A course every science undergraduate should take?

Science is becoming increasingly inter-disciplinary.
Most science graduates do not end up working in scientific research or an area related to their undergraduate major.
Yet most undergraduate curricula are essentially the same as they were fifty years ago and are copies of courses at MIT-Berkeley-Oxford designed for people who would go on to a Ph.D and (hopefully) end up working in research universities.
Biology and medicine are changing rapidly particularly in becoming more quantitative.
How should we adapt to these realities?
Are there any existing courses that might be appropriate for every science major to take?

Sometimes my colleagues get upset that advanced physics undergrads don't know certain things they should [Lorentz transformations, Brownian motion, scattering theory, ....]. But, my biggest concern is that they don't have certain basic skills [dimensional analysis, sketching graphs, recognising silly answers,  writing clearly, ....]. These skills will be important in almost any job that has a quantitative dimension to it.

For the past few years Phil Nelson has been teaching a course at University of Pennsylvania that I think may "fit the bill." The associated textbook Physical Models of Living Systems will be published at the end of the year.

Previously, I have lavished praise on Nelson's book Biological Physics: Energy, Information, Life. I used it in a third year undergraduate biophysics course PHYS3170 and think it is one of the best textbooks I have every encountered. Besides clarity and fascinating subject material it has excellent problems [and solutions manual], makes use of real experimental data, has informative section headings, often discusses the limitations of different approaches, and uses nice historical examples.

The new book covers different material and focuses on some particular skills that any science and engineering major should learn, regardless of whether they end up working in biology or medicine or biophysics. Below I reproduce some of Nelson's summary.

Readers will acquire several research skills that are often not addressed in traditional courses:

• Basic modeling skills, including dimensional analysis, identification of variables, and ODE formulation.
• Probabilistic modeling skills, including stochastic simulation.
• Data analysis methods, including maximum likelihood and Bayesian methods.
• Computer programming using a general-purpose platform like MATLAB or Python, with short codes written from scratch.
• Dynamical systems, particularly feedback control, with phase portrait methods.

[Here modeling does not mean running pre-packaged computer software but developing simple physical models].

All of these basic skills, which are relevant to nearly any field of science or engineering, are presented in the context of case studies from living systems, including:

• Virus dynamics
• Bacterial genetics and evolution of drug resistance
• Statistical inference
• Superresolution microscopy
• Synthetic biology
• Naturally evolved cellular circuits, including homeostasis, genetic switches, and the mitotic clock.

This looks both important and fascinating. The Instructors Preface makes an excellent case for the importance of the course, including to pre-medical students. The Table of Contents illustrates not just the logical flow and interesting content but again uses informative section headings that summarise the main point.

So, what do you think?

Is this a course (almost) every science undergraduate should take?

Are there specific courses you think all students should take?

Are you nervous? Its just physics!

One of the things I really liked about Nelson's chapter on Nerve Impulses was the figure below. (Left click to make it larger.)



In the caption he says, "Perhaps the most remarkable experiment described in this book."

Why is this data so important and profound?

I would say that it is another defeat for "vitalism" and victory for both reductionism and emergence.

It is a victory for reductionism because it shows how a specific biological phenomena (nerve impulses) can be essentially reduced to a purely physical effect.
It is a victory for emergence because it shows how the shape and speed of the voltage pulses is universal and independent of many of the biological and biochemical details.

The right panel shows the time dependence of the voltage across the membrane of a "live" axon (a single nerve) cell.
In contrast, in the left panel the contents of the cell (a complex biochemical mix!) have been removed and replaced with just a solution containing the same amount of potassium ions as the "live" cell. [But the cell membrane and its ion channels are intact].

In passing, I mention that this does not mean that consciousness is "just" electrical activity. But that is another story....

Nervous and impulsive

I am really enjoying the last chapter of Nelson's Biological Physics. It discusses pioneering work of Hodgkin and Huxley the 1940's which laid the foundations for our understanding of nerve impulse propagation.

Hodgkin and Huxley received the 1963 Nobel Prize in Physiology of Medicine for this work.
[They shared it with John Eccles from ANU]. The Nobel Foundation has a really nice educational "game" on Nerve Signaling.

Nelson notes,

"Many biophysicists regard this work as one of the most beautiful and fruitful examples of what can happen when we apply the tools and ideas of physics to a biological problem."

Biological question: How can a leaky cable (e.g., a neuron) carry a sharp electrical signal over long distances?

Physical idea: Nonlinearity in the cell membrane's conductance turns the membrane into an excitable mdedium, which can transmit waves by continuously regenerating them.

