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25%-quiz 1
25% quiz 2
50% final exam
Grading Format
~8 MCQs
~4 Assays with calculations
Open book
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Agenda • Jan 16 --- Lecture 1 ( Cell, bacterial, and biomolecule) • Jan 23 --- Lecture 2 (statistics and Diffusion) • Jan 30 --- Break (Chinese new year) • Feb 6 --- Lecture 3 (Thermodynamics and Chemical reaction) • Feb 13 --- No class • Feb 20 --- Lecture 4 (Characterization technologies) • Feb 27 --- Exam I (open book) • Mar 6 --- Recess week • Mar 13 --- Guest lecture 1 (optical imaging strategies) Dr. Audrey Shi
(Leica) • Mar 20 --- Guest lecture 2 (MRI for biology/physiology) Prof. ShaoYing
Huang (SUTD) • Mar 27 --- Guest lecture 3 (cell-cell/substrate interaction) Dr. Nils Gauthier
(NUS) • Apr 3 --- Guest lecture 4 (development of electron microscope for studying
plasmid, protein, and cell) Prof. Utkur Mirsaidov (NUS) • Apr 10 – Exam II (open book) • Apr 17 – Overview
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We are mostly made of
water (H2O): ≈75%
C —very versatile: everything made of: Nucleic acids,
Proteins, Lipids (fat), Carbohydrates.
O —bonding, proteins, fats, nucleic acids
N — proteins, genetic material
Ca, P — bones
What are we made of?
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Biophysics • Biophysics is a bridge between biology and
physics
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Biophysics Applications
• Biomolecular interaction analysis
• membrane protein and lipid studies
• Drug discovery and development (protein-small molecular interaction)
• Protein-metal ion interaction
• Biomolecular structure and stability
• Protein crystallography studies
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Two areas of BioPhysics
Method Development
New techniques to see better Model Development
What it means (lectures 2-3)
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Model Development
• Statistics
• Random Walks, Friction and Diffusion
• Thermodynamics
• Chemical reaction and biological machines
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Statistics
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Probability in Science
You can NOT tell the exact state of each gas molecular in the room; BUT you can measure the precise probability distribution of gas molecules
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0.259X60=
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• For the babies distribution, find the variance of x
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What is the probability of getting a 6 with a dice plus getting head with a coin? What is the probability of getting a 6 with a dice plus getting a 1 with another dice?
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Integral of P(r) from R0 to infinite
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Low-density gases obey a universal law
• The number of gas molecules in a box at atmospheric pressure is proportional to its volume. (V↔N)
• Further, p*V=N*kB*T (Ideal gas law) 1. kB is Boltzmann constant and is 1.38*E(-21) joules
per degree
2. T is absolute temperature. (t+273C)
3. At room temperature (22C), kB*T equals 4.1E(-21)J or 4.1pN*nm
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What about a dirt particle with 1.25E(-10)kg?
Compared mgh and 3/2KT
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Simple case: Ball in gravitational field.
Thermal fluctuations, finite probability of being at height, h.
E = ??
Partition Function for 2-state system
1
o 1
1
o
-E /kT
1 -E /kT -E /kT
- 1 E
- o E
eP E =
e +e
o
1
E = mgh
E h = 0
E h =(mg)(h meter)
P(h) =
P(0)
As ball gets smaller, probability gets smaller / larger ?
“Ball” the size of O2? Why can you breathe standing up?
For O2, 1/e height is ~10 km ~height of Mt. Everest.
(10 kM is “death zone”)
What is 1/e height for O2?
-mgh/kT e
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Random Walks, Friction and Diffusion
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http://youtu.be/STLAJH7_zkY
1. Why does the dye spread through the solution?
2. Why does the diffusion take a random/unpredicted path?
3. Why is the diffusion quicker at higher temperature?
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http://youtu.be/cDcprgWiQEY
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Probability for getting back to the starting point
L=1; R=-1 To return to the starting point, the head has to be same as the tail
P=M0/M M0=possible combinations M=total way of flip coming out
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HT or TH
HHTT or TTHH HTHT or THTH THHT or HTTH
http://www.math-prof.com/Prob/Prob_Ch_05.asp https://www.khanacademy.org/math/probability/probability-and-combinatorics-topic/probability_combinatorics/v/probability-using-combinations
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Probability using Combinations
• Total number of way all the flip can come out
• 5000 heads out of 10000
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The exclamation point denotes the Factorial function
Factorial function is a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n
4!=4X3X2X1=24
0!=1 N!=(n-1)!Xn
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Displacement and diffusion law
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RRR RRL RLR LRR LRL LLR RLL LLL
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When L=1cm
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The diffusion law is model independent
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Key: image the bin to be very narrow; the difference between a function, line N(x), at two nearby points is L times the derivative of N
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Key: the development of the density won’t depend on how big the box is; the important thing is the number per unit area of a
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1. J measures the net number of particles moving from left to right;
2. A net drift to the right ensures, tending to even out the distribution, or make it more uniform.
3. If there is structure in the original distribution, Fick’s law says that diffusion will tend to erase it.
4. Diffusion constant D enters the formula because more-rapidly diffusing particles will erase their order fast
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B: partition coefficient of solute in oil versus water D: diffusion constant in oil
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Constant I=J*4πr^2
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More than diffusion
+
+ +
+ + +
?
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112
http://youtu.be/Md0PtdRxXvw http://youtu.be/Ya-jpBgzcc8
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113
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C(z): profile of particles density
Adapted from Nernst relation
114
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Scale height
115
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1g/ml
Not a stable suspension
116
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Scale height also depends on the acceleration constant
117
Comparable with z and cause a significant difference between Cx and C0
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118
Sedimentation equilibrium in centrifuge
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119
Or sedimentation coefficient
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-1
49
120
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Log-log plot of diffusion constant D of polymethyl methacrylate in acetone as a function of the polymer’s molar mass M.
P=0.57
121
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Log-log plot of sedimentation coefficients of polymethyl methacrylate in acetone as a function of the polymer’s molar mass M.
122
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http://youtu.be/_dbnH-BBSNo
123
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Definition of laminar flow
124
Fixed
Pushed to right
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125
f
Any fluid obeying is called a Newtonian fluid.
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Characteristics of Newtonian Fluid
1. Obey ;
2. Completely characterized by its viscosity and mass density;
3. Isotropic (the same in every direction)
126
𝑓 = −𝜂𝑣0𝐴
𝑑
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127
f
𝑓 ∗ 𝜌𝑚𝞰2
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128
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129
http://youtu.be/fma5WBl90Sw
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130 Now we want to compare ftotal with ffrict
If one is much bigger than another, we could drop the smaller on in Newton law
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131
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133
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134
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135
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136
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138
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139
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140
Calculate travel distance
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141
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142
Cilia motion is periodic but not reciprocal
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143
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144
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145
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146
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148
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149
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150
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151
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152