Statistical Postulates in Quantum Mechanics

This paper is reasonably accessible, and talks about the Information Theoretic approach to Statistical Mechanics. It is written using Quantum Mechanics, because Classical Statistical Mechanics is conceptually harder. But, the same results apply in both cases.

Balian, R. (2005). Information in statistical physics. Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics, 36(2), 323–353. doi:doi: DOI: 10.1016/j.shpsb.2005.02.001

Salt Rejection and Water Transport Through Boron Nitride Nanotubes

Abstract: http://onlinelibrary.wiley.com/doi/10.1002/smll.200900349/abstract

Full PDF: http://onlinelibrary.wiley.com/doi/10.1002/smll.200900349/pdf

My talk on the paper: A Bipedal DNA Brownian Motor with Coordinated Legs

Hello everyone

The paper I gave my presentation on was titled: A Bipedal DNA Brownian Motor with Coordinated Legs
By Tosan Omabegho, Ruojie Sha, Nadrian C. Seeman

A copy of it can be accessed at the websites below.

Abstract:
http://www.sciencemag.org/cgi/content/abstract/324/5923/67

Paper:
http://www.sciencemag.org.ezproxy.library.uq.edu.au/cgi/reprint/sci;324/5923/67?maxtoshow=&hits=10&RESULTFORMAT=&searchid=1&FIRSTINDEX=0&resourcetype=HWCIT.pdf

Practice final exam

Here is the final exam from last year.

Structure of the torque ring of the flagellar motor and the molecular basis for rotational switching

Hi all,

I will be presenting the paper titled "Structure of the torque ring of the flagellar motor and the molecular basis for rotational switching" by Lee et al on Wednesday. Have a look at some of the supplementary videos on this site - the torque ring in particular.

http://www.nature.com/nature/journal/v466/n7309/full/nature09300.html

Cheers,

Calvin

Our Video!

How do neurons perform calculations?

If the brain is analogous to a computer is it possible to describe a small number of neurons as similar to a logic gate? What would this analogy leave out?

Paper presentations

Before you presentation please post a link to the paper you will be discussing.
After the presentation (or even better before) post a copy of your presentation.

When axons get on your nerves

Thanks to the work of Camillo Golgi and Santiago Ramon y Cajal, we have been able to understand the functioning of neurons. Between each neuron is a synapse. On either side of this synapse is the presynaptic (axon) and the postsynaptic (dendrite) components. As it goes, information passes from the pre- to the post-synaptic side.


Axon Terminals are capable of releasing various neurotransmitters, which can be used to alter the membrane potential in another dendritic tree.
Arrivign action potentials at the presynaptic cleft can cause depolarization or hyperpolarization of the postsynaptic, based around the released neurotransmitters, and on the postsynaptics ion channels.
The synapse can be considered excitatory or inhibitory based on whether it is depolarizing of hyperpolarizing.Often, single action potentials just aren't good enough to do anything, soi cells incorporate integrate-and-fire model of neuron activity.

Electrophysiology

Also known as the axon's electrical response, there are several features that are key to the functioning of an action potential.

1. It's all or nothing - either you're going to have an action potential, or you're not. The membrane depolarization must reach a certain threshold (commonly quote in textbooks as -50mV). If subthreshold, electrotonus occurs (no response far from the point of stimulation), but if above the threshold, a wave of excitations will occur, with each peak potential non-determined by the input stimulus.

2. action potentials move at a constant speed of 0.1 to 120 m/s.

3. Action potential peaks are independent of distance, though the decaying behaviour of hyperpolarization or subthreshold stimuli are. This is to say, one input of stimulus can send an action potential along the longest axon (very important, think of your leg)

4. action potential shape remains constant over time.

5. afterhyperpolarization is where the membrane potential overshoots, become more negative than at rest.

6. The neuron is harder to stimulate during what is known as the refractory period.

Proof that ion channels exist?

The experiment that produced the graphs in figure 12.13 is described as the most remarkable in the book. I suppose it is the most remarkable because showing that the action potential of an intact axon is identical to that of an axon with replaced internal contents proves that: a) the internal contents of the axon do not matter and b) there must be some way for the ions thought to be responsible for the action potential to enter the axon. Could that way be the ion channels?

Threshold stimulus effect on crab axon

Figure 12.2 shows the effect of depolarizing (upper traces) and hyperpolarizing (lower traces). It shows a quick dying off (electrotonus) behaviour below a threshold but large propagating potential once this threshold is reached.

Movement of an Action Potential

Initiation of an action potential.
Most voltage-sensing channels have voltage-sensing ‘paddles’. These paddles consist of charged helices that can move according to the charges of its surroundings. Movements of these voltage-sensors create conformational changes in the channel that leads to their opening/closing.



Action potentials move in one direction.
Na+ channels can also be inactivated. After activation Na+ channels are inactivated for a time (refractory period). In the ‘ball and chain’ model the channel is blocked by a ball-structure which binds in the channel pore. This ensures that the action potential does not propagate backwards. The channel will remain inactivated until the membrane has reached its resting potential.



