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BI 559 Lecture 2: how big is a bacterial cell?

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BI 559 Lecture 2

Notes and announcements:

  • HW1 is due 2/12/24 on Blackboard
  • I will post several links on the course website to help people with essential python stuff
  • As needed, we can do sessions to help people with python

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BI 559 Lecture 2: how big is a bacterial cell?

Today:�

  • What are the primary microbial length scales?�
  • How do those length scales impact the concentrations of different key biomolecules?�
  • How do we measure the concentrations of those molecules?�
  • How do microbes transport cargo over those lengths inside their cytoplasms?�
  • Try to get in the “quantitative” mindset!

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How big is a bacterial cell?

Milo, Phillips, and Orme, Cell Biology by the Numbers

microbe length scale, ~1 µm

1 µm

our bodies

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How big is a bacterial cell?

Bacteria infecting a mammalian cell (sped up x150)

Listeria monocytogenes

*CDC

*wikipedia

Long-nosed Potoroo

(food-borne pathogen)

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What’s the significance of this size?

1 µm

3 µm

1 µm

Approximate cell volume:

 

 

 

 

 

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What’s the significance of this size?

1 µm

3 µm

1 µm

Approximate cell volume:

 

 

 

 

 

 

 

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What’s the significance of this size?

1 µm

3 µm

1 µm

Approximate cell volume:

 

 

 

~3 femtoliters

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What’s the significance of this size?

3 µm

1 µm

 

3 femtoliters

If there is one of a particular kind of molecule in a bacterial cell, what is its concentration?

 

 

 

 

 

Rounding up, 1 molecule in 1 bacterial cell has roughly a concentration of

 

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What’s the significance of this size?

3 µm

1 µm

 

3 femtoliters

# in one bacterium

concentration

1

1 nM

1,000

1 µM

1,000,000

1 mM

1,000,000,000

1 M

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What’s the significance of this size?

3 µm

1 µm

 

3 femtoliters

# in one bacterium

concentration

1

1 nM

1,000

1 µM

1,000,000

1 mM

1,000,000,000

1 M

molecule

# in one bacterium

concentration

citation(s)

inorganic ions

~108

~100-500 mM

H+

100 (!)

10-7 M (~pH 7)

DNA basepairs

5×106

5 mM

protein

2-3×106

2-3 mM

Neidhardt and Umbarger Vol. 1, Ch. 3

ribosomes

2×104

20 µM

Neidhardt and Umbarger Vol. 1, Ch. 3

mRNA

2×103

2 µM

Neidhardt and Umbarger Vol. 1, Ch. 3

ATP

1×107

10 mM

*these values are mostly from E. coli under lab conditions!

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What’s the significance of this size?

3 µm

1 µm

 

3 femtoliters

# in one bacterium

concentration

1

1 nM

1,000

1 µM

1,000,000

1 mM

1,000,000,000

1 M

molecule

# in one bacterium

concentration

citation(s)

Highly expressed protein (TufB, ribosome component, in exponential E. coli)

58,000

58 µM

Low expressed protein (EnvZ, osmoregulation, in exponential E. coli)

100

100 nM

Highly expressed mRNA (ompT, outer membrane protein, in exponential E. coli)

100

100 nM

Low expressed mRNA (yhiJ, unknown maybe inositol metabolism, in exponentialE. coli)

0.1

100 pM

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What’s the significance of this size?

3 µm

1 µm

 

3 femtoliters

# in one bacterium

concentration

1

1 nM

1,000

1 µM

1,000,000

1 mM

1,000,000,000

1 M

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How do people measure these values?

mRNA

RNA sequencing

RNA:

Field of “transcriptomics”

  1. Extract RNA from cells�����
  2. Convert RNA to DNA with reverse transcriptase enzyme������
  3. Sequence DNAs and associate number of each sequence with the corresponding gene in the known genome

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How do people measure these values?

Mass spectrometry

Proteins:

Proteins

  1. Take a sample of cells and extract proteins�����
  2. Ionize proteins�����
  3. Run ionized proteins through an electric field to determine masses
  4. Compare masses to known masses of proteins

+

+

+

+

+

+

+

Field of “proteomics”

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How do people measure these values?

Common method: MALDI-TOF

Proteins:

Proteins

Matrix-assisted laser desorption/ionization:

method of ionizing and evaporating proteins

Time of flight:

method of determining mass

protein sample and gel matrix

detector

laser

-

+

high voltage

+

+

+

  • Laser charges proteins by transferring electrons from the sample to the matrix and simultaneously vaporizes them�
  • Charged proteins accelerate through an electric field�
  • The time of flight of each molecule is measured, correlated with its mass to charge ratio, and a spectrum of the # of molecules of each mass is made�
  • Masses are then associated with specific proteins in the sample species’ genome

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MALDI-TOF system

(much $$$)

Each circular spot contains one sample

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What makes a cell?

3 µm

1 µm

nucleic acids

cell envelope

(lipids, cell wall)

storage & misc

protein

metabolites

?

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Let’s plot the makeup of an E. coli cell

  • Open the Week 2 python template in jupyter

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What makes a cell?

