# cell growth rate, model - (Jul/24/2006 )

when calculating growth rate, some people use Nt = N0*2^(tf), while others use exponetial model, dN/dt = µN, or N = N0*exp(µt).

anyone know the reason why one researcher would choose one model over the other?

All these models are **exactly ** the same.

dN/dt = mu * N

This is the differential equation. It means that the growth rate is directly proportional to the number of cells because more cells means more divisions. mu is the rate constant

N = N0 * exp ( mu t)

This is the solution of the diff equation. It gives the number of cells as a fuction of time. They grow exponentially, until they reach saturation. The latter phase is not captured by the model.

N = N0 * 2^(t/td)

This notation is exactly like the former equation, but has some more biological intuition. td is the average doubling time of the cells. There is a mathematical relation that states

2^x = e^(ln(2)*x) = exp(ln(2)*x)

where ln(2)~0.69. So you can easily find that mu=ln(2)/td.

THANKS!

so...

when people talk about growth rate in papers, do they usually put 1/td or mu?

Rate must have units of 1/time.

mu is the rate constant.