Biocurious

/ a biophysics blog

Philosophical Saturday: George Wald

Posted 5 April 2008 by PhilipJ under &

George Wald made considerable progress in our understanding of the chemistry and physiology of vision (which just so happens to be the area I find myself in now). He won the Nobel Prize (physiology or medicine) in 1967, and his lecture in Stockholm opened with a beautiful description of experimental science:

I have often had cause to feel that my hands are cleverer than my head. That is a crude way of characterizing the dialectics of experimentation. When it is going well, it is like a quiet conversation with Nature. One asks a question and gets an answer; then one asks the next question, and gets the next answer. An experiment is a device to make Nature speak intelligibly. After that one has only to listen.

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Michaelis-Menten enzyme kinetics

Posted 26 September 2007 by PhilipJ under &

Enzymes are the workhorses of the cell. They are proteins which help facilitate reactions, such as RNA polymerase adding nucleotides to form new strands of RNA. The polymerase is the enzyme (E), the nucleotides are the substrate (S), which react to form a product (P), the newly formed RNA strand.

It can often be the case that there are very low copy numbers of enzymes in the cell, meaning only one to a handful of a specific kind of enzyme. It is also possible that there is significant substrate present. You might then wonder, how fast can the enzyme of interest, given basically unlimited substrate, carry out its reaction? Let’s simplify the situation and assume only one enzyme in a cell filled with substrate*. The below treatment was first outlined by Haldane, and then by Leonor Michaelis and Maud Menten.

The enzymatic reaction described above looks like this:

where the concentration of the substrate, cS, comes into play, and it is assumed that the second step, ES reacting to make product P, is irreversible. Thinking of the reaction in terms of probabilities (which we will denote using lowercase p), if the enzyme is unbound there is a probability per unit time cSk1 of binding a substrate, if the enzyme is bound with the substrate there is a probability per unit time of k2 of reacting to form product, or probability per unit time k-1 of returning back to its unbound state. Explicitely,

In the steady-state (dpE/dt = 0), you can solve for the probability of being in the enzyme-substrate complex:

The rate at which product is created is then k2pES as per our original reaction equation, and multiplying by the enzyme concentration (in our case just a single enzyme) gives you the velocity of the reaction.

We can simplify the formula further by introducing these two substitutions:

where KM is called the Michaelis constant, and is a measure of concentration, while vmax is a measure of the rate of change of concentration. Substition gives the famous Michaelis-Menten rule:

This rule helps explain the observed kinetics of some enzyme reactions, such as the mechanochemical cycle RNA polymerase (free link to the paper at the bottom of the post).

So, why the primer on enzyme kinetics?

Maud Menten

Because Maud Menten and I are schoolmates, so to speak!

* This treatment is based on P. Nelson’s Biological Physics, Ch. 10.

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Ultimate Scientific Distillations: Deep insight, simple representations

Posted 14 June 2007 by Andre under &

At its best, the scientific method can reduce profound questions about our universe to their barest essence and answer them compellingly with simple observations. The greatest experiments achieve the most complete distillations because of the principles and theories that guide them and the knowledge that has already been well established. Once this context is internalized, even grainy images or barely visible spikes in a line of noise can become moving pieces of art.

Here’s the image that got me thinking about this most recently:

It’s a postcard that Walther Gerlach sent to Niels Bohr after Gerlach’s experiment seemed to confirm Bohr’s prediction about the magnetic moment of atoms. The caption says “Attached [is] the experimental proof of directional quantization. We congratulate [you] on the confirmation of your theory.” According to the delightful Physics Today article where I found this figure, at the time these results were considered “among the most compelling evidence for quantum theory.” This is an amazing distillation. Magnetic field off, no splitting. Magnetic field on, splitting. Magnetic moment is quantized. For background, some complications, and to learn about how cigar smoking in the lab played a crucial role in this discovery you’ll have to read the article.

I don’t want to talk about the details of the experiment here though. Instead I want to ask for other great scientific distillations. There must be excellent examples of this from the early days of molecular biology. Something like: this spot is radioactive, this spot is not, so DNA is the molecule of inheritance. Let’s see your nominations. Include a link to an image if you have one.

How far can this go? In theoretical physics, people often discuss reducing all of physics to a single theory, maybe something you could fit on a t-shirt. But why must the universe on a t-shirt be represented by an equation? With such a theory in hand, could there be a simple representation of an elegant observation that, in context, encapsulates the nature of the universe?

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Pierre-Gilles de Gennes, 1932-2007

Posted 23 May 2007 by PhilipJ under &

I just read (via some complicated series of links that started with the Bourbaphy seminar page) that Pierre-Gilles de Gennes passed away on the 18th.

He was a true giant in the field of soft condensed matter physics, and was the sole person awarded the 1991 Nobel Prize in physics for “discovering that methods developed for studying order phenomena in simple systems can be generalized to more complex forms of matter, in particular to liquid crystals and polymers”.

Le Monde has a nice writeup (for those who can read French), here.

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The Brain and the Fancy

Posted 26 June 2006 by PhilipJ under &

The truth is, the Science of Nature has been already too long made only a work of the Brain and the Fancy: It is now high time that it should return to the plainness and soundness of Observation on material and obvious things. It is said of great Empires, That the best way to preserve them from decay, is to bring them back to the first Principles, the Arts on which they did begin. The same is undoubtedly true in Philosophy, that by wandring far away into invisible Notions, it has almost quite destroy’d itself, and it can never be recovered, or continued, but by returning to the same sensible paths, in which it did at first proceed.

Robert Hooke in Micrographia, 1665

It is amazing to me that a complaint of science in the 1660s could, without the flowery language and odd punctuation, be said readily today as well. I’m not able to critique with any authority the trendy subjects in quantum gravity, but their lack of connection to experiment has made me question the validity of the entire enterprise. That the mathematics may be beautiful isn’t in question, but how long do we have to wait for some predictions to test before trying something new?

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Biology is unmathematical?

Posted 31 May 2006 by PhilipJ under &

More from The Character of Physical Law, this time from the second lecture on the relation between physics and mathematics:

In thinking out the applications of mathematics and physics, it is perfectly natural that the mathematics will be useful when large numbers are involved in complex situations. In biology, for example, the action of a virus on a bacterium is unmathematical. If you watch it under a microscope, a jiggling little virus finds some spot on the odd shaped bacterium – they are all different shapes – and maybe it pushes its DNA in and maybe it does not. Yet if we do the experiment with millions and millions of bacteria and viruses, then we can learn a great deal about the viruses by taking averages. We can use mathematics in the averaging, to see whether the viruses develop in the bacteria, what new strains and what percentage; and so we can study the genetics, the mutations and so forth.

Much has changed since 1964 when Feynman gave this set of lectures at Cornell, and I think he would be excited about the “mathematisation” of biology. We now can study the physics of viruses using optical tweezers and fluorescent techniques. In particular the beautiful work by the Bustamante lab on the φ29 packaging motor, showing the viral genome being packaged in its protein capsid (subscription required) and the microscopy studies on viral entry into cells by the Zhuang lab (click here to watch a cool movie). So while it might have been true in 1964, it is no longer true that biology is unmathematical at any scale.

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