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).

Meeting summary 06.10.10 CH10 Enzymes & Molecular Machines

Sorry about the late posting of this summary!
Last week we discussed chapter 10 of Nelson which was on enzymes and molecular machines. A definition of molecular devices can be found on pages 402-403 where there is a distinction between catalysts and 1-shot machines. An example of a 1-shot machine is translocation of a protein across a membrane.

We discussed where the motive force used by Listeria fits in to there definitions of molecular devices. At the tail end of Listeria an actin nucleation site where actin polymerizes is found. This polymerization causes listeria to be pushed forward. Should the Listeria motive force be considered a one-shot machine or a cyclic motor? p402 definition of a cyclic motor suggests that by using a renewable fuel (ATP) this it should be considered cyclic.

Mitch wondered where the data in fig 10.8 comes from.

Megan mentioned that the fact that these molecular machines do work on both local and global random fluctuations was not emphasized in this chapter. They tended to be represented by a smooth switching function when they would be better represented by an energy funnel.

Gilbert & Sullivan keep interrupting the chapter.

Figure 10.26 compares rachets to kinesin. The question was raised: what role does ADP or ATP play in this mechanism? It must be coupled to free energy difference but it is not clear how this happens. p463 mentions assumptions hold for large deltaG.

ATP, ADP provides large energy that allows weak, strong binding.

Figure 10.24 load is moved on upper right, hydrolysis on lower left. motion is not coupled to fuel burning. Are the events connected irreversibly?

A nucleotide sandwich dimer was mentioned where ATP is between myosin & kinesin.

The Smoluchowski equation (10.4) was discussed. Which describes diffusion with drift with ohmic/linear response/damped/dissipitive where velocity is linear in force - this basically means low reynolds number.

We discussed section 10.4 on Michaelis-Menten kinetics and discussed non- vs un-competitive binding. See Matt & Mitch's blog posts from last for further information.

We discussed the lack of statistics/probability knowledge in science - this seems to be a common theme.

Brief discussion on potential surfaces and their usefulness.

S-rachet was presented as protein translocation through membrane. When considering molecular machines even the best once go both ways due to thermal motion KbT.

We discussed molecular models of ATP & ADP + Pi and how it is difficult to model both as a single system.

Alan posed a question: What is the cause of catalysis? Could proteins have evolved to fluctuate randomly in one degree of freedom & can this enhance the rate of reaction. Is it possible to tell the difference between the different proposals for how enzymes work? Thermodynamically they all appear the same.

Your Turn 11F

As this is a fairly short chapter, and I wanted to leave things for other people to blog about, I’m taking a leaf out of Heather’s book and making my second post my solution to Your Turn 11F.

a) Torque, τ is force, f × (cross product) distance from the pivot to the point the force is applied, r. The force described in equation 11.17 is for the force acting perpendicular to the long axis of the rod, so the angle between the force vector and the position vector is 90o. So the cross product can be treated as a regular product. I will assume the force applied to the rod is uniform along the rod, so the average position of the point where the force is being applied is just the halfway down the rod. Thus, τ= f ×r≈3.0ηLvr=1.5ηL^2v.
The velocity of a point rotating at ω rad/s is the angular velocity times the distance that point is from the pivot. The average distance a point on the rod is from the pivot is again just halfway down the rod. So the torque becomes τ≈0.75ηL^3ω.

For a rod of length 1μm and an angular velocity of 6 rev/s=12π/s, the torque is 2.83x10^-20Nm.

b) The work done by torque is just the torque times the angle moved. In this case, the angle moved is one third of a revolution, which is ⅔π. So the work done by the F1 motor every third of a revolution is 5.92x10^-20J. Thermal energy at room temperature is 4.1x10^-21J, which is less than the value calculated, which is a good sign.

Differences between normal cells and neurons

After reading this chapter I was confused about which cells had sodium pumps, which cells had voltage drops across their membrane, and which had voltage gated ligand channels. The giant axon of the squid is used when introducing this topic, and is the cell in which the values in table 11.1 come from. Because a nerve cell was used as the example, I wasn’t sure if the topics discussed are specific to a nerve cell or to cells in general. So I took to the internet.

First of all, all cells have sodium-potassium pumps. This makes sense, as all cells need to osmoregulate. According to Wikipedia, the sodium-potassium pump in a normal cell expends a third of the cell’s energy.

All cells do have a membrane potential, around that of the resting potential of a neuron. It is used to power some of the molecular devices in the membrane. However, not all cells can use it for signalling like neurons.

Voltage-gated ion channels are necessary in neurons, but again, according to Wikipedia, can be found in many kinds of cell. I had trouble finding examples other than muscle and neuronal cells, but I found one example. The Transient Receptor Potential Channels are voltage triggered. An example of a protein in this family is the capsaicin receptor, which responds to the chemicals which make chilli taste hot. Voltage gated ion channel are not found in every cell.

So everything that I found out here is pretty much what I expected. But I am glad I found out for sure, and I hope this helps confirm things for you too.

P.S. I can’t remember if I was taught this last year in BIPH2000, but in case I wasn’t, I thought I’d share: The research done on squid giant axons was not performed on the axons of a giant squid, but the giant axon of a regular sized squid. You probably already know this, but I didn’t realise this until it was pointed out to me.

Your Turn 11B

Consider a fictitious membrane permeable to Cl- but not to K+:

Assuming only the negative ions can permeate the membrane, and then the negatively charged chloride ions will leak. The concentration of ions inside the membrane is higher than the outside, c2 > c1, therefore the ions will move outwards. This will increase the negative charge just outside the membrane and decrease it just inside. This is the reverse of the situation shown in Figure 11.2 a.
The electrostatic potential across the membrane will also be opposite. Visualise a positively charged test object. As the object moves from the outside of the membrane in its potential energy will increase; as it moves from a complementary-charged negative region to a repulsive positively-charged region. Thus the potential curve decreases moving from the inside to the outside of the membrane. This again is the reverse of the situation shown in the text, Figure 11.2 b.

