Quantcast

Posts tagged with speed


World record progression for the men’s Long Jump.

A jump process.
…
…
PUN FULLY INTENDED.

World record progression for the men’s Long Jump.

A jump process.

PUN FULLY INTENDED.

(Source: Wikipedia)


hi-res




inside the cell

…how fast things happen inside cells.

…a white blood cell responding to inflammation.

Cells are very crowded


image
Image: “The structure of the cytoplasm" from Molecular Biology of the Cell. Adapted from D.S. Goodsell, Trends Biochem. Sci. 16:203-206, 1991.

… a synaptic vesicle, which is the part of a neuron that releases neurotransmitters from one neuron to another. …I assumed that the authors crammed all the different proteins into the [diagram]…. But in fact, the diagram below omits ⅓ of the proteins so real membranes are even more crowded…. paper … we should think of membranes as packed with proteins like a cobblestone pavement.
A neural vesicle studded with proteins
Image: “Molecular Model of an Average SV" from Molecular Anatomy of a Trafficking Organelle, Takamori et al, Cell. 2006 Nov 17;127(4):831-46.

Molecules move very very fast

You may wonder how things get around inside cells if they are so crowded. …[M]olecules move unimaginably quickly due to thermal motion. A small molecule such as glucose is cruising around a cell at about 250 miles per hour, while a large protein molecule is moving at 20 miles per hour. Note that these are actual speeds inside the cell, not scaled-up speeds. I’m not talking about driving through a crowded Times Square at 20 miles per hour; to scale this would be more like driving through Times Square at 20 million miles per hour!

Because cells are so crowded, molecules can’t get very far without colliding…. In fact, a molecule will collide with something billions of times a second and bounce off in a different direction. Because of this, molecules are [on] a random walk through the cell … diffusing…. A small molecule can get from one side of a cell to the other in ⅕ of a second.

As a result of all this random motion, a typical enzyme  … interact with 500,000 [molecules] every second. …[Y]ou might wonder how the different pieces just happen to move to the right place. In reality, they are covering so much ground in the cell so fast that they will be in the “right place” very frequently just by chance.

In addition, a typical protein is [spinning] a million times per second. Imagine proteins crammed together, each rotating at 60 million RPM, with molecules slamming into them billions of times a second. This is what’s going on inside a cell.

The incredible speed and density of cells also helps explain why it’s so difficult to simulate what’s happening inside a cell. Even with a supercomputer, there’s way too much going on inside a cell to simulate it without major simplifications. Even simulating a single ribosome is a huge computational challenge.

Molecular motors sprint, not walk

.. Like a mechanical robot with two lumbering feet, a kinesin motor protein can be seen in the video at the 2 minute mark dragging a monstrous bag-like vesicle along a microtubule track. (This should be what you see in the YouTube preview frame at the top of the page.) These motor proteins move cargo through the cell if diffusion isn’t fast enough to get things to their destination, which is especially important in extremely long cells such as neurons. …

… these mechanical walkers…sprint at 100 steps per second. If you watch the video again, imagine it sped up to that rate.

Cells are powered by electric motors spinning at 40,000 rpm

Mitochondria also provide a fascinating look at just how fast things are inside cells. You may know that mitochondria are the power plants of cells; they take in food molecules, process it through the famous citric acid cycle, and then use oxygen to extract more energy… ATP….

image

Image from David Goodsell, ATP Synthase, December 2005 Molecule of the Month


… Mitochondria use the energy from oxidizing food to pump protons out of the cell, creating a voltage of 170mV across the cell. This voltage causes a complex enzyme to spin, and the mechanical energy of this spinning enzyme creates the ATP molecules that energize the rest of the cell.

…these enzymes spin at up to 700 revolutions per second, which is faster than a jet engine. …

If you’re interested in more about this mechanical motor, you’ll probably enjoy PDB’s molecule of the month article.

(There’s also a longer narrated version at the BioVisions website.)

The above text is by Ken Shirriff.

It makes sense to me that if my muscles do things on the order of hundredths of seconds, then the chemical interactions to cause something like “arm, go up” has to be happening several orders of magnitude below what my consciousness evolved to notice.

Hearing the speeds of biological molecules made me wonder how heavy / fat these fast-moving molecules are relative to hydrogen (familiar Schroedinger stuff) or quantum chemistry. DNA is apparently 6 orders of magnitude heavier than hydrogen ion.

Follow-up thought on gerontology: If you think on the decades scale, your body starts falling apart after 3 or 4 and is pretty much useless by 8, 9, or 10 — if it even lasts that long. But think about how many molecular things have to happen to make you be yourself for even a minute. Let’s say it’s tens of millions. Then multiply that by 100 trillion cells and a 60×24×365×10 = 6½ orders of magnitude difference between a minute and a decade, for a total O(10^28) molecular thingies to make a life. That’s not so short.




As every sci-fi geek knows, matter may travel faster than the speed of light as long as its mass is imaginary (a multiple of √−1). A so-called tachyon would not overturn special relativity—and it would provide a handy way of resolving any conflicts in a given Star Trek plot.

  • 14th Law of How to Write Star Trek: Whenever you’ve written yourself into a hole, instead of re-writing the show so that it’s better, simply make characters issue the word “tachyon” several times toward the end. Everything is magically resolved, returning all aspects of life to the way the show started with no long-term consequences for the characters—which by the way is a great lesson to teach to young adults—and then Spock or Data has an “a-ha!” moment wherein he throws around jargon to further justify the deus ex machina.

The only problem with tachyons, as any sci-fi geek can attest, is that “imaginary” mass is pure fiction! How could anything weigh an imaginary amount?

 

Well, I’m not sure that tachyons do exist—although if someone wants to post some arXiv links to relevant papers that would be awesome—but, I will say that “imaginary mass” isn’t that ridiculous of a concept.

As Tristan Needham said in the best book about complex numbers ever, the “imaginary” descriptor only reflects the historical prejudice against √−1.

Do imaginary numbers exist? No. But neither do counting numbers. Numbers are linguistic entities that humans communicate with. Sort of like how trees, flowers, bushes, shrubs, brambles, and vines all exist in nature, but those classifications, concepts, words, groupings are human-language mental constructs. “Five” doesn’t “exist” per se, but mathematical models built with the-thing-that-satisfies-the-properties making five five, do wonderfully at prediction of physics experiments.

Anyway, imaginary numbers exist just as much as other numbers. Just like rational numbers, they’re generated by an operation that comes up as a matter of course in algebra. And algebra seems to have something to do with nature. God knows why. (ohh! which way did I mean it?!)

So I’m not saying imaginary mass exists, but here are some good ways to think about imaginary numbers.

  • imaginary numbers are twisted numbers
  • imaginary numbers are phase-shifted like a sine wave versus a cosine wave
  • an imaginary current heats up a wire but does no useful work

If the mass of a particle is an imaginary number, then … that might help you make sense of tachyons.

 

Nerdy side note: E=MC² is not the real equation to describe the conversion of energy into matter or vice-versa.

  • E=MC² tells you how to convert stationary matter into energy.
  • The real equation is E² = [mc²]² + [pc]².
  • (p is momentum.)
  • (Notice that the real equation is of the form A²+B²=C². i.e., Energy is the hypotenuse (C) to the triangle sides B=mc² and A=p•c)

You can casually start/interrupt conversations with this knowledge the next time you attend a kegger / black-tie affair. Doing so will win handsome glances from potential sex partners. Also, there is a 0% chance that anyone will think you’re an insufferable know-it-all.