The Universe Marches to Its Own Drummer

Blink your eyes. Are you done yet? Okay, that took about one-third of a second. For us humans, that seems like a very short time, occurring in "the blink of an eye." But by the time the early Universe was about an eye-blink old, a lot of the interesting stuff had already happened. For example, by about a millionth of a second, the sub-microscopic particles making up all ordinary matter- electrons, protons and neutrons- had been produced. But it would be a very long time- 380,000 years in fact- before the Universe contained any stable atoms. Only then would the blazingly hot Universe have cooled down enough to let those tiny building blocks stick together long enough to form atoms. And perhaps prophetically, most of those early atoms were hydrogen, the most abundant atom in our bodies.

But we need a far less anthropomorphic view of Time to think about the seminal events in the early Universe. During the first fraction of a second after its birth, the Universe was much more tumultuous and rapidly changing than at any later time.

First came the Big Bang that started it all about 13.7 billion years ago. This was of course really "big", since it was the beginning of our Universe, when space, mass-energy, and even time itself somehow appeared, apparently out of nothing. But scientists now believe that, for a time extremely shorter than a millionth of a second, the nascent Universe expanded in a rather leisurely fashion- not at all like a Big Bang. Then, according to a 1979 theory of Alan Guth, the true "Bang" began an exceedingly short time later. Guth termed his theory Inflation, a mild term indeed for the posited tremendous exponentially increasing explosion in the size of the Universe.

This proposed Inflation "explosion", occurring very early in the life of the Universe, could answer a number of otherwise very puzzling questions about our present-day Universe, 13.7 billion years later:  1. Why is the Universe (on a very large scale) the same, and in fact so smooth, in all directions?  2. Why is the Universe so "flat"? Yes, it seems strange to describe the three-dimensional Universe using a word conventionally applied to two-dimensional objects like a perfect plain. But for the Universe, "flat" simply means that the angles in any gigantic triangle add up to 180 degrees,  just like those triangles featured in our high school trigonometry classes.  3. Any magnet contains both a North and South magnetic pole, and so do the pieces we get by cutting the magnet in half again and again. But any electrical charge has only a single "pole": it's  either positive or negative. So why hasn't anyone ever found an analogous magnet (a "magnetic monopole"),  that also has only a single pole? Inflation provides the answer to that question too.

Because Inflation yields answers to all three of these profound questions about today's Universe, it is a widely accepted theory. But there are two fundamental unanswered questions about this proposed enormous explosion:

1.  We don't know know why or when Inflation might have either started or stopped. We do know that the beginning and end of Inflation (at least in our local part of the Universe) must have occurred at times unimaginably soon after the birth of the Universe, something like a trillionth of a trillionth of a trillionth second later. And during this extremely short time, the Universe doubled in size at least 90 times, growing from inconceivably small to the size of something we can actually imagine, for example a golf ball or a basketball. During Inflation, parts of the Universe expanded far faster than the speed of light- surely the greatest explosion that ever has or ever will occur. A "big bang" indeed! [For anyone concerned about a possible contradiction here with Einstein's Special Theory of Relativity: although Einstein's theory states that no information or (real) matter can travel within the Universe faster than light, there is no limit on how fast the Universe itself can expand.] When Inflation ended (if indeed it ever started), the Universe returned to a more laid-back expansion rate. 
    But curiously, this rate is being accelerated by a very mysterious form of energy discovered in the 1990s, Dark Energy . The expansion caused by Dark Energy is fairly mild today, but its rate increases as the Universe itself expands. So scientists hypothesize that, many billions of years from now, the effect of Dark Energy will become strong enough to cause a Big Rip, ultimately tearing apart the Universe and even its constituent atoms. The Universe would then turn into a vast thin dark and cold gruel, with the sad probable fate of forever becoming only ever bigger, darker, and colder.

2.  Unfortunately, we don't yet have any direct experimental evidence that Inflation ever happened. A part of the problem is that we can't detect the light of the Universe at any age earlier than 380,000 years after its birth. This is because, as noted above, only then could stable atoms form from sub-atomic particles. So light particles could finally cease incessantly bumping off of the charged sub-atomic particles; and so voyage freely through space for 13.7 billion years, finally to reach our telescopes today. What we can see today of the 380,000 year-old Universe is termed the Cosmic Microwave Background (CMB), whose discovery in 1964 provided convincing evidence for the Big Bang theory. It does seem poignant that we will very probably never pierce this barrier that prevents any glimpse of our Universe during its frenzied early infancy. 

Quite recently, there was optimism that direct evidence for Inflation had finally been obtained. Early in 2014, observations by astronomers using the BICEP2 telescope at the South Pole, of particular light patterns in the CMB, indicated that these patterns arose from the effects of Inflation. But data produced by the Planck spacecraft later that year showed that the BICEP2 data could have arisen entirely from effects of dust in our own galaxy, instead of from Inflation.

