on 20-Jan-2017 (Fri)

nucleosides in DNA and RNA have the base attached cova- lently to the sugar by a single bond from the C1ʹ atom of the sugar to the N1 or N9 atom of the pyrimidine or purine base

Th e glycosidic bond is a sin- gle bond, and so rotations about it are possible.

Th e conformation with the lowest energy, and hence the one most frequently observed, places the sugar H1ʹ atom and the base C6 or C8 atoms (for pyrimidines and purines, respectively) in a trans conformation about the glycosidic bond

Although the anti conformation is lower in energy and occurs more frequently, there are situations that can enforce adoption of the syn conformation. For exam- ple, in some structures there is much better stacking of the bases in the syn con- formation, as seen in a form of DNA known as Z-DNA (see Section 2.12) and in some RNA loop structures. Chemical modifi cations of bases may also aff ect the relative energies of the anti and syn conformations

Another important conformational parameter for DNA and RNA is known as the sugar pucker, which refers to the diff erent out-of-plane distortions in the deox- yribose or ribose rings of nucleosides

When the out-of-plane atom is located on the same side of the plane as C5ʹ, the conformation is referred to as endo (“inside”). When it is located on the side opposite C5ʹ, the conformation is referred to as exo (“outside”)

pucker in which the C2ʹ atom is out of the plane and is on the same side of the plane as C5ʹ, is referred to as C2ʹ endo, whereas a sugar pucker in which C2ʹ is on the side opposite C5ʹ is called C2ʹ exo. Likewise, a C3ʹ endo sugar pucker has C3ʹ out of the plane, but on the same side as C5ʹ, whereas a C3ʹ exo sugar has C3ʹ on the side opposite C5

In nucleic acids, endo sugar puckers are more common than exo. In DNA, the sugar pucker can be either C2 ʹ endo (in B-form DNA) or C3ʹ endo (in A-form DNA). In RNA, however, the C2ʹ endo sugar pucker cannot be adopted because of steric hindrance between the OH group on C2 ʹ and the phosphate group on C3ʹ

RNA cannot adopt the standard Watson-Crick double- helical structure because of constraints on its sugar pucker

In the standard Watson-Crick model of DNA, all of the sugar groups have the C2ʹ endo conformation. Th is results in close contact between one of the oxygen atoms of the 3ʹ phosphate group and the hydrogen atom at the 2ʹ position of the ribose ring in DNA (Figure 2.8). Th e distance between the phos- phate oxygen and the hydrogen atom is 1.9 Å. If the 2ʹ hydrogen were replaced by a hydroxyl group, as in the ribose ring of RNA, the two oxygen atoms would repel each other strongly. Instead, in RNA, the sugar adopts a C3ʹ endo conformation (Figure 2.9), which causes a change in phosphate separation and a general modi- fi cation of the double-helical structure

Th e structure of double-helical DNA, as originally described by Watson and Crick on the basis of Franklin and Wilkinsʹ x-ray diff raction data, is known as B-form DNA or B-DNA

h e base pairs, for example, are perpendicular to the axis of the helix. Each base pair is centered on the helix axis, so that when viewed from above, the base pairs all cross each other, in projection, at the central axis

Th e complementary chains are parallel, but run in opposite directions, and together they twist into a right-handed double helix. Th e helix forms two grooves of unequal size (Figure 2.10). Th e wider and more accessible major groove (Figure 2.11) allows regulatory proteins or other molecules to gain access to nucleotide functional groups on the edges of the groove. Th e narrower, less acces- sible minor groove (Figure 2.12) allows much more limited access to the func- tional groups lying within the groove.

Th e B-form helix rises ~34 Å per helical turn and there are 10–11 base pairs per turn, so the rise per base pair is ~3.1–3.4 Å.