Some extra info on glycolysis...

Here’s a simplified Biologists look at glycolysis, the citric acid cycle and oxidative phosphorylation. Three processes involved in ATP production.

Watch these:
http://www.youtube.com/watch?v=x-stLxqPt6E
http://www.youtube.com/watch?v=aCypoN3X7KQ&feature=related
http://www.youtube.com/watch?v=Idy2XAlZIVA&feature=related
http://www.youtube.com/watch?v=H0RchC0FbYU&feature=related

Glycolysis involves two stages. All the reactions are catalysed by specific enzymes. First glucose is prepared for catabolism by adding phosphates to its structure. This actually uses some ATP energy. The glucose is then processed and broken down to produce pyruvate.
The pyruvate is passed into the citric acid cycle (also named the Krebs cycle) it undergoes a number of changes involving a different enzymes and metabolites.
Two of these reactions are described by Nelson. Equations: 11.14; 11.15.
These reactions produce reduced NADH and FADH2 molecules. NADH is then used to generate a hydrogen ion gradient in the mitochondrion. The chemiosmotic gradient is generated using four protein complexes. Complex 1 is a NADH dehydrogenase; it catalyses NADH -> NAD+ and pushes 4 protons across the membrane. The electrons captured in this reaction are passed through to the other complexes in succession. Complex 2 is a succinate dehydrogenase; it doesn’t directly transfer hydrogen ions but instead donates further electrons by converting succinate to fumarate. Complex 3 couples the transfer of the electrons (from 1 and 2) with the transport of 4 protons. Complex 4 then reacts the electrons with oxygen to create water and transports a further 2 protons across the membrane. These successive reactions work to fully capture the energy generated from glucose. Without these incremental energy-capturing steps most of this energy would be lost to heat.

Landscaping

From figure 10.6, figures (a) and (b) both follow one-dimensional landscapes.

For (a) there is a negative slope (lower dashed line) related to the Umotor = -t(theta), the coiled spring contribution, while the positive slope (upper dashed line) relates to the external load contribution. This results in an overall downward slopes. the total potential energy (equal to (w1R-t)(theta)) decreases as time increases (theta is constant).

For (b) the graph is rather similar to (a) except is related to an imperfect shaft. What can be noticed is that due to the set up of (b) the contributation by the spring follows a sine-wave like curve, which is then reflected in the total potential energy line.

From figure 10.6, figure (c) contains a 2D landscape graph, since it depends on both the angles alpha and beta. Figure 10.8 displays the landscape graph for an unloaded machine, containing both valleys and barriers. Travelling along a valley is ideal but impossible to do indefinitely, so movements over the barriers are necessary. For a loaded machine, figure 10.9 shows the landscape graph, explaining that it is simply a tilted version of figure 10.8

Week 9 Session Notes - sorry for late upload

Point 9.1

Using a set number of degrees of freedom – we don’t overanalyse, we save ourselves a huge amount of mathematics etc

Elasticity comes from entropy. Entropy determines the elasticity of an object

Rubber band force pulling it back becomes less at high temperature

Elastic energy cost increases with temperature

Shape of curve determines elastic energy (equation 9.4 assumes circular curve)

Approximate a curve as a bunch of little circular segments

Figure 9.4

C) still a coil

d) unwinds and becomes straight

slope of A = entropic elasticity

figure 9.5

gives 4 different models to describe 9.4’s regime A and part of B

talked about reasons why we’d stretch out dna and other things

1D chain model – chain containing segments that pointed either left or right. Only two parameters occurring are temperature (which is fixed), and the persistence length (length of segment)

3D chain – segments can point in any direction. Adds two degrees of freedom (the two extra dimensions)

Elastic rod model – 3dfjc model plus an energy cost for every bend. Each segment cares about what’s going on with its neighbours

Figure 9.7

Find it weird that the structure become more ordered at higher temperatures, as opposed to denaturing. Does show however that at low temperatures it is denatured, and for all we know, it may denature again at a higher temperature.

Cold denaturing – loss of electrostatics, lowering of disulfide bonds

Long protein can be approximated as an infinitely long coil

Short protein – ends can’t be stabilised as easily, due to fraction of residues that can’t become part of the helix

Figure 9.8

Rotation determines fraction of helices

Double conc = double rotation

One helical rotation turns light to the left, the handedness of rotation turns light to the right.

CD

Figure 9.9

Effects of changing degree of cooperativity

In long chains, hard to tell if cooperativity matter

In short chains though, makes a hell of a difference

Cooperativity allows for sharp transitions

Figure 9.10

HbO2 -><- Hb + O2

Keq = [Hb][O2]/[HbO2]

Y = [HbO2]/([Hb] + [HbO2] = fraction bound

Bad to have myoglobin.....20% oxygenation difference in tissue

Haemoglobin has 4 binding sites....effective value of 3 due to its binding nature

Small fraction have 1, 2 or 3 bound

Response to Mitch's Post on Enzyme Inhibition

So when inhibitors are involved with our simple enzyme reaction system, there are two main ways in which this inhibitor can incorporate itself.

The first way in which it can be involved is to bind to the enzyme while not bound to the substrate. By forming the EI complex, the inhibitor can prevent the substrate from binding and forming the ES complex, thereby prohibiting the formation of a product.

