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  1. Illinois Institute of TechnologyPHYSICS 561 Radiation Biophysics Lecture 5: Survival Curves and Modifiers of Response Andrew Howard 17 June 2014 Survival Curves; Modifiers

  2. Looking forward • Be alert for changes in the posted assignments: I may add a few things • Midterm will cover chapters 1-7 and the bit of extra material on free radicals that we discussed last week; therefore, it will not include the material from today’s lecture Survival Curves; Modifiers

  3. Survival Curves • We discussed models for cell survival last time • We looked at various ln(S/S0) vs. dose models and the logic behind them • Today we’ll focus on the graphical implications and how we can look at the numbers • Then we’ll talk about cell cycles and other good solid cell-biology topics. • (Warning: I’m more of a biochemist than a cell biologist, so don’t expect high expertise in this later section!) Survival Curves; Modifiers

  4. Errata in Chapter 8 • Page 169, Paragraph 2, 1st sentence:Until the later 1950’s it was not possible to use … • Two sentences later:BacteroidesBacillus • Fig. 8.1, p. 173:The label that says Dq is pointing at the wrong thing:it should be pointing at the place where the dashed line crosses the (Surviving faction = 1.0) value. Survival Curves; Modifiers

  5. What Fig. 8.1 should have said n Dq = D0lnn = quasi-threshold Dose, Gy Surviving Fraction Slope = k = 1/D0 A B Survival Curves; Modifiers

  6. Shoulder of the Survival Curve • We recognize that with MTSH dose-response we have a region where the slope is close to zero. We describe that region as a shoulder: Survival Curves; Modifiers

  7. Slopes in the MTSH model • Remember that the MTSH model saysln(S/S0) = ln(1-(1-exp(-D/D0))n) • Because S/S0 = 1-(1-exp(-D/D0))n • So what is the slope of the S/S0 vs. D curve? • … and … what is the slope of the ln(S/S0) vs. D curve? • In particular, what is the slope’s behavior at low dose? • Answer: calculate dS/S0/ dD and d(ln(S/S0))/dD and investigate their behavior at or near D = 0. • Note: we’re looking here at the n>1 case. Survival Curves; Modifiers

  8. Slope investigation, part I • For S/S0 itself,d(S/S0)/dD = d/dD(1-(1-exp(-D/D0))n) • The 1 out front doesn’t affect the derivative: d(S/S0)/dD = -d/dD(1-exp(-D/D0))n) • We’ll do the rest of this calculation now based on the general formulas • dun/dx = nun-1du/dx • deu/dx = eudu/dx Survival Curves; Modifiers

  9. Arithmetic & Calculusof Survival Models • MTSH says S/S0 = 1 - (1-e -D/D0)n • What I want to investigate is the slope at low dose, I.e. for D << D0, • And at high dose, I.e. for D >> D0. • But are we interested in the slope of S/S0 vs. D or ln(S/S0) vs. D? • Both! • Slope = derivative with respect to D. So • Slope = d/dD(1 - (1-e -D/D0)n) = -d/dD(1-e -D/D0)n Survival Curves; Modifiers

  10. MTSH slope, continued • Recalling that dun/dx = nun-1du/dx, for n>1, • Slope = -n(1-e -D/D0)n-1 d/dD (1-e -D/D0)= -n(1-e -D/D0)n-1 [-d/dD(e -D/D0 )] • But we know deu/dx = eu du/dx,so d/dD(e -D/D0 ) = e -D/D0 (-1/D0) = -1/D0 e -D/D0 • Therefore Slope = -n(1-e -D/D0)n-1 (-)(-1/D0)e -D/D0 • i.e. Slope = (-n/D0)(1-e -D/D0)n-1e -D/D0 Survival Curves; Modifiers

  11. Slope at D << D0 • This formula for the slope is valid for all values of D,including D << D0 and D >> D0 • For small D, i.e. for D << D0,Slope is -n/D0 (1-e -0/D0)n-1e -0/D0= (-n/D0) (1-e0)n-1e-0; for n > 1 this is= (-n/D0)(1-1)n-11 = 0. Shazam. Survival Curves; Modifiers