Th ere is, in addition, a fundamentally dif- ferent way of reading information stored in DNA that neither opens the helix nor copies the sequence, but instead reads the base sequence from the “outside” (via the grooves), leaving the helix largely intact. Th is process of reading the surface signposts of the base pairs is particularly important in the mechanisms by which DNA replication and transcription are controlled

How do these proteins, known as transcription factors, recognize their target sites on DNA? Th ey do so by interacting with the edges of the base pairs in double-helical DNA, which are exposed within the major and minor grooves. Th ere are four potential types of interactions with complementary base pairs, illustrated in Figure 2.13. Th ese involve, on the DNA, hydrogen-bond donors (for example, the amino group of adenine in Figure 2.13C and D), hydrogen-bond acceptors (for example, the N7 nitrogen atom of guanine in Figure 2.13A and B), hydrophobic groups (for exam- ple, the methyl group of thymine in Figure 2.13C and D), and nonpolar hydrogen atoms (for example, the ring proton of cytosine in Figure 2.13A and B).

Th e patterns of recognition elements in the major groove are unique for each of the four base pairs (G-C, C-G, A-T, and T-A). In the minor groove, however, the pattern for G-C is indistinguishable from that for C-G, and the pattern for A-T is the same as that for T-A. Th us, the major groove of DNA allows each of the four kinds of base pairs to be distinguished from each other, whereas the interactions in the minor groove do not.

ecall from Section 2.7 that RNA cannot readily adopt the C2ʹ endo sugar pucker characteristic of B-DNA. However, RNA does form a double-helical structure known as the A-form helix, in which the sugar pucker is C3ʹ endo.

DNA can also adopt the A-form helical structure (Figure 2.15), but it is usually only favored when limited water is available to hydrate the DNA. When DNA molecules that are in the B-form are allowed to dry out slowly, they switch spontaneously to A-DNA. Th e A-form helix is also adopted by RNA-DNA hybrids

A-form DNA or RNA is similar to B-DNA in several aspects. Th e two polynucle- otide strands are antiparallel, and form a right-handed spiral with the phosphate groups on the outside and the bases on the inside. Th e precise number of base pairs per turn depends on whether the double helix is DNA-DNA, DNA-RNA, or RNA-RNA, but it is generally close to the ~10 base pairs per turn of B-DNA

One important diff erence between B-form DNA and A-form DNA or RNA is the position of the base pairs with respect to the helix axis. In B-DNA, they are all parallel to each other and perpendicular to the axis of the helix. In A-form heli- ces, however, the base pairs are tilted away from perpendicular and are moved away from the center of the helix

the major groove in the A-form is deeper and narrower than it is in B-form DNA, while the minor groove is wider and shallower (Figure 2.18 and Figure 2.19). Th e narrowing and deepening of the major groove in A-form helices means that it is more diffi cult for proteins to read out the sequence-specifi c information at the edges of the bases in A-form helices (that is, α helices cannot readily enter the narrower major groove of the A-form helix).

the double-helical structure of RNA impedes access to the major groove, so access to sequence-specifi c information in RNA is usually through its nonpaired regions

Z-form DNA or Z-DNA, discov- ered by Alexander Rich.

Unlike the A- and B-forms, Z-DNA is a left-handed helix ( Figure 2.20). Th e Z-form is adopted preferentially by segments of DNA that have strictly alternating C and G nucleotides.

Charisma in a Crisis CHARISMA IS PARTICULARLY effective during times of uncertainty, ambiguity, or crisis. “Leaders perceived as charismatic are rated higher when times are tough and anxiety is high,” Omar Sultan Haque of Harvard’s department of psychology told me. It’s easier to be perceived as charismatic during a crisis because people facing an emergency are more readily affected by a leader’s magnetism; 1 they become “charisma hungry.” Whether it was Churchill’s ability to rouse England’s spirits and inspire her people to stand while the rest of Europe fell, Napoleon taking France by storm as it was reeling from the French Revolution, or Gandhi voicing a clear path during India’s identity crisis, people who respond to crisis with bold, decisive actions will be perceived as charismatic. If you find yourself in a crisis, it’s actually an opportunity to gain charisma—if you play your cards right. This chapter will show you how. First, retain at least a certain measure of equanimity. Most charismatic leaders are known for their ability to remain (or appear) calm even in the midst of turbulent circumstances.

