The biophysics department here at Hopkins had invited Dr. Alexander Van Oudenaarden from MIT physics to give a student invited seminar. I was a bit familiar with his work through my junior thesis. He is trying to understand noise and random behavior of cellular signaling pathways through experiments and computer simulations.
The talk had a lot of good things, but what caught my attention the most was a topic I could directly relate to the heading of the post. In our cells (except mine!) , or in any other eucaryotic cell there is a signaling pathway called the GAL switch. When the cell is put in an environment which lacks any other nutrients except galactose (which is a kind of sugar present in milk) the GAL switch operates and produces carriers which help the transport of galactose from outside of the cell in the cytoplasm (inside of the cell). I genetically lack that system and that's why I cannot consume milk which is a major source of galactose.
Suppose we start with a bunch of cells which at time t = 0 do not have the machinary to transport galactose in. We then supply galactose to this culture. What we expect to find and do find is that the internal GAL switch starts functioning and builds up the transport machines which take the galactose in. This makes a lot of evolutionary sense, that to a given change in environment, the cells are able to cope up accordingly. (case A)
Now suppose we start with a bunch of cells which at t = 0 already have the machinery present to transport galactose in. And suppose now we put this culture in a solution where there is a lot of galactose (case B) or there is no galactose (case C), what we would expect is that the cells would continue living with their existing machines in case B and that they would shut off the factory of transporting galactose in case C (since there is none in the environment).
Counter intuitively what we find experimentally is that in case A, there will be some cells which do not produce the machinery, in case B there will be some cells which shut off their machines and in case C, there will be some cells which will keep on maintaining the machines though they are rendered useless. This phenomena is no accident and is a persistent feature of the culture. It is counter intuitive because the cells which are going against the popular vote are eventually going to die because of their apparently stupid decision. If the organism were to evolve such that the selfish unit of evolution were the individual itself, this kind of suicide does not make much sense.
Cleverly when the experiments were performed in a medium/solution where the concentration of external galactose was changed in time, the lab found that this suicidal behavior makes a lot of sense for the gene! During evolution of the yeast, the species was exposed to a time varying environment the nature of which we surely don't know. The gene's way of predicting the future environment or differently put, the gene's way of coping up with random changes in the future environment was to produce individuals of all kinds some of which are unsuitable for the current environment (but might be suitable for the future). By maintaining a population which has some members which are suitable for the present and some members which are not, the gene ensures that for any reasonable change outside of the cells the species as a whole is not wiped out. In other words (I suppose) the gene makes sure that it does not follow a path to extinction by maintaining a pool of suicidal members (who potentially may cope better with random change in the environment in the future).
I thought this is a direct evidence to the selfish gene rather than a selfish individual or a selfish species. And that made me happy :-) This is a direct evidence because neither selfish individual nor selfish species hypothesis can explain this kind of a behavior.
And to conclude, it is important to give some definitions as I understand them. By selfish X (X = gene, individual, species) we understand that X is the unit which will try to survive in case of competition by perhaps eliminating other members of X. For example in case of food shortage, a selfish individual theory would imply that individuals will kill each other to survive so that they can acquire sufficient amount of the limited resource for themselves, a selfish species on the other hand would perhaps imply that humans would kill off other animal and plant species so that they don't have any competition for food resources. The most counter intuitive selfish gene would imply that individuals would take actions in such a way that individual genes are retained in further generations.
Showing posts with label Nerdy. Show all posts
Showing posts with label Nerdy. Show all posts
Monday, April 14, 2008
Thursday, September 27, 2007
The arrow of time
Some days ago, I had come across an intriguing article about how our intuition about the forward direction of time or the celebrated arrow of time is linked with the theoretical predictions arising from fundamental and applied physical theory.
Consider a world full of objects obeying classical laws of mechanics. A little inspection would trivially show that the equations of motion are time reversible i.e. as far as the equations are considered, there is no preferred direction of time. This observation became a major worry for physicists with the advent of the second law of thermodynamics which stated that the entropy should always increase (thus giving a direction to time).
Though entropy was not a directly accessible experimental quantity, it had become obvious for a lame physicist to determine the positive direction of time. As trivial as the problem might sound in a common sensical way, consider that you are given a movie about a real life experiment and then you are asked to identify if the movie is played backwards or forwards. This question is certainly a non-trivial one (e.g. waves on water, where forward and reverse might look the same. I must mention that this strictly is not a very good example!) With the aid of the entropy law, the physicist will be quickly able to tell which is the positive direction!
This entropy law was a shocker to all the physicists and notably, since it hasn't been proved yet for a classical system, it is legitimate to believe that we will find instances where given a movie we exactly determine the arrow of time. In the realms of classical mechanics, though the law has not been proved, it's limitations are well known. E.g. a ball rolling on the floor does not indicate any direction of time. It is only when the system becomes macroscopic (A rolling ball, though is macroscopic in nature, here is modeled as a point particle for simplicity) that the entropy law is valid and it is the only case where we can with firmness determine the direction of time.
