Lecture 5: Exponential Growth Part 1
Our initial thought experiment
Our initial thought experiment
Liquid broth
?
+
Growth
etc . . .
etc . . .
Process not perfect
evolution
Why should we study exponential growth if it is likely not the state of most cells in the wild?
Highly repeatable and quantitative laboratory phenotype!
Capability of exponential growth essential for expanding into new territory, creating multicellular structures, etc.
What is our goal studying exponential growth this week?
Understand dynamics: how does population size evolve in time?
How do cells regulate their genes and physiology to achieve this state of growth?
Define quantitative parameters of growth dynamics
How do we measure microbial growth?
1. Colony counting
Gel with nutrient mixture
Liquid nutrient mixture with growing cells
Early growth > few colonies formed
Late growth > many colonies formed
How do we measure microbial growth?
2. Turbidity
Low turbidity > few cells
High turbidity > many cells
How do we measure microbial growth?
2. Turbidity
How to measure turbidity
shine light through sample
light detector
measure transmitted intensity
Light attenuation ~proportional to biomass density
How do we measure microbial growth?
2. Turbidity
How to measure turbidity
shine light through sample
detector
measure transmitted intensity
Light attenuation ~proportional to biomass density
attenuation or absorbance, measured
path length, set by measurement container
extinction coefficient, property of the growing cells/biomass (assumed to be constant)
concentration/density of biomass
How do we measure microbial growth?
3. Microscopy
Methods for measuring growth
Method | Pro | Con |
Colony counting | -can estimate cell number/density -can directly observe decline in viable cell number during death phase | -cannot measure biomass -takes many plates and much time to county colonies |
Turbidity | -quick/easy -sensitive to biomass | -not sensitive to cell number |
Microscope | -can observe differences in cell shape/length/morphology -with time-lapse, can observe cell-to-cell heterogeneity | -specialized equipment -limited to the number of cells in fields of view -generally limited to single-cell layer growth |
Let’s take a look
Let’s take a look
1 cell
Let’s take a look
2 cells
Let’s take a look
2 cells
Let’s take a look
5 cells
Let’s take a look
13 cells
Let’s take a look
31 cells
Let’s take a look
108 cells
Let’s take a look
316 cells!
Let’s take a look
586 cells!!
What’s this?
What’s this?
↓ This looks like a line! ↓
How can we describe bacterial growth in time?
↓ This looks like a line! ↓
The cells grow exponentially!
Some notes on exponential growth
↓ This looks like a line! ↓
What is a simple model for exponential growth?
If there’s only 1 cell that can divide, the population’s rate of increase should be small.
If there’s tons of cells that can divide, the rate of increase should be big!
The simplest equation then is one where the rate of population growth is proportional to the population size.
A differential equation!!
constant
How do we solve this equation?
Important notes on exponential growth
What must happen to synthesize new cells?
A very simplified molecular picture
A very simplified molecular picture
Within our exponential growth model, somehow all of this complexity is subsumed under one parameter, the doubling time!
We’ve seen that to build a new cell, the parent cells must incorporate carbon, nitrogen, phosphorous.
How can we determine what biochemical processes determine the doubling time?
How do we start understanding growth?
We carefully control what resources bacteria are given to make new cells and observe how this impacts growth.
Investigate the physiological state of the cell under these different conditions
A very powerful tool here is that we have identified a single, quantitative parameter we can measure: the doubling time!
Laboratory growth conditions
“Rich medium” / ”Broth”
“Defined medium”
“Minimal medium”
Laboratory growth conditions
“Rich medium” / ”Broth”
Common: LB (Lysogeny Broth)
Some rich media get pretty wild!!
Laboratory growth conditions
“Defined medium”
Liquid made of water and purified chemicals.
We know the precise concentration of every single component.
Always contains
Defined media allow precise control of the bacterial growth environment
Laboratory growth conditions
“Defined/minimal media”
Common minimal medium:
M9 medium (most E. coli experiments, for example)
Often people (including me) will say something like bacteria “growing on glucose”; this refers to cells growing in a minimal medium with glucose as a carbon source.
How does growth rate depend on the available nutrients?
Intuitively, the exponential growth rate should depend on the concentration of nutrients, no?
What’s my response to any question like that in this class (and in general)?
Basic experiment
What determines doubling time?
What determines doubling time?
What determines doubling time?
Exponential growth rate strongly dependent on nutrient conditions
Next time: What aspect of cell physiology determines these growth rates?�
A large fraction of the cell mass is protein.
Proteins are synthesized by ribosomes.
We will see that to grow faster, cells dedicate more of their available biosmass to ribosomes.
We will find quantitative relationships between the fraction of cell mass that is in ribosomes and the per capita growth rate.