  12. Slope of ln(S/S0) vs D • The behavior of the slope of the ln(S/S0) vs D curve is not much harder to determine. • Recall d lnu /dx = (1/u)du/dx. We apply this here: • d ln(S/S0) / dD = (1/(S/S0)) d(S/S0)/dD. • For very small D, S/S0 = 1,so d ln(S/S0) / dD = (1/1) * d(S/S0)/dD = d(S/S0)/dD . • But we’ve just shown that that derivative is zero, so d ln(S/S0) / dD = 0. Survival Curves; Modifiers

  13. High-dose case • We’ve covered the low-dose case. • What happens at high dose, i.e. D >> D0? • What we’d like to show is that the slope of lnS/S0 vs. D is -1/D0. Let’s see if we can do that. • Slope = d ln(S/S0) / dD = (1/(S/S0) d/dD(S/S0) • Thus slope =(1 - (1-e -D/D0)n-1)d/dD(1 - (1-e -D/D0)n) • For D >> D0, D/D0 is large and-D/D0 is a large negative number;therefore e-D/D0 is close to zero. Survival Curves; Modifiers

  14. High-dose case, continued • Slope = limD∞{(1 - (1-e -D/D0)n)-1(-n/D0)(1-0)n-1e-D/D0)} • That’s messy because the denominator and the numerator both go to zero. There are ways to do that using L’Hôpital’s rule, but there are simpler ways that don’t involve limits. • The trick is to recognize that we can do a binomial expansion • I’ve done that in the HTML notes • The result will be slope = -1/D0 and ln n is the Y intercept of the extrapolated curve Survival Curves; Modifiers

  15. What constitutes a high dose here? • The only scaling of the dose that occurs in the formula is the value of D0, so we would expect that we are in that high-dose regime provided that D >> D0. • In practice the approximation that the slope is -1/D0 is valid if D > 5 D0. Survival Curves; Modifiers

  16. Linear-Quadratic Model • This is simpler. ln(S/S0) = aD + bD2 • Therefore slope = d/dD (ln(S/S0)) = d/dD(aD + bD2) • Thus slope = a + 2bD. That’s a pretty simple form. • At low dose, |a| >> 2|b|D, so slope = a. • At high dose (what does that mean?) |a| << 2|b|D,so slope = 2bD. • What constitutes a high dose?Well, it’s a dose at which |a| << 2|b|D, so D >> |a / (2b| • Thus if dose >> |a / 2b|, then slope = 2bD. Survival Curves; Modifiers

  17. Implications of this model • At low dose slope = a is independent of dose but is nonzero; thus ln(S/S0) is roughly linear with dose. • At high dose slope = 2bD,i.e. it’s roughly quadratic. • How can we represent this easily?We discussed this last time:ln(S/S0) / D = a + bD, • so by plotting ln(S/S0) / D versus D, we can get a simple linear relationship. Survival Curves; Modifiers

  18. LQ: Plot of ln(S/S0) / D versus D ln(S/S0)/D By observation, both a and b are negative. a < 0 tells us that radiation harms cells; b < 0 is an observed fact. Thus the intercept is below the axis and the slope is negative. D Y-intercept = a Slope = b Survival Curves; Modifiers

  19. LQ graphical analysis: one step further We can read -a/b directly off an extrapolation of the plot: at D = Dz,ln(S/S0)/D = 0,a + bDz = 0,a = -bDz, Dz = -a / b.Note a < 0, b < 0,so -a/b < 0. ln(S/S0)/D Dz D Y-intercept = a Slope = b Survival Curves; Modifiers

  20. Where do linear and quadratic responses become equal? • At what dose does the linear response equal the quadratic response? • At that dose, aD = bD2, D = a/b • So the value we read off the X-intercept of the previous curve is simply the opposite of the dose value at which the two influences are equal. • We mentioned this last time, but we’re reminding you now Survival Curves; Modifiers

  21. How plausible is all this? • Model studies suggest reasons to think that ln(S/S0) = aD + bD2 is a good approach. • Much experimental data are consistent with the model • Some of these LQ approaches allow for time-dependence to be built in. Survival Curves; Modifiers

  22. LQ vs MTSH and thresholds Response • How does the question of comparing the LQ model to the MTSH model relate to the question of threshold doses? • A typical real-world question is a dose-response relationship for which the only reliable experimental results are obtained at high doses; at lower doses the confounding variables render the experiments uninformative. Dose Survival Curves; Modifiers

