Transcript lecture 31 slides no animationsx

Recap from last time: perspective on
DG of ATP hydrolysis, -50 kJ/mol
At room temperature,
kbT = 1.38 x 10-23 J/K * 298 K * 6 x 1023 mol-1
= 2.5 kJ/mol
The energy required to break a typical covalent bond
= 400 kJ/mol
Recap from last time: enthalpies of formation
for major biological macromolecules
Carbohydrates:
Proteins:
Fatty acids:
4 kcal/g
4 kcal/g
9 kcal/g
1 lb of fat ≈ 450 g or 4000 kcal
Typical burn per mile: 100 kcal
Recap from last time:
energy density of macromolecules
Solubility limit of carbohydrates
in water: 2000 g/L
-- coke: 160 g/L
-- glycogen: 4% of muscle
mass, or 40 g/L of muscle
-- “pre-diabetic” blood
glucose: 1.8 g/L (10 mM)
Adipose tissue density: ~1 g/mL
-- lipid fraction: ~70% (nearly
as good as stacked oranges)
Plan for this unit
Explore the energy budget of the cell:
• How much energy is available? 1000 W/m2
• How do we capture it? e- excitation -> ATP
• How do we store it? bio. macromolecules
• How much do we need to make the
components of a cell?
• How efficient is the process?
To double, an E. coli cell in LB
uses glucose as a primary source of
both carbon and energy
How much sugar do we need to
double an E. coli cell’s carbon #?
(i.e., roughly 2 x 109 glucose
molecules for raw materials)
How much more sugar is needed for
energy to build macromolecules?
1. Calculate the total energy needed to synthesize
all of an E. coli cell’s protein
– Half of the dry mass of the cell is protein, so for
simplicity, we’ll just double that value to estimate the
total energy needed for cell component synthesis
2. Find the energy we can obtain through
respiration of one glucose molecule
– Somewhat less than the energy originally required to
synthesize the sugar
3. Divide to find the theoretical minimum number
of sugar molecules needed for energetics
How much energy is needed to synthesize amino acids
and incorporate them into protein?
Dry mass of protein per cell:
1.5 x 10-13 g
Typical amino acid mass:
100 Da or 1.5 x 10-22 g
# of amino acids per cell:
1.5E-13 / 1.5E-22 = 109
Cost to synthesize*:
~ 1 ATP/amino acid
Cost to incorporate:
~ 4 ATP/amino acid
Total: 5 x 109 ATP equivalents
Valine
2O
5C
11 H
1N
x 16
x 12
x1
x 14
Total
=
=
=
=
=
32
60
11
14
117 Da
How many glucose molecules do we
need to get that much energy?
• Can generate ~40 ATP
equivalents per glucose
molecule through
respiration
– For comparison,
photosynthesis required
2700 kJ/mol or roughly 50
ATP equivalents to
construct the glucose
molecule in the first place
How many glucose molecules do we
need to build an E. coli cell?
• Can generate ~40 ATP equivalents per glucose
molecule through respiration
– For comparison, photosynthesis required 2700 kJ/mol
or roughly 50 ATP equivalents to construct the glucose
molecule in the first place
• 5 x 109 / 40 ≈ 1.2 x 108 glucose molecules needed
for energetic purposes
– x 2 to account for synthesis of NTs, lipids, etc.
– Add to glucose molecules needed for raw materials
• Grand total: ~ 2 x 109 glucose molecules
– Dominated by need for carbon, not energy
How many glucose molecules does an
E. coli cell typically use to double?
Fresh media:
0.1 mol glucose/L, ~ 1 cell
Spent media:
0 mol glucose/L, ~ 1012 cells
0.1 mol * 6 x 1023 / 1012 cells
= 6 x 1010 glucose molecules/cell
Why is much more glucose used than
predicted in this calculation?
Predicted: 2 x 109 glucose molecules/cell
Observed: 6 x 1010 glucose molecules/cell
E. coli growing on LB are fermenting, not respiring
• 2 ATP equivalents/glucose molecule vs. 40
• Accounts for most of the discrepancy!
• Note that fermenting E. coli need more glucose
for energetics than for raw carbon
Plan for this unit
Explore the energy budget of the cell:
• How much energy is available? 1000 W/m2
• How do we capture it? e- excitation -> ATP
• How do we store it? Biolog. macromolecules
• How much do we need to make the
components of a cell? 1-10x own dry mass in
glucose!
• How efficient is the process?
How much of the available solar
energy are plants able to capture?
