Synthetic biology and data analysis companion to "Gene regulation at a single cell level" (2005)

 Inspired by the statistical companion by Lior Pachter to the paper on "stochastic gene expression in a single cell" from 2002 by Elowitz, Levine,  Siggia and Swain, shortened to ELSS, I decided as a part of some reading with the really talented new student Tanvi, to work on a followup for the related (it seems like a follow-up) paper by Rosenfeld, Young, Alon, Swain and Elowitz (RYASE) on "Gene regulation at a single cell level" (2005). The RYASE paper uses a neat gene expression control system which is negatively regulated by anhydrous tetracycline addition, to produce a cI-YFP (that's c-one) fused to the yellow fluorescent protein, which in turn binds to a promoter pR that drives the expression of CFP (cyan fluorescent protein). The most interesting result to my mind was the dose-dependent inheritance of the copy numbers of YFP between equally sized daughter cells. The question is then framed as:

What is the dependence of the difference between protein copies in the two daughter cells [abs(N1-N2)] as a function of the total protein copy number [N1+N2]. 

 The answer found by RYASE paper was that the difference between two daughter cells that has quite a spectacular scatter, nicely to fits a [$ \SQRT{Nt}/2 $] dependence with Nt, where Nt=N1+N2. This is expected from the binomial theorem.

Interestingly enough the data is sort of all over, but the binned average of the data seems to nicely follow a  dependence of error (|n1-n2|)/2 with number of total molecules N (x-axis) as \sqrt(N)/2.  Could there have been alternative views? How about exactly symmetric segregation- well we'd see the graph linearly increase with N. Fully asymmetric (depending on N1 > N2) would give something parallel to the x-axis. 

So are all proteins expected to follow the same distribution? Does it matter? 

More on this soon.

 

1/ Cones thrown from high places in biophysics class

I also thought of titling this post "Teaching how to think about the drag equation in biophysics by demonstration", but it's more verbose and less amusing to write.

Compass required for drawing a circle, to make a well proportioned cone (screen grab from Amazon.in. Easily purchased in a local stationery shop).

Foot rule

As it is nearing the end of my teaching semester I reminisce (and procrastinate setting the question paper) about the fun I had teaching Cellular Biophysics 2 (Out of equilibrium approaches to cellular scale biophysics) at IISER Pune, I am reminded probably of a demo-experiment that actually worked quite well.

Paper cone (Image taken from https://www.cutoutandkeep.net/projects/cone-shaped-frog) based on the half-circle using the compass (above) and a simple measuring scale to mark the straight part.

Borrowing heavily from the excellent book by Sunjoy Mahajan [1], a professor at Olin College of Engineering and visiting faculty at MIT, Boston, this is a mixture of DIY and order of magnitude estimates, to hone the intuition of the class. Our day to day intuition suggests that dropping cones of different sizes will result in differing amounts of drag and weight of the cone, and hence possibly lead to a different time of arrival. Indeed in a vote I took in class (2019-Jan), we had a 1:6 split (same time:different times of arrival).

Big cone, small cone: Paper cones made using the same sizes of semi-circle with different overlaps to ensure mass was the same.

Doing the experiment in a classroom:
The first step was to get paper, a ruler (foot-rule, scale) and scissors. Indeed, the need for a this high-school equipment was part of the excitement of doing the experiment. Also, a break in normal classroom teaching is a delight- for both students and professors.

Once the semi-circles were ready, we glued their overlapping edges together, such that we had atleast a pair of cones with 2-fold differences in base-diameters (big-cone, small-cone).

Finally it was time to let it all fly- off to the bridge (literally) we went. The bridge is a part of the lecture hall complex (LHC - yes, really!) which connects the ellipsoid corridor across the short axis. From the second floor (Indian 2nd, USAmerican 3rd) at about the height of 7-10 metres, we then held our hands out and let the cones drift.

For any good experiment we needed repeats. So the same cones with little damage were allowed to fly down three times. Also considering the class lasts only 55 minutes, we really had to keep it tight.

And (not so surprisingly) our average measurements of the time of arrival at the bottom, which allowed us to estimate a mean velocity (which we consider to be terminal velocity). And these turned out to be THE SAME for both big and small cones.

In the next post, I will discuss the maths of this very exciting result. And perhaps, if time permits interpret what that could mean for biological systems - animals flying and fish moving.



References:
[1] Mahajan S.  2010 Street Fighting Mathematics OpenAccess & FREE https://mitpress.mit.edu/books/street-fighting-mathematics

Indonesian Superman

Museum Wayang the centre of Jakarta Barat is a spectacular place to witness the collections of leather (usually buffalo hide) puppets, used in traditional Wayang Théâtre. Indeed if you want to see both a shadow theatre, as well as the diversity of puppets from tbe various islands, this is the place. Indeed in that sense it's not a 'traditional' ceremony you will witness, but as a tourist to get a first impression it should suffice. What excited me most was the life sized puppet of Ghatotkach घटोत्कच whom the museum assistant referred to as Indonesian Superman! The son of the mythical Bhim भीम and rakshasi Hidimba हिडिंबा from the Mahabharata, he is endowed with a special place in Wayang. More on this in the coming months.

Transiting Ethiopia, Travelling to Zuid Afrika and Vaccines

It has been a long while since I blogged about anything, and it can be blamed perhaps on my teaching commitments, unfinished research papers and PhD students whose defence dates are up and the levels of stress are just a little more than anybody should have to deal with.