The second way in which an inhibitor can be involved is by binding to the ES complex to form the ESI complex. Again, by binding to this, the production of the product in prevented. In this case, it is because the binding of the inhibitor usually distorts the shape of the enzyme thereby making it lose its fitting bind to the substrate disabling the catalytic effects that come from a fitted binding of the ES.

I have heard that there can be some situations where there is the step EI + S <-> ESI, but I cannot name any examples, and I personally find it hard to imagine that happening, as surely the EI complex would straight away prevent it from binding the substrate due to either being bound in the same pocket that the substrate would be binding it, or it would distort the conformation of the enzyme, and as such the binding pocket of the substrate.

Michaelis-Menten and simple kinetics

Let's start with the general procession of an enzymatic reaction (which is unaffected by inhibitors). We have:

E + S <-> ES<-> EP <-> E + P

In the case where the is none, or next to no product present initially, the chemical potential is a large negative number, resulting in a steep downhill slope for the third step, allowing us to write EP -> E + P

We now have:

E + S <-> ES <-> EP -> E + P

We shall also assume that E+S, ES, and E+P are separated by large barriers, allowing each transition to be treated independently. The transition involving binding of substrates from solution is characterised by a first order rate, proportional to the substrate concentration.

Throwing a single enzyme into a vat of substrate at initial concentration cs, and negligible product, will spend a fraction of time Pe unoccupied, and the rest (1-Pe) bound to substrate. These two times can be said to be nearly constant in time, so the enzyme converts the substrate at a constant rate.

We are now left with the final reaction of:

E + S <-> ES -> E + P

Forward rate of the first step = csk1

Reverse rate of the first step = k-1

Forward rate of the second step = k2

Michaelis constant = (k-1 + k2)/k1

vmax = k2Ce

Michaelis-Menten rule

v = vmax(cs / (Km + cs))

Ratchet?

I have to say Nelsons use of analogies in this chapter seems overly complicated, such as his introduction of the G and S-ratchets.



So in order to understand his analogy I propose to consider a different analogy. Instead of a rod moving through a membrane driven by thermal fluctuations; take a simple chemical reaction.

A + B <-> C + D

The reaction can move either left or right. There is only a small difference in energies which can easily be supplied by thermal fluctuations.
The equilibrium can become biased when the activation energy for the products becomes large. In this way the amount of product will increase and reactant decrease (like the sliding of the rod).
By simply removing amounts of the product (Le Chatelier’s Principle) the reaction will keep forming products and use up the available reactants (like applying a force on the rod).

Molecular Machine Example

One amazing molecular machine is ATP synthase.



It operates in a rotational catalysis mechanism. The β subunits perform the catalysis of ADP + Pi -> ATP. The γ subunit is responsible for rotating the β subunits and is driven by the influx of Hydrogen ions.

As the β subunits are rotated their conformation changes depending on their contacts with the γ subunit. Firstly ADP and Pi are bound loosely within one β subunit. The rotational conformation change then produces ATP by binding the reactants tightly and stabilizing the ATP form. In the next rotation, the ATP molecule is only loosely bound by the β subunit and the molecule can dissociate. There are many videos of this process available on Youtube.

This synthase is a great example of both a cyclic machine (10.1.1) and an enzyme catalyses a reaction by binding to the transition state (10.3.3). Can you think of any other examples?

(Information taken from textbook: Lehninger- Principles of Biochemistry
Image from article: Molecular Motors: Turning the ATP motor, Richard L. Cross, Nature 427, 407-408(29 January 2004), doi:10.1038/427407b)

Enzyme Inhibition

The Lineweaver-Burk equation

 

As my first post this week was quite long, I’ll make my second a short one and save you some reading time. I’m pretty sure we’ve all done CHEM2002, and have learnt about enzyme competition before. This chapter mentions competitive inhibition and noncompetitive inhibition. To refresh our memories, competitive inhibition is where the inhibitor molecule binds to the same site as the enzyme’s substrate. Thus they are in direct competition with each other at the binding site.

Noncompetitive inhibition is where the enzyme has two binding sites, which are effectively mutually exclusive. When the inhibitor binds to its binding site, the enzyme cannot bind the substrate any more, and thus the reaction again is inhibited. We learnt a third kind of inhibition, uncompetitive inhibition. This is where the inhibitor binds to the enzyme substrate complex.

These three kinds of inhibition have different effects on the Lineweaver-Burk plot as the inhibitor concentration is increased. If the inhibition is competitive, the y-intercept of the Lineweaver-Burk plot is constant, but the gradient changes. If the inhibition is noncompetitive, the x-intercept of the plot is constant, but the slope changes. If the inhibition is uncompetitive, the gradient is constant, but the y-intercepts changes (it increases). This means that competitive inhibition does not affect the vmax of the reaction and noncompetitive inhibition does not affect Km. Uncompetitive inhibition lowers both the Km and vmax.

Kinesin Motion

I thought a key topic in this chapter was the motion of kinesin. I was confused at first about how this molecule works, but I think I understand now. Please correct me if I am wrong anywhere. Each head of the kinesin molecule has two sites, one which binds one ADP molecule and one which binds to the microtubule. Both these sites bind strongly to their respective substrates. However, the head cannot bind strongly to both substrates at once. This is an example of non-competitive inhibition.

Because these sites bind strongly, and there is an abundance of ADP and microtubule binding sites in the cell compared to kinesin molecules, at least one of these sites is bound at any time. So if the molecule is not bound to the microtubule, then both these heads of the dimer have ADP bound. When the molecule is near a microtubule, eventually one of the heads will lose its ADP and bind to the microtubule. I suppose that a backward step could be taken at this point, and the head bound to the microtubule releases the microtubule and rebinds ADP. However, as the concentration of ATP in the cell is much higher than the concentration of APT, an ATP molecule is more likely to bind to the vacant site on the kinesin head bound to the microtubule.

