cell biology - Does electricity cause damage on a cellular level?

Regarding the moss or lichen on the third rail on British train lines: there is no current passing through the moss/lichen as they are not completing a circuit. They are just sitting on one connector. If another connector passed over them, completing the circuit across them, then a current might pass across them for a very short time. But I doubt they grow on the top of the rail (which is the contact part in the UK system) as that is constantly being polished smooth by the contacts from trains sliding across it.

Regarding cell damage: Apart from fibrillation in animals, and burns caused by Joule heating, electricity does cause cellular damage.

At low frequencies (<10kHz), electricity disrupts cell membranes and makes them much more permeable (we actually harness this when we use electroporation to transform bacteria). All organisms rely on electrochemical potential differences across membranes for their metabolism (Berry, 2002). The exact effect is dependent on the previous electrical state of the cells, for example the electrical potential difference across the membrane, and on the surface area to volume ratio of the cell (greater volume relative to surface area leads to more disruption). In any case, extreme electroporation can cause solutes to flow in or out of a cell, and generally disrupt the balance of solute concentrations and cause organelles and other bodies to move out of a cell. When the electrical stimulation stops, the contents are then fixed in a disrupted state. The cell then has to expend enormous amounts of ATP using ion channels and transport proteins in an attempt to reinstate the necessary chemiosmotic potentials, and in doing so exhausts the entire ATP supply and goes into biochemical arrest (no metabolism occurs), which is when a cell is dead. Dead cells break apart because there are is no maintenance occuring.

At higher frequencies (10-100kHz) proteins become permanently denatured. Many proteins carry charges which give them an overall polarity. When placed in an electric field, the proteins reorient themselves and will undergo conformational change to achieve the optimum dipole moment in the direction of the field. Ion channels and pumps are particularly sensitive to these disruptions (since their charges are crucial to their function).

Rather than provide lots of references, there is one excellent review from which I drew all this information, and which you should read for more of the physical detail (Lee et al., 2000).

References:

• Berry, S. (2002) The Chemical Basis of Membrane Bioenergetics. Journal of Molecular Evolution. [Online] 54 (5), 595–613. Available from: doi:10.1007/s00239-001-0056-3 [Accessed: 9 February 2012].


• Lee, R.C., Zhang, D. & Hannig, J. (2000) Biophysical injury mechanisms in electrical shock trauma. Annual Review of Biomedical Engineering. [Online] 2 (1), 477–509. Available from: doi:10.1146/annurev.bioeng.2.1.477 [Accessed: 9 February 2012].

exoplanet - Has the Kepler data been examined for light curves due to phase changes of non-transitting hot Jupiters and other?

I found this article http://www.epj-conferences.org/articles/epjconf/pdf/2011/01/epjconf_ohp2010_03005.pdf from 2011 announcing that two dozen secondary eclipses of "hot Jupters" have been seen in Kepler data. I even think I have seen a light curve showing phase changes of a transiting planet. This makes me think that there should be evidence in the Kepler data for non-transiting planets since the amplitude of the light curve due to planetary phase changes shouldn't be much different from that of a secondary eclipse as long as there is a fairly high inclination (say over 60 degrees).

Is anybody aware of such an examination of the data?

star systems - How many planets does Omicron Persei have?

Currently http://exoplanet.eu/ (which lists more exoplanets than the official NASA archive) lists no known planets of Omicron Persei. So currently we know of none, it is outside of the Kepler field so has no Kepler candidates either.

Though just because none are known that does not mean it has none, it may be that their mass and or orbital plane is such that it is very difficult to identify planets or no one has looked with a suitable instrument.

gravity - Existence of gravitons?

The metric describes the curvature of the space. For space around a massive object this is the Schwarzchild metric

$$
ds^2 = -left(1-frac{r_s}{r}right)dt^2 + left(1-frac{r_s}{r}right)^{-1}dr^2 + r^2(dtheta^2 + sin^2theta dphi^2)
$$

Clearly, if $r>>r_s$ this looks like

$$
ds^2=-dt^2+dr^2+r^2(dtheta^2 + sin^2theta dphi^2)
$$
which is the metric for flat space. So effectively the space gets flatter and flatter at a rate of $1/r^2$, which is the inverse square that you're looking for.

But where does the Schwarzchild metric come from? Without getting into the gritty maths, it can be proven that it is the unique metric that possesses spherical symmetry, without which nothing would make much sense. This is called Birkhoff's theorem.

I want to talk about where gravitons come from, but first lets talk about curvature.

If you want to measure the curvature of a space one way of doing it is to move in some closed loop, ending up back where you started. If the space is curved though, you won't be facing the same direction (this idea is called parallel transport)

Let's say we're parallel-transporting a tangent vector, as in the picture. We get a tangent vector from the derivative at a point (a slighly special derivative called a covariant derivative, because the space is curved). Let's take the tangent vector and move forwards then left. And we try again this time moving left then forwards. We end up the same point both ways, but like in the picture, the derivatives will be different in some way. We summarise this up with a commutator (where $D$ is the covariant derivative) like so

$$
[D_mu,D_nu] = D_mu D_nu - D_nu D_muneq 0
$$
It basically means "doing it one way is not the same as doing it the other".

Now let's back up a tiny bit and talk about how electromagnetism and other forces are typically discussed, using quantum field theory.

We describe the theory in terms of a Lagrangian, for a fermion (like an electron) it looks like this

$$
mathcal{L}=barpsi(igamma^mu D_mu-m)psi
$$

If I take the field $psi$ and give it a transformation
$$
psitopsi'=e^{ixi(x)}psi
$$
then the Lagrangian will remain unchanged. This type of transformation belongs to a group called $U(1)$. We say that the Lagrangian possesses $U(1)$ symmetry. Notice that this $D_mu$ is in there again? Its the same thing, a covariant derivative, here in QED as well. We can try taking a commutator again

$$
[D_mu,D_nu] = -iF_{munu}psi
$$
where
$$
F_{munu} = partial_mu A_nu - partial_nu A_mu
$$

From this we form the complete QED (the quantum theory of electrodynamics) Lagrangian
$$
mathcal{L}=barpsi(igamma^mu D_mu-m)psi-frac{1}{4}F_{munu}F^{munu}
$$

Don't get bogged down in the maths. The point is very simple. See the $A_mu$? Its a new field, we had to introduce it to make things work. In QED this field corresponds to a photon (particles are quanta of a field, like a small bump in the field). We had to introduce it becuase we had curvature. How do I know we have curvature? Becuase the covariant derivatives do not commute, just like in GR, above. This time though, the curvature is not of phyical space, its of an abstract object called the $U(1)$ gauge bundle.

So you're totally on the right track when you say that other forces may curve space. Its nice that gravity curves space-time, its very physical and easy to imagine, for the other forces its not so simple to picture, even though its fundamentally the same.

If you want the full picture of Einstein's gravity you do some maths and arrive at something called the Einstein-Hilbert action (an action is just an integral over a Lagrangian), one tidy object that sums up the whole theory

$$
S=int R sqrt{g} d^4x
$$
where $R$ comes (more or less) from the commutator of covariant derivatives we saw at the top. When talking about QED I brushed over the fact that its a quantum theory (it is). This EH action, however, does not describe a quantum theory. So, you might say, lets make it one! Hold on a second though, because it doesn't actually work. The problem is something called renormalisability - QED is renormalisable, GR is not. This is the root of the incompatibility between GR and quantum field theory. If we could carry out the resultant qunatum particle would be a graviton. You're right to doubt their existance as they haven't yet been observed, however...

We saw QED, which desribes particles of light, photons. They are quantised. Then we saw how in many ways GR and QED are very similar. We can't properly quantise GR but if we could we would have gravitons, exactly like photons popped out in QED. The duality between QED (and other gauge theories, QCD, etc) is clear, which leads a lot of people to believe that probably should have gravitons, even if they have not yet been observed, nor consistently formulated.

A note on other theories

There are many theories where gravitons are present from first principles without the problems of renormalisability, string theory or supergravity for instance.

A note on errors in the above

Sorry, I'm tired and rambling. Please point them out if you find them!

How far apart is the dust in the Sombrero Galaxy's dust lane?

The sizes of dust particles varies enormously, and thus the density of dust particles depend upon which sizes we are talking about. The dust size distribution can be described by a power law with a slope of roughly $-3.5$; that is, the density of 0.1 µm particles of is $10^{-3.5}$ times that of 0.01 µm particles, or roughly 3000 times smaller.

Moreover, the discussion is complicated by the fact that we don't really have a formal definition of what is dust. But one "definition" takes the minumum size as a conglomeration of a few molecules, and the maximum size as "what has time to grow in a formation process" (these dust particles can later "stick together" and grow to form pebbles, rocks, asteroids, and planets. That's why any definition will be arbitrary).

In a dust-dense region of the interstellar medium, this results in a typical mean density of roughly one dust particle per cubic centimeter.

evolution - Why did the process of sleep evolve in many animals? What is its evolutionary advantage?