Again, Nelson has really helpful section headings, including:

12.1.2 The cell membrane can be viewed as an electrical network
12.1.3 Membranes with Ohmic conductance lead to a linear cable equation with no traveling wave solutions

12.2.4 The time course of an action potential suggests the hypothesis of voltage gating
12.2.5 Voltage gating leads to a nonlinear cable equation with traveling wave solutions

12.3.1 Each ion conductance follows a characteristic time course when the membrane potential changes
12.3.2 The patch clamp technique allows the study of a single ion channel behavior

Moving beyond structural biology

One of the key ideas in biophysics is that structure determines property determines function. On the PHYS3170 blog one of the students, Alex (aka. ack!) had a profound observation about chapter 11 of Nelson. Here is my paraphrase/version/extension of her point.

Today both biology teaching and research is driven by a paradigm: first determine the biomolecular structure, then deduce the relevant properties of the structure, and then explain the function of the biomolecule.

However, historically this is NOT how biology has operated, and Nelson illustrates this nicely when considering the case of molecular ion pumps and the mitochondria. One starts with a knowledge of the biological function, e.g., energy production and distribution, and one then deduces what physical property the system must have (e.g., the ability to maintain a non-equilibrium concentration gradient of ions), and one then makes a hypothesis about what kind of structure is necessary to have this property (e.g., an ion pump embedded in the cell membrane wall).

In the 21st century biology is moving away from a preoccupation with molecular biology to systems biology. Since this involves emergent properties the actual details of biomolecular structures are less important than the collective properties that they have as they interact with one another.

Not the ghost in the machine, but the machine in the membrane

Here are a few highlights from Chapter 11 of Nelson's Biological Physics. It is entitled, "Machines in Membranes."

Indirect physical arguments led to the hypothesis of the existence of the active ion pumps, long before the biochemical identity of these amazing molecular machines was known.
This is analogous to how the existence of a molecular carrier of genetic information (DNA) was proposed to exist long before its chemical or physical structure was known.

Biological question:
The internal and external chemical composition of cells is very different. Why doesn't osmotic flow burst (or shrink) the cell?

Physical idea:
This nonequilibrium, osmotically regulated state can be maintained by active ion pumps located in the cell walls.

The invention of batteries (i.e., voltaic cells) was stimulated by Volta's skepticism towards Galvani's claim that muscles could be a source of electricity.

The Nernst potential is the voltage that must be applied across a membrane to maintain a concentration gradient of a particular ion species across the membrane.
All animal cells have a sodium anomaly, i.e., the Nernst potential for sodium is much more positive than the actual membrane potential, i.e., the ion concentrations deviate significantly from equilibrium values.

This non-equilibrium is maintained by an ion current across the membrane which is proportional to the conductance per unit area of the membrane.

Ion pumps are embedded in cell membranes and hydrolyze ATP to obtain the free energy they use to pump sodium ions out of the cell.

Consider the industrial factory below. It generates, distributes, and utilizes energy.


Mitochondrion are like factories, systems of coupled machines. See the figure below.
They act as bus bars to generate, distribute, and utilize energy in a cell. The chemiosmotic mechanism proposes that ATP synthesis is indirectly coupled to respiration:

NADH + H+ 1/2 O2 -> NAD+ + H2O

Note that proton transfer plays a key role here.

Ratcheting up my understanding

Something I have never quite understood has been discussions of ratchets which are driven by thermal fluctuations. Today in PHYS3170 we discussed these in the context of molecular motors. In Chapter 10 of Biological Physics, Nelson considers:

Biological question: How does a molecular motor convert chemical energy, a scalar quantity, into directed motion, a vector?

Physical idea: Mechanochemical cuoupling arises from a free energy landscape with a direction set by the geometry of the motor and its track. The motor executes a biased random walk on this landscape.

The figure below shows a protein (i.e., chain of amino acids) being irreversibly dragged to the right through a membrane.
Nelson considers the mechanical model below.
[We thought the S-ratchet and G-ratchet were from some profound nomenclature. But they are G&S = Gilbert and Sullivan!, who Nelson often uses for Socratic dialogues.]

This can be described by the potential energy curve below. On top of this random thermal motion (i.e, Brownian motion) occurs. One can see that this will lead to a nett motion to the right because the random thermal motion leads to small reversible displacements, except near the steps.
I did a web search for a simulation (e.g., a Java applet) of such a ratchet but could not find anything. Please let me know if you are aware of something like that.

The power of thermodynamics

Chapter 6 of Nelson's Biological Physics ends with a nice extract from a 2001 Science paper describing optical tweezer experiments which reversibly unfold single RNA molecules.