This brings me to the lecture I attended today, by one of the notable statistical physicists of our times. The main topic of the talk was violation of the second law of thermodynamics in systems which are neither microscopic nor macroscopic but lie on the boundary and give rise to interesting results. For concreteness, suppose we are given a movie about stretching a rubber band. By a movie, I mean every possible accessible detail about the experiment. It would be trivial to find out if the rubber band is being stretched or if it is being compressed based on our intuition. But when it comes to molecular level rubber bands, like RNA molecules. To put things in the lecturers own words, we only have a maximal likelihood of predicting if the RNA molecule is going forwards in time or backwards. To add more spice and mysticism to the story, the molecules itself doesn't know if it is going forward or backward in time. There is a probability associated with that :-)
On a more fundamental level, these issues have been resolved thanks to the asymmetry in the realms of quantum mechanical world, or the world which we live in. But nevertheless, for systems like the molecular rubber bands, which can still be treated classically for good reason, time might not know which direction is forward!
Consider a world full of objects obeying classical laws of mechanics. A little inspection would trivially show that the equations of motion are time reversible i.e. as far as the equations are considered, there is no preferred direction of time. This observation became a major worry for physicists with the advent of the second law of thermodynamics which stated that the entropy should always increase (thus giving a direction to time).
Though entropy was not a directly accessible experimental quantity, it had become obvious for a lame physicist to determine the positive direction of time. As trivial as the problem might sound in a common sensical way, consider that you are given a movie about a real life experiment and then you are asked to identify if the movie is played backwards or forwards. This question is certainly a non-trivial one (e.g. waves on water, where forward and reverse might look the same. I must mention that this strictly is not a very good example!) With the aid of the entropy law, the physicist will be quickly able to tell which is the positive direction!
This entropy law was a shocker to all the physicists and notably, since it hasn't been proved yet for a classical system, it is legitimate to believe that we will find instances where given a movie we exactly determine the arrow of time. In the realms of classical mechanics, though the law has not been proved, it's limitations are well known. E.g. a ball rolling on the floor does not indicate any direction of time. It is only when the system becomes macroscopic (A rolling ball, though is macroscopic in nature, here is modeled as a point particle for simplicity) that the entropy law is valid and it is the only case where we can with firmness determine the direction of time.
This brings me to the lecture I attended today, by one of the notable statistical physicists of our times. The main topic of the talk was violation of the second law of thermodynamics in systems which are neither microscopic nor macroscopic but lie on the boundary and give rise to interesting results. For concreteness, suppose we are given a movie about stretching a rubber band. By a movie, I mean every possible accessible detail about the experiment. It would be trivial to find out if the rubber band is being stretched or if it is being compressed based on our intuition. But when it comes to molecular level rubber bands, like RNA molecules. To put things in the lecturers own words, we only have a maximal likelihood of predicting if the RNA molecule is going forwards in time or backwards. To add more spice and mysticism to the story, the molecules itself doesn't know if it is going forward or backward in time. There is a probability associated with that :-)
On a more fundamental level, these issues have been resolved thanks to the asymmetry in the realms of quantum mechanical world, or the world which we live in. But nevertheless, for systems like the molecular rubber bands, which can still be treated classically for good reason, time might not know which direction is forward!
Wednesday, June 20, 2007
Pacman
In an academic discussion (hmph!), it was pointed out that Lysozyme is equivalent to Packman in it's job. It' lyses ie. cuts and kills proteins when they are vulnurable to attack. It also turns out that they are isomorphic in shape as well.
Tuesday, March 27, 2007
A B argument
An AB argument is a conversation between two people PD and VK which proceeds as shown below:
VK : A
PD : B
VK : A
PD : B
VK : A
PD : B
.. ad infinitum (or till one of them gives up)
If VK is replaced by AM, PD always looses the AB argument. The essence of the conversation is that VK claims A is true while PD claims B is true where B<==> ~A (or !A) and both of them want the other to believe that what they believe is true is the truth. Do not take this construct lightly for its triviality, this has been proved to be a useful model for explaining adamant people.
Recently I had to perform a technical survey, all the scientists were people who have achieved a significant amount of discovery (some of them Nobel laureates) and all the papers I read were either in Nature or in Science. And the argument goes like this:
RM: S4 linker moves 20 angstrom
RH: S4 linker does not move 20 angstrom
RM: See results from XYZ experiment, S4 linker moves 20 angstrom
RH: See results from XYZ (the same XYZ as above) experiment, the S4 linker does not move 20 angstrom
They continue this way for every other aspect of the problem. There are around 5-10 aspects to the problem and each of them results in atleast 10-20 Science or Nature papers.