Repolarisation is also delayed by the hyperpolarisation that occurs from K+ channel flux. This is seen as a further dip in Figure 12.8a in Nelson. K+ voltage gated channels are opened once the action potential depolarisation has occurred. They then remain open until the membrane potential returns to its resting state.



Information taken from: Molecular Cell Biology, Lodish, 6th edn, Chapter 23.
Information and Channel figure taken from: The Voltage Sensor in Voltage-Dependent Ion Channels, F. Bezanilla, 2000, Pysiological Reviews.
1st polarisation figure taken from: http://www.ncbi.nlm.nih.gov/bookshelf/br.fcgi?book=mcb&part=A6125

Myelination allows the Action Potential to jump down the axon.

The myelin sheath provides insulation for the neuron and increases the speed of the action potential transmission. For neurons with no sheath the speed of the action potential is proportional to the axon diameter (you may remember this from Krassen’s lectures in Biph2000).

The region of the axon covered in the sheath does not have any channels present in the membrane, they are instead localised to the nodes between the sheaths. In this way the potential can jump to each node with practically no loss of signal. This type of transmission is called “salutatory conduction”.

Information taken from: Molecular Cell Biology, Lodish, 6th edn, Chapter 23.
Image taken from: http://www.arts.uwaterloo.ca/~bfleming/psych261/lec4se21.htm

The Hodgkin and Huxley Equations

In the biological maths course I took last semester, we looked at the Hodgkin and Huxley model for action potential. I hoped that this chapter would mention it, but it didn’t go into many of the details. So I thought I’d share a bit of what I learnt here.

They modelled the rate of change of the potential as a function of the current injected into a cell minus the change in voltage caused by the change in conductance of each ion (Ex is the equilibrium Nernst potential of the ion x).

They had to find a relation to model the conductances of each ion as function of membrane potenial. They chose the equations below. The variables n and m measure (respectively) the probability of the potassium or sodium voltage gated ion channels being open and thus 0 <= n <=1. The term for the sodium conductance has an extra variable, h, which measures the probability of the sodium gated ion channel being inactivated. As section 12.3.2 on page 540 of Nelson points out, it’s ok to use a probabilistic model for the activation of ion channels, as there are many of them in a single cell.

A model must then be found for these probabilities. Each of the variables n, m and h were assumed to have first order kinetics, where there was one rate constant governing the opening of the channel, and one rate constant governing the closing. These rates are α and β in the equations below, and are assumed to be the same for each variable m, n and h. It is these variables, α and β, which are membrane potential dependant.

This model might seem complicated, and it is, but it produces quite realistic results. One of our assignments for this course was to solve these equations numerically. This is an example of the action potentials produced by this model.

I think this chapter would have been better off discussing this model rather than the model in section 12.2.

The Goldman Equation

This chapter derived some interesting models for the way action potentials are generated. But I noticed they let out an equation which I thought was quite important when considering the membrane potential. This equation is the Goldman-Hodgkin-Katz equation. This equation is effectively just the Nernst equation, but for multiple ionic species. But there is one important difference. The Nernst equation uses relative concentrations on each side of the cell membrane to determine the potential, whereas the Goldman equation goes a step further, and includes a permeability term for each ion.

Px represents the permeability of ionic species x, F is Faraday’s constant, and R and T have their usual meaning, the gas constant and temperature.

The permeability term allows this equation to remain valid during the entire action potential, unlike the Ohmic hypothesis used in Nelson. To convince yourself this equation will still give an accurate measurement of the membrane potential during an action potential, consider what happens to V as the permeability of sodium (PNa) increases. [Na+out]>[Na+in], so the numerator in the natural log increases, increasing the membrane potential V.

A realistic ratio of the permeabilities of these ions in the resting state is PNa:PK:PCl = 1 : 0.03 : 0.1. Using these pemeabilities and the values in table 11.1 on page 477 of Nelson, I calculated a resting potential of -63.8mV, which is very close to the measured value of 60mV. The ratio of permeabilities for the excited state is PNa:PK:PCl = 1 : 15 : 0.1, which yields a membrane potential of +43.7mV, which is again close to the accepted value of the peak potential of an action potential.

If you don’t want to repeat these calculations again, but would like to play around with values, I suggest going to this website: http://www.nernstgoldman.physiology.arizona.edu/. It allows you to vary the permeabilities of the ions and observe the effect on the membrane potential using the Goldman equation.

Meeting Summary 13th of October

As today was the first time we had seen the sun in a few days, we decided to have this meeting outside. On our way we discussed aspects of the biophysics course, such as the prerequisites, the textbook, etc. We came back to this topic briefly a number of times during the meeting, but I didn’t think it was necessary to record these digressions.