Unlike ADP, kinesin is able to bind ATP and the microtubule strongly. When the ATP molecule binds, the head does not let go of the microtubule. The neck linker of the bound head then attaches to the head. This state is a local energy minimum. The other head is free to diffuse around; however, the position of the neck linker biases this diffusion. This is the asymmetry which is necessary for directed molecular motion.

Eventually the other head diffuses close enough to the next microtubule binding site for it to bind. However, this head still has ADP bound, so it can only bind weakly to the next site. It is likely that it binds and unbinds several times. However, eventually the head will spontaneously release the ADP, and will be free to bind the microtubule.

The protein chain connecting the two heads is only just long enough to reach the next microtubule binding site, so when both heads are bound, the molecule is strained due to stretching. Since the protein chain is only just long enough to reach the next microtubule binding site, even with the bias in the neck linker, it is nearly impossible for the unbound head to accidentally diffuse close enough to the previous site ad take a step backwards, because the neck linker will always point in the forward direction.

Perhaps this added strain on the molecule deforms the ATP binding site on the initially bound head, which causes it to hydrolyse the ATP bound to it. The head only weakly binds the resulting ADP and the microtubule, so the molecule will likely release one of these substrates. Due to the extra strain the molecule is under in its stretched state, the head preferentially releases the microtubule, to cancel this stress.

The energy released by ATP hydrolysis detaches the neck linker from the head, and the molecule is left with one head bound to the microtubule and one head bound to an ADP molecule. This is the state it began in, thus the cycle is available to repeat, providing the substrate concentrations remain the same. I presume this process will repeat until an ADP binds to the head bound to the microtubule instead of an ATP molecule, and the kinesin molecule detaches from the microtubule altogether.

Myosin and actin are the force generating units of muscle fibres

The most intuitive example of a motor in the human body would be the skeletal muscles. When researches were using optical and electron microscopy to study the muscle fibres they found that at each level of resolution the larger unit was made up of smaller force-generating subunit. At the molecular level myosin and actin were found. See Fig 10.1 pp405: muscles -> muscle fibres bundle -> individual muscle fibres -> myofibril -> myosin filament & F-actin filament -> myosin molecule & G-actin molecule.

The first experiment to provide direct proof of the force generation of myson & actin was by Finer et al., 1994 here they used the familiar combination of adhesion to glass beads which are trapped by optical tweezers which can measure force. When ATP was added to the setup shown in a. a sideways displacement of the actin filament was inferred by the measurement of a force in b.

Figure 10.2 provides a good summary of the experiment.

As this technique seems to be fairly common (optical tweezers + glass bead adhesion) I am wondering how they get the molecules to adhere to the glass?

Supplementary Video Material Matching Chapter 10

Nelson chapter 10 is the first time I had heard of the interesting way that Listeria moves. The Julie Theriot group at Stanford has done a lot of work on the motility of Listeria and other organisms, and are experts in the field of cytoskeletal dynamics and motor proteins. They have produced many videos which are an easy way to learn some neat stuff.

First, there is a triple of YouTube videos on the organization of the Cytoskeleton:

http://www.google.com.au/url?sa=t&source=video&cd=1&ved=0CC8QtwIwAA&url=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DU-IiQ2CsFqQ&ei=PEGdTN-IJoTmvQPi_Ny1DQ&usg=AFQjCNG9UIOKPkA22AJbpNgZIbWyRMpAQA&sig2=cbztQribbbByP7hYFyYyEw
http://www.google.com.au/url?sa=t&source=video&cd=3&ved=0CDkQtwIwAg&url=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DKs_xePZxe0E&ei=PEGdTN-IJoTmvQPi_Ny1DQ&usg=AFQjCNFcdH2BH51RJl8lqHc9kPixrH3Hpg&sig2=C9v7zPohfMq8mm9-nrya8w
http://www.google.com.au/url?sa=t&source=video&cd=2&ved=0CDQQtwIwAQ&url=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D8DJtbWWs9yo&ei=PEGdTN-IJoTmvQPi_Ny1DQ&usg=AFQjCNEPEts0HU6jPWvJGvB5bhb35AiAlw&sig2=CR6q_D7fVLo-fuz3SEjojw

And the Theriot Lab at Stanford hosts a heap of videos generated with their video microscopy work. The group web site is http://cmgm.stanford.edu/theriot/

Week 8 Discussion

To get a closer look just click.

Rubber Band Heat Engine

First of all, I want to try this out, it looks really cool

Second of all, the idea behind this is so simple, and yet really interesting.

So the idea of this machine is based around idea 9.6, which states that "The retracting force supplied by a stretched rubber band is entropic in origin." On the basis of this idea, we can see that it's not the elastic energy which will decrease as the rubber band retracts, but the free energy F.

When we heat up rubber, it causes the rubber to shrink, due to its negative coefficient of thermal expansion. By setting up a heat contraption like in figure 9.3, we can see that by shrinking the exposed side, we cause contraction in the rubber bands exposed, causing an unbalancing in the wheel, resulting in rotation to expose the cool bands to the heat, which eventually leads to a cyclic process, thereby creating out heat engine.

Limitations? I'm sure the rubber bands will eventually snap on us

DNA Extension

The following post is in relation to figure 9.4

In figure 9.4, we are shown the idea of what happens to the extension of a DNA strand as the force increases. The DNA used was 10416 bps in length, with one side anchored to a glass slide, the other to a bead which was pulled by optical tweezers.

