Transcript Tutorial 1 - Frederick H. Willeboordse

Nature’s Monte Carlo Bakery:
The Story of Life as a Complex System
Tutorial 1
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Who am I?
Hong Chong Ming, Kenneth
B. Sc. (Hons.), 2002, NUS
Teaching assistant
Graduate student (part-time)
Dept. of Physics
Office: Block S13, Room 04-03
Tel: 68742631
Email: [email protected]
URL: http://staff.science.nus.edu.sg/~phyhcmk/
Research: Theoretical Physics
(General relativity, Black hole solutions)
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Topics covered
1.
2.
3.
4.
Solubility in water
The structure of proteins
Logistic map
Kinks in phospholipids
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Solubility in water
Recall
Water (H2O) is formed by covalent bonding of two Hydrogen
atoms and one Oxygen atom.
The Oxygen atom pulls the electrons a bit harder
than the Hydrogen atom. Consequently, there is a
slight charge shift towards the Oxygen atom.
bit
--
bit
Since equal charges repel, the two
+
hydrogen atoms will be pushed out a bit.
This then leads to water’s ‘V’ shape.
bit
H
O
H
bit
+
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Solubility in water
Ionic Substances
The ionic bonds linking the
atoms are relatively weak in
an acqueous medium.
The negatively charged oxygen
ends are attracted to the positively
charged ions; similarly, the
positively charged hydrogen ends
are attracted to the negatively
charged ions.
The ionic bonds are broken because of the competitive
attraction of the water.
Copyright  W. W. Norton & Company
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Solubility in water
Polar Substances
When a polar substance is placed in contact with water,
the water molecules are attracted to the polar atoms of the
substance.
The water form hydrogen bonds with the substance,
surrounding it with water molecules and so dissolve it.
Copyright  W. W. Norton & Company
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Solubility in water
Non-polar Substances
Dispersed non-polar molecules disrupt the polar bonding
pattern of pure water, so that few hydrogen bonds can form in
the solution.
As non-polar molecules encounter one another randomly in a
solution of water, they tend to become trapped in clumps by
polar bonding of water molecules to one another.
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Copyright  W. W. Norton & Company
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Proteins’ structures
Recall
Proteins are made up of one or more polypeptides folded
and coiled into specific conformations.
A polypeptide is a polymer of amino acids connected
via peptide bonds.
The structure of amino acid:
Polar  soluble
Often gains an H+ 
becomes positively
charged base
H
H
N
H
C
O
C
OH
Polar  soluble
Often looses the H+ 
becomes negatively charged
acid
R
Amino group
Carboxyl group
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Proteins’ structures
Four levels of protein structure
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Proteins’ structures - Primary
Primary Structure
The primary structure of proteins is the sequence of amino
acids in the polypeptide chain.
N-terminus
C-terminus
Copyright http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/P/PrimaryStructure.html
The amino end is called the N-terminus and the carboxyl end
is called C-terminus.
It was first pioneered by Frederick Sanger with his colleagues
at Cambridge University on insulin.
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Proteins’ structures - Secondary
Secondary Structure
Secondary structures are the result of interactions between
non-R groups along the polypeptide backbone.
a-helix: hydrogen bonding between every fourth amino acids.
b-pleated sheet: hydrogen bonding between the parts of the
backbone in the parallel region.
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Proteins’ structures - Tertiary
Tertiary Structure
The tertiary structure of a protein is the three-dimensional
arrangement of the atoms within a single polypeptide chain.
It basically consists of interactions between R groups from
various amino acids.
It is the highest level of
structure that is attained for
a protein
composed of single
polypeptide molecule.
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Proteins’ structures - Quatenary
Quaternary Structure
Quaternary structure is only present if there is more than
one polypeptide chains.
Quaternary structure is the overall protein structure that results
from the aggregation of these polypeptide subunits.
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Logistic Map
What is chaos?
Chaos is also called non-linear dynamics.
Non-linear: a system that can not be described by linear
functions, eg. straight lines.
Dynamics: a deterministic process in which a functions’
value changes over time according to a rule that is
defined in terms of the function’s current value.
Chaos is NOT the same as random!!
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Logistic Map
What is chaos?
A simple non-linear dynamics system can exhibit a
completely unpredictable behaviour which might seem
to be random.
In popular terms, a linear system is exactly equal to the
sum of its parts, whereas a non-linear system can be
more than the sum of its parts.
The basic operations in chaos are stretching and folding.
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Logistic Map
Stretching and folding
Stretch
Fold
Back to the original shape
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Logistic Map
Stretching and folding
Stretch
Fold
Back to the original shape
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Logistic Map
Sensitive dependence on initial conditions
The distance between points on opposite end of the bar.
The distance
grows
exponentially!
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Logistic Map
Sensitive dependence on initial conditions
The distance
grows
exponentially!
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Logistic Map
Logistic Map
The original motivation of the logistic map was the
modeling of populations.
The logistic map can be expressed as:
xn 1  1  ax
2
n
We have already known the logistic map is a chaotic
system for certain value of the parameter a.
Let’s us see how do stretching and folding appear in the
logistic map.
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Logistic Map
Logistic Map
The maximum value of 1 for
xn+1 occurs when xn= 0.
The set of values of xn in the
interval (-1,0) map into xn+1
values in the interval (-1,1),
while xn values in the interval
(0,1) also map to (-1,1) but in
the reverse order, from 1 to -1.
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Logistic Map
Logistic Map
xn
xn+1
-1
-1
0
0
1
1
xn+1
xn+2
The logistic map stretches (-1,1), the domain of xn, to twice
its length and folds it back This repeated again as xn+1 is
mapped to xn+2.
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Logistic Map
Logistic Map – Population Dynamics
There exits two opposing forces:
•
tendency of population to grow exponentially
stretching
•
limitations by the environment.
folding
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Phospholipids
Why there is a kink in the structure of Phospholipids?
Brief answer: carbon-carbon double bonding
WHY???
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Phospholipids
Carbon-Carbon single bonding
The carbon and two of the hydrogens
form a plane that perpendicularly bisects
the plane formed by the carbon and the
other two hydrogens.
Copyright  Houghton Mifflin Company
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Phospholipids
Carbon-Carbon double bonding
Each carbon atom of a double bond is connected to only three
other atoms.
The two carbon atoms of a double bond and the four atoms
that are attached to them lie in a single plane.
Copyright  Houghton Mifflin Company
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Phospholipids
Copyright  Perarson Education
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