Of all incident light:
• ≈ 37% is absorbed by a pigment molecule
• ≈ 28% successfully mobilizes an e• ≈ 9% of energy is used to synthesize sugars
• ≈ 7% of energy remains usable after
respiration (0.3% after fermentation)
How much energy do organisms really
need to collect?
Need 5 x 109 ATP equivalents
= 4 x 10-10 J per cell division
20 minutes = 1200 s per cell division
-> 3 x 10-13 W
E. coli’s surface area is 1 x 10-12 m2
-> 0.3 W/m2
For a human (2000 kcal/day, 2 m2 surface area)
-> 50 W/m2
Energy budget of the cell summary
•
•
•
•
How much energy is available? 1000 W/m2
How do we capture it? e- excitation -> ATP
How do we store it? Biolog. macromolecules
How much do we need to make the
components of a cell? 1-10x own dry mass in
glucose!
• How efficient is the process? Not very – but
good enough!
Where are we headed in LS 50?
• Two lectures on cooperativity
– Biochemical approach and stat mech approach
• Four lectures on diffusion
– Chemical potential differences as a driver for
molecular motion
• Three lectures on natural and synthetic gene
regulation
– Applications of cooperativity and diffusion
Diffusion tends to equalize concentrations by driving
molecules from regions of high conc. to regions of low conc.
• For thin organisms, diffusion is
enough to ensure that oxygen
continually flows from the air or
water into tissues (where the
concentration is lower since it’s
being consumed)
• No circulatory system or other
bells & whistles necessary
• Steady-state concentration
profile same as for the Bicoid
problem on PS6 (falls off
rapidly) – big problem for thick
organisms!
A circulatory system can help transport O2,
but is also limited by diffusion
That’s
all?
RB
C
Once the concentration of oxygen is the
same inside the red blood cell as in the
lung, the net flow of oxygen into the RBC
Nature’s solution:
molecular hoarding with hemoglobin
Step one: Stash the oxygen
RB
C
Nature’s solution:
molecular hoarding with hemoglobin
Step one: Stash the oxygen
RB
C
Bound oxygen does not count toward the
concentration in the red blood cell’s
cytoplasm, so more oxygen can enter by
Nature’s solution:
molecular hoarding with hemoglobin
Step one: Stash the oxygen
RB
C
Nature’s solution:
molecular hoarding with hemoglobin
Step two: Advection
(flow of red blood cells in the
circulatory system)
Nature’s solution:
molecular hoarding with hemoglobin
Step three:
Unloading
RB
C
Cooperativity Lecture Outline
•
•
•
•
Introduction to heme and hemoglobin
Limitations of simple binding
Cooperativity as a potential improvement
Mechanistic understanding of cooperativity in
biology
The iron atom in heme binds oxygen
Heme
The protein hemoglobin has four subunits,
each cradling a heme group
~ 4 nm
PDB May 2003 Molecule of the
Iron oxidation state and coordination
state change on oxygen binding
Superoxide (O2-)
Fe2+
Fe3+
Reminder: some transition metals with
close d orbital spacing absorb visible light
Chlorophyll
Heme
Oxygen binding changes the
absorption spectrum, reflecting more
red light
Courtesy of Scott
Prahl
The fraction of hemoglobin bound by
oxygen bound can be estimated from
an absorption spectrum
Courtesy of Scott
Prahl
Liu et al., 2012
The fraction of hemoglobin bound by
oxygen bound can be estimated from
an absorption spectrum
Liu et al., 2012
This curve should surprise you!
Recap: Simple binding curves
are hyperbolic
How hard is it to switch from
“mostly not bound” to “mostly bound”?
How hard is it to switch from
“mostly not bound” to “mostly bound”?
What is [A] when 10% of B is bound to A?
What is [A] when 90% of B is bound to A?
…we must increase [A] by a factor eightyone!
Hemoglobin, an oxygen-binding
protein, has a sigmoidal curve
Switches from 10%
to 90% bound over
an ≈ four-fold
change in oxygen
availability
Hemoglobin has four oxygen binding
sites:
Is this responsible for its sigmoidal
curve?
Suppose all four sites are identical and independent
(i.e., each site is unaffected by the binding of O2 elsewhere)
with binding reaction rate kon and dissociation reaction rate koff
P: Protein (hemoglobin)
X: Ligand (O2)
Finding the binding curve when
sites are independent
What is the total concentration of binding
sites?
What is the total concentration of bound
sites?
What is the fraction of sites bound?