  23. Dose-Response in Epidemiology Human health effect • #2 is the linear non-threshold (LNT) model • Is #3 more realistic? • This has regulatory consequences! Experimental data Extrapolations Limit of reliable measurement #1 #2 #3 Threshold Baseline Dose Tolerable dose #3 Tolerable dose #2 Tolerable dose #1 Survival Curves; Modifiers

  24. Studying repair • We’ve been suggesting that LQ models and even some MTSH models are dependent on the idea that some DNA damage can be repaired accurately. • Let’s look for approaches to studying DNA damage that might provide a fuller understanding of the effects of repair. Survival Curves; Modifiers

  25. The Elkind-Sutton Experiment • Provides a way of probing repair functions in cells • Procedure: • Irradiate and establish survival curve(“conditioning dose”) • Take cells surviving at S=0.1 and subject them to further irradiation at varying time intervals after reaching S=0.1 • If repair is taking place, then the appearance of a curve similar to the original shoulder is indicative of full recovery Survival Curves; Modifiers

  26. Results Survival Curves; Modifiers

  27. Interpretation • If slope and implied n value are equivalent to the original curve, then repair is complete • Smaller n values indicate insufficient time has elapsed • n=1 implies repair has not begun Survival Curves; Modifiers

  28. Elkind-Sutton and LET • We might expect more complicated results if we vary the LET for the two dosing regimens • Low-LET first, high-LET second gives two lines of different slope, independent of the time interval • High-LET first, low-LET second gives line followed by usual Elkind-Sutton distribution Survival Curves; Modifiers

  29. Low-LET followed by High-LET Survival Curves; Modifiers

  30. High-LET, then Low-LET Survival Curves; Modifiers

  31. The Cell Cycle • Cells have a definite cycle over which specific activities occur. • Particular activities are limited to specific parts of the cycle • Howard and Pelc (1953) characterized four specific phases: • M (mitosis, i.e cell division) • G1 (growth prior to DNA replication) • S (synthesis, i.e DNA replication) • G2 (preparation for mitosis) Synthesis(S) Presynthetic(G1) Post-synthetic(G2) Mitosis(M) Survival Curves; Modifiers

  32. What happens in S phase? • DNA is replicated; thus, we have twice as much DNA at the end of S as at the beginning. • During mitosis the two duplexes of DNA can separate • One goes to one daughter cell, the other to the other Survival Curves; Modifiers

  33. How much time do these segments take? • Depends on the overall mitotic rate and the type of cell: • Cell Cycle Times in hours: Segment CHO HeLa M 1 1 G1 1 11 S 6 8 G2 3 4 ------------------------------------------ TOTAL 11 24 Survival Curves; Modifiers

  34. Pie charts of cycle percentages • The point is that different kinds of cells spend differing amounts of time in the various phases Survival Curves; Modifiers

  35. Phase Sensitivity • Many cells are much more sensitive to radiation in some parts of the cell cycle than they are in others. • Why? • Repair is more vigorous in some stages • Unrepaired damage has more opportunity to manifest itself as clonal alteration close to mitosis • Access of repair enzymes to damaged DNA is sometimes influenced by how organized the DNA is. Survival Curves; Modifiers

  36. What phases are sensitive? • In general, cells are radioresistant when they are synthesizing DNA. • Cells that are synthesizing DNA are taking up label;the time that they’re doing that is correlated with survival: 90 % of labeled cells 0.4 Surviving Fraction Surviving Fraction % of labeled cells 24 0 Time in Hours Survival Curves; Modifiers

  37. Survival Curves in Various Phases • See fig. 8.8: • Late S is least radiosensitive • Early S next least • G-1 somewhat sensitive • G-2 and M most radiosensitive • M and G2 curves are essentially straight lines (log-linear dose-response), suggesting that repair is unavailable or of little influence Survival Curves; Modifiers

  38. Figure 8.8, reimagined with LQ model Survival Curves; Modifiers

  39. Radiation-InducedCell Progression Delay • Note that various biochemical signals regulate progression from one phase of the cycle to another. • To study this, you need synchronized cells . . . • Sample study (Leeper, 1973): • CHO cells exposed to 1.5 Gy in mid-G1 experienced a delay of 0.5 h in cell division • 1.5 Gy in late S or early G2 caused a delay of 2-3 h • Dose-dependent: (4h for 3Gy, 6-7h for 6 Gy) Survival Curves; Modifiers

