Transcript Lecture 3 (9/2/14) "Entropy Matters"

Today
Review quiz
Homework
Written HW #1 due Thursday
Reading #2, Scientific American by Mattick,
assigned today, due next Tuesday
(a few question quiz next Tuesday)
(Talks about what is the purpose of the “junk” DNA.)
Quiz
1. There are 3 families of life on earth. Name them. (Hint: recall Carl Woese)
Eukaryotes, Prokaryotes, Archea
2. Despite the tremendous diversity of life-forms, they all have a common
property and therefore likely arose from a common ancestor. What is this
common property? Central Dogma Biol: DNA RNA Proteins,
or Nucleic Acids Proteins
3. All reactions are governed by the free energy DG (sometimes written as
DGsystem). This is made up of two separate terms.
a. Write an equation for DGsystem in terms of these components and tell
what they are called? DG=DHsystem (enthalpy) –TDSsystem (entropy)
b. In order for a reaction to be spontaneous (therefore happens
automatically), DGsystem should be positive, zero, or negative?
c. Does the system tend to want to go towards the first and second terms
being positive, negative, or zero? DH < 0 ; DS > 0
4. Explain how biology --and life-- is consistent with the first and second
laws of thermodynamics. (The first law says that the total energy of a system
and its surrounding is constant; the second law states that the total entropy
of a system plus its surrounding always increases for a spontaneous
process.) Use the biochemical process of converting carbon dioxide and
nutrients into a leaf as an example.
DStotal must increase = DSsystem +DSsurrounding
5. Given the reaction below, tell why water plays an important role in
biochemistry/ protein-folding.
DHtotal = constant = DHsystem +DHsurrounding
(Either one can go up or down)
Water will H-bond with
itself but also w amino
acids. Therefore where Hbonding occurs within
protein is often regions
that water is excluded
from.
Basic Biology
& some calculations
[Read Chpt 1 of Berg et al.: lots of
important things about Molecular
Binding, Central Dogma, Entropy, DG]
1. Size of Cells and King Kong
2. Entropy Matters, DG, ATP.
The Cell is the Fundamental Unit
of Life
from Latin cella, meaning "small room"
Three types:
A bacteria and archea,
(w/o nucleus): 1 x 2 mm
A eukaryotic cell, (w nucleus): 10-100 mm.
What determines how small a cell can be?
.
Minimum size to have enough room for ~1000 reactions
necessary for life.
What determines how large a cell can be?
Maximum size to make sure molecules find each other rapidly
enough so metabolism can take place
--will study more, but partly based on diffusion. Bacteria small
enough that don’t need anything else beside diffusion. Eukaryotes
also have molecular motors to cause molecules to get close
together and react.
(Bacteria has about 10x faster metabolism than eukaryotic cells.)
Mass? (density is the same): 10 x 10 x 10 = 103
Strength? a Cross-sectional area (rope): 10 x 10 = 102.
Strength/Mass ratio? 1/10… 1/dimension
King Kong is proportionally speaking
is 10x weaker than regular gorilla!
Regular gorilla with 10 gorilla’s on him—couldn’t walk.
Whales
In water– held up by buoyant force.
Bones do not need to support weight
If have to, have super big bones– would sink.
If whale stranded on the beach?
Bones break; also overheat (because warm-blooded and
water is going at conducting away heat, whereas air is not.)
Thermal energy matters
a lot!
Everything (which goes like x2 or v2 in PE or
KE) has ½ kT of energy.
If a barrier has on this order, you can jump
over it and you will be a mixture of two
states.
Boltzman distribution = Z-1 exp (-DE/kBT)
kf
kb
DE
Keq =
kf/kb
Entropy also matters
(if lots of states can go into due to
thermal motion)
Probability of going into each state increases
as # of states increases
DE1
DE1
DE1
DE2
DE2
DE3
Add up the # of (micro-)states, and take
logarithm: ln si = Si = Entropy
Boltzmann factor & Degeneracy
In general, there can be a number of different
states, Wi, that are degenerate—have the same
energy, but can put a molecule into, with P(Ei)
W=1
W=1
W= 1
W=1
3

