μίτος (Mitos)

Every one of us starts our life’s journey as a single cell. How do we grow up to become what we are? (Of course several other processes go into making a human being but just consider the sheer increase in the number of cells in your body from 1 to billions). You fall down playing football injure your knee, but after few days the knee looks as it was before. How does mould grow on your bread to such huge amount when you had left it just for few days? Let’s do a bit of time traveling and try finding out.

It’s late 1870s (somewhere around 1876-77). Enter the University of Kiel, Germany; into the lab of Prof. Walther Flemming. He pioneered the use of aniline dyes to stain and observe the nucleus. His discovery – the chromosomes (Greek for colored bodies) would become one of the 10 most important discoveries in cell biology. He seems to be busy observing something under the microscope and making some drawings. Come closer let’s have a look at what he is up to. Can you see the red colored thread (figure below are sketches made by Prof. Flemming, with black ink though) like structures at different locations in different cells? They are nothing but the chromosomes, the packaged form of DNA. Walther Flemming is observing and recording various stages of cell division for the 1st time.

Courtesy: Wikipedia

What he had seen in the 17th century is mitosis (From Greek word Mitos- for thread). Mitosis is the process of multiplying a cell’s chromosome into two sets which is generally followed by division of the cell into two daughter cells (cytokinesis), each one getting one set of the chromosome.
To embark on the journey of mitosis (cell division) the cell has to equip itself. This is what it does in the interphase (or the in between phase-in between two mitosis). The entire cell’s machinery starts to work in full swing. Lets have a 1st hand information from the cell himself as to what he is upto.

“Hello there! Oh don’t get intimidated by the hurry burry happening around. Lots of work going on…. got to prepare for the big event you see. So I am taking in the nutrients, making proteins and lots and lots of energy, soon I will have to start duplicating my DNA. By the way, I am currently in G1 phase of interphase (that’s what you humans call it). Sometimes some of my brother cells decide to take a break at this phase (may be because of lack of nourishment or bad conditions around) and do not go ahead to synthesis DNA. But no breaks for me now, so I am going ahead with DNA synthesis such that there are two copies of my DNA (S phase). I got to distribute the DNA equally to my daughters. That’s a tiring process, takes up huge energy to do that, since I have to ensure no mistakes are made else my progeny will pay heavily for it. But since everything till now has gone well I can’t afford to rest now, have to keep synthesizing proteins (G2 phase) that will help in the mitosis. For successful occurrence of interphase and mitosis (that is yet to occur), the credits go to two groups of proteins that are mainly responsible for it, which together are called the cyclin-CDK complexes.

Now I am all set to start off mitosis. The 1st step in the process of mitosis is the prophase (the before stage). As you might have already noticed, the DNA, which was present as loose coil (chromatin) till now, has started to condense, forming the chromosome (dividing/distributing is easier when things are compact). The two copies of each region of the chromosomes also appear in doublets (sister chromatids) attached at a region called centromere. The architect who helps maintains shape and structure - the centrosome - jumps into action (centrioles making up the centrosome have also replicated during the interphase) and you can see the centrioles going to the two poles of the nucleus, as things proceed centrioles are going to be doing the chromosome separating job.Whoosh goes the nuclear membrane!!! I have broken it down so that for the 1st time ever, in my existence, the nuclear contents are going to mingle with the rest of the regions that make me up. It is now prometaphase. Can you see centrioles and the chromosome playing search and capture game? Well that’s actually a serious business. Some of the microtubules (now also called the mitotic spindles) bind (with the help of motor proteins) at the centromere (kinetochore microtubules), few at the arms of the sister chromatids (astral microtubules) and still others with the spindles arising from the opposite poles (nonkinetochore microtubules).

Into the metaphase, which is exactly half way through the process you can notice that my chromosomes are getting aligned one by one along my centre plane. They are all set to be separated into two, once the check proteins finish their last minute testing to ensure everything has been fine till now (similar to the checking before a rocket launch that you people do). As I had told you before, I cannot afford any mistakes. The final GO is yet to arrive from the kinetochore (which is the centromere bound by various proteins). Ahh!! There…. got it.

Now my next task is to separate out the sister chromatids (named Anaphase, Ana in Greek means up. Weird how humans come up with such names!) and bring them to the two poles. Any guesses how I am going to manage that? Well I have got a simple old strategy which I learnt from my mom. Make one set of the microtubules, which is holding the chromosomes at the centre, short and the others to elongate. Yes creating a pull and a push force, ripping the sister chromatids to two (Its now daughter chromatids) and stretching the cell as well. I will be handing down each of the pair of chromatids to my daughter cells.

Oh boy! Oh boy! I can’t contain my excitement. I have finally reached the final leg (Telophase) of my journey and all set to give the finishing touch to this long and tedious but well planned and executed journey of mine by first forming a nuclear membrane around the two segregated set of chromosomes.”

Well what happened next to our cell is anybody’s guess. He distributed his contents equally to two daughter cells in a process called cytokinesis (considered to be separate from that of the phases making the process of mitosis). A kind of constriction (cleavage furrow) occurred around the region where the chromosomes were present during the metaphase, to bring about the separation. (Cytokinesis usually starts off along with telophase and by the time the nuclear membrane forms completely the cell has also divided into two with all the organelles and the constituents in a parent cell, divided equally among the daughter cell).