So stay tuned. It seems likely that current intense and ever more precise investigations of the CMB will determine whether Inflation- potentially able to explain profoundly puzzling aspects of our current present Universe- ever actually occurred.

(sciencequandaries.blogspot.com)

Infinities Galore

What do you see when you picture Infinity? Perhaps you imagine a very, very large number. If so, please don't. Infinity is not a number at all, but a concept. Infinity is actually a seeming oxymoron, an unreachable limit of a never-ending series of numbers. A simple example is a list of all the positive integers: 1,2,3....., where the dots indicate that this list never stops. And, to further complicate matters, there is not just one infinity, but instead multiple ones, each larger than the one before.

A warning is in order here: The concept of Infinity is initially quite mysterious and unintuitive, because in the mathematics of our daily life we deal with actual numbers such as the cost, weight, and speed of a new cell phone. Thus thinking about the enigma of Infinity might cause headaches, hallucinations, or other adverse reactions. So proceed at your own risk!

An often-used example, The Infinite Hotel, illustrates the properties of the smallest infinity. Here is my version: 

Picture a hypothetical hotel with an infinite number of rooms, named imaginately Room 1, Room 2, ... This is the hotel's high season, and so the hotel is completely full with, of course, an infinite number of guests. Then, very late one night, a young couple shows up. These two are clearly in love (or at least lust), and just as clearly in desperate need of a private place with a bed, and so ask the hotel manager for a room. The aged night manager patiently explains to the young lovers that the hotel is full. But the couple entreats him to use all of his powers to try to find them a room. Well, who among us could not open his/her heart (and hotel) to such a plea? The old manager, remembering well the urgency of youthful desires, is deeply moved by the duo's plight. And he also knows that he could actually provide the lovers a room in the hotel. But doing that would require a lot (actually an infinite amount) of distasteful interactions with an infinite number of sleepy, irate guests. So with a heavy sigh (but a light heart!), the manager moves the guests in Room 1 to Room 2, those in Room 2 to Room 3, and so on right up the line. The lovers of course then get to move into Room 1. And since the hotel is infinite, none of the hotel's current guests will have to sleep out in the cold.

Clearly there's a problem here, since no real-world hotel could work like this. Though the room list of this hypothetical hotel will eventually reach any whole number we can think of, the list will never reach the non-number Infinity. And because Infinity is not a number, it is meaningless to use this concept in standard numerical equations; e.g., Infinity - Infinity = ?  

But surprisingly, there are many different kinds of infinity. The brilliant mathematician Georg Cantor showed in 1878 that infinities come in different sizes. Cantor gave the name Aleph-Null to the smallest Infinity: the set of all "rational numbers", which include the whole numbers in the hotel example above, plus all fractions like 3/4, 1/137, 20/21 that can be written as a ratio of two integers. Cantor showed that it is possible to count all of the Aleph-Null numbers, including the fractions, in a diagonal manner that would eventually arrive at any specified number. So he termed Aleph-Null the countable ("denumerable") Infinity. It turns out that even if you multiply Aleph-Null by itself, the result s still Aleph-Null. So what manner of infinity could possibly be larger than Aleph-Null?

Cantor showed that there is indeed an infinity larger than Aleph-Null, termed Aleph-One, that contains all of the "real" numbers. The real numbers include all the Aleph-Null rational numbers. But these real numbers 
additionally contain all the "irrational" numbers (like the square root of 2 and pi), that can't be expressed as a simple ratio of integers. These irrational numbers  can instead be represented only by a never-ending series of digits. Cantor demonstrated that Aleph-One is a non-countable infinity, since between any two rational numbers lie infinitely many irrational numbers. 
So Aleph-One is a larger infinity than Aleph-Null. Cantor's proofs clearly showed that Infinity could no longer be viewed as a single concept. In fact, Cantor showed that there are infinitely many infinities!

Could there be any infinities lurking between Aleph-Null and Aleph-One? Cantor believed the answer is no (and
long attempted to prove this), a conjecture now termed the "continuum hypothesis". It is not known whether Cantor was correct. Even worse, this question is an undecidable problem, of the type shown in 1931 by Kurt Godel's incompleteness theorems to plague the basis of arithmetic. So Cantor's conjecture can't be either proven or disproven within any standard (e.g., ZFC) arithmetic system. Sadly, we will thus never know for sure whether there is a long-lost middle sibling lying between the two smallest known infinities. 

So not only is Infinity a concept or limit rather than a number, there is actually an infinite number of infinities, each larger than the one before. When it comes to infinities, size does indeed matter.