A) What happens initially as we pull the bead is that the molecule remains very nearly a random coil the ends have mean-square separation of Lseg(N)^(1/2)

B) After this initial part of the curve, we see that the relative extension quickly curves off and plateaus around 20pN force. This is the point where the DNA is virtually straight, since z approximately equals L.

C) Along this minutely increasing slope, the DNA starts to become stretched out to be longer than the actual total contour length. This is known as "intrinsic stretching"

D) "Overstretching Transition" - around 65pN force, a sharp transition occurs as the molecule jumps to 1.6 times the length of its relaxed state.

E) Molecule continues to be stretched until the molecule breaks (like when you decide to stretch that rubber band to launch paper too far)

Allostery helps deliver oxygen to our tissues

Section 9.6 describes haemoglobin as an allosteric macromolecule i.e. that the binding of a molecule (e.g. oxygen) on one part of the macromolecule can affect the binding of a spatially distant binding site. Allostery is important for haemoglobin as it must be able to bind oxygen strongly enough at the lungs and release oxygen quickly enough at the tissues. If haemoglobin displayed simple binding properties this would not be possible.

It mentions that CO2 has an effect on the binding of oxygen to haemoglobin. I am told that it is the presence of CO2 in the blood and not that lack of O2 that stimulates breathing. This is a reason often given for people accidentally drowning while holding their breath as they often expel air (including CO2) before diving to increase the dive time.

DNA - melt it, stretch it, rip it, and unfold it

The first point of the DNA double-stranded helix which I shall talk about is the idea of "melting" it or making it fall apart into two strands. Sometimes referred to as another "helix-coil" transition, the degree of melting is a sigmoid curve, but the disorded state occurs at a high temperature (meaning that the sharp transition occurs past a definite melting point temperature). As melting occurs though, there are many things to consider.
1) A minor net change in free energy occurs as the basepair hydrogen bonds break and then reform between the bases and water.
2)The bases will stop being stacked neatly, causing the breaking of energetically favourable interactions (i.e. van der Waals). The energy coast however is slightly offset by gain of electrostatic repulsions.
3)Compression of counterion clouds released, leading to increased entropy. Single strands of DNA are also more flexible, to the backbone entropy also increases.
4) hydrophobic surfaces will become exposed to the water.

Now, for the fun we can have with DNA by applying forces.
1) Unzipping DNA - using a stretching apparatus, Heslot et al found that applying a force of 10-15pN could unsip the strands. Of course these days we also know that we can use helicase to do a similar job (though we need to also consider the provision of ATP, topoisomerase etc).

2) Overstretching - by applying a critical force (i.e. 65pN for lambda phage) we can force the DNA Duplex to go from being in the B-form (spiral staircase) and into a "ladder".

3) Unfolding - by increasing tension, we can cause proteins to undergo a change in structure. However, like a rubber band, when we release the tension, the protein returns to its original structure (though not quite in the same snapping motion)

Figure 9.10

Figure 9.10 on page 377 is very significant. This figure shows the saturation curve of haemoglobin as it moves from low oxygen concentration to high.




This is a great example of the cooperativity effect, particularly in proteins.

It is also biologically relevant, concerning a process that occurs while we breathe.

It can relate information on the structure of haemoglobin without the use of imaging techniques. As fitting the data estimates that haemoglobin is made up of more than one oxygen-binding subunit, which is in fact true.

Protein Substates

In early biochemistry subjects proteins (enzymes) are described as catalytic switches. With their on/off modes corresponding to whether they are occupied by a substrate or unoccupied. The conformation of the protein was suited to find its one specific substrate, and accordingly the substrates would fit into the protein like a key into a lock. This ‘lock and key’ mechanism implies that the protein would be held in the static ‘lock’ conformation waiting for its substrate.

However when considering the Boltzmann distribution it seems unlikely that a protein (consisting of many individual molecules) could remain in a fixed position. In fact it is known that proteins can exist in many different structures and depend on many different parameters outside of their substrates. But if proteins can have a vast number of conformations how do they perform their highly specific functions? Section 9.6.3 of the text gives an interesting viewpoint: within a bulk sample of the myoglobin protein there are many different ‘conformational substates’ (shown by R. Austins experiment, figure 9.13). These substates are able to perform the overall protein function of binding oxygen, but they each have slightly different binding affinities due to their structural differences. Thus proteins are able to satisfy the Boltzmann distribution while still maintaining their function. However in regard to the lock and key fit, proteins are not so easily typified. In this context the proteins would be more aptly described as the lockpicker’s toolkit.

Water water everywhere (9.5.2)

Alpha-helix formation is another phenomenon that can be explained by the ‘hydrophillic effect’. As it seems water prefers water over amino acids. The hydrophilic interactions can drive the apparently energetically unfavourable formation of an amino acid alpha-helix.

∆E(bond) : the energy change for DNA when moving from a random coil formation to an alpha-helix. The helix has higher energy as ∆E(bond) > 0.
∆S(conf) : the entropy change from restricting the movements of the DNA monomers. This is usually < 0.
∆S(bond) : the entropy of redistributing hydrogen bonds interacting with the environment to interacting with other monomers to create helix. Can be > 0 depending on the environment.

∆S(tot) = ∆S(bond) + ∆S(conf)

If ∆S(bond) is larger enough it can overcome the entropy decrease of ∆S(conf). Which can then overcome the effect of the energy difference ∆E(bond) creating a favourable reaction.

∆G(bond) = ∆E(bond) - T∆S(tot)

Nelson defines a parameter
α = [∆E(bond) - T∆S(tot)]/[-2k(b)T]
Where if α is positive, extension of the DNA helix is favourable in the current environment.

