Keeping the Physics in Biophysics -- and vice versa Phil Nelson University of Pennsylvania For these slides see: www.physics.upenn.edu/~pcn What we face Our Physics colleagues are still saying -- • “That’s not really physics.” • “That’s already offered in some other department.” • “We don’t have the resources for that.” Our Biology colleagues are still not sending their students to our courses. “Biology students cannot/will not do math.” “Physics students get uncomfortable with biological physics -- there are too few `Tripos questions.’” I’ll discuss those questions in the context of describing a course that works at U. Penn. If you don’t face these particular questions, you may still be interested in the choice of topics. Why do we even have classes at all? ✴To tell them facts? No -- facts are now free in infinite quantity. ✴To tell them the latest, most trustworthy facts? No -- facts go out of date in the blink of an eye. Well -- skills and habits still matter a lot. When you walk into a room with your toolbag and encounter a problem you’ve never seen, which tool should you pull out of your bag? Knowing where to begin is a difficult but learnable skill. Students need to develop the right skills and habits for that, but many (most?) courses don’t really help. A class should help them do that -- in some specific context. Biological physics is an interesting context for that purpose, regardless whether a student goes on in that field. The interesting questions in science are those where we shake our heads and ask, “How could anything like that possibly happen at all?” And biophysics is full of such questions. The boffins speak Students have got to learn how to get computers to do useful things from scratch. They also need to get used to extracting useful information from big datasets. http://books.nap.edu/ A course that works at Penn Physicists are pretty comfortable teaching about molecular biophysics. It’s a good fit -- we like to talk about entropy It’s still an exciting, opening field. A number of modern textbooks are now available. But... Maybe you’ve already got one of those. Molecular biophysics is not so obviously connected to medicine, which many of our students plan to study. Students are intrinsically interested in themselves, e.g., their own visual system. Physicists have a lot to say about Systems, although we’re somehow ceding a lot of the high ground to mathematicians and computer scientists. Let’s see how a Physics department could offer an useful course to a wide variety of students, including the more numerate Bio majors, and the burgeoning group of Engineering majors interested in bio applications. Much inspiration from Bialek/Botstein 2004; Wingreen/Botstein 2006. Genetic switching Monod found something funny in the growth of bacteria in mixed medium. He asked, “how could that possibly happen at all?” And he ended up with the operon model. Monod 1949 Could bacteria somehow be implementing a two-state switch like the ones that changed human civilization in the mid-20th century? (Ahem -- Why doesn’t this icon appear anywhere else in our Physics curriculum?) R E P O R T S data (12, 13). However, biochemical parame- ters are generally unknown in vivo and could Gene Regulation at the depend on the environment (12) or cell history (14, 15). Moreover, gene regulation may vary Single-Cell Level from cell to cell or over time. Three funda- mental aspects of the GRF specify the behav- 1 Physics 280, 3Fall 2001 9 Phil’s version 16 Nitzan Rosenfeld, * Jonathan W. Young, Uri Alon, ior of transcriptional circuits at the single-cell Peter S. Swain,2* Michael B. Elowitz3. level: its mean shape (averaged over many cells), the typical deviation from this mean, The quantitative relation between transcription factor concentrations and the and the time scale over which such fluctua- rate of protein production from downstreamwgeneshereis centralonetoothef tfunctionhe derivatitoinsvpeersist.eAqlthuouaghlsfastzfleucrtuoat.ionsYshoouuld may prefer to draw a graph for which all of genetic networks. Here we show that this relation, which we call the gene average out quickly, slow ones may introduce regulation function (GRF), fluctuates dynamicallyarrowinsindividualare slivingcalecells,d to therrosrsainmthe opleerantiogn tofhg,enestioc cirycuoitsuandcan see what’s happening right up near the thereby limiting the accuracy with which transcriptional genetic circuits can may pose a fundamental limit on their ac- transfer signals. Using fluorescent reporterfixgenesed andpofusionintsproteins,(belowew rightcu)r.acy. In order to address all three aspects, it characterized the bacteriophage lambda promoter PR in Escherichia coli. A is necessary to observe