3 µm

1 µm

nucleic acids

cell envelope

(lipids, cell wall)

storage & misc

protein

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Great resources for these kind of numbers

Note: the point of these things is not strictly the numbers themselves, but that comparing numbers and thinking about how they relate to biological processes forces you to think differently about biology!

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How do bacterial cells transport things in their cytoplasm?

DNA

gene

RNA polymerase

?

10 µm

Mikael Häggström/wikimedia

Short answer: diffusion—stuff constantly bumps into each other.

We’ll see quantitatively why bacteria don’t have the transport systems like you see on the left.

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Brownian motion

(gif from Wikipedia)

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Diffusion is a means of molecular transport!

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Ballistic motion vs. Brownian motion

 

Ballistic

Brownian/diffusive

  • Well-defined direction
  • “Deterministic”: if you know the position and speed, you can perfectly predict the position later

  • Direction of motion constantly changes
  • “Stochastic”: You cannot predict the position later; you can only hope to predict the average

Can we quantitatively predict this average? What does that tell us about transport within microbes?

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Ballistic

Brownian/diffusive

 

 

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If you are randomly bouncing around, there are many possible trajectories you can take.

So there are many distances you could travel. We can only talk about the average distance after a certain amount of time!

Let’s take a look then.

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Simplifications:

  1. We’re moving in 1 dimension��
  2. We treat all collisions as steps of length 1���
  3. Collisions happen at regular time intervals so that the time passed is proportional to the number of steps

0

1

2

3

-3

-2

-1

 

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How far do you go on average after N steps? Let’s actually compute the average for different values of N in one dimension

N = 1

What are all the possibilities?

Series of steps

Displacement, r

{+1}

{-1}

1

-1

 

Hmmmm . . .

Squared displacement, r2

1

1

 

 

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How far do you go on average after N steps? Let’s actually compute the average for different values of N in one dimension

N = 2

Series of steps

Displacement, r

{+1, +1}

{+1, -1}

2

0

 

Squared displacement, r2

4

0

 

{-1, +1}

{-1, -1}

0

-2

0

4

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How far do you go on average after N steps? Let’s actually compute the average for different values of N in one dimension

N = 3

Series of steps

Displacement, r

{+1, +1, +1}

{+1, +1, -1}

3

1

 

Squared displacement, r2

9

1

 

{+1, -1, +1}

{+1, -1, -1}

1

-1

1

1

{-1, +1, +1}

{-1, -1, +1}

1

-1

1

1

{-1, -1, +1}

{-1, -1, -1}

-1

-3

1

9

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How far do you go on average after N steps? Let’s actually compute the average for different values of N in one dimension

N (number of steps)

1

0

1

2

0

2

3

0

3

 

 

 

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Distance traveled squared

Number of collisions

Proportionality constant

 

 

 

A constant that has to do with

  1. How often the particle collides
  2. How far it travels between collisions

(temperature, medium, particle size)

 

 

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Distance diffused depends on the number of spatial dimensions

Protein on DNA: 1D

 

Protein in a cell membrane: 2D

 

 

 

 

 

 

 

 

Protein in the cytoplasm: 3D

(images from Wikipedia)

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Very physics/math derivation

 

 

 

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Very physics/math derivation

 

 

 

(mean of sums is sum of means)

 

Diffusion constant: inversely proportional to molecule size

 

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Why am I making such a big deal about this?�

  • Diffusion is fundamental to all sciences�
  • Despite its ubiquity, this non-linear transport property is very counterintuitive for us�
  • We will see that this mathematical law has deeply impacted intracellular transport across length scales

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What does transport in the cytoplasm look like?

Well maybe it looks like this?

We’ve never actually observed this, but why do we believe it?

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How does this compare to ballistic transport?

 

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How does this compare to ballistic transport?

 

 

Motor proteins in eukaryotes (e.g. dynein)

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How does this compare to ballistic transport?

 

 

 

It’s proportional to the square root of time. This is highly unintuitive. Let’s see how it impacts how microbes transport things in their cytoplasm.

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What do these equations mean for our bacteria?

The question I’m going to ask is: for a given distance, how long does diffusive vs. ballistic transport take to transport something that distance?

Driving an average of 20 miles/hour on Rt 9, how long does it take to drive the ~20 miles from Symphony Hall to Framingham, MA?

 

 

Let’s examine this in the context of a bacterium vs. a neuron.

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What do these equations mean for our bacteria?

We’ll compare the transport times for:

 

*image from wikipedia

 

 

Bacterial cell

Neuron

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Let’s compute how long it takes it to transport by diffusion vs active transport

  • Open the Week 2 python template in jupyter

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What do these equations mean for our bacteria?

 

 

You can transport things way faster with these motor proteins. Why are bacteria not using these?!

Let’s zoom in on our relevant microbial length scale . . .

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What do these equations mean for our bacteria?

 

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Laws of physics and the size of microbes has revealed something quite deep across the entire living kingdom!

Microbes

Small size enables rapid transport across the cell for 0 cost with diffusion

Large cells

Must spend large protein and energy resources on elaborate transport machinery