To keep cool, use all the internal tools—this is where they really shine. I particularly recommend the following techniques: Check your physiology often, both for your own sake (it affects your psychology) and for that of others (it will be “caught” by them and will spread). Skillfully handle internal negativity: destigmatize, dedramatize, and neutralize the negative perceptions that may be crowding your mind. Rewrite reality to whatever degree is helpful. To get out of a pessimistic state, find a few different ways of viewing the situation positively. Use visualizations to keep yourself in the right state. For instance, a responsibility transfer could be useful for reducing anxiety.

Second, express high expectations. Sometimes, simply assigning to people the labels you want them to live up to is enough.

Making someone feel validated and heard is the carpool lane to deeper friendships, especially when you combine it with humor.

Conversation tactics are like the background music in a television scene. When they’re there, you don’t notice that everything is flowing smoothly. But when they’re gone, you notice (sometimes immediately)

Compliments are meant to make people feel better about themselves, which ultimately builds comfort and rapport.

The response was probably one of the following:

- False modesty – Oh, my muscles? I just started going to the gym and apparently it’s working!

- Awkward stuttering – Um… you mean my biceps? Thanks… I guess… Um…

- Flat-out denial – What are you talking about? I’m fat, ugly and out of shape. You’re blind.

- Evocation of a deep insecurity – I’m fit? I don’t know, I used to be the fat kid and I never really see myself as attractive or deserving of anyone…

- Direct gratitude – Hey, thanks! Now how about the weather? …


Each with its varying negative implications. Only the last example doesn’t derail a conversation and make both parties feel weird about being positive.

After analyzing more than three dozen studies of charismatic leadership, Wharton School professor Robert House concluded that “expressing high performance expectations” of people while “communicating a high degree of confidence” in their ability to meet those expectations was the hallmark of charismatic leadership. Think of the people you want your charisma to impact. What standard would you like them to live up to or exceed? Express this expectation as if you have full confidence that they can live up to it. Better yet, act like you assume they already are meeting these standards.

Third, articulate a vision. A charismatic vision is what will give your charisma staying power when the crisis is over.

To be charismatic, your vision must vividly illustrate the difference between the way things are now and the way they could be.

Once you have expressed your vision, be bold and decisive.

You’re going to have to compensate for your charisma in order to limit the jealousy and resentment others may feel. You have three choices: you can refuse the glory, reflect the glory, or transfer the glory.

Refusing the glory means trying to self-efface—to minimize the praise you’re getting.

You can try to bring yourself back down through self-deprecation, downplaying compliments and praise. But we’ve seen how this can backfire, as you’re essentially contradicting your admirers and making them feel wrong.

Reflecting the glory means highlighting others’ contributions. This works well, and has the additional bonus of making you look modest. Something as simple as “Thanks! We were really lucky to have Susan checking the financials and Bill doing his graphic magic.” But sometimes, no matter how much you reflect, some people will still become envious or resentful of your magnetism and your success. You may need to go a step further, which is to transfer the glory

Giving people a sense of ownership for your success is a great way to prevent resentment and engender good feelings, such as pride and loyalty, instead. This technique is, in fact, known as a Clinton classic.

Justification. Create an excuse for contacting the person

Appreciation. Thank the person for what they’ve done for you. You can thank someone for taking time to meet you, whether in person or by phone, especially if you spoke with them for the first time or for a long time. You can also acknowledge good advice or interesting information someone gave you. Lay it all out. Demonstrate exactly how the person helped you. Acknowledge their effort: “I know you didn’t have to do…” or “I know you went out of your way to do…” Impact. Let them know the positive impact they’ve had on you. What did they do or say or what example did they set that changed you for the better? What do you do or say differently because of what they did or said or because of the example they set for you? How is your life or your behavior different? Tell them the difference it made to you personally; make it dramatic. People love to feel important. Responsibility. The Justification-Appreciation-Laying-out-the-Impact sequence creates a feeling of Responsibility (JALIR). It gives people a feeling of vested interest in your success. Give them as much credit as you can. Make them feel that they own your success and they will feel driven to help you continue to succeed