Figure b above shows how the amount of unfolded RNA as a function of applied force can be fit simply that predicted for a two-state equilibrium distribution (which has the same mathematical form as a Fermi-Dirac distribution!) The fit also gives a good estimate of the free energy of unfolding (about 80 k_B T at room temperature).

Nelson also gives simple arguments that give the probability distribution P(t) for the different waiting times t for folding and unfolding, P(t)=kexp(-kt) where k is the rate. The right panel of c. above shows the RNA length as a function of time for different applied forces. The resulting range of distribution times (note they are the order of seconds) are shown in panel d.

What is real new and cool here is observing all this for single molecules. Decades ago people found that the two-state model could describe the folding and unfolding of many biomolecules.



Here are slides for a lecture I have given previously on how this two-state equilibria can quantitatively describe the unzipping of DNA and unfolding of proteins. The right panel figure above is just one example of a measurement the amount of unfolded molecule as function of temperature. It can be fit to the same two-state distribution.

As Nelson note, it is amazing and impressive that such incredibly simple expressions based on simple thermodynamic considerations can describe such complex systems and processes.

Informative section headings

As I posted before, I really like the way that Phil Nelson uses informative section headings in his book, Biological Physics: Energy, Information, and Life. More of us need to do this in papers we write. Specifically, we need to go beyond Introduction, Methods, Results, Discussion, and Conclusion!

Here are some headings from the chapter I am currently reading:

6.2.2 Entropy is a constant times the maximal value of disorder

6.4.1 Entropy increases spontaneously when a constraint is removed

6.5.1 The free energy of a subsystem reflects the competition between entropy and energy

6.5.2 Entropic forces can be expressed as derivatives of the free energy

6.5.3 Free energy transduction is most efficient when it proceeds in small, controplled steps

6.6.3 The minimum free energy principle also applies to microspcopic subsystems

6.6.4 The free energy determines the populations of complex two-state systems

Here is a challenge for you. How many of these can you prove without looking at the book?

Finding the protons in proteins

X-ray crystallography has proven to be an extremely powerful tool to determine the structure of proteins. However, it does have several limitations:

• real biology happens in water not in a crystal (How do we know the protein structure is the same in a crystal as in the native state in water?)
• one can't see the location of protons (many important biochemical processes involve proton transfer and so knowing where the protons are is extremely important)

An alternative probe is neutron scattering. It does not have as high as resolution as X-ray scattering but one can see deuterium (which can be substituted for protons). It can also see water molecules.
A recent PNAS paper, Low-barrier hydrogen bond in photoactive yellow protein, illustrates the power and importance of the technique. Using nuetron scattering they were able to identify the positions of 819 H atoms out of 942 . More importantly, they showed that the hydrogen bond between the chromophore and the carboxylic acid group of the Glu46 residue was particularly short. The authors propose that in the excited state the fast relaxation of this bond into a normal hydrogen bond is the trigger for the photo-signal.

[I stumbled across this paper while looking at the Protein Data Bank as part of the PHYS3170 course]

I am curious as to how this relates to an earlier JACS by Gerrit Groenhof et al, which uses an extensive Quantum-Classical Molecular Dynamics study to argue that the Arg52 residue controls the photo-isomerisation process.

Dancing with the molecules

Here are some things I learnt from chapter 3, of Biological Physics by Nelson.

Biological question: Why is the nanoworld so different from the macroworld?
Physical idea: Everything is (thermally) dancing.

Activation barriers control reaction rates.
i.e., the rate of a typical chemical reaction depends on temperature largely via a factor of exp(-Eb/k_B T) where the activation energy Eb is independent of temperature, characteristic of the reaction and usually of the order of an eV (10^{-19} J) . Note this energy scale is two orders of magnitude larger than k_B T. Knowing this helps understand why genetic information must be coded at the molecular level. (Schrodinger emphasized this in What is life? which heavily influenced James Watson).

Early in the twentieth century, T.H. Morgan performed a series of experiments on genetic linkage that led him to deduce that genetic factors (alleles) must be encoded in a linear sequence. By the 1940's there were partial maps of the fruit fly genome:


In the 1930's Miller and Timofeeff found that the frequency with which a specific mutation (of fruit flies) occurred varied linearly with the total X-ray exposure of the system. Max Delbruck was able to deduce from this that genes are single molecules.

Biological physics vs. Biophysics

On the PHYS3170 blog, on of the students, Alex posted a perceptive question about clarifying the relation between biophysics and biological physics.

Certainly, different people will have different definitions. But, the question is worth thinking about if it helps clarify different approaches (which there certainly are).
Similar issues arise with physical chemistry vs. chemical physics.

