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

The deepest Humiliation

I'm not using this as one of my necessary blog posts for assessment, but I just wanted to mention that quote at the very beginning of the chapter. I've heard this before, and it's quite a true statement. We've now spent quite a bit of time looking at the second law of thermodynamics and the resulting phenomena of this law. Not to mention also that the maths of the law has also been successfully proven. Indeed, if something were to work against the second law, it would have such an impact upon everything around it, that it just couldn't be possible.

Entropy Phenomena

I learnt a lot this chapter. I didn’t realise how many of the principles I had learnt in biology and chemistry could be explained in terms of entropy. From osmotic pressure, to molecular crowding, to surface tension, to charge shielding by ions. When I read about the molecular crowding section, I was surprised to see that entropy could increase order, but I knew I’d seen something like it before. I later remembered that it was phenomenon of granular convection. Shaking a jar of nuts results in the largest nuts (Brazil nuts) rising to the surface (depending on the ratios of the sizes of the nuts). This is an example of a process which creates order. It is similar, since the larger objects are separated from each other, allowing the smaller objects more room to move in. However, I can also see the flaws in this comparison. First of all, the brazil nuts move in a specific direction, that is opposite to gravity. In molecular crowding, there is no preferred direction, or at least not on the scale of molecules. Also, the length scales are not quite right; obviously nuts are much too big to be effected by the energy kbT, and the nut size ratio is much smaller than the ration of water molecules to proteins. But I can see similarities in these two phenomenon.

I have to say though, I’m a little annoyed at this chapter. The explanation of many of these phenomena includes suggesting that the particles “are willing to pay some … energy in order to gain entropy” (pp268-269). I think this is a little too simplified. Explaining it like this implies that the particles are aware of their surroundings. But we know that they cannot be. They do not measure the entropy or free energy of their environment, and then act according to that. The just act in a random manner, or in a manner as random as they can given the constraints they are under. The behaviour of individual particles is unpredictable. It is only the whole distribution of behaviours that we can make inferences about.

Your Turn 7D

7.5.1 inroduced the hydrogen bond network observed in water and some of its consequences (boiling points, hydrophobic effect). Another interesting effect of the hydrogen bond network is proton hopping also termed the "Grotthuss mechanism".

The structure of the hydrogen bond network allows a charged proton to 'hop' across multiple water molecules. This is a way in which the charges can be quickly distributed throughout the water volume and is related to the conductivity of water.
This effect must also be prevented within water channel transport. As cells utilise proton transport as a way of generating energy, this proton hopping would act to discharge the potential energy from localising the protons. Thus water channel proteins eliminate proton hopping by disrupting the hydrogen bond network of water as it moves through the channel. They can achieve this in a few ways. For example by moving single water molecules across one at a time or by twisting the orientation of the water molecule to dislocate the linear hydrogen bond.

The wikipedia file on Grotthuss mechanism has a quick video on proton hopping.

Osmosis - a tale of dilute solutions, and semipermeable membranes.

So my first blog for this chapter is going to be focussing around osmotic pressure, and some of the details surrounding it.

So to describe osmosis, the book detailed the example where water is placed into a two part chamber, with a semi-permeable membrane seperating the two parts. If we add solute to one side such that there is a concentration difference, the water passes through the membrane till the concentrations and pressures of the two systems have come to equilibrium.
If you'd like another way to describe this, I'll explain the way I once heard it told. Take two connected chambers like before, except this time put in a sliding membrane. As we add more solute to one side, the interactings of the molecules moving about forces the piston away to the point where the forces on either side of the piston equilibrate.

There are a couple of points we should look at in relation to pressure.
Pi = cRT (which is essentially the same as p = nRT / V, since n/V = c)
We can treat a dilute solution the same way that we can treat an ideal gas, since the molecules don't interact much with each other.

Next up we have the vant Hoff relation, which in section 7.3.2 is clarified as being the pressure needed to stop osmotic flow, or as a better way of putting it, the pressure drop if the system were brought to equilibrium.

While on the topic of equilibrium, it will be worth mentioning that our cells have yet again proven their awesomeness, by being created to have the ability to fine-tune internal solute concentrations, so as to survive in a world of osmosis, especially since the book performs calculations which confirm that our cells could be destroyed quite easily by osmosis.