It’s not easy, however, to slow people down when they’re in the middle of this kind of experience without leaving them feeling hurt and rejected. Here are a few “soft landing” approaches to try: 1. Pay attention. When they start sharing, ask yourself: Will they regret having said this tomorrow? 2. As soon as you hear them start to say something you think they may regret, interject a “me, too” story. This is the one case where interruption is warranted. Ideally, this would be something you’ve personally experienced, second best would be something that someone close to you has experienced, and third best would be something you’ve heard about. The “me, too” interjection accomplishes three things: First, this forces them to pause, interrupts their flow, and gives them a chance to slow down the stream of personal revelations. Second, they get to hear something similar to what they’ve just shared told by someone else, and with this switching of roles, a chance to hear how revelatory their own sharing was. They can then decide whether they feel comfortable continuing on that path. Last, this will help them when they come off the high. If their ego recoils in shame over having shared too much, they can cling to the fact that the person they shared so much with revealed something similar. 3. If it’s too late and they’ve already gone too far, show them that you are placing their revelations in the whole-scope context of all you know about them—that whatever they are revealing is just one piece of a much bigger picture that contains many elements they can be proud of. Say something like, “Wow, I never would have guessed you had such a strong impostor syndrome, too, considering all your accomplishments.” 4. You can also aim to make them feel admired for having shared and revealed so much. Remember, what you’re trying to counteract is shame, and few things work better for this than admiration. For example: “You’re showing some serious courage to be delving so deep. That’s impressive.”

Showing Vulnerability Think of the next three or four conversations you’re going to have. Pick one or two that have low stakes. Now find a small vulnerability you could share. This should not be something major. Any minor fear, hesitation, concern, or regret will do. You might share something you’re worried about, something you think you did wrong, or something you wish you could have done better. Before the conversation, do a compassion visualization and a responsibility transfer for the outcome of this exercise. This gets your body language right and prevents anxiety from overwhelming you, though you should expect discomfort—that’s what vulnerability is all about. During the conversation, here are a few good ways to ease into the sharing: ♦ “You know, I have to tell you…” or “I have to admit…” are good preambles. ♦ Prepare the terrain by saying “I’m feeling a bit nervous about saying this, but…” ♦ You can also ask them to keep this conversation confidential. Not only will this make you feel safer, it will make people treasure the moment more. People love secrets

Set a timer for one minute. Close your eyes and try to focus on one of three things: 1. Sounds: Scan your environment for sound. Imagine your ears are satellite dishes, passively registering sounds. 2. Your breath: Focus on your breath and the sensations it creates in your nostrils or stomach as it goes in and out. 3. Your toes: Focus your attention on the sensations in your toes

Whenever you feel your brain rehashing possible outcomes to a situation, try a transfer of responsibility to alleviate the anxiety. 1. Sit comfortably or lie down, relax, and close your eyes. 2. Take two or three deep breaths. As you inhale, imagine drawing clean air toward the top of your head. As you exhale, let it whoosh out, washing all your worries away. 3. Imagine lifting the weight of everything you’re concerned about off your shoulders and placing it in the hands of whichever benevolent entity you’d like to put in charge. Now that everything is taken care of, you can sit back, relax, and enjoy whatever good you can find along the way

The next time an uncomfortable emotion is hindering you, try this step-by-step guide to destigmatizing: 1. Remind yourself that this is normal and that we all experience it from time to time. 2. Think of others who have gone through this, especially people you admire. 3. Remember that right now, in this very moment, many others are going through this very same experience.

The guidelines below will help you broadcast power through your voice. 1. Speak slowly. Visualize the contrast between a nervous, squeaky-voiced teenager speaking at high speed and the slow, emphatic tone of a judge delivering a verdict. 2. Pause. People who broadcast confidence often pause while speaking. They will pause for a second or two between sentences or even in the middle of a sentence. This conveys the feeling that they’re so confident in their power, they trust that people won’t interrupt. 3. Drop intonation. You know how a voice rises at the end of a question? Just reread the last sentence and hear your voice go up at the end. Now imagine an assertion: a judge saying “This case is closed.” Feel how the intonation of the word closed drops. Lowering the intonation of your voice at the end of a sentence broadcasts power. When you want to sound superconfident, you can even lower your intonation midsentence. 4. Check your breathing. Make sure you’re breathing deeply into your belly and inhale and exhale through your nose rather than your mouth. Breathing through your mouth can make you sound breathless and anxious.