Much of biophysics seems to be concerned with applying physics techniques to understand biological systems and processes.

Biological physics is particularly interesting when studying biological systems illuminates physical concepts and principles which hold independent of the system under study.
A master at this is John Hopfield, best known for his work on neural networks, which is now applied in computer science.

Another example, is how studying the protein folding problem led to energy landscape theory by Joseph Bryngelson and Peter Wolynes. Their approach introduced a Principle of minimal frustration and the notion of "folding funnel" energy landscapes which allow a protein via a large number of pathways. Such ideas of rugged energy landscapes are also relevant in non-biological systems such as glasses and artificial neural networks.

Two articles that discuss some of these ideas are a short Physics Today piece by Hopfield and a
Reviews of Modern Physics paper by Austin, Frauenfelder, and Wolynes.

How can it be?

Ch. 2 of Biological Physics by Nelson reviews a myriad of exquisite biological structures and processes. It is easy to get lost in the detail. But, he ends nicely, emphasizing the need to focus on the question:

How can all these "miraculous" processes occur?

Is there some common underlying physics?

The key physical phenomena we will need to understand are

• specificity
• self-assembly
• active transport

Other things to keep in mind and pay attention to are

-the hierarchy of length scales
-the hierarchy of energy scales associated with different types of bonding
-water with its unique properties is crucial, the hydrophobic interaction which drives many processes
-structure determines property which determines function

Keeping track of everything without accountants

Biological question:
How do cells organise their myriad ongoing chemical processes and reactants?

Physical ideas:
a. Bilayer membranes self-assemble from their component molecules; the cell uses them to partition itself into separate compartments.
b. Cells use active transport to bring synthesized materials to particular destinations.
c. Biochemcial processes are highly specific . Most are mediated by enzymes, which select one particular target molecule and leave the rest alone.

Nelson, Biological Physics, page 37

Some key ideas for biophysics from basic physics and chemistry

Section 1.5 of Biological Physics by Nelson lists

1.5.1 Molecules are small

He describes how in 1773, Benjamin Franklin estimated the linear size of a single molecule from observing that one teaspoon of oil covered half an acre of pond!

1.5.2 Molecules are particular spatial arrangements of atoms

1.5.3 Molecules have well-defined internal energies

1.5.4 Low-density gases obey a universal law

Boltzmann's constant is universal, i.e., it does not depend on the chemical or structural details of the system being described.

At room temperature

k_B T = 4.1 pN nm (most important formula in this book!)

I tend to think k_B T = 25 meV since this is a useful scale in solid state physics.
But, Nelson deliberately writes it terms of a force scale (picoNewton) and length scale (nanometer) that is relevant to the physics of cells.

How to do better on exams (and discover new physical laws)

This is the title of section 1.4 in Phil Nelson's book, Biological Physics.
I really like the way he uses subsection titles which convey useful information. Here are some:

1.4.1 Most physical quantities carry dimensions

1.4.2 Dimensional analysis can help you catch errors and recall definitions

1.4.3 Dimensional analysis can also help you formulate hypotheses

I think something that we just have to keep "hammering" students on is keeping track of units at each step of a calculation and canceling them out.

Why physicists and biologists need each other

I really enjoyed reading the rest of Chapter 1 of Biological Physics in preparation for thursday's class discussion. Section 1.3 has a nice discussion of the relationship between physical and biological sciences. Physicists seek the universal and simple in any system. In contrast, biologists when confronted with the complexities of the biosphere are more likely to emphasise "frozen accidents of history" and focus on details.

Figure 1.4 is nice but does not scan well and so I don't reproduce it here.

How does one synthesize these complementary approaches? First appreciate the value of each. Nelson suggests 3 steps for scientific advance:

"a) select a simplified but real model system for study
b) represent this system by a mathematical model with as few parameters and variables as possible.
c) deduce from the mathematical model some nonobvious, quantitative, and experimentally testable predictions."

He emphasises that a) and b) are inductive whereas c) is deductive.
a) and b) require a thorough knowledge of the biology.
Physicists need to be wary of proposing models that "lead to a large body of both theory and experiment culminating in irrelevant results."

Nelson points out that the best models may lead "to postulating entities whose very existence wasn't obvious from the observed phenomena."
Historical examples of this include:

Max Delbruck's deduction of the existence of a hereditary molecule (chapter 3)

the discovery of ions pumps and ion channels in cells (chapter 11,12)

George Gamow's proposal to find the genetic code

How can living organisms be so highly ordered?

This may seem to violate the second law of thermodynamics.

In the Intermediate Biophysics class meeting today we agreed to start reading through Philip Nelson's excellent book, Biological Physics: Energy, Information, and Life.