gene regulation in in- novel technique based on binomial errors in protein partitioning enabled dividual cells over time. calibration of in vivo biochemical parameters in molecular units. We found Therefore, we built Bl-cascade[ strains of that protein production rates fluctuate over a time scale of about one cell nullclines and flow field for geneticEsche switchrichi equationsa coli, containing the l repressor cycle, while intrinsic noise decays rapidly.1.4Thus, biochemical parameters, and a downstream gene, such that both the 1.4 noise, and slowly varying cellular states together determine the effective amount of the repressor protein and the rate single-cell GRF. These results can form a basis for quantitative modeling of of expression of its target gene could be natural gene circuits and for design of synthetic1.2 ones. monitored simultaneously in individual cells 1.2 Switching, II (Fig. 1B). These strains incorporate a yellow The operation of transcriptional genetic cir- rate at which their downstream gene products fluorescent repressor fusion protein (cI-yfp) cuits (1–5) is based on the control of pro- are p1roduced (expressed) through transcrip- and a chromosomally integrated target pro- 1 moters by transcription factors. The GRF is tion and translation. The GRF is typically moter (PR) controlling cyan fluorescent pro- the relation between the concentration of represented as a continuous graph, with the tein (cfp). In order to systematically vary active transcription factors in a cell and the acti0.8ve transcription factor concentration on repressor concentration over its functional 0.8 Students can write a model of two the x axis and the rate of production of its range (in logarithmic steps), we devised a tac2 rget gene on the y axis (Fig. 1A). The shape Bregulator dilution[ method. Repressor pro- 1Departments of Molecular Cell Biology and Physics mutually repressing genes, makeof Comple thex Syst ems, Weizmann Institute of Science, of t0.6his function, e.g., the characteristic level of duction is switched off in a growing cell, so 0.6 Rehovot, 76100, Israel. 2Centre for Non-linear Dy- repressor that induces a given response, and that its concentration subsequently decreases phase-plane analysis, and find namithecs, Department of Physiology, McGill University, the sharpness, or nonlinearity, of this response by dilution as the cell divides and grows into 3655 Promenade Sir William Osler, Montre´al, Que´bec, 3 (1)0.4determine key features of cellular behavior a microcolony (Fig. 1C). We used fluores- 0.4 Canada, H3G 1Y6. Division of Biology and Depart- such as lysogeny switching (2), developmen- cence time-lapse microscopy (Fig. 1D; fig. region of bistability in Matlab. ment of Applied Physics, Caltech, Pasadena, CA 91125, USA. tal cell-fate decisions (6), and oscillation (7). S1 and movies S1 and S2) and computational Its properties are also crucial for the design image analysis to reconstruct the lineage tree *These authors contributed equally to this work 0.2 0.2 .To whom correspondence should be addressed. of synthetic genetic networks (7–11). Cur- (family tree) of descent and sibling relations E-mail: [email protected] rent models estimate GRFs from in vitro among the cells in each microcolony (fig. 0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 c1 Fig. 1. Measuring a A B C aTc gene regulation func- 1 T l l 4 tion (GRF) in individual 10 CI-YFP o e ( t a l c CFP 0.8 i E. coli cell lineages. (A) n l ) r P -TetR e C e Rate c e l The GRF is the depen- a F p a 0.6 r P c Γ 3 P Not assigned: Here is a corresponding plot for thes bistable case (n = 2.4, = 2): dence of the produc- s aTc 10 c p F g a 0.4 e tion rate of a target Y o l r l l It’s not speculation -- now the e ( c a ) promoter ( y axis) on P -cIYFP P -CFP t tet R 0.2 e o l Production 2 l the concentration of T 10 transfer functions of each elementone (o r more) tran- !"##$%&'()*Repressor+')"%,-Concentration! unit-2 !-1length0 1 2 flow3 4 5field6 7 for8 genetic switch equations scription factors (x ax- Time (cell cycles) have been measured. The era ofis) . (B) In the l-cascade * D 2.5 strains (16) of E. coli, CI-YFP is expressed synthetic biology has arrived. from a tetracycline promoter in a TetR background and caþn be induced by anhydro- tetracycline (aTc). CI- YFP represses produc- 2 tion of CFP from the PR promoter. (C) The reg- ulator dilution experi- ment (schematic): Cells are transiently induced to express CI-YFP and then experiment using the OR2*–l-cascade strain (see fig. S3) (16). CI-YFP protein observed in time-lapse microscopy as repressor dilutes out during cell growth is shown in red and CFP is shown in green. Times, in minutes, are indicated on (red line).