In R, running a script is called source-ing the script, because you are redirecting the source of commands from the command line to the script.

Let’s arbitrarily select x values from −2to+2, separated by intervals of 0.1. We have R set up the list of x values by using the built-in sequence function: x = seq( from = -2, to = 2, by = 0.1 ) .

ordered list of numerical values is called a “vector” in R

Conveniently, R has a built-in function called plot, which we call by entering plot (x,y,type="l"). The segment of code, type="l" (that’s a letter “ l” not a numeral “1”) tells R to plot connecting lines between the points, with no distinctive symbols marking the points. If we omitted that part of the command, then R would plot only points by default, not the connecting lines.

A comment in R begins with the “ #”symbol, called a number sign or a pound sign.

Type the command ?"plot" and you can read all about it. In particular, the information directs you to another command, par, that controls all the plot parameters. To learn about it, type ?"par". In general, it actually is helpful to use R’s built-in help. To get a list of all sorts of online documentation, much of it written in readable prose instead of telegraphic lists, type help.start()

While ?"plot" returns the single help page that explains the plot function, ??"plot" returns a list of dozens of help pages that contain the word “plot.”

The double equal sign for testing equality, used above, is brittle and can give unintended results due to the limited precision of representing numbers in the computer’s memory. For example, in most computers, the value of 0.5 − 0.3 does not equal the value of 0.3 − 0.1, even though mathematically they are equivalent. Therefore, R has another function, all.equal, for testing equality up to the degree of precision for the computer being used.

A vector is not technically a class in R, but a vector is the fundamental data structure.

A vector is simply an ordered list of elements of the same type

By “ordered” I mean that R knows the elements by their position in the list, not that the elements themselves somehow go in increasing or decreasing value.

The combine function, c (yes, the single letter “c”),makesvectors.Actually,thecombine function can combine different types of data structures, but at this point we consider only its ability to create vectors by combining elements. For example, c( 2.718 , 3.14 , 1.414 ) combines the three numbers into a vector.

R defaults to component-by-component vector operations. In particular, if x and y are two vectors of the same length, then x*y is the vector consisting of the products of corresponding components.

R automatically applies a scalar operation to all elements of a vector. For example: > 2 * c(1,2,3) [1]246 > 2 + c(1,2,3) [1]345

The colon operator, :, makes sequences of integers. For example, 4:7 creates the vector 4, 5, 6, 7 .

The colon operator has precedence over basic arithmetical operators, but not over the power operator.

The sequence function, seq, is very handy for creating vectors that consist of regular sequences of numbers. In its basic form, the user specifies the starting value of the sequence, the ending value, and the increment between successive values, like this: > seq( from=0 , to=3 , by=0.5 ) # length not specified [1] 0.0 0.5 1.0 1.5 2.0 2.5 3.0

If the increment is not an exact divisor of the distance between the starting and ending values, the sequence will not exceed the ending value.

The seq function is clever and will infer whatever value is omitted by the user. This capability can be very useful, for example if we want a sequence of a certain length and do not care about the exact end point or the increment.

44 Doing Bayesian Data Analysis > seq( from=0 , by=0.5 , length.out=7 ) # end not specified [1] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 > seq( from=0 , to=3 , length.out=7 ) # increment not specified [1] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 > seq( to=3 , by=0.5 , length.out=7 ) # start not specified [1] 0.0 0.5 1.0 1.5 2.0 2.5 3.0

The replicate function, rep, is also very useful for creating vectors. Here are some examples: > ABC = c("A","B","C") # define a vector for replication > rep( ABC, 2 ) [1] "A" "B" "C" "A" "B" "C" > rep( ABC, times=2 ) [1] "A" "B" "C" "A" "B" "C" > rep( ABC, times=c(4,2,1) ) [1] "A" "A" "A" "A" "B" "B" "C" > rep( ABC, each=2 ) [1] "A" "A" "B" "B" "C" "C" > rep( ABC, each=2, length=10) [1] "A" "A" "B" "B" "C" "C" "A" "A" "B" "B" > rep( ABC, each=2, times=3) [1] "A" "A" "B" "B" "C" "C" "A" "A" "B" "B" "C" "C" "A" "A" "B" "B" "C" "C"