2

1

0
Usual Boltzmann Faxtor:
P(Ei) = (1/Z) e-Ei/kT
With degeneracy
W=3
W=2
W=3
W=2
3

2

1

0
P(Ei, Wi) = (2/Z) e-0/kT + (3/Z) e-/kT + (2/Z) e-2/kT +…
P(Ei, Wi) = (Wi/Z) e-Ei/kT
Boltzmann factor & Degeneracy
•
•
Generalize the definition of the free energy to include
degeneracy. Like flipping a deck of cards twice.
Each energy level may be populated with several
molecules, i.e. have many accessible states. We define
the multiplicity Wi as the number of accessible states
with energy Ei. For example:
W=3
W=2
W=3
W=2
3

2

1

0
Assume that a more general formula for the probability
P(Ei, Wi) = (Wi/Z) e-Ei/kT
of finding a molecule with energy Ei, with the multiplicity factor Wi.
Using Wi = exp[ln Wi]
P(Ei, Wi) = (Wi/Z) exp(-Ei/kT) = (1/Z) [exp(lnWi)] exp(-Ei/kT)
= (1/Z) exp -(Ei – kTlnWi)/kT
Define S= kln[Wi]
P(Ei, Wi) = (1/Z) exp -(Ei – TS)/kT = = (1/Z) exp –[Fi /kT]
where F = Helmholtz free energy which is same as Gibb’s
Free Energy for liquids (non-gasses).
Note: ∆G because always energy w.r.t. some zero (like E,
∆E); define E and S. Typically, 1M concentration.
DG vs DF
Up till now we said change in energy
= kinetic + potential energy.
In some cases, there is a change in volume
(e.g. explosives work)
H (enthalpy) = E (energy) + pV.
Takes into account changes in pressure and
volume.
In biochemical reactions, Dp and DV are ~ 0, so
you can use either DF or DG.
F = E – TS
G = H – TS
(F ~ G)
Can use either.
Bottom line:
Whenever you usually use E, use G,
and entropy is taken care of!
Equilibrium
How stable is one state over
another?
A  B
Probability of being in B = Z-1exp(-GB/kT)
Probability of being in A = Z-1(exp-GA/kT)
Keq = B/A = exp (-GB/kT+ GA/kT)
= exp –([GA- GA]/kT)= exp –(∆G/kT)
Keq = exp –(∆G/kT)
∆G = -kTlnKeq
What about A B + C
Keq = [B][C]/[A].
But how to figure out in terms of ∆G?
This tells about equilibrium.
Tells nothing about why two are
stable
Stability and thermal activation
Both systems are stable because they
have activation energy to convert!
All chemical reactions involve changes in energy.
Some reactions release energy (exothermic) and
others absorb it (endothermic).
Keq= [B]/[A]
[Says nothing about
∆G+rev/forward]
∆G+forward
∆G+rev
Keq = f(∆G)?
Keq = exp(-∆G/kT)
∆G
∆G = -kT ln (Keq)
Enzymes
(Catalyst)
∆G+rev
∆G+forward
∆G
If Activation Energy < kT, then rxn goes forward. If not,
need to couple it to external energy source (ATP).
ATP, Energy, Entropy
ATP  ADP + Pi

Take energy from a couple of photons, and convert
ADP + Pi into ATP
You must add up not only the energy (two vs.
three negative charges forced together), but the
free energy arising from loss or gain in Entropy.
Energetics of ATP
1 ATP= 80-100 pN-nm of energy at 37 ºC
= 20-25 kT of energy
(much more than kT = 4 pN-nm)
A lot of energy
Why do I say 80 to 100 pN-nm? Why not an exact amount?
Let’s say that you let reaction in a (small) box.
Start out with no ADP and no Pi. Then there are a
ton of places for each to go and so you have tons of
places to go where negative charges are far from
each other.
Now if there is a lot of ADP and Pi around, not
much energy from splitting ATP.
ATP sometimes gives 20 kT, sometimes 25 kT
You will have to calculate this.
(Easiest to do in moles/liter,
rather than by single molecules.)
How can use 90 lbs?
Net weight = WATP-WADP
Class evaluation
1. What was the most interesting thing you
learned in class today?
2. What are you confused about?
3. Related to today’s subject, what would you like
to know more about?
4. Any helpful comments.
Answer, and turn in at the end of class.