Lecture notes. Written from the material of MIT 8.591J 2014, licensed CC BY-NC-SA 4.0. These are notes, not a transcript: the material has been reorganised and rewritten. This adaptation carries the same licence, and the original is linked above.
7. Anticipatory Regulation and Bet Hedging¶
What this covers¶
Why does a clonal bacterial population sometimes look genetically diverse when it is not? This chapter works through three distinct evolutionary answers, built around two papers the lecture treats as a matched pair: one on gene regulation that anticipates a predictable future environment (Tagkopoulos et al., Mitchell et al.), and one on gene expression that goes heterogeneous in a population facing an unpredictable one. It assumes the reader already has the idea of a Nash equilibrium from an earlier lecture in the course (game theory is used but not re-derived here), and basic comfort with fitness as a growth rate.
Direct sensing versus anticipating the future¶
Take a bacterium moving between two environments that present two different cues, \(S_1\) and \(S_2\), each of which calls for its own response, \(R_1\) and \(R_2\). The naive strategy is direct sensing: \(S_1\) drives \(R_1\), \(S_2\) drives \(R_2\), and that is all. (These arrows need not even be all-or-nothing — \(S_1\) could drive \(R_1\) strongly and \(R_2\) only weakly.)
The interesting alternative is that a cue pre-activates the response to a cue it hasn't seen yet, because in the organism's normal life history the two cues are correlated. This is anticipatory regulation, and the lecture's classic frame for it is Pavlovian conditioning: ring a bell, then give the dog food, and eventually the bell alone makes the dog salivate. The bell (\(S_1\)) has come to drive the food response (\(R_2\)) because in the dog's experience one reliably precedes the other. The question for a cell is whether something structurally identical could evolve without any nervous system at all, just from selection acting on a gene network — and whether it has.
Two versions of this idea appear in the readings, and they differ in exactly one thing: whether the cross-activation runs both ways.
Symmetric anticipatory regulation: temperature and oxygen¶
E. coli live part of their life cycle in the mammalian gut, and entering it means a characteristic, correlated change in conditions: temperature rises and oxygen availability drops at the same time. Tagkopoulos et al. (Science, 2008) showed that exposing E. coli to a temperature rise turns on not only the genes needed to survive heat, but also the genes needed to survive low oxygen — and exposure to low oxygen turns on the heat-response genes too. The cross-activation runs both ways, hence symmetric.
A cheap objection is that this could just mean the same genes happen to help against both stresses — not a "predictive" regulatory link at all, just one response that happens to cover two problems. The way to rule that out is to break the correlation experimentally: evolve a population in an environment where temperature changes but oxygen doesn't, and see whether the unnecessary cross-activation arrow disappears. It does — the cross-regulation can be selectively removed, which argues that it really was a distinct, evolved link between the two cues rather than a side-effect of two response programs sharing components.
Why would symmetric — cross-activation both ways — ever be worth it, rather than each cue only predicting its own future need? Two considerations came up. First, when both cues are individually noisy predictors of "you are now in a gut," seeing both together is much stronger evidence than seeing either alone, and this also controls false positives: if each cue fires spuriously at some low rate, the two firing together at the same time is far rarer, so requiring (or reinforcing on) both lowers the false-alarm rate. Second, if there's no reliable temporal order between the two cues — they arrive together rather than one before the other — there's no basis for making one of them the "leading" predictor, which pushes the design toward symmetry.
Asymmetric anticipatory regulation: lactose before maltose¶
Mitchell et al. (Nature, 2009) is built around a case where there is a reliable order: bacteria entering a mammalian gut typically encounter lactose before they encounter maltose (lactose comes from milk, and young mammals drink milk; adults mostly do not, so an adult gut may present maltose with no lactose at all). What they found is that exposure to lactose pre-activates the maltose (mal) genes — not to the same level as exposure to maltose itself, but well above the baseline for other carbon sources — while exposure to maltose does not pre-activate the lactose genes. The cross-activation only runs one way: asymmetric.