The end of the AB argument as told above comes only when t --> infinity or one of them gives up. The giving up has been observed within 30 minutes with probability 1 when the mode of conversation is speaking in front of each other. But we believe that it is really difficult to observe the giving up phenomena when the mode of communication is writing up 1 page papers in Science or Nature. Thus a more evolved type of argument is needed to to settle the issue.
VK : A
PD : B
VK : A
PD : B
VK : A
PD : B
.. ad infinitum (or till one of them gives up)
If VK is replaced by AM, PD always looses the AB argument. The essence of the conversation is that VK claims A is true while PD claims B is true where B<==> ~A (or !A) and both of them want the other to believe that what they believe is true is the truth. Do not take this construct lightly for its triviality, this has been proved to be a useful model for explaining adamant people.
Recently I had to perform a technical survey, all the scientists were people who have achieved a significant amount of discovery (some of them Nobel laureates) and all the papers I read were either in Nature or in Science. And the argument goes like this:
RM: S4 linker moves 20 angstrom
RH: S4 linker does not move 20 angstrom
RM: See results from XYZ experiment, S4 linker moves 20 angstrom
RH: See results from XYZ (the same XYZ as above) experiment, the S4 linker does not move 20 angstrom
They continue this way for every other aspect of the problem. There are around 5-10 aspects to the problem and each of them results in atleast 10-20 Science or Nature papers.
The end of the AB argument as told above comes only when t --> infinity or one of them gives up. The giving up has been observed within 30 minutes with probability 1 when the mode of conversation is speaking in front of each other. But we believe that it is really difficult to observe the giving up phenomena when the mode of communication is writing up 1 page papers in Science or Nature. Thus a more evolved type of argument is needed to to settle the issue.
Tuesday, October 31, 2006
Piano and PDEs
The story goes back to a conversation between me and analytique de maximus, Lothar. "Which instrument do you like the most Purushottam?", He asked. "Piano", I answered quickly. Though I played only guitar, piano was my favorite always. " And why is that?", he insisted. Why one likes anything is a different issue altogether and I am not going to dwell into that here. Important to this context was the answer I gave. "I like the pure sound, the notes, without mircrotones, not like violin, piano has a definite sound". I was able to satisfy his ultra-inquisitive mind with this. I was relieved for that.
Some years later, that is today, I was sitting in in my PDE class. And the prof. was teaching something about wave equation. It's not that I hate it or something. Being the geek I am, I was enjoying the mathematical aesthetics in the problem. Now, I am going to write something which you might not understand or like, but it's a graduate course and never mind :)
In the wave equation, the initial conditions on time are the initial velocity and the initial displacement on the string. The string is assumed to be bolted at the two ends so that given a displacement, it vibrates periodically. The solution generally is a fourier series, each term representing a definite mode of vibration of the string. If we solve a problem where the initial velocity is zero while the initial displacement is finite and linear, we find that the fourier coefficients die down as 1/n^2. While in the initial velocity (no displacement) case, the fourier coefficients die down as 1/n^4. Even this part was enough interesting for me. But then, the professor started talking about piano.
In a piano, sounds are produced by pressing the keys which in turn results in a small hammer striking the string. Hence an initial velocity is given to the string problem. While playing a guitar, you pluck the string and give it an initial displacement. But since in an initial velocity problem the coefficient which are nothing but the amplitude, decrease rapidly, the higher overtones of the frequency are not heard, while the higher overtones are powerful in guitar and what we hear is a mixture of frequencies. That is why a piano sounds pure and single frequency and the guitar doesn't.
Math is beautiful in her own right. But then you can see her in nature, and in things you love and then it feels like adding more stars in her crown.
Some years later, that is today, I was sitting in in my PDE class. And the prof. was teaching something about wave equation. It's not that I hate it or something. Being the geek I am, I was enjoying the mathematical aesthetics in the problem. Now, I am going to write something which you might not understand or like, but it's a graduate course and never mind :)
In the wave equation, the initial conditions on time are the initial velocity and the initial displacement on the string. The string is assumed to be bolted at the two ends so that given a displacement, it vibrates periodically. The solution generally is a fourier series, each term representing a definite mode of vibration of the string. If we solve a problem where the initial velocity is zero while the initial displacement is finite and linear, we find that the fourier coefficients die down as 1/n^2. While in the initial velocity (no displacement) case, the fourier coefficients die down as 1/n^4. Even this part was enough interesting for me. But then, the professor started talking about piano.
In a piano, sounds are produced by pressing the keys which in turn results in a small hammer striking the string. Hence an initial velocity is given to the string problem. While playing a guitar, you pluck the string and give it an initial displacement. But since in an initial velocity problem the coefficient which are nothing but the amplitude, decrease rapidly, the higher overtones of the frequency are not heard, while the higher overtones are powerful in guitar and what we hear is a mixture of frequencies. That is why a piano sounds pure and single frequency and the guitar doesn't.
Math is beautiful in her own right. But then you can see her in nature, and in things you love and then it feels like adding more stars in her crown.
Monday, January 30, 2006
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