(sciencequandaries.blogspot.com)

How Eukarkyotic Cells Should Work- But Apparently Don't

[Note: The essay below was originally published in 2006 on the LabLit.com website, with quite helpful editing by Jennifer Rohn, editor of this "webzine" website. I wrote the essay mainly to present to fellow biologists a hypothesis about information flow in the nucleated ("eukaryotic") cells of humans and other multi-cellular organisms. The style is informal, and I sought to explain scientific concepts and jargon in plain English. However, the essay may still be a difficult read for non-biologists.  -CB]

Parallel cell universe

How eukaryotic cells should work - but apparently don’t

Carter Bancroft 19 November 2006

I have been a biologist for many years, but my early college and graduate school training was in physics. One of the hardest parts of my transition from physics to the life sciences was the realization that it is not possible to deduce everything in biology from first principles. Instead evolution involves a quite random series of changes in the genome of an organism, followed by selection of the phenotypic (apparent) changes that work best.

It took me some time to recover from the implication that one can’t use theory to predict how living organisms work. And maybe, in my musing about biological systems, I am still a recovering physicist. So I can’t help thinking that eukaryotic cells, in their own transition from primordial soup to now, somehow missed an elegant solution to solving a biochemical problem.

A process central to the functioning of any type of cell is information flow: the cell’s use of the information in DNA to produce its macromolecular products such as proteins and other building blocks. There are three well-known examples of this information flow. First, we have replication, where the DNA sequences of our chromosomes are employed for self-copying (in other words, making more DNA). Then there is transcription, in which the DNA sequence of a protein-coding gene is used as a template to produce messenger RNA (mRNA). And finally, there’s translation, when the mRNA is in turn is used to direct the amino acid sequence of the final protein product.

In both prokaryotic cells (such as bacteria) and eukaryotic cells (such as our own), major steps in the types of information flow described above are transmitted via highly specific hybridization (sticking) between a nucleic acid template, and either a nucleic acid sequence or a nucleotide building block. In either cell type, specific hybridization permits DNA to act as a template for both its own replication and for production of a complementary mRNA, while synthesis of proteins is directed by hybridization of specific transfer RNAs (tRNAs) to specific sequences in the mRNA.

So far so good. However, in eukaryotic cells, the flow of information from the chromosomal DNA to a protein product involves an extra step. The initial product of gene transcription is not the final mRNA, as occurs in bacteria. Instead, our cells produce a larger pre-mRNA made up of information stretches separated by junk sequences, rather like the dashed yellow line on a highway. The informational stretches (the yellow paint, known as exons) are bits of genes, periodically interrupted by filler DNA (the asphalt in between, known as introns) which don’t code for anything. In eukaryotes, production of the final mRNA thus requires further processing of this long pre-mRNA: by processing, I mean the removal of the filler introns followed by the splicing together of the informational exon sequences.

This intron removal step is amazingly accurate, even for genes that encode a pre-mRNA containing tens or even hundreds of introns. This requisite conversion of pre-mRNA to processed mRNA is clearly an essential component of information flow in eukaryotic cells, involving as it does the selection of a specific subset (exon sequences) of the total sequence information in the pre-mRNA molecule for inclusion in the final mRNA product. It seems unnecessarily complicated, but the process probably evolved so that cells could be flexible in the proteins they make, as alternative splicing of different exons can make different modular proteins from the same initial DNA sequences – and that gives a cell flexibility in responding to its environment. Okay, so if I, the recovering physicist, were using first principles to design a eukaryotic cell, how would I ensure the precise specificity of the removal of the introns from a pre-mRNA molecule to yield the final mRNA product? Clearly (to me, anyway), I would employ the great specificity provided by precise hybridization of complementary nucleic acids, just as replication and transcription do. This would involve using a cellular nucleic acid molecule, precisely complementary to the mRNA, as a template that would guide the specific selection of the exons in the pre-mRNA for inclusion in the final mRNA product. This additional RNA processing step in the synthesis of proteins by eukaryotes would thus take advantage of the same powerful and elegant principle of specific hybridization employed at the other stages of cellular information flow.

But eukaryotic cells apparently employ a rather less elegant biochemical route to process their pre-mRNA to mRNA. This processing, both intron excision and exon splicing, involves the action of a monstrously large multi-component cellular structure called a "spliceosome," bristling with an array of proteins and RNAs. The spliceosome seems to require recognition of common and thus fairly general “consensus” sequences at the ends of introns in pre-mRNAs to correctly identify intron-exon splice junctions.

However, it was recognized some time ago that, at least in the cells of organisms that have a backbone, the limited information in these consensus sequences is not sufficient to specifically identify intron-exon splice junctions amid the sea of DNA in all the chromosomes. As far as I know, this central informational problem in pre-mRNA splicing specificity has not been solved – how are all these needles found in the haystack? And I also don’t think that there have been any previous suggestions, like mine, that precise spliceosome-mediated processing of a specific pre-mRNA might involve a nucleic acid template complementary to the final mRNA product.