Why asymmetric survives even though the correlation is weak. Only about 10% of the time that E. coli encounter maltose did they see lactose first. That sounds like it should scotch the whole idea, but the cost-benefit accounting is one-sided. When maltose shows up with no preceding lactose, the anticipatory strategy and plain direct sensing behave identically — both are simply surprised and switch on the mal genes on contact, at the same cost. The only place the two strategies diverge is after seeing lactose: the anticipatory strategy pays a cost by activating the mal genes early, and that cost is worth paying only if maltose reliably follows lactose closely enough in time. It has nothing to do with what fraction of maltose encounters were preceded by lactose — only with what fraction of lactose encounters are followed by maltose soon after.
What it takes to show the mechanism actually evolved for this purpose, and not just observed by chance in one strain, the lecture distilled to three requirements the paper had to establish:
- Fitness: pre-exposure to \(S_1\) (lactose) increases fitness under \(S_2\)/\(R_2\) (maltose) — i.e., seeing lactose first genuinely helps when maltose arrives.
- Cost: there is a real cost to up-regulating \(R_2\) (the mal genes) when it turns out not to be needed — otherwise there's nothing to explain, since a free response would always be worth having.
- Specificity: it is specifically lactose that pre-activates the mal genes, and other sugar sources should not.
The evidence assembled for each: cross-activation is present in more than one E. coli strain, not just theirs (adding generality, and also — worth noting honestly — this particular cross-regulation of the mal genes by lactose had already been reported by someone else). Most tellingly, they compared the wild-type strain to one that had been laboratory-evolved for 500 generations in lactose alone — evolved by a different group, for a different purpose, and simply reused here rather than repeated from scratch, since redoing three months of daily dilutions to get the same strain would have been pointless. In that lactose-evolved strain, the anticipatory arrow is gone: lactose exposure no longer pre-activates the mal genes. And in a separate measurement (their Figure 3), the fitness benefit of pre-exposure is specific to the lactose-then-maltose ordering — not maltose-then-lactose, not galactose-then-maltose, not sucrose-then-maltose — and that fitness benefit is likewise absent in the lactose-evolved strain that lost the regulatory arrow. Losing the regulation and losing the benefit together, in the same strain, is a stronger case than either result alone.
A brief aside on reading the figure itself: the lecture points out that the paper's fitness data (Figure 3) is presented as a figure with color-coded points — one color for the main comparison, others for the various control orderings and for the extinction control — precisely because a table of the same numbers would not make the argument visible. The advice offered for writing one's own figures was to choose a color scheme that stays legible printed in black and white, not only on screen (Bang Wong's series of short articles on figure design in Nature Methods was named as a good source for this, but not itself part of the lecture's content).
The paper also treats a "stochastic switching" mechanism as a third alternative to direct sensing and anticipatory regulation — cells switching into different response states at some rate independent of a specific predictive cue. That is exactly the segue into the rest of the lecture: stochastic switching between phenotypes, and why it might be favored by selection at all.
Heterogeneity in a clonal population¶
Even a genetically identical population can look strikingly heterogeneous in one environment. The lecture is explicit that observing this is not, by itself, evidence of anything adaptive: a trait can be observed without having been selected for — it could be a side effect of something else entirely. But when there is an evolutionary explanation, the lecture identifies three, and warns against reflexively reaching for the first one:
| Explanation | Idea | Lecture's example |
|---|---|---|
| Bet hedging | stochastic diversification against an unpredictable environment | persister cells / antibiotic tolerance |
| Mixed strategy | equilibrium of a game played within the population | glucose/galactose bimodal expression in yeast |
| Altruistic self-sacrifice | division of labor, some individuals pay a lethal cost for relatives | colicin production |
Bet hedging and the geometric mean¶
The seed germination problem. A desert annual plant releases seeds. Suppose it rains in 75% of years and doesn't in the other 25%. A seed that germinates and gets rain goes on to produce, on average, 2 seeds the following year; a seed that germinates without rain has only a 10% chance of surviving, so its expected contribution is \(0.1\) seed. A seed that does not germinate simply survives to try again next year, contributing exactly 1 seed regardless of rain.