There you go, the cell just showed you a way it has learnt and perfected through the course of evolution to increase in number, a means of replacing the dying cells, a process employed in making you (development of all multicellular organisms) and repairing you.

Reference :
Molecular biology of the cell. Bruce Alberts, Alexander Johnson, Julian Lewis, Martin Raff, Keith Roberts, and Peter Walter. Garland science 4th edition.

A quick story of quicksand!!!

Many years ago, when I had been to my ancestral village as a kid, the people there excitedly showed us around places, telling us the history behind each and every place-from the temple to the fort. Near one of the cannons located on the edge of a hillock was a big sign that read: “DANGER! QUICKSAND AHEAD”. The guide accompanying us saw my eyes moving in that direction and started describing how dangerous that place was. Apparently a monster that had been living inside for ages, pulls in any animal or people going that way and eats them.

Lots of myths surround the very idea of a quicksand. Many movies also showcase quicksand, where the villain slowly sinks and dies. What is this quicksand? Why does it pull things in? Can people sink in a quicksand and die?

Firstly how does quicksand come into existence? A quicksand is composed of water, clay, salt and of course, as the name suggests lots of sand. You would have seen a house made of cards. A quicksand also has a similar structure, with sand for cards, water in the gaps and clay gluing the cards. When water saturates a region with loose sand and this sand gets agitated (due to flowing underground water or due to earthquakes, wherein shaking ground increases the pressure in the ground water, which then liquefies the sand) the water gets trapped between the agitated sand and liquefies the sand. That’s why one finds quicksand mainly near the river beds and marshy places.


What happens when you disturb a house of card? It collapses of course. That’s exactly what happens to a quicksand into which, say, the hero of our movie falls. So what happens next? Nope….he is not going to sink and die (heroes don’t die in our Indian films). In a series of events, rapidly following the collapse of the structure called the liquefaction of the quicksand, the water and sand separate out into different layers. And the clay particles come together and get packed nicely due to the salts. The densely packed (nearly double of what it was in the undisturbed quicksand) wet sand and the clay is what traps the hero in. Would he sink further? No he can’t, because the sand below and around him is a lot denser than his body weight. So he is just trapped in and can rest assured that he won’t die by sinking.



How do we get our hero out? Definitely not by throwing a rope to him and pulling him out. That would be nearly impossible. The researchers who have studied quicksand behavior have estimated that a force equivalent to lifting a mid sized family car is what is required to pull just a leg out of the quicksand. So if you try pulling him out with that force you will get our hero back…..but minus his limbs.

The only way out is to rebuild the house-of-cards structure again around the trapped hero. All that needs to be done is to reintroduce the water (now in a separate layer) into the sand and the clay and decrease their viscosity. It is easier said than done. This again needs lots of force estimated around to introduce water at a speed of 1 cm s-1, say, a pressure of 106 pascals (Pa) is needed (Ref 2). But persistently making small circles around his trapped body parts, our hero can help rebuild the house of cards and then someone can pull him out.

Now you know for sure that, as shown in the movies, people cant die in quicksand by sinking in. Nor are there any quicksand monsters (by the way I had brushed off that story even as a kid ).


References:
1. http://science.howstuffworks.com/quicksand1.htm (How Quicksand Works )
2. Khaldoun, Bonn et al., Nature 437; pp 635

The joy of joymetry-3

Previous

For comparison, here’s another proof. It’s equally famous, and it’s perhaps the simplest proof that avoids using areas.( Routine text book stuff)
As before, consider a right triangle with sides of length a and b and hypotenuse of length c, as shown below on the left.


Now, by divine inspiration or a stroke of genius, something tells us to draw a line segment perpendicular to the hypotenuse and down to the opposite corner, as shown above on the right. (I use to wonder why during my school days, is it just for the sake of proving it or there is no remote chance of proving it with out the line?)
This clever little construction creates two smaller triangles inside the original one. It’s easy to prove that all these triangles are “similar” — which means they have identical shapes but different sizes. That in turn implies that the lengths of their corresponding parts have the same proportions, which translates into the following set of equations:


We also know that

because our construction merely split the original hypotenuse of length c into two smaller sides of length d and e.
At this point you might be feeling a bit lost, or at least unsure of what to do next. There’s a morass of equations above, and we’re trying to whittle them down to deduce that

Nevertheless, by manipulating the right three equations, you can get the theorem to pop out. See the notes below for the missing steps.
Would you agree with me that, on aesthetic grounds, this proof is inferior to the first one? For one thing, it drags near the end. And who invited all that algebra to the party? This is supposed to be a geometry event.
But a more serious defect is the proof’s murkiness. By the time you’re done slogging through it, you might believe the theorem (grudgingly), but you still might not see why it’s true.

Reference :
E. Maor, The Pythagorean Theorem: A 4,000-Year History (Princeton University Press, 2007).
New york times.

• Here are the missing steps in the second proof above. Take this equation:

and multiply it by a on both sides to get

Similarly massaging another of the equations yields

Finally, substituting the expressions above for d and e into the equation c = d + e yields

Then multiplying both sides by c gives the desired formula: