So what is Entropy?
To follow in the tradition of Maimonides. Entropy is NOT a tendency to disorder! I need to thank Joe Felsenstein for directing me to Frank L. Lambert’s insights on a previous thread probably best left alone. Here is a great site to elucidate Lambert’s insights:
http://entropysite.oxy.edu/
What about Evolution? Can complex systems arise naturally and spontaneously into higher tiers of complexity and order and opportunity—according to the Second Law of Thermodynamics— and all without divine intervention commonly described as Intelligent Design or Irreducible Complexity?
Sean Carroll has much to offer on this question:
Participants should refrain from arc-reflex boiler-plate diatribes echoing previously held opinion and first examine what Carroll has to say. Failure to do so will merit cyber-smack downs.
What are they competing for, who has the highest fitness?
Allan doesn’t mean competing. He doesn’t mean ignore. He doesn’t mean its silly. He doesn’t mean because. He doesn’t mean difficult.
Its just convenient to write this way, because he readers should know what he really means.
I now see why he says he never said fitness means the ones that survive best. Because if he said it, probably its not what he meant.
No, the “it’s silly” part he definitely means.
Mung,
Yawn.
Distinguish means measure. A measurement can’t be made on a system without affecting the system. That may not be obvious in macroscale systems like an airplane where you can measure its velocity by the light bouncing off of it (and not affecting its velocity much) and you seeing it, but it’s a different story at the molecular level where the measuring apparatus (the enzyme) is of the same order size as the measured object.
The enzyme pays the price of measuring the orientation of a molecule by borrowing now and paying later, so it’s not cost free. Homochirality will be generated only to give it up when it becomes racemized or destroyed (like L-aspartic acid going back to an uncertain orientation of fumarate) as I’ll show below. The increase in Gibbs free energy for gain homochirality now is paid back by an equivalent decrease in Gibbs free energy later by loss of homochirality.
Nope! The proper word is enantiotopic not isomer. 🙂
For example, in the book I linked to which you should read for yourself:
Another name for aspartase:
https://en.wikipedia.org/wiki/Aspartate_ammonia-lyase
A description of this reaction is detailed here:
http://www.jbc.org/content/233/4/1010.long
But you see, the reduction in uncertainty of position or orientation (like recognizing the face of fumaric acid in the production of L-aspartic acid) is a reduction of entropy, a temporary increase in Gibbs free energy that must be paid back when the L-aspartic acids become racemized or turned back into fumaric acid of unknown orientation.
Not to mention there is a subtle application of energy not immediately obvious. For the reaction of L-aspartic acid to be constantly generated, it has to be transported out lest the equilibrium constant become realized and the L-aspartic acid production stops. Soooo, there is an energy cost, there is a de-mixing (removal of L-aspartic acid to another part of the organism), which is an energetic activity.
Agreed, yes indeed.
I think I figured out how the book I linked to on stereochemistry arrived at the equivalent of the Landauer Principle. It alludes to two ways of framing the equilibrium constant.
One could frame the equilibrium as:
L == D (for case already at equilibrium) where equilibrium constant K = [.5]/[.5] = 1
or
L == L + D (for the case starting at non-equilibrium)
which implies K = [ L ] / [L][D] = [.5] / ( [.5] [.5] ) = .5
plugging into
K = e^(- delta-G/(RT) ) =
ln (K) = ln (.5) = -delta-G/(RT)
delta-G = RT ln 2
which is the book result. As pointed out, the energy of setting an amino acid bit (so to speak) in this system agrees with the Landaur principle.
So whatever number of particles with degrees of freedom and associated equilibrium expectation there is, in principle, an associated delta-G. But as Allan Miller pointed out, the answer is likely intractable, except to say delta-G of formation of complexity is positive. 🙂
There are such systems. They are called racemases:
https://en.wikipedia.org/wiki/Epimerase_and_racemase
stcordova,
Since when? Neither pops up as a synonym of the other.
Yurgh. If there is some analogue of the enzymatic ‘lock/key’ system, the distinction is made by binding energies, which determine which is the lowest-energy state. No price is paid; the molecule with the higher affinity is the one more likely to be bound – the bound state has lower energy than the unbound state. Isomers interfere with this process, by providing an alternative low-energy state whose energy is higher than the lowest possible state – it is still thermodynamically downhill, and reduces reaction yield. Nonetheless, being of higher energy, and there being an available path to shed this energy, it is more readily displaced, which provides another opening for the ‘preferred’ orientation to follow its thermodynamic gradient.
Your vision of the enzyme somehow expending energy groping over the surface of these molecules to find the right one is ludicrous.
On a completely different time scale, and by a completely different process. You can’t bring two different kinetic processes together. This is fundamental thermodynamics, and you are mangling it badly from your ten minutes on Google.
The correct equivalent word is actually enantiomer, if you are trying to be clever, but in fact all isomers will be subject to the same element of competition for the active site, so I’ll stick with the more general term, if you don’t mind. My point is that you are looking at molecules in a highly ‘designed’ environment – one which fits the chemistry texts: a pure racemic solution of two molecules at 25 degrees and one atmosphere pressure. That is not a realistic model for any applicable system, primitive or later. It is not a simple contest between enantiomers, with all the left/right sock, coin-toss intuitions that this unleashes.
The rest of your post, relating to the Gibbs-energy ‘cost’ of more complex sets of solutes, and subsequent rearrangements, is equally irrelevant – particularly since the overwhelming thermodynamic cost is the energy of condensation of the peptide bond. You’ll notice that no ATP is consumed in the ribosome in ensuring that the ‘correct’ tRNA docks – convertible energy (ATP and GTP) is only needed for the bond (eta – some of the bond energy, incidentally, comes from the docking energy of the ‘right’ tRNA).
The relative cost of competing molecules is relatively trivial – and it’s pointless trying to work out the mixture ‘costs’ of an unknown mixture.
stcordova,
I know. I’m hardly going to appeal to a biological process though, am I?
stcordova,
Intractable actually means intractable.
A bitwise approach is way too simplistic anyway. Thermodynamic and informatic entropy are mathematically related, at the level of primary sequence. But chemistry has more layers.
Consider a system in which monomers had a higher free energy than the condensed state. Then, they would ‘spontaneously’ bind. Consider also the possibility that a bond between homochiral pairs of such monomers had lower energy than the opposite. It is certainly possible, because the monomers interact, potentially asymmetrically – something Shannon bits do not do. Thus, such dimers would be more stable.
Additionally, consider the possibility that short strings of such monomers may interact with each other, by hydrogen bonding. This makes the doubly-bound state more stable still. If, additionally, such pairings are also more stable homochirally than mixtures, we have a means of enrichment. Clumps of both orientations would arise, but crucially, the initally racemic mixture has been partitioned.
Now, this is hypothetical, and it doesn’t take a genius to see what molecule I’m hinting at here. And, I know that there are problems with the scenario, so spare us a hastily-constructed Google-fest.
My point is that organic molecules can, in theory, ‘self-purify’ – they can partition a racemic mixture. Proteins can’t, of course, but one should not export protein intuitions to all of chemistry.
stcordova,
Actually becomes a weird argument at this point. It’s positive unless one can prove it’s negative …
We are being invited, as the first part of this argument to agree that the Second Law is absolutely rigid. Of course we agree that, yes indeed, there is no way Life can get going if it requires a violation of the Second Law. Cos, ‘y’know, the Second Law cannot be violated. Well, except that there’s this bloke, you see, and …
Nope. I’ve agreed that the Second Law cannot be violated. End Of. You can’t just chuck away your starting premise.
ALL solutions to the OoL need to pay attention to thermodynamic constraint, I agree with that. Which is (one reason) why I reject Proteins First.
To the extent it is a statistical law, it is not very appropriate for sparse gases like say 2 molecules in a box. In that case it is possible heat (as in the two molecules) can spontaneously go from one side of the box to the other.
In that vein there is the Poincare recurrence theorem, meaning given hypothetically enough time, a system like a gas in a box goes back close to the original state, which means — the gas in thermal equilibrium can spontaneously go back to having hot and cold spot! But Poincare time is usually far beyond the expected age of the universe.
https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theorem
Agreed, they can cheat by borrowing. If we accept that racemic mixtures have a higher Gibbs energy than homochiral mixtures, the Gibbs free energy is borrowed in the present and paid back in the future when the enzyme causing the purification is removed. Of course the value of the Gibbs energy is contingent on derivations of K constant being something like 0.5 when it is usually regarded as 1.0! Some may balk at the derivation I provided (which actually was suggested by the stereo chemistry book, but not explicitly save the end result).
I searched long and hard for Aspartase! The other amino acids get their homochirality via a transfer such as L-glutamate “donating” its chirality to an alpha keto acid. So I had to search for where a non-chiral molecule got its left-handedness, and then the left-handedness can spread.
The Aspartase mechanism is a hypothetical (not true) route for spreading homochirality, and it had the correct mechanism of being able to recognize one side of a molecule (fumarate) vs. the other. Hypothetically Aspartase can create L-aspartic acids, which can then transfer its left handedness to alpha keto glutarate and make L-glutamate which can then synthesize the other amino acids via amino transferases to other alpha keto acids. That’s not the way it’s actually done, but it shows the principle anyway.
It’s not really clear from literature searches the exact path in biological systems how homochirality is spread in an existing organism, but the presumption is that there is a net Isomerization going on, and given there are lots of isomerases in biological systems, there must be a pathway somewhere deep in the weeds. I just can find it in any typical biochem books.
So I see Salvador has changed his tune. Good. Next he’ll be saying he never said otherwise.
stcordova,
Hang on, why would we accept that? What we have are two binding energies, one for one enantiomer and one for the other. If we removed all of one, replacing each molecule by an instance of the other, we would not change the binding energy of its interaction; we would reduce the number of bindings interfered with by the ‘other’ one. We’d affect the rate, possibly the yield.
The Gibbs energy of the solution, assuming the same number of molecules in each case, must be the same too.
You must allow that there must be some occasions where one’s words, leaving the brain, deserve reconsideration and clarification when reflected back, and it’s not for the reader to insist what the author’s intent was against all protestations.
stcordova,
Enzymes are highly stereospecific, and hence can only make one orientation. So this is what you get, in abundant excess. There’s not much isomerisation.
Under certain conditions they are not just mathematically related they are mathematically the same.
Can the law of large numbers ever be violated?
Fortunately we have a very long thread between DNA_Jock, keiths and Salvador to refer back to.
Because a system of homochiral amino acids is not in chemical equilibrium, the L-amino’s will spontaneously racemize toward the equilibrium condition. I hear it’s some quantum mechanical thing, I don’t know exactly. We do know equilibrium is reached faster by increasing the temperature, and it obeys the Arrhenius equation.
Given that it is not in equilibrium, and knowing where the equilibrium point is, one can calculate the Gibbs free energy, but according to the Stereochemistry book the reaction equation from the non-equilibrium condition is not described by:
L ⇔D
but rather by
L ⇔ L + D
You get a different Gibbs free energy depending on which equation you accept. The Sterochemistry book I linked to did not accept the first equation as representing the non-equilibrium initial condition. However, it didn’t specify the second equation but left it as an exercise for the reader!
So Allan, I know you’re quite busy defending your many definitions of fitness, but could you spare a moment o clear up the matter of where energy goes?
Is that what black holes are for? The energy that has to go somewhere goes into black holes? I remember learning about holes back in basic electricity and electronics class in the Navy.
Yes, I’ve been watching this interaction with much amusement.
I particularly enjoyed Sal’s noting that “Distinguishable chemicals have an associated entropy of mixing, therefore delta-G applies for exclusion of isomers”
Gee, why do they have to be distinguishable?
He also completely fails to understand the fact that, in the presence of a chiral agent, enantiomers are no longer equivalent. We’ve know this about tartaric acid since 1848…
Hey, at least he appears to have figured out how Landauer came up with his “estimate” <LOL> of the entropic contribution of a bit of information, although – with Sal – you can never be sure. He certainly doesn’t realize how small it is, compared with, say, a hydrogen bond…
So says the guy who made this legendarily stupid claim:
That wins a Darwin award. If you google “dQ/T is rarely informative” guess where the #1 hit for that is? Right here on TSZ by our very own Darwin award winner of 2016, DNA_Jock.
Have you figured out how to draw a straight line yet DNA_Jock?
I mean, I learned how to use a ruler to do that in elementary school.
And by the way, did you see Tom Meuller favorably quoting Lambert. Seems I made a convert to the Lambert view of entropy rather than the DNA_Jock school of entropy which says:
Hi Sal,
Glad to see you haven’t changed a bit.
Would you care to explain, exclusively in terms of dQ/T, how Landauer derived the 0.012 eV value. (And no, examples of people experimentally confirming Landauer don’t count – show me, in your own words and in terms of dQ/T, how Landauer originally came up with the 0.012 eV value. I have a funny feeling the concept of “information” is going to show up…)
Also, if you’re promoting Lambert, could you please explain to me, exclusively in terms of “dispersal of energy”, why the entropy of a mixture is non-zero at absolute zero?
I get bonus points if you use Hess’s Law in your answer.
Dear Tom Mueller:
I advise you don’t learn from the DNA_Jock school of thermodynamics. Because DNA_Jock says stupid stuff like this:
You did well by referencing Frank Lambert. Some here at TSZ were on an anti-Lambert campaign possibly fueled by the fact I was Lambert’s biggest promoter at TSZ.
PS
You hear that Mung and Keiths and DNA_Jock! Tom Mueller references Lambert, the guy you kept lambasting after I promoted his work here at TSZ. Why isn’t Keiths not teeing off on Tom Mueller for promoting Lambert? Where is Keiths. Did he get so badly ignored and no-one except Mung was willing to talk to him anymore?
lol
Yep. I told Sal this, and his answer was that he’s talking about the origin of life. My answer was that we don’t really know that the origin of life had to involve going from a racemic mixture to homochirality.
Sal is betting that if there was a mix, there had to be a conversion. I doubt that, separation might suffice.
Then again, we don’t know if there was ever a time that truly involved amino-acid racemic mixtures, or RNA racemic mixtures, or DNA racemic mixtures. Maybe yes, maybe not. Either way, the most that can de demonstrated under each scenario is that these things did not happen in isolation, but we know this already.
I respect Sal’s attempts at making those calculations. What I don’t find too convincing is the pretension that those calculations represent an “entropy problem” for the origin of life, or for evolution.
Sal,
This is to inform you that you miss-attributed this to me. I never wrote that.
Furthermore, while I understand Allan’s point in the first sentence, I would not have written “for free,” because I know that can easily be misinterpreted, especially because we’re talking about entropy, and because you seem to be very happy to make your calculations, and conclude that there’s a subtle entropy problem by ignoring that reactions don’t happen in abject isolation. That there’s a context.
Entropy,
It looks like it was Allan Miller who said that. My sincere apologies.
It may or may not be an entropy problem, I consider it moot because there is a probability problem. It is however an interesting academic question related to the Laundauer Principle and the Gibbs free energy. So my discussion about this wasn’t to say entropy is necessary a problem, I was simply pointing out the homochiral configuration can be considered a lower entropy state relative to a racemic configuration — all other factors being equal (like temperature). This may raise a question about whether designed systems have a slightly lower entropy as well based on the Landauer Principle and pure statistics alone. For example if we happened upon a poly peptide with the chiral configuration:
L D L D L D L D L D L D L D L D L D L D L D L D L D L D L D L D L D L D ….
It might be considered “designed” or at the very least statistically astonishing. It would be regarded in a lower entropy state according to the Landauer Principle and even the calculation from the book on Stereo Chemistry I linked to, but not according to typical considerations (such as involving specific heat or standard molar entropies as I used for the ice cube).
Linus Pauling did something about the configuration entropy of ice, but I still haven’t figured the issue out clearly for my own understanding, but it seems possibly related to these issues. I don’t know. There is some ID literature on Configurational Entropy by Walter Bradley that may make sense to Material Science engineers who work with the concept of Configurational Entropy, but it is even confusing to physicists!
Pauling’s paper:
http://pubs.acs.org/doi/abs/10.1021/ja01315a102
The question of homochirality in amino acids is at two levels, the first in the monomer or unpolymerized state, the next is in the polymerized state.
Homochirality is essential for formation of particularly of Alpha-Helicies. Thus if there is some molecular replicator that needs proteins, it is reasonable (according to a paper by NASA) that homochirality is needed.
Even hypothetically supposing one could make a replicator that could replicate the amino acid sequence independent of whether it was L or D, the protein would not be actually duplicated because the Alpha helices and other secondary structures would not be replicated.
The the ribosome in the cell circumvents this problem because the monomer supply is all L (in general).
One could invoke a sterospecific enzyme to cause an L excess of building block monomers. But then, this runs into the chicken and egg paradox because where did the sterospecific enzymes come from in the first place?
Next, in the polymerized state (a polypeptide), if there is even some moderate racemization, this is a problem, and the stereospecific enzymes or catalysts optimized to cause L excess in the monomer state won’t likely work for the polymerized state.
This is assuming the polypetides can self-assemble in the first place since it is a positive energy step involving a condensation reaction. Now, condensation can be done by having the amino acids in a pool of water and letting it dry, the solar energy can supply the energy for the condensation reaction. The reverse hydrolysis reaction may be slower, so hypothetically the polypetide can be slowly constructed this way. From what I hear, the chiral amplification experiments that get excess L also rely on wetting and drying cycles. The problem is that these require specific conditions, and even then there has to be some sequence specificity and proportional amounts among a set of polypetides and spatial attachment to get something functional — (the problem of the proverbial Frog in a blender).
Now Allan Miller rejects proteins first, and for good reason. My hypothesis is “everything first”, which would be a miracle, but at least it would work in principle if miracles happen. A miracle-free origin of life is the problem facing abiogenesis researchers.
Although I would agree with Allan the problem in exact detail is mathematically intractable, I would say one doesn’t need a very exact answer to make an educated guess at the qualitative question of how likely life will eventually arise without a statistical miracle.
NOTES:
Pictured below is an alpha helix in a protein made possible by L homochirality. I recall the first time I saw such a diagram, the professor spent about two-hours explaining the geometry and chemistry from first principles. It still makes my head spin trying to understand it.
stcordova,
I know that homochiral sequences would be in a lower entropy state than racemix mixtures. Again, what I keep saying is that this doesn’t mean that there’s an entropy problem. Life forms today build the versions of the molecules that they use.
That the built molecules are in a lower entropy level is evident, besides the obvious of being homochiral, when the molecules, if stable enough, start “inverting.” That still doesn’t make it either an entropy problem, nor a probabilistic one. The process is such that only one molecule is built, and its stability is more than enough for the time they’re in “use.”
That homochirality “plays a role” in how alpha-helices form, and how DNA gets its structure, etc, is not a problem. Why so? Precisely because if homochirality is required, then homochiral polymers will be successful, at least more than heteropolymers. Tendencies towards naturally forming polymers from homochiral molecules would be advantageous, regardless of how this is accomplished: by building homochiral monomers, by “selecting” the appropriate enantiomer from a racemic mixture, by inverting the “offending” enantiomer, etc. My point, yet again: the “all thing being equal” doesn’t justify forgetting that these reactions don’t happen unconnected. There’s a context to them, and then there’s that thing called evolution.
That homochiral molecules are at a lower entropy state than racemic mixtures doesn’t mean that the cells should produce racemic mixtures. It just means that they are at a lower entropy state. Then again, who cares? A lot is at a lower entropy state than other stuff. That doesn’t translate into an entropy problem. That doesn’t translate into a probabilistic problem. You seem to be looking too hard into a tiny detail in hopes of finding something that looks like a problem (for evolution? for nature? for us?). However, that’s no different to the usual creationist “argument” that any life form is a probabilistic problem, a clock by the beach. Meh!
What on earth do probability and statistics have to do with entropy. Come on Sal, you can do better than this. All that advanced education. Put it to use man!
If entropy is statistical does that mean it’s probabilistic? You mean we might find probability distributions involved? Just like in Shannon’s measure of information?
Revisiting the question of Linus Pauling’s configurational entropy of ice vs. the configurational entropy of amino acid chirality, I realized Pauling was describing a system in equilibrium where after the ice’s temperature is raised by the environment around it, it goes into equilibrium as the change in heat spreads inside the ice. Hence this will affect changes in specific heat of ice rather noticeably. Further, the changes are easily reversible with temperature changes…
In contrast, the chiral configuration of a homochiral mixture is NOT in equilibrium. One probably won’t see changes in things like specific heat with temperature changes as seen with the Linus Pauling ice situation. Only when the mixture is racemic will it be in equilibrium, and further the changes are NOT easily reversible. You can’t change the temperature and expect the racemic mixture to spontaneously go to the homochiral mixture.
So I think that explains the issue I had reconciling the Ice configuration vs. the homochiral configuration and the effect of adding or subtracting heat.
I predict that Salvador won’t have an answer. Doesn’t have an answer.
Sal doesn’t see your comments “by design” (he said he has you on ignore), and he doesn’t see mine by virtue of incapacity to read (or lazyness). I doubt much advance can be done. For a second there I thought I could talk to him, but now I’m not so sure.
I also suspect that he might be impervious to sarcasm. More properly, maybe he would not understand the sarcasm because he doesn’t understand the relevant concepts.
Just a hunch. He also seems to get lost in quotes and irrelevant sidetracks, which might be his way of ignoring “inconvenient” explanations. Who the hell knows.
Salvador and I go way back.
He started out by changing my posts at UD to make it appear as if I had written something that I did not actually write. Then he resorted to just deleting my posts from threads where he could delete them.
His excuse was that I was a troll, by which he meant that I disagreed with him and he had no good answer.
Some things never change.
If homochirality is required for life and it doesn’t exist, no life. No life, no evolution. That’s a problem which you say is no problem.
Just a hunch. He also seems to get lost in quotes and irrelevant sidetracks, which might be his way of ignoring “inconvenient” explanations. Who the hell knows.
I refrained from saying things because some of the stuff you said was pretty idiotic and I didn’t want to embarrass you nor was I willing to invest time on well covered ground. I didn’t want to strain our cordial relationship by pointing out some of your confusions and illogic. But maybe now I might not be so nice.
For now, I think I’ll put you on ignore too. Have nice weekend!
You did not read that carefully enough Sal, either that or you missed the main message. We’re talking about a hypothetical situation when there’s some racemic mixture. Good so far? OK, now, if homochirality is required for polymers to function, then the formation of polymers is the issue to focus on. Is it possible that polymerization produces mostly homochiral polymers? Is it possible that some catalyst might bias the polymerization towards homochiral polymers? Is it possible that the polymers are formed starting from crystals that might consist, each, of homochiral molecules? All of those situations might produce homopolymers, some “right-handed,” some “left-handed.” Evolution can proceed.
I’d find it much kinder for you to point to my mistakes. Laving me in the dark on some egregious mistake would be like letting me drive drunk. How else could we get to solve problems, or reach some conclusion, if we don’t pay attention to both, the mistakes and the good points?
It’s not kind, either, to ignore the points and respond with a load of quotes that you don’t seem to understand either, or that have nothing to do with the point of the discussion?
Anyway, if I’m in ignore, then not much to try and clarify.
Have a good week end too.
Exactly. Just in case Sal doesn’t notice…
I meant homochiral polymers …. 🙂
Entropy,
It was clear enough from the context. 🙂
stcordova,
The requirement for life is more then homochirality. It is homochirality formed with rapid reactions due to the short life of many enzymes that require the availability of these amino acids.
You seem to think that the homochirality is one more step. It isn’t. Amino-acids are directly synthesized in the homochiral configuration. There’s no mixture that needs separation afterwards.
Homochirality applies across the board in proteins, RNA and DNA. All life works with the same enantiomers. Not a coincidence, perhaps?
Entropy,
Sure they are if you assume the existence of enzymes that catalyze rapidly enough to sustain life. Assuming the existence of enzymes means the availability of enzymatically produced amino acids exist. How can one exist without the other?
Did you already understand that the enantiomers are synthesized as such?
You seemed confused about current circumstances. Are you telling me that, instead of looking at my answer to Salvador, you were mixing current circumstances with imagined closer-to-origin-of-life ones to try and imagine a “problem” with the origin-of-life circumstances? If so, then I suggest you to read my answer to Salvador before continuing, rather than add, mindlessly, a supposed problem with “speed,” when you don’t even know if Salvador’s problem is a problem at all. Then we could try and have a less convoluted conversation.