Molecular Crowding

After looking at Figure 7.2 I wondered how on earth could anything move within a cell that crowded. Even with ATP powering the movements of vesicles and the like, with something so densely packed surely no movement was possible. Furthermore specific reactants would never be able to find each other. It would be like trying to push to the front of a mosh pit at an epic concert.

However, a great explanation followed this picture. Nelson was able to explain that movement of larger molecules was possible due to the entropic forces of smaller molecules. By removing the depletion layer surrounding large molecules the entropy of the smaller ones could increase. This was achieved by sheparding the larger molecules together.
The depletion layer is a result of the smaller particles not being able to occupy (or concentrate in) the space directly surrounding the larger particles i.e they cannot occupy the maximum number of states, they're not at the maximum entropy. The entropy is maximised by decreasing the size of the depletion layer. Where the biggest decrease is seen when the large molecules are 'matching'. That is the larger molecule reactants are pushed toward the recognition sites of their specific enzymes speeding up the reaction. It's more like crowd surfing in a mosh pit, with everyones hands (the smaller molecules) propelling your body (the larger molecule).
It is amazing how so many processes, that at first seems backward, happen because of entropy.

It also made me wonder. Is this how bacteria are able to feed in laminar fluid? Do these 'sheepdogs' herd the food particles for the bacteria to eat?

Your turn 7A

Hey guys I'm having trouble with Your Turn 7A my integration by parts never seems to simplify. Has anyone managed to get the result? I'm lost.

Week 6 (1.09.10) meeting minutes

The topic for this weeks meeting was Chapter 6: Entropy, Temperature and Free Energy from Biological Physics by Nelson.

Students were asked what they thought the most important concepts from the chapter were, the topics mentioned were:

• Gibbs Free Energy
• The Fundamental Definition of Temperature
• The Sakur-Tetrode formula for Entropy
• The example of RNA folding
• The Partition Function
• The Zeroth Law
• What is Phase Space?
  

Sakur-Tetrode formula for Entropy:

The Sakur-Tetrode formula gives an exact description of entropy for non-interacting particles. This is good for non-interacting particles at a large volume: as the volume is reduced the ideal conditions break down. In general this formula cannot be applied to cells due to these constraints. Essentially it is correct for an ideal gas or osmotic pressures at equilibrium at low concentrations.

Some of the terms in the full expression of the formula were queried.

Ross described the reasons for the inclusion of Planck's constant in the formula as profound. He summarized this idea by saying that in phase space there is one quantum state per volume, and this volume corresponds to Planck's constant. For simple purposes it is included to fix the units required for the formula.

The factorial term comes from the definition of entropy and accounts for the particles with identical chemical composition being indistinguishable. The exclusion of this factorial, for example using just N instead of N!, leads to Gibb's paradox. Gibb's paradox results from an incorrect form of the the entropy equations which does not lead to entropy being additive.

The Partition Function:

The partition function, Z, gives the sum over all the possible configurations for the particle with energy Ej. The example given in Chapter 6 was if you want to minimize the free energy of system a, Fa, by calculating Z you can show the Fa_min is just:

It was stated that calculating Z for any interacting system is not trivial, and in fact very clever people spend careers trying to calculate Z for interacting systems. One application of this partition function in terms of free energy is calculating the free energy of a drug bound in a binding pocket of an enzyme.

Gibbs Free Energy:

The terms Ea + pVa is known as the enthalpy (at fixed volume and temperature). pVa is the work done and Ea is the internal energy.

The Zeroth Law

The Zeroth Law is named as such as it was discovered after the first three laws of thermodynamics, however, it logically underpins the following three laws.

Lastly we discusses phase space.

What is Phase Space?

Instead of representing a system in three dimension of space, in phase space each particle is represented by a vector in each of 6 dimensions, one for each spatial dimension of both the particles position and momentum. An example of a representation of a Phase space diagram is a porcupine diagram of a protein.

Lastly the famous Australian scientist Dennis Evans was name dropped. He was the first to analytically prove the second law of thermodynamics, what a fantastic result.