  40. Shape of the culture matters! • How the cells grow influences how much the cells’ progression is altered by radiation • Monolayers’ progression is altered less than cells in a multicellular spheroid geometry 0.53 hours per Gray 0.22 hours per Gray Survival Curves; Modifiers

  41. Is that such a big deal? • Probably not: • The cells in the spheroidal mass divide half as fast even in the absence of radiation, possibly due to contact inhibition. • Therefore it may simply be that the whole mitotic clock has been slowed down, including the clock as it’s been influenced by radiation. Survival Curves; Modifiers

  42. Causes for these effects • Why are cells more radiosensitive in M and G2? • Reduced availability of repair enzymes • Repackaged DNA is hard to repair • How is cell progression influenced by radiation? • Damage to protein kinases and cyclins involved in cellular checkpoints • Premature degradation of p21, maybe… • Sample 1994 study:Edgar et al, Genes Dev. 440: 52 (1994) Survival Curves; Modifiers

  43. Effectors of Radiation Sensitivity • Biological • Cells go through life cycles & are much more sensitive to radiation damage at some stages than at others • Chemical • Physical Survival Curves; Modifiers

  44. Assignment related to amino acids • 1. There are exactly twenty amino acids that serve as the building blocks for proteins in almost all organisms. The general formula for 19 of these 20 amino acids is +NH3-CHR-COO-, where R is any of 19 different side-chain groups. The simplest of these R groups is H, for which the amino acid is called glycine; the most complicated is a moiety known as indole, for which the amino acid is called tryptophan. Survival Curves; Modifiers

  45. Upcoming Problem 1, cont’d • Much of the chemistry that these R groups participate in in proteins is ionic in nature, involving charges or partial charges; but usually these ionic interactions involve pairs of electrons rather than unpaired electrons. An exception is the amino acid tyrosine, which can participate in free-radical (unpaired-electron) interactions. Draw a structure of the tyrosyl free radical and explain why it might have a reasonably long lifetime, as compared to a hydroxyl radical or some other short-lived free radical. Survival Curves; Modifiers

  46. Second upcoming problem • 2. Most biochemical oxidation-reduction reactions involve transfers of pairs of electrons and therefore do not involve free radical mechanisms. A sizeable minority, however, do involve free radicals. Which of the following biochemical oxidizing or reducing agents are capable of participating in single-electron (free-radical) reactions, and which are not? Explain briefly. You may need to look up the structures of some of these compounds. • (a) ferric iron, Fe3+ • (b) nicotinamide adenine dinucleotide, oxidized form (NAD) • (c) flavonamide mononucleotide (FMN)(also spelled flavin amide mononucleotide; it’s an instance of what are generally known as flavin prosthetic groups) Survival Curves; Modifiers

  47. Errata • Page 205, in the EXAMPLE:4.0 µM l-1 should be 4.0 µM, or 4.0 µmol l-1 • Page 206, last sentence:If the lesions produced by high LET radiation are predominantly of type II (irrepairable), then m-1 will be disappearingly small and no oxygen sensitization will be detectable. • Page 213, last paragraph: cysteine, not crysteine Survival Curves; Modifiers

  48. Cellular Life Cycles (review) Phases • Mitotic M (short) • Sensitive • Presynthetic G1 (variable) • Radiation causes 1/2 h delay here • Synthetic S (4 - 8 h) • DNA synthesis • Least sensitive • Postsynthetic G2 (usually short 1 - 2h) • Radiation causes 3 - 4 h delay here • End of G2 sensitive __________ Overall Process 14 h Survival Curves; Modifiers

  49. What happens in G1? • Routine cellular metabolism • Both buildup of new cellular structures and gathering energy to do so, i.e. both catabolism and anabolism: Metabolism as a whole consists of: • CatabolismAnabolism • Energy-producing Energy-requiring • Breakdown of complex Build-up of complexmolecules into simpler molecules from simplerones, producing ATP precursors, using ATP Survival Curves; Modifiers

  50. A mitotic cell Other organelles Nucleus(DNA location;cellular organization) Mitochondrion(energy metabolism) Mitotic Spindle Ribosomes(protein synthesis) Survival Curves; Modifiers