α=((∆E-T∆S))⁄(-2kT)
α= 1/2×((T∆S-∆E)∆E/∆S)/(kT ∆E/∆S)
α= 1/2×∆E/k×(T-∆E/∆S)/(T ∆E/∆S)
α= 1/2×∆E/k×(T-Tm)/TTm
T= ∆E/∆S (Eq 6.9)

When T = Tm, α = 0 Therefore at Tm there is no free energy cost of extending the alpha-helix.

Which is the most important figure in chapter 9?

Please post the relevant figure and your view on why it is so significant.

Sharp transitions

Yet another issue I had with the concept of entropy is being resolved by this book. I was always curious as to how scientists can say anything concrete about the state of any system, given that it is constantly changing states. If the state of a system is governed by statistical distributions, how can processes occur with distinct boundaries?

For example, we can predict the average kinetic energy of the particles in a litre box at 278K, but at any moment the particles could adopt positions which are unusually close to each other, thus converting some of their kinetic energy to potential energy, and changing the average kinetic energy of the system. But this book explained we can be confident of the exact average energy of the box, because the variance around this mean is so incredibly small, as there are such a large number of particles in the box.

This chapter explains another way we can get sharply defined transitions and values. The concept of co-operativity can explain why some systems can be in discrete distinct states. If the change of state for one molecule can increase the likelihood of another molecule changing state, then a positive feedback loop can occur until all the available molecules switch into the opposite state. The book gives the example DNA stretching and ice melting, but co-operativity comes up everywhere. The reaction of hydrogen gas with oxygen gas to produce water has elements of co-operative behaviour, as the heat produced by the reaction of two molecules can provide the extra necessary heat energy for further molecules to react.

When trying to reconcile this concept with my understanding of entropic processes governed by statistical distributions, I realised that I was still making the assumption that each element in the system is independent of each other. This is clearly not true in these cases when co-operativity is involved. So it seems that in cases where the elements of the system do not behave independently, we can have processes with distinct states that still obey entropic laws.

Phenomenological Parameters

The discussion in this chapter compared many theoretical models to experimental data. It reminded me of section 8.5 from last chapter, which I made a post about last week. This chapter gave us a name for some of the constants which we can fit to a model, the phenomenological parameters. The subtle difference between the constants needed to fit a model and phenomenological parameters are that constants involved in a model can be definite traditional variables, like the length of a bond, or the number of particles in a situation. The phenomenological parameters only describe a bulk behaviour of a model; they only make sense in the large scale, and they break down when applied to individual constituents of the bulk substance. In other words, the constants in a model can exist outside the model, but the phenomenological parameters only make sense when the model is used, such as the co-operativity parameter γ in the helix-coil transition model.

This distinction comes back to the two methods for creating scientific models discussed in section 8.5. When a model is built from the theory up, and then compared to experimental data, constants that exist independently of the model are being used. When the model is created after analysing experimental data, constants which describe the observations are discovered, and are named phenomenological constants.

This distinction was also obvious in the way this chapter was constructed. When discussing simpler topics and models, the chapter would discuss the theory that lead to the model, and only after the model had been made would the experimental data be shown, to verify that the model is sound. This chapter however was different; we saw the data very early (p351, figure 9.4) and didn’t finish discussing it until p362. This approach is quite necessary for the analysis of the extension profile for the stretching of DNA, as it has a very complicated behaviour, and it would be very unlikely that a model which predicts this behaviour would have been developed before the data was discovered.

I like that this textbook demonstrates both methods of model development. I can see strengths and flaws in both approaches, and I am glad that as scientists we have both models available to us.

Assignment 6: due friday october 8

Your turn 10C, 10D, 
Problems 10.1, 10.4
and any two of 10.5, 10.6, 10.7, 10.8, C10.10 to C10.14

Assignment 5: due friday september 24

Complete any ten of the following:
Your Turn 7E, 7H, 8F, 8G, 9B, 9E, 9I, 9M
Briefly discuss the historical significance of Figure 8.2 for medical research
Problems 9.1, 9.2, 9.5, 9.6, 9.7, 9.8, 9.9, 
C9.12, C9.13  (see pages 594 ff.)


If you complete more than 10 you will receive extra marks on a pro rata basis.

8.6 Self Assembly In Cells

How can amphiphilic molecules account for their hydrophobic tale in a water environment? Figure 8.5 solves this self-assembly by using a sphere. To form a sphere the hydrophilic head must be wider than its tail. Not all amphiphiles can take this arrangement, for example two tailed molecules can form a bilayer membrane.

These two tailed amphiphiles are usually of the class phospholipids. These are the major component of cell membranes. The reasons for this are:

• Self-assembly of phospholipids is more frequent than one chain surfactants because the hydrophobic cost of two chains exposed to water is twice as great as a single chain
• Phospholipids spontaneously form closed surfaces (vesicles) to avoid exposing hydrocarbon chains
• They are easy to synthesis in cells
• The permeability of phospholipids membranes have favourable values
• The fluid mosaic allows ease of changing shape
• The fluid mosaic can accept embedded objects

All these factors make a working cell possible.

In the Kitchen

In chapter 8 Nelson describes how to curdle milk. Milk is simplistically made from water, fat and the protein casein. The casein is a phosphoprotein that assembles into micelles. Curdling occurs when coagulation of the casein micelles (by overcoming the electrostatic repulsion between them) turns the milk into a gel. By adding acid (H+) the effective charge on the micelles is reduced, in turn decreasing the repulsion allowing the micelles to aggregate and curdle the milk.

But milk can also curdle over time when left on the bench instead of the fridge.