But my proposed scheme would solve the splicing specificity problem so neatly! Picture this as yet unknown perpetrator, which I’ve dubbed “cNA” – a nucleic acid (made of either DNA or RNA) which is complementary to a processed mRNA, in other words the mRNA that has had all its introns removed and exons stitched up. When this cNA hybridizes specifically to the unprocessed pre-mRNA, the resulting structure would be a partially double-stranded molecule, in which the pre-mRNA exon sequences are hybridized to the cNA, zipped up like a zipper, while the pre-mRNA introns would form single-stranded loops bulging off of the zipper. To correctly form the final mRNA product, the eukaryotic cell would then just have to employ a single-strand-specific RNA cutter (RNAse) to clip away all the intron bulges, then an RNA stitcher (ligase) to sew together all the exons.

So, what are the problems with my model, and how might I counter them? Here are some of the problems – I am pretty confident that I have not yet thought of them all.

1. There is no evidence whatsoever to support the existence of my proposed class of “cNA" molecules. However, I would point out that we are in an exciting era of discovery, and new classes of RNAs with novel cellular roles are being discovered all the time. In fact, the 2006 Nobel Prize in Physiology or Medicine was recently awarded to Fire and Mello for their characterization in 1998 of RNA interference (“RNAi”) via a novel class of small RNA molecules termed microRNAs. So my proposed “cNA" molecules might also represent a novel class of complementary RNAs that just haven’t been discovered yet. So get to work, all you graduate students!

2. That specific single-stranded nuclear RNAase cutter I mentioned, needed to chew up the spliced-out intron bulges, would have to be fastidious enough to leave intact all other single-stranded RNA, such as the final mRNA itself. And a related biochemical problem: following the splicing out and ligation step, the mature mRNA would still be (perfectly) hybridized to the cNA template. How would the mRNA be released from this hybrid structure, permitting it to direct specific protein synthesis? Who would unzip it? I don’t have a ready solution for either of these problems. There is yet another related problem: part of the RNAi mechanism I mentioned above involves a “Dicer” enzyme that cleaves double-stranded RNA. So, if my proposed cNA is a cRNA, Dicer could be a distinct threat – one could imagine that it would be hard to keep this protein from cutting up the double-stranded regions of the pre-mRNA:cRNA complex, because this is exactly the snack that Dicer favors. I believe the answer to this problem is that Dicer is located in the cytoplasm, while my proposed cNA would be in the nucleus – these two compartments are safely separated most of the time.

3. My scheme would require that a eukaryotic cell contain a specific cNA for each mature mRNA produced by the cell – that’s a lot of extra stuff to make, and the cell is very busy at the best of times. This does seem at first like a strong objection. But it seems likely that my proposed cNAs would in fact be cRNAs (complementary RNA). And since these cRNAs would be complementary to mRNA, they would of course be anti-sense RNAs. They might thus represent a subset of the products of the widespread antisense transcription of the human genome that we already know about – we still don’t know what a lot of these antisense RNAs actually do.

4. One might also ask how this whole process could have arisen during evolution. That is, if a template were needed for production of each type of mRNA in a eukaryotic cell, how would the first mature mRNAs ever have been made? I don’t have a good solution to this “chicken and egg” problem.

Finally, let us suppose a fairly likely proposition: that eukaryotic cells actually don’t employ the model I have described here. But if my model represents such an elegant mechanism for a eukaryotic cell to guide the flow of information through the pre-mRNA processing step, why didn’t this type of cells develop it during the evolution of multi-cellular organisms? It is of course difficult (perhaps even dangerous) to try to answer questions about why evolution has taken a specific path since, as noted at the beginning of this article, temporal genomic changes (mutations, etc.) are blind and random, and it is only environmental selection among the phenotypic results of these changes that is at all guided.

But the best answer I presently have for this question was suggested by Jennifer Rohn, the editor of this magazine. Simply put, eukaryotic cells may have just plain missed the boat. Cellular information flow based on specific hybridization originally developed in non-nucleated single cell organisms such as bacteria. But since the transcripts of these primitive organisms lack introns, the organisms had no need for a mechanism to process pre-mRNAs to mRNAs via splicing out of introns. So at the time eukaryotic cells evolved from prokaryotes, the latter might have lacked key specialized biochemical mechanisms required for my proposed scheme. Instead, eukaryotic cells apparently had to go another route, and develop a complex, less elegant spliceosome-based mechanism for this step in specific information flow.

Ah, well, as the poet e.e. cummings said: “listen: there's a hell of a good universe next door; let's go”. Maybe over there eukaryotes (if there are any!) have managed to go the more elegant route, and employ the beautiful theme of information flow via specific nucleic acid hybridization for all of the steps in the transmission of information from the genome to protein synthesis.

[Reprinted by permission from www.lablit.com/article/174]

(sciencequandaries.blogspot.com)