I found this paper by Benington and Heller that expands on the previously mentioned theory of sleep as a mechanism to renew metabolism. They hypothesise that sleep is necessary to replenish glycogen stores (mainly within astrocytes) in the brain. These stores are normally used to supplement blood glucose due to the high energy demands of the brain.

It is suggested that this may also result in the manifestation of feeling sleepy as a consequence of the exhaustion of glycogen supplies in specific small areas of the brain. Brief and localised depletion of glycogen stores mean that cells are operating with less energy than they normally have to work with. This causes an increase in synthesis of adenosine from the breakdown of AMP. The paper maintains that the increased levels of adenosine are detected by adenosine receptors which then triggers or increases (as seen on EEG scans) the feeling of the need for sleep:

In NREM sleep (which may lend some support to the theory as NREM sleep accounts for 80% of sleep and is most physiologically different to waking), this glycogen is most efficiently replaced. During NREM sleep the release of glycogenolysis inducing neurotransmitters is reduced, allowing glycogen-synthase to predominate and glycogen levels to be restored. However, these same neurotransmitters are key in the processing sensory stimuli (by tonically depolarising neurons in the sensory cortex). Therefore glycogen replenishment will always be associated with a (strongly) reduced response to stimuli.

This leads to finally answering the question as to why sleep has an evolutionary advantage, which I will quote verbatim to maintain the authors momentum:

Glycogen replenishment during waking would be maladaptive because it would impair the organism's ability to to process and respond to sensory stimuli. Sleep has therefore evolved as a state where animals retreat to a safe environment, behaviour is suppressed and glycogen stores are replenished.

How can we tell how many exoplanets a star has?

What you are describing is a basic signal processing problem. The doppler shift that one observes is due to the motion of the star in the system around the system's centre of mass. The star will be influenced by the gravitational pull of each of the planets in that system, each of which exerts a gravitational pull that increases with the mass of the planet and decreases with the orbital radius of the planet.

The overall motion of the star will be the sum of the effects of all the planets. Importantly, the effect of each planet will have its own amplitude and will be periodic with a period equal to the orbital period of that planet.

Let's imagine that each planet is in a circular orbit (elliptical orbits are more complicated, but the principle is the same). Each planet would cause a circular motion in the star about the centre of mass of the planet-star pair, leading to an observable doppler signal which has the form of a sine wave with a period equal to the orbital period of the planet. The amplitude of that signal will increase with the mass of the planet and increases with decreasing orbital radius.

The overall signal is the sum over all the planets in the system. Fortunately the decomposition of this signal back into its individual components is a well-trodden problem in physics, electronics and many other fields and is known as Fourier Analysis. Whether you can successfully recover the original signals from each of the planets depends on how long you observed the system (ideally you want to observe for longer than the longest orbital period) and the amplitude of the signals compared with the noise in your observations.

In general it is easier to recover high-mass planets with short orbital periods and more difficult to recover low-mass planets with long orbital periods.

The image below might be helpful. It shows the track of the solar system centre of mass compared with centre of the Sun over a period of several decades. Notice how the Sun executes a complex trajectory (with respect to the solar system centre of mass) that is mainly caused by the orbit of Jupiter, but then there are smaller, superimposed, signals caused by the smaller planets. In principle, if you observed for longer than the period of Neptune and had a detector which gave perfect measurements, you could reconstruct how many planets there were in the solar system, what their orbital periods were (and then from Kepler's 3rd law, what the planet-star sepration was) and what their masses were (multiplied by the inclination of their orbits with respect to the line of sight of observation, which is generally an unknown in doppler measurements).

In terms of what we could currently see if we observed the Sun as a star: basically we would (assuming we observed for 20 years) detect Jupiter quite easily with a doppler amplitude of about 13 m/s. We would also see that there was a drift in Jupiter's signal due to the influence of Saturn, but we would have to observe for >Saturn's orbital period in order to confirm the presence of Saturn, its orbital period and mass. The inner planets produce an amplitude that is too small to be visible using the technology currently available. e.g. The Earth would produce a doppler wobble of amplitude $<8$ cm/s, but the current precision of doppler measurements is limited to about 50 cm/s.

The doppler amplitudes in m/s due to each of the planets (assuming we view them edge on) are:

Mercury <0.01
Venus 0.08
Earth 0.08
Mars <0.01
Jupiter 12.5
Saturn 2.6
Uranus 0.28
Neptune 0.26

Thus with current technology, only Jupiter and Saturn are detectable.

Below I simulate what the doppler signal due to these two planets would be. I hope you can see that the overall signal consists of the superposition of two sinusoidal signals with different periods and amplitudes. Myriad computational tools are available to do the fourier decomposition to establish these.