Previously Nelson stated that the value of the critical micelle concentration typically decreases at higher temperature. Therefore when not in the fridge the number of micelles in milk will increase. Would this decrease in separation space be enough to induce the aggregation of the micelles?
The problem is, milk can also be heated to higher temperatures (in the microwave, on the stove, using a coffee machine) and this coagulation will not occur. Furthermore when curdled by acid the milk does not give off a pungent aroma. The smell of bench-top milk points to the idea that the proteins are actually denaturing within the mixture. But we know that heating proteins to high temperatures can also denature them. So what exactly is going on? How can milk curdle with acid, curdle over time yet not with extreme heat?

The Potential of Neutrality

Thanks to the existance of surface charges (namely, overall surface charges) existing on proteins, we can make sure of it to seperate proteins using a method known as electrophoresis. Electrophoresis, the migration of macroions as goverened by pH and electric fields, drifts proteins across a surface or differing pH levels, to the point where the pH of the surface allows for the protein to achieve its Isoelectric point (the point where its overall net charge is zero, thereby preventing any more movement caused by applied potentials). Noted is that the protein doesn't just instantly stop at this point, it has to oscillate a bit first as it slows down.

One of the great discoveries from electrophoresis is the differing of sickle cells from normal red blood cells. Despite not knowing the sequence of hemoglobin, Pauling et al found that there had been a change in the sequence as the titration curve of sickle cells was 1/5 of a pH unit different to normal hemoglobin. As it has since been found, a valine is replaced with glutamic acid, which is more acidic, causing the lowering of the titration curve.

Amino Acid pK Values

On page 312, Nelson briefly mentions:

...in a protein uncharged and charged residues will affect each other...

meaning that the pK of amino acids within the protein can be affected by the presence of other amino acids. And this is true, in fact many enzymes work on this basis using what is known as general acid/base catalysis.

pK values of residues within the active site of an enzyme can be significantly altered relative to the outside of the protein. The pK of an acid will increase when near a non-polar group as the anionic (deprotonated) form is not stabilised. But the pK will decrease when near a positive charge as the deprotonated form is favoured. Conversely, the pK of a base decreases in a non-polar environment as the positive (protonated) form is not as stable yet the pK will increase when next to a negative charge as its protonated form is stabilised by the opposing charge.

Furthermore the dielectric constant inside a protein can be vastly different to water. Protein centres are typically described as the 'oily core', which will again affect the pK values of the amino acids present.

For more details: enrol in BIOC3000

Let's Get Vesicle

Before anyone asks, yes, I did take Olivia Netwon Johns' "Let's get Physical" and give it a scientific application (it was one of my ways of remembering lipid arrangements.

So we know that lipids are amphiphilic (meaning that they have both a hydrophobic head, and hydrophilic tail, or on occasion the other way around). Either way, due to the hydrophobic effect (which as we were told last week, should more aptly be called the hydrophilic effect, as water loves water more) the lipids aggregate themselves into different types of arrangements so as to decrease the overall energy of the system. These arrangements include:
* micelles - like a soccer ball, where each of the hexagons making up the ball have a tail attached, which exists inside the ball (except replace the hexagon with the hydrophilic head)
* bilayer - the classic arrangement we've all been taught for cell membranes, where there are two layers of lipids which come together to create a semipermeable layer.
* vesicle - like a fusion of a micelle and a bilayer. There is the micelles structure, with then what we can consider a reverse micelle within the micelle, interacting with the micelle in the same way that the two layers of the bilayer interact.

Associated with the micelles is a term known as the critical micelle concentration. This term, the CMC, refers to the point where the concentration of lipids is high enough to spontaneously form structures such as a micelle.

Fitting Models to Data

Section 8.5 is possibly the shortest section in the whole book. It was the section about fitting models to data. I was intrigued by the meaning of the quote at the beginning of the section

“If you give me two free parameters, I can describe an elephant. If you give me three, I can make him wiggle his tail.” –Eugene Wigner

I think it’s supposed to say that two free parameters are enough to describe most situations. Any more than that are unnecessary, and don’t actually allow for a more complicated model. This is a good point; if a set of data only has two degrees of freedom then any more degrees of freedom don’t increase the accuracy of the model. Too many degrees of freedom and you start modelling effects in the data that aren’t really in the model, such as experimental errors.

Any number of equations and models could be found to describe a given set of data. This section summarised what makes some more interesting than others. If the data set is exceptionally accurate, and a simple model with few parameters can be fit to the data, within in the low uncertainty, then that model can suggest a relationship in the data. What the parameters physically mean can then be deduced.

The opposite approach can also be taken. A model can be made based built out of physical principles, and then applied to a data set which it attempts to describe. The model is successful if the parameters it predicts match the parameters described by the data.

I personally think this second approach is a better, as it reveals the physical principles underlying the data. However, when investigating a completely new phenomenon, where the processes behind the model are unknown, the first approach can be better. This method gives a scientist attempting to understand the phenomenon a foundation to build a model from.

Does anyone have any other ideas about which scientific model construction process is better?

Curvature of a Lipid Bilayer

I didn’t like the discussion of the energy required to bend a lipid bilayer on page 326-327. It analysed quite rigorously what might happen at the outer surface of a planar lipid bilayer if it were bent, and how much energy would be required to do that. But it left out a number of features, such as the compression of the internal layer of lipids when the membrane is bent. My first thought upon reading this section was that all the bilayer needs to do, if exposed to a force which is trying to bend it, is move some lipids from the inside layer to the outside layer. Extra lipids on the external side would fill the gaps made by spreading apart the polar heads of the outer layer. This post investigates this idea.

