Q1#$Ans$b.$For$a$signaling$circuit$capable$of$adaptation,$plot$the$downstream$output$when$the$input$has$the$following$form$(you$may$assume$that$the$adaptation$mechanism$operates$on$the$timescale$of$several$minutes):$$$

$$$Ans$for$b:$It$can$be$shown$mathematically$that$any$perfect$adaptation$mechanism$works$the$following$way.$There$are$two$quantities$that$both$track$the$input:$(i)$a$rapidly$varying$‘signal’$component$(e.g.$receptor$activity,$shown$in$blue);$(ii)$a$slowly$varying$‘offset’$component$(e.g.$rate$of$receptor$internalization,$shown$in$red).$The$actual$output$is$a$difference$between$signal$and$offset$(black$curve).$$$If$the$output$is$operating$at$the$middle$of$its$range,$so$that$it$can$swing$both$positive$and$negative,$it$will$look$as$shown$in$the$figure.$Sometimes$the$output$is$operating$at$its$minimum$possible$level$and$cannot$swing$below.$In$that$case,$all$negative$portions$of$the$curve$will$be$cut$off$by$the$x#axis$at$zero.$$In$the$figure$we$have$assumed$that$the$signal$responds$with$a$time$constant$of$0.2$min,$while$the$offset$responds$with$a$time$constant$of$2$min.$

$

Q2#Answer:#a)#Find#the#homolog#in#a#model#organism#(specify#which)#and#study#it#by#a#genetic#approach.#Details#of#how#this#will#be#done.##Generate#a#mutant#and#see#if#it#re@capitulates# the# disease# phenotype.# Cell# specific# RNAi# knockdowns# and# over@expression#studies#based#on#the#disease#phenotypes.#Details#of#the#methods#that#will#be#used#depending#on#which#model#organism#is#chosen.##b)#Bioinformatics# to# find#smaller#domains#within# the#protein.#Specify# the#nature#of#domains#you#will#search#for#and#why.#Existing#programs#that#can#be#used#for#finding#such#domains.# #This# should#be# followed#by#a#biochemical#approach# to# test# if# those#domains# function# in# the# predicted# fashion# by# mutant# and# deletion# constructs#expressed#and#tested#in#cell#lines.###Q3!a.#In#globular#proteins,#residues#can#form#backbone@water#hydrogen#bonds#and#thus#do#not#pay#a#large#energetic#penalty#for#failing#to#satisfy#these#interactions#with#other#backbone#atoms.##In#contrast,#in#the#membrane#the#lipid#tails#do#not#provide#hydrogen#bond#donor#or#acceptors.#Additionally,#there#is#no#energetic#gain#from#burying#a#hydrophobic#core#in#the#membrane#since#the#hydrophobic#environment#negates#the#importance#of#the#hydrophobic#effect.#Secondary#structure#formation#is#an#efficient#mechanism#for#completely#satisfying#the#hydrogen#bonding#requirements#of#the#peptide#backbone.#These#hydrogen#bonds#provide#the#major#energetic#force#driving#folding#in#the#membrane.##b.#A#30#Angstrom@length#alpha#helix#will#have#3.6*30/5.4#=#20#residues.#Given#the#amino@acid#sequence#of#a#protein,#we#can#make#a#hydropathy#plot#which#highlights#hydrophobic#residues#as#we#traverse#the#length#of#the#protein.#Any#stretch#of#20#or#more#hydrophobic#amino#acids#is#a#putative#transmembrane#segment;#however,#the#length#cannot#be#much#longer#than#20#due#to#tile#(see#next#answer).##c.#Long#hydrophobic#transmembrane#segments#will#be#tilted#in#the#membrane,#whereas#short#(20#amino#acid)#segments#will#run#straight#across.##

Q4#ANS#a.#If#pollinator#density#is#low#at#high#elevations,#plants#might#self.#b.# The# niches# have# to# be# separate# in# some#way.# Temporal# differences# in# # flowering# time.#Differing# flower# morphology# to# attract# different# # pollinators.# They# depend# on# wind#pollination#etc##

Q 7There are many possible solutions. One is: Follow these instructions in order of priority, with

(i) being the highest priority. (i) If you can make three in a row, make that move and win. (ii) If the opponent could make three in a row in the next move, then block that possibility. (iii) If

you can make a move that simultaneously sets up two possible three-in-a-rows for your next move, then make that move. (iv) If your opponent could make a move (say on square A) that

simultaneously sets up two possible three-in-a-rows for his/her next move, then make your own two-in-a-row that threatens a three-in-a-row that does not include square A. (v) If your

opponent could make a move that simultaneously sets up two possible three-in-a-rows for his/her next move, then block that move by playing in that square. (vi) Play in the center. (vii)

If the opponent has played in one corner, play in the opposite corner. (viii) Play in a corner. (ix) Play on the edge.]

Q8

[Answer: All you need to remember to solve this is that the probability of two independent events both occurring is the same as the product of their individual probabilities. Here, the independent events are you carrying an umbrella (or not), and

it raining (or not). Then if the probability of you carrying an umbrella is p, and happiness counts as +1 points and unhappiness as -1 points, your net happiness can be calculated to be 0.4p-0.2. This is maximum when p=1, so you should always carry an umbrella. (Bonus for realising that choosing other numbers for happiness or

unhappiness doesn't change the answer!) Instead of doing this maximization you could also calculate the happiness of each of the four strategies and compare them.]

!

Part. A – Q -13

1. Our gut grows when we regularly increase food intake and shrink we regularly

manage to diet severely. Imagine a simplified gut with epithelial cells and

smooth muscle. Keep in mind that food is digested, nutrients taken up and sensed inside the animal. Write outa signalling mechanism that can detect levels of food intake and respond to it by increasing gut size and reducing it on starvation. Link the specific signalling pathways you choose, their ligands, receptors, output with the cell biology of secretion, detection of systemic read-

outs of nutrient levels and how this detection in turn feed back from the body to the gut to regulate its size. You don’t have to know ‘the answer’: You just need to present a well-thought out credible answer.

ANS: Let’s start at the end and work backwards. Intestinal muscles secrete Insulin (say), which act on the intestinal stem cells to make them proliferate. These muscles

secrete insulin in response to nutrient levels inside the animal. Nutrient levels are sensed by the ingestion of food, amino acids. These nutrient sensing mechanisms in adipose or hepatic tissue would typically involve the mammalian Target of Rapamycin pathway. As a consequence of nutrient sensing, adipose and hepatic tissue derived signals ( choose any!) will act on visceral smooth muscle ( choose a receptor)

to activate the expression ( choose a pathway) of insulin and its secretion to activate

an intestinal stem cell niche. Q-15

2. Stem cells can expand the size of tissues they make by switching from

asymmetric cell division (linear increase in cell number) to symmetric

(exponential) division. Write down a plausible molecular mechanism for asymmetric division where one daughter of a stem cell is a stem cell and the

other a daughter, which divides once and differentiates its two progeny. Write another plausible molecular mechanism by which a stem cell gives rise to a daughter stem cell and a ‘transit’ cell which then divides to give two more

transit cells, a process that continues for 6 rounds of symmetric transit cell division. The amplified transit cells then divide once more to differentiate. You

answer need not be based on what we have learnt from research on this question: We just need a plausible molecular model that is inspired by what we know of the cell biology of signalling, sub-cellular localization and transcriptional response.

ANS: There are two mechanisms operating: Asyymetric division and symmetric division of a stem cell. Asymmetric division of a stem cell can take place ( classically) by the asymmetric segregation of a factor (such as Numb) to one daughter cell and not the other. This daughter cell then is unable to activate the Notch pathway, divides to give two

daughter cells that differentiate. The daughter of the stem cell that does not get Numb remains a stem cell. It responds to a Notch signal by synthesizing Numb, which again is asymmetrically segregated to give rise to a stem cell and a sibling that will divide once and differentiate. Symmetric Division can take by one daughter cell getting a factor [say brain tumor (brat), but you can hypothesize any such factor] that promotes

symmetric cell division till it is diluted out. The other daughter cell does not get Brat and remains a stem cell, which will then synthesize Brat to carry on the process.