dt = -(k+m)(t-E)

where m is metabolic (turnover) rate constant, d/dt is the change in isotope value with time, t is the isotope value at time t, and E is isotope value at equilibrium with new input.

Integrating between t = 0 and t at equilibrium yields:t-E = (0-E )e-(k+m)t

ort = E + (0-E )e-(k+m)t

or t = E + (0-E )e-t

where is overall rate constant for isotopic incorporation

Half-life (time for signal to shift by 50%): t1/2 = (ln2)/

Dealing with Growth and Turnover(MacAvoy et al. 2005)

QuickTime™ and a decompressor

are needed to see this picture.

QuickTime™ and a decompressor

are needed to see this picture.

QuickTime™ and a decompressor

are needed to see this picture.

13 weeks old on day 1: sexually mature, adult?

Dealing with Growth and Turnover(MacAvoy et al. 2005)

Blood Muscle Liver

Expected due to growth alone (m=0): t = E + (0-E )e-(k+0)t

Dealing with Growth and Turnover(MacAvoy et al. 2005)

Blood Muscle Liver

Expected due to growth and turnover (m≠0): t = E + (0-E )e-(k+m)t

Dealing with Growth and Turnover(MacAvoy et al. 2005)

QuickTime™ and a decompressor

are needed to see this picture.

m = k + (ln[(t-E )/(0-E )])/t

Dealing with Growth and Turnover(MacAvoy et al. 2006)

QuickTime™ and a decompressor

are needed to see this picture.

Adults (?) given 120 to equilibrate to control diet before start of experiment.

No change in size during experiment.

Dealing with Growth and Turnover(MacAvoy et al. 2006)

Mouse Rat

Dealing with Growth and Turnover(MacAvoy et al. 2006)

QuickTime™ and a decompressor

are needed to see this picture.QuickTime™ and a

decompressorare needed to see this picture.

Reaction Progress Variable(Cerling et al. 2007)

QuickTime™ and a decompressor

are needed to see this picture.

QuickTime™ and a decompressor

are needed to see this picture.

Reaction Progress Variable(Cerling et al. 2007)

QuickTime™ and a decompressor

are needed to see this picture.

Fractional approach to equilibrium: scale 1 to 0

Linearizes and normalizes exchange:

y = mx + bln(1-F) = - t + b

eb is the size of the fractional size of the pool(i.e., 1 when b=0)

Reaction Progress Variable(Cerling et al. 2007)

Can deal with up to three pools (j) of size (ƒ) with different s

QuickTime™ and a decompressor

are needed to see this picture.

QuickTime™ and a decompressor

are needed to see this picture.

QuickTime™ and a decompressor

are needed to see this picture.

Each pool changes as:

Reaction Progress Variable

QuickTime™ and a decompressor

are needed to see this picture.

Pool 1size: 0.7t1/2: 2 days

Pool 2size: 0.3t1/2: 20 days

Reaction Progress Variable

Example 1: Mouse breath (combining experiments)

QuickTime™ and a decompressor

are needed to see this picture.

QuickTime™ and a decompressor

are needed to see this picture.

Reaction Progress Variable

Example 2: Horse hair (multiple pools)

QuickTime™ and a decompressor

are needed to see this picture.

Reaction Progress Variable

Example 2: Horse hair (multiple pools)

QuickTime™ and a decompressor

are needed to see this picture.

Reaction Progress Variable

Example 3: Warbler blood (dealing with delays)

QuickTime™ and a decompressor

are needed to see this picture.

QuickTime™ and a decompressor

are needed to see this picture.

Reaction Progress Variable

Example 4: Horse diet from horse hair (inverse modeling)

QuickTime™ and a decompressor

are needed to see this picture.

QuickTime™ and a decompressor

are needed to see this picture.

Each pool changes with time incrementally as:

Reaction Progress Variable

Example 4: Horse diet from horse hair (inverse modeling)

QuickTime™ and a decompressor

are needed to see this picture.