The main topic of chapter 11, and thus our discussions, was ion channels. Much of the maths derived for topics that we have studied in previous chapters, which deal with bulk solutions and continuums, breaks down when applied to ion channel physics. Before the structures of the ion channels were known, many models were suggested, but were not able to reflect reality. This is because ion channels often allow transmission of single molecules at a time, and statistical assumptions like those made for the Boltzmann distribution break down at this level.

We briefly discussed voltage gated ion channels, and how a potential can be stored in a cell membrane. This discussion moved on to how electric eels generate charge, and how the charge hurts/kills prey. They have thousands of cells in series called electroplaques which generate and store potential, like a capacitor.

The sodium anomaly was discussed, which lead to the concept of the anion gap. This is where a coma patient’s electrolyte count is measured, to indicate how the coma was induced. Brain injury patients are at risk of low electrolyte concentrations, as brain swelling increases the amount of water in the brain.

The unusual features of the chlorine channels were mentioned. These channels come in pairs, and have inward curving channel walls, and have a glutamate residue gating the channel, which only allows chlorine ions to pass through in one direction. KcsA channels were also brought up and the way that the protein mimics the hydration sphere of the potassium ion, to allow only potassium ions to pass through, rather than sodium ions, which as smaller. The concept of the potential mean force on an ion as it passes thorough a channel was introduced. Ligand gated ion channels were also mentioned.

The nature of torque was discussed, and how it relates to the ATP synthase motor experiment in section 11.3.4. The mitochondrial role in glycolysis was touched upon, as well as the molecule pyruvate, but most of us were happy with this area.

How some toxins work as ion channel blockers, and how lethal they can be was also discussed. We then moved into Megan’s lab to view some videos illustrating how detergents can affect crystallised protein structures and how ions travel through ion channels.

How to Make the Most of Your Chemiosmotic Coupling

So the body needs ion pumping across membranes as a necessity. It can be used for segregating macromolecules inside cellular components (often they need to be in a certain environment for optimal activity), to give macromolecules an overall net negative charge (to prevent clumping), and to maintain osmotic balance, or to osmoregulate.

So from pg 497, here are some you can make use (or more appropriate, cells force an organism to make use) of chemiosmotic coupling.

Proton pumping in chloroplasts and bacteria.

Chloroplasts are ATP-generating organelles, which use the free energy of the sunlight they absorb to pump protons across their membrane, and this proton gradient drives the "CF0CF1" complex, similar to the mitochondria complex "F0F1"

Bacteria also find their proton gradient and contain F0F1 synthases.

Flagellar Motor.

The flagella motor converts the electrochemical potential jump of protons into a mechanical torque. (to quote from pg 497 of the text)

Other Pumps.

Pumps such as the calcium ATPase are powered by ATP. There are others known as symports, and antiports.

How now to blow your cells up 101

Unfortunately, unlike plant, algal, fungal and bacterial cells, human cells just don't have a lot of strength behind them. They are weak, flexible and easily broken by the osmotic pressure occuring during Donnan Equilibrium. So, to maintain this equilibrium, the body has developed a method of being able to unsure that our cells don't swell up to the point that they burst, nor remove solution away to the point that the cells shrivel up like an old person. This solution - allow both the cell to swell and shrivel at the same time in such an equilibrium that neither burstage nor complete shrivelling occur. The cells allow for continuous pumping of the sodium ions by using metabolic energy. This creates a nonequilibrium system, but a steady state.

The text provides another example of this as the water fountain. Allow the fountain to keep running without a pump will cause it to eventually stop, but by using a pump, one can move the water back to the water source, and the cycle of fountain flow can continue.

Finally, the text eludes to some genetic defects which can interfere with osmoregulation. If one has spherocytosis, then their red blood cells become more permeable to sodium. Because the cells have to work a lot harder to remove the sodium, then it results in some cells surcoming to the eventual swelling and bursting. As the text says, "Entropic forces can kill"

Finally (this time it actually is finally) I was going to elude to action potentials. These are an example of continuous pumping of ions in and out of the cell but which can perform a useful action. Once a certain energy threshold has been achieved in the cells, a cascade of ions can be pumped in and out of the cell, allowing the muscle to perform useful work.

Evidence for the chemiosmotic mechanism: generation and utilization

ATP synthase is independent of the electrochemical potential generating proteins. In the words of the text: generation and utilization of chemiosmotic mechanism are independent. An experiment confirming this was done by E. Racker and W. Stoeckenius in which an artificial system resembling an ATP factory was constructed. Artificial lipid bilayers with the light-driven proton pump, bacteriorhodopsin from a bacterium, was confirmed as generating a pH gradient in response to light. A foreign ATP synthase from beef heart was added. With these two elements ATP was synthesized when the experiment was exposed to light. Because of the very different nature and source of the two proteins it was concluded that the two events are independent.

Figure 11.9 from page 493 shows an example of oxidative phosphorylation and the independence of proton (black dots) gradient generation and ATP synthasis (far right).