I looked up in my biology text book how often lipids switch layers, and in an unstressed membrane, they flip very rarely, only about once a month, or once every 2600000 seconds. However, Nelson says there are ‘tens of millions’ of lipid molecules in a membrane. 10000000/2600000 = 3.9 molecules per second. A second is a long time on the cellular clock (proteins fold on micro to milli second timescales), but this value is for a membrane in equilibrium. The increase in internal energy of the curved bilayer system would cause this rate to increase.

Let the lipid heads have a cross-sectional area of A, an average tail length L, and are in a bilayer membrane where the radius of the external layer is R. The surface area of the outer layer is 4πR^2. The internal layer has a surface area of 4π(R-2L)^2. The difference in area these two layers is 4πR^2-4π(R-2L)^2=16πL(R-L). So the difference in the number of lipids between each layer in the bent membrane is 16πL(R-L)/A. Taking L=1.3nm, R=10μm (page 327) and A to be π(0.3nm)^2 (the size of a few atoms), we calculate the necessary difference in the number of lipids in the inner and outer bilayer is 16*1.3E-9(1E-5-1.3E-9)/9E-20=2.3E6. At four molecules a second, it would take 5.7E5 seconds, or 6.7 days, for enough lipids to flip to cause enough curvature required for a 10μm cell.

I can understand why this was not discussed in detail in the book, but I think it should have been mentioned, even as a Your Turn investigation, as it was an idea that seems quite reasonable at first. I suspect in actual cells, there is a combination of these two ideas, lipids flipping to cause curvature, and an increase in the internal energy of the membrane. The internal polar heads have a shorter distance to travel through the hydrophobic centre of the membrane when curvature is first applied, as the external heads are separating and exposing the extracellular water. This would increase the rate of lipid flipping. As the external spaces are filled, the flipping rate would decrease, and the internal energy of the membrane would increase instead.

Liquids in space

Because we were talking about water in space today I thought you all might enjoy this video.

Meeting Summary 8th of September

We began by watching a short video of an acidic solution and indicator in a semi-permeable membrane bag becoming dilute after it was placed in a beaker of pure water. The indicator turned pink in acidic solution, and yellow when neutral. However, two distinct phases were observed, the lower one pink and the upper yellow. This was unexpected; we expected the pink to become lighter shades over time. We didn’t come to a consensus on why this was.

We then discussed figure 7.1. We discussed how the external force term, such as gravity, affects a liquid element at equilibrium. We also discussed how osmotic pressure would affect the system that is not experiencing gravitational force, and whether the pressure would cause movement. Figure 7.3 was discussed, and how the depletion layers affect the entropy of the system when they overlap, in different concentrations of large molecule.

Figure 7.6 was analysed, as it caused some confusion. Parts a and b were straight forward, but we decided that part c was a situation that had no external pressure, and part d had an external pressure, the dotted line representing reverse osmosis. We can imagine there is a piston on the far right compressing the volume on the right side of the membrane. The solid line appears as thought it should be flat along the whole graph, but we attributed the dip in the pressure to the depletion layer; if there are no solute particles in this layer, then there is no cause for osmotic pressure, thus the pressure drops. It was also determined that the direction of the applied pressure can be deduced from the gradient of the pressure line on the graph.

The exercise from Your Turn 7D was briefly discussed, and why the energy goes down as the radius decreases, despite the charge being confined to a smaller area. This is due to the larger surface area to volume ratio of the smaller drops.

Figure 7.8 was discussed, and the effects of the depletion layer compared to the electromagnetic effects. We discussed why the hydrophobic effect should be called the hydrophilic effect, as it is the hydrophilicity of water which drives the phenomenon. Also, after looking at figure 7.14, we discussed how the solubility of hydrophobic molecules can decrease as temperature increases, due to the increase in the entropy of the ‘sheepdog’ solvent molecules. This principle allowed Walter Kauzmann to make predictions on the structure of proteins, before structural data was available.

Finally we discussed how the hydrogen bond gave water an unusually high melting and boiling point compared to other small covalent molecules. The hydrogen bonds decrease the rotational freedom of the water molecules, which decreases their entropy, so it takes more thermal energy to disrupt this order. Oxygen – hydrogen bonds have the highest potential for forming hydrogen bonds, as oxygen is a very electronegative atom.

We decided not to have a assignment this week, and we will read chapter 8 for our meeting next week.

Proteins and Hydrophobic interactions: basics and history

Basics are discussed in this lecture I used to give in PHYS2020 and sometimes in the predecessor to this course.

For more on Walter Kauzmann here is the first post on my condensed concepts blog. I particularly encourage you all to read his, "Reminiscences of a life in a Protein Science,"
linked in the blog post.

Which is the most important equation in the chapter?

Please give your opinion and why?

Charged Surface Chemistry

With this chapter eluding to diffuse charge layers, I thought that I would share some insight from my CHEM3013 course of last semester. The following images have been taken from the CHEM3013 lecture slides prepared by Prof. Matt Trau.

In the above image you can see that to a positively charged surface, the anions are the ions that are most concentrated around the surface, while the cations are a bit more scattered, though some are held close to the surface by the surrounding anions. There are also two graphs there, the first depicting the ion concentrations as a function of the distance away from the surface, and the second depicting the potential as a function of the distance.

This is a depiction of what is known as the Stern Layer. In the stern layer, counter-ions adsorb to the surface, and it's their size which determines the stern layer thickness. Since the cations in this case (since the surface is negative) are adsorbed to the surface, and are hydrated, the stern plane is said to be "one hydrated ion radius from the surface"

Finally, to wrap up this blog post, here is the graph from before, but now with the stern layer included in the system. As you can see, the potential drops quite linearly to begin with, then drops linearly.

By the way, in case you want to know the maths of the potential, it's

for the situation without the stern layer, or

for the situation with the stern layer, where psid is the stern potential