Each chapter begins with a biological question, and a terse slogan encapsulating a physical idea relevant to the question. Chapter 1 begins with:

Biological question: How can living organisms be so highly ordered?
Physical idea: The flow of energy can leave behind increased order.

He introduces the idea of free energy as the useful energy or quality of energy. The distinction between high and low quality energy is a matter of order or organisation.

Living beings consume order not energy.
Free energy transduction is what the biosphere does to create order.

The figure below is a nice way to illustrate transduction of free energy.
A machine uses osmotic flow to convert disorder (random molecular motion) into work in the upper part of the figure.

In the lower part of the figure doing work pulling on the weight increases the order in the system, i.e., the sugar solution becomes more concentrated (reverse osmosis).

Teaching biological physics

Preparing to teach PHYS3170 Intermediate Biophysics I have been looking at some material on Phillip Nelson's website. He is author of one of the nicest texts, Biological Physics: Energy, Information, and Life.

Several things particularly worth looking at are:

Teaching biological physics, an article in Physics Today.

A course on physical models for biological systems, a talk to the Biophysical Society.
(the syllabus of the actual course is here).

Key concepts in biophysics

Thinking through what to include in the PHYS3170 Intermediate Biophysics reading course it is good to reflect on what do we really want the students to learn. Here, off the top of my head, are some of the important ideas in biophysics that I have learned from scratch the past 5 years.

* Structure determines property which determines function

* Function is often about transduction (e.g., conversion of energy) and optimisation of efficiency, speed, and selectivity.

* Water is an amazingly unique substance.

* The hydrophobic interaction has a big effect on how proteins fold and the emergence of other biomolecular structures. (A dry protein is a dead protein!)

* The hierarchy of energy, time, and length scales.

* Both excitonic and vibrational energy transfer occurs via resonant energy transfer.

* Hush-Marcus theory describes electron transfer in proteins and elucidates the role of the environment.

* The size of kBT sets the scale for many phenomena.

* Entropy and Gibbs free energy (the chemical potential) are key concepts.

* Entropy describes elasticity of DNA, the hydrophobic interaction, and concentration gradients producing electrochemical potential differences.

* Transition metals play a key role in many biomolecular functionalities.

* The interplay of Emergence and reductionism associated with the hierarchy of energy, time, and length scales.

* What details matter? Physicists say none, chemists, most, and biologists all!

* Biochemistry is the search for the chemistry that works.

* Enzymes work by lowering the energy of the transition state over which the reaction proceeds.

* Biomimetics: understanding the underlying physical principles behind specific biomolecular functionalities (e.g., conversion of light energy to chemical energy) may allow us to design synthetic analogues which have optimum efficiency.

* Skepticism I. Heed Kauzmann's maxim: people will tend to believe what they want to believe rather than what the evidence before them suggests they should believe.

* Skepticism II: just because someone can do a simulation on a computer that looks what you expect to see does not mean:
1. the simulation is reliable, reproducible, and correct
2. you actually understand the phenomenon that is being simulated.

* More skepticism: von Neumann on wagging the elephants trunk.

* Biological physics vs. Biophysics vs. Biologists using tools that physicists invented

A radical (emergent) approach to teaching a course

Below is an email I sent out to the 5 students enrolled in a third year undergraduate class. I was wondering if anyone has any experience with this approach to teaching a course. Subconsciously, I was inspired by the two pages on "Synergy in the classroom" in The 7 Habits of Highly Effective People, by Stephen R. Covey. I just re-read it. He says:

As a teacher, I have come to believe that many truly great classes teeter on the very edge of chaos. Synergy tests whether teachers and students are really open to the principle of the whole being greater than the sum of the parts.

----------------------------------

Dear students,

Currently only 5 students are enrolled in PHYS3170 Intermediate Biophysics.Normally, this would mean that the course would be cancelled.

However, Dr. Seth Olsen and I are willing to offer to run the course in an alternative mode of delivery, where you all take greater ownership for learning and administrative activities.

There would be no formal lectures. Most learning would take place via readings and a class blog. Emphasis will be on co-operation rather than competition.

We would meet face to face on thursdays at 12 noon and possibly 2pm. This would be an informal discussion and question section. Students would each give at least one presentation during this time.

I would propose we try and negotiate an assessment arrangement which will be based on your extent of involvement and contribution to the learning activities of the class. You would collectively write the course profile.

The main role of Seth and I would be to select the readings/topics and help you understand them.

I believe you would actually learn more and have more fun.

But, I can understand why you might prefer the safety and predictability of a conventional course.

Please let me know if you are still interested.

cheers,

Ross McKenzie