So it was with glee that I registered for a conference in Zuid Afrika (ZA) on bacterial virulence in November 2019 (BMSV, Cape Town) organized by a group of experts on Tuberculosis.

Yellow Fever Virus Particle: A rendering from RayUr.com

Little did I know what extra adminisrative burden I was bringing onto myself. However, adding to my task-overload was the fact that I needed to prepare for the journey in a manner I had not so far required - vaccination! Indeed with all the strange rumour mongering about vaccines, it was surprising to come accross some clearly detailed list of places which if one transits or travels through, to re-enter India I will compulsorily need to be vaccinated against the Yellow Fever (1).  To quote the site "Any person, Foreigner or Indian, (excluding infants below six months) arriving by air or sea without a vaccination certificate of yellow fever will be kept in quarantine isolation for a period up to 6 days if :

• He arrives in India within 6 days of departure/transit from a yellow fever endemic area.
• Has come on a ship which has started from or transited at any port in a yellow fever endemic country within 30 days of its arrival in India provided such ship has not been disinfected in accordance with the procedure laid down by WHO."

 The insistence on "He" is theirs not mine. I would have preferred (the now archiac) s/he or even "Person(s)" to be gender neutral and non-binary.

The world health organization (WHO) describes the illness as an "...an acute viral haemorrhagic disease transmitted by infected mosquitoes...." (2) and the yellow-tag name comes from the fact that affected patients show jaundice (yellow) pallor. Jaundice in turns is a symptom of excess bilirubin in the blood, an effect of an underlying condition. The origins of bilirubin are of course the famed hemoglobin. The breakdown is described by the following (schematic) reactions (3,4):

Hb ----> Globin + Fe + Haeme
Haeme -----> Biliverdin -----> Bilirubin

The location of this degradation process is in the liver, spleen and bone marrow.

Thus the kind of infections that trigger excess breakdown of RBCs and Hb are grouped under haemolytic jaundice (as opposed to hepatic jaundice caused by liver dysfuntion कवेळी ).

To once more quote WHO, "The yellow fever virus is an arbovirus of the flavivirus genus and is transmitted by mosquitoes, belonging to the Aedes and Haemogogus species." In short it means transmission by mosquitoes and viral with surprisingly (acc. to WHO) no cure available, with help to prevent dehydration and liver failure improving patient outcomes (5).

Interesting the virus is a +ve sense ssRNA virus, i.e. its genome acts like an mRNA when it enters a host cell! The capsid structure of this Flavivirus (Latin "flavi" = yellow) is similar to that of the dengue and west-nile virus. Indeed endocytosis and ER targetting appear to be the modus operandi at the level of the single cell.

 Much more remains to be done on this account, and perhaps as I expectantly wait for a jab, thoughts about potential engineering vaccines as opposed to the live, weakened virus that is currently administered (6).

So more to travelling scientists and spreading the good science, and better understanding the world around us.

References:
1) Bureau of Immigration, Govt. of India https://boi.gov.in/content/health-regulation
2) Yellow Fever, WHO https://www.who.int/news-room/fact-sheets/detail/yellow-fever
3) Hemoglobin catabolism and bilirubin http://chemistry.elmhurst.edu/vchembook/634bilirubin.html 
4) Bilirubin Metabolism http://www.meddean.luc.edu/lumen/MedEd/orfpath/bilirub.htm
5) Yellow Fever Treatment https://www.who.int/csr/disease/yellowfev/en/
6) Yellow fever vaccine https://www.cdc.gov/vaccines/hcp/vis/vis-statements/yf.html

बांस Bamboo Mast

Bamboo has many legends and sayings associated with it, especially in asian cultures. In hindi (हिंदी) in India we say "Na rehaga baans, na bajegi bansuri", that is there is no hope of hearing sweet reed melodies if the bamboo stops growing. Many chinese charachteristics of strenghth, flexibility and virtue have been attributed by philosophers and poets to bamboo 

(the taller the bamboo grows, the more it bends ~ i.e. truly great people are humble).
From the perspective of the premise of this blog of patterns in nature, Bamboo mast (मास्ट) flowering or the mass synchronized flowering of these plants at the same time, with a long gap (30-120 years) counts with the big mysteries of "snychronization", with an added evolutionary and ecological context. The current ideas suggest a this mass flowering and seeding results in overwhelming the seed eaters by synchronization, giving the plants a survival chance exceeding the normal. Add on to that, bamboos out of sync do not do as well. And in such a context, changes in flowering time can only be integer multiples of the existing period. These integer values can also be reduced to primes by integer factorization (the same thing that lies at the heart of RSA encryption). And add to it, there is the excitement of a plant-biological alarm clock, ticking away. 

Further reading:
1) Synchronization http://www.scholarpedia.org/article/Synchronization
2) Keeley, JE; Keeley, J.E.; W.J. Bond (1999). "Mast flowering and semelparity in bamboos: The bamboo fire cycle hypothesis". American Naturalist. 154 (3): 383–391 https://www.ncbi.nlm.nih.gov/pubmed/10506551
3) Janzen, DH. (1976). "Why Bamboos Wait so Long to Flower". Annual Review of Ecology and Systematics. 7: 347–391. http://www.annualreviews.org/doi/10.1146/annurev.es.07.110176.002023