Growing a crystal of a protein often starts by mixing a solution of protein with a solution of a salt. If you imagine sitting on a point that starts in the protein solution, as mixing occurs protein diffuses away into the salt solution and is diluted, so the protein concentration decreases, while as the salt arrives, the salt concentration increases. This means that in a plot with the x-axis the salt concentration, and the y-axis the protein concentration, the concentrations at the point move down and to the right. It will start at the point marked above by the blue circle, and finish at the magenta circle. If the mixing is just diffusion of the protein and salt, and if they diffuse equally fast, the point will follow the path of the straight dashed-red line above. But if protein diffuses much slower (which it does) and there is flow of the solutions (almost unavoidable except for the smallest volumes*) the point should follow the path of the dashed black line — this is a very different path of course.
A recent paper argues, and provides some experimental evidence for, droplets that as soon as they form, promptly head off to a region where they are unstable and so dissolve. The droplets are forming in what is sometimes called the ouzo effect, which is illustrated above. When water is added to ouzo (or similar aniseed-flavoured spirits like pastis, absinthe etc), the drink turns cloudy due to small droplets forming — these scatter light turning the drink cloudy. Above, the neat absinthe is on the left and and is clear, the drinks in the middle and on the right have added water and so are cloudy.
This is a tequila sunrise cocktail, made with 45 ml of tequila mixed with 90 ml of orange juice, which together forms the orange layer on top, plus a layer of 15 ml of grenadine (flavoured and red coloured sugar syrup) on the bottom. The grenadine is carefully added to the bottom of the cocktail, using a spoon to minimise flow during the process of adding the grenadine to the tequila/orange-juice. The red shading into yellow gives the cocktail its name of sunrise.
In a final year course that I co-teach, I teach Fermi estimation* (my notes are here). Fermi estimates are simple back-of-the-envelope calculations. Let’s say you want a Fermi estimate of how many people in the UK take a train journey on a normal week day. You start by saying “Well the population of the UK is about 60 million people”, then you say “I guess about 10% take a train journey on a given day, as 1% of people taking a train looks too low, while it is clearly not 100%”. The Fermi estimate is then that about 6 million people take the train in one day. To check this estimate, I did a little Googling, and there are about 6 million journeys per day in the UK, so assuming that people who travel in a day take two trips (eg to and from work), it looks like I am about a factor of two, too large. Not bad for a simple estimate.
I am continuing to play around with transient phase separation, as you can see in the movie above. Droplets of a blue phase appear then disappear. In the experiments that I am trying to understand, the experimentalists mix salt, which diffuses fast and promotes protein phase separation, with protein, which diffuses slower. So I have developed the model so that the ‘protein’ in my model diffuses slowly and downwards, and there is also a faster diffusing component, the ‘salt’ in the model, that diffuses upwards. Then the blue ‘protein’ droplets start to form when the ‘salt’ has diffused into the top half of the system, but then as the ‘protein’ diffuses downward and out of the top half, this causes dissolution of the droplets.
The human body is a colony of about 30 trillion cooperating cells, each of which needs to burn energy to survive. Within the cells, a lot of the energy is carried around in the form of a molecule called ATP. A single one of our cells may have ten billion or more molecules of ATP, and these molecules are very dynamic. A single ATP molecule may be used to release its energy, then regenerated only a second later. So, there are huge ATP currents and gradients inside cells. And ATP is a big molecule, its structure is above. From left to right, there are three charged phosphate groups (each with a P = phosphorous), a sugar in the middle, and at the part at the top right is also found in one of the bases in DNA. Continue reading
The government has introduced the Teaching Excellence Framework (TEF) which purports to assess the excellence or otherwise of teaching in English universities. Surrey was awarded the highest score, a gold, in 2017*. But measuring teaching is hard, it is subjective, and so mostly what the TEF measures is statistics about a university, plus a text summary. There is no actual observation, let alone direct assessment of, teaching, in the TEF. The august body, the Royal Statistics Society (RSS), has just issued a critique of the TEF. The critique reads like the feedback on a piece of statistics coursework submitted by an unusually weak student.
I am continuing to play around with systems that start to separate into two phases (the green and the red phase in the movie above) but don’t get very far before one phase (the green one) dissolves. I have tweaked some parameters above, so that green droplets form, and the system is a bit bigger (I also changed the orientation, sorry if that is confusing). if you follow the movie carefully, it seems clear that the dissolution of the green droplets is via fronts that are pretty straight (horizontal), one front that moves upwards, dissolving droplets as it goes, while another moves downwards. When they meet in the middle, the green droplets are all gone.
Oils and water often spontaneously separate to form two coexisting liquids, one mainly oil, and one mainly water. For example, if you add olive oil to vinegar the two liquids separate out into droplets of oil in the vinegar. But at least for some oils, they mix in at least some proportions with water at higher temperatures, so you can have a single hot mixed liquid, that on cooling separates out into oil droplets in water. This is a well studied and common phenomenon. But what if you simultaneously cool, and mix in more water? For example, what if you start with with hot oil in water, with for example, 20% oil, that is sufficiently hot that water will dissolved all the oil? Then you cool to a lower temperature, where water can only dissolve say 15% oil, but at the same time you mix in an equal volume of pure water?
Just before Christmas I wrote a blog post about Baron Rayleigh’s work on convection, he showed how a layer of colder fluid (eg air or water) on top of warmer fluid, would lead to convection — flow of the colder fluid downwards to be replaced by warmer fluid from the bottom. Rayleigh’s work is a classic, and has been built on to help us understand, amongst many other things, Earth’s weather/climate. Rayleigh assumed that the flow was driven by gravity. The colder fluid on top falls because it is denser. Convection is everywhere in Earth’s atmosphere and oceans. It is sometimes called Rayleigh-Bénard convection, to honour Baron Rayleigh who developed the theory, and Henri Bénard, who did the experiments that inspired the theory.