Chapter 3 Lecture

Biological PhysicsNelson

Updated 1st Edition

Slide 1-1

The Molecular Dance

Slide 1-2

Announcements

• Study methods

– Read each chapter BEFORE class

– Pair study groups (if class big enough)

• Grading format

– Participation 30%

– Midterm report/presentation 35%

– Final report/presentation 35%

• Those of you taking Advanced Physics 1 (AP1)

will be encouraged to take AP2, sorry.

Slide 1-3

Summary Chapter 1

• Don’t forget:-

– The Belousov–Zhabotinskii experiment

– Free energy transducers and reverse osmosis

– High to low quality energy in plants and

animals

– The 1st law: dEtherm=dU= dQ - dWext

Slide 1-4

Summary Chapter 1

• The First Law of thermodynamics:

Etherm= Q - Wext

can be rephrased for different cases as:

• Just depends on what you’re interested in ...

• We’ll discuss μ the chemical potential later

Slide 1-5

Chapter 1 Homework

• You should have:

– Made a presentation on Chapter 2 or your

own them and pleas upload to Goggle Drive

– Homework Problems

• 1.4 (Earth’s temperature)

• 1.5 (Franklin’s experiment)

• Example solutions later please ...

Slide 1-6

Chapter 3: The Molecular Dance

• Cover previous material to tie in with the

beginning of chapter 2 and chapter 4

• 3.1 Probability & normalization

• 3.2 Gaussian, Maxwell & Boltzmann

distributions (Kinetic Theory of Gases)

• 3.3 Physical carrier of genetic information

(extra reading)

Slide 1-7

Question?

• Heat is disorganized molecular motion and

hence the lower the temperature the more

organized things are (lower entropy)

• So, do cells work best at the coldest

temperatures? No, then what is happening?

• It is amazing that a tiny cell can contain your

own personal database (the genome) without

loss of information over many generations ...

Slide 1-8©1991 by Larry Gonick.

3.1 Probability

Slide 1-9

Probability Rules

• Discrete measurements xi , x1, x2,.... with each

measurement made N times then probability is𝑁𝑖

𝑁→ 𝑃 𝑥𝑖 , 𝑁 → large

• For the continuous case we have

where we divide the range x into small bins x+dx

• They are normalized as (cf. quantum mechanics)

Slide 1-10

Mean, Variance

• Mean

• Variance

• For a Gaussian: mean = x0 and var = σ

• Exclusive events add:

and independent event multiply:

Slide 1-11

Gaussians

σ

Slide 1-12

Useful Mathware

• Maxima is a free Computer Algebra System

(CAS) unlike Maple or Mathematica

• Octave is a (Matlab-like) free package which

uses GnuPlot to make plots

• Finally we will also try Wolfram Alpha an

online free version of Mathematica

• Alternatively use a graphical calculator ... :-)

Slide 1-13

2D Gaussian: Shooting Arrows

Slide 1-14

Homework 1: 3D Case & 3D Gaussian

distribution?

Slide 1-15

3.2 Kinetic-molecular model of ideal gas

• The assumptions of the kinetic-molecular model are:

• A container contains a very large number of identical molecules.

• The molecules behave like point particles that are small compared to the size of the container and the average distance between molecules.

• The molecules are in constant motion and undergo perfectly elastic collisions.

• The container walls are perfectly rigid and do not move.

Slide 1-16

Molecular Pressure

𝑝 = 𝑚 𝑣𝑥2 𝑁/𝑉 ⇒ 𝑝𝑉 = 𝑁𝑘𝐵𝑇 ⇒ 𝑚 𝑣𝑥

2 = 𝑘𝐵𝑇

Slide 1-17

Molecular speeds

• The Maxwell-Boltzmann distribution f(v) gives distribution of molecular speeds.

• Figure right helps interpret f(v):

– Part (a) shows how the shape of the curve depends on temperature.

– Part (b) shows the fraction of molecules within certain speed ranges. The most probable speed for a given temperature is at the peak of the curve.

Slide 1-18

Theory vs. Experiment

Slide 1-19

An experimental apparatus*

Slide 1-20

The Boltzmann Distribution

Slide 1-21

The Boltzmann Equation

Slide 1-22

IN CLASS DISCUSSION

Discuss the following Figures 3.8 and 3.9:

Why does evaporating water cool?

How does an activation barrier affect the cooling of

evaporating water or chemical reaction rates?

Slide 1-23

Activation barriers

Slide 1-24

Relaxation to equilibrium

Slide 1-25

Homework/In class time

1. Make 2D/3D Gaussians with plots for different

σ using Wolfram α or similar software.

2. Derive Your Turn 3E/3F (darts in 1D & 3D)

3. Do Problem 3.1 (The Dodgy Bakery)

4. Suppose you role 3 fair dice. What is the

probability that you will get a 5 on at least one

dice?

5. Read Excursion 3.3. and think about Mendel’s

rules of heredity information.

See slides for Chapter 4 for next week.

Slide 1-26

3.3 How is bio-information stored?

• First how is the information replicated?

• Aristotle correctly argued (roughly) that life is

copied/created through

– software stored in a carrier to direct own

construction (genotype)

– duplicates/outputs the software (and carrier)

for transmission of offspring (phenotype)

Slide 1-27

Heredity Information

Slide 1-28©1961. Used by permission of Dover Publications.

Mendel’s Peas

Slide 1-29

Meiosis

Slide 1-30©1961. Used by permission of Dover Publications.

Slide 1-31(b) Andrew Syred/Science Photo Library/Photo Researchers, Inc.

Slide 1-32

Slide 1-33