| Rain (75% of years) | No rain (25% of years) | |
|---|---|---|
| Germinate | \(\times 2\) | \(\times 0.1\) |
| Don't germinate | \(\times 1\) | \(\times 1\) |
Which is the better strategy, in the long run? The tempting shortcut — average the two outcomes weighted by their frequency — is the wrong average. What matters for a quantity that multiplies across generations is the geometric mean, not the arithmetic mean. Over a representative run of four years matching the 3-to-1 ratio (three rain years, one drought), always-germinate multiplies the population by $\(2 \times 2 \times 2 \times 0.1 = 0.8,\)$ so the population shrinks by a factor of \(0.8\) every four generations, while never-germinate multiplies it by \(1 \times 1 \times 1 \times 1 = 1\) — flat. In this instance, always sitting out beats always germinating, even though germinating is the better bet in any single rainy year.
The reason the geometric mean is the right quantity, and not the arithmetic mean, is starkest in the limit where the bad-year payoff goes to zero. If a germinated seed's survival probability in a drought is exactly \(0\), then always-germinating guarantees eventual extinction, full stop — the population is certain to encounter a drought eventually, and one factor of zero erases everything before it, no matter how good the good years were. An arithmetic mean of the two payoffs can still look attractive (three factors of 2 outweigh one factor of \(0\), arithmetically) while the true long-run growth rate is exactly zero. It is precisely in this regime — a rare, catastrophic environment with a payoff near zero for the "committed" phenotype — that bet hedging earns its keep: instead of an all-or-nothing strategy, germinate with some probability \(p\) and hold the rest in reserve. That reserve need not be large — a small \(p\) that leaves most seeds ungerminated most of the time can still maximize the population's long-run growth rate, because it buys insurance against the catastrophic year while still capturing most of the benefit of the good ones.
Persister cells are the microbial version of the ungerminated seed. In a population exposed to antibiotics, only about one cell in \(10^5\)–\(10^6\) enters a slow-growing, drug-tolerant "persister" state. Growing slowly is a real cost — but because so few cells pay it, the cost to the population as a whole is small. Add antibiotic and wait 12 hours, and the persisters are what's left; this looks like resistance, but it is not: regrow that surviving population and it is once again fully sensitive to the antibiotic. That reversibility is exactly what distinguishes phenotypic (persister) tolerance from true genetic resistance, which arises independently at a much lower rate (around one cell in \(10^8\)) and, being a mutation, is stable across generations rather than reverting. The mechanism proposed for entering the persister state involves toxin–antitoxin modules that are normally repressed but triggered stochastically at a low rate — though the lecture flags this as a genuinely unsettled debate, complicated by the fact that any slow-dividing cell tends to be broadly protected against many stresses, which makes it hard to tell a specific persister mechanism apart from generic dormancy.
Mixed strategies: heterogeneity from a game within the population¶
Bet hedging is about coping with an unpredictable environment. Mixed strategies are a different mechanism entirely: heterogeneity that arises from a game played among members of the same population, with no environmental uncertainty required at all.
Hawk–Dove. Two individuals meet over a resource worth \(b\). A dove backs down rather than fight; a hawk fights. If two doves meet, they split the resource: each gets \(b/2\). If a hawk meets a dove, the hawk takes the whole resource, \(b\), and the dove gets \(0\) (and avoids the fight). If two hawks meet, they fight: each has a 50% chance of winning the whole resource and a 50% chance of losing and paying the cost of the fight, \(c\), for an expected payoff of \((b-c)/2\).
Assume the fight is not worth it on average, \(b < c\) — the interesting regime. Then neither pure strategy is a Nash equilibrium: starting from all-dove, a single individual does strictly better by switching to hawk (getting \(b\) instead of \(b/2\), since it never has to fight); but hawk isn't stable either, since \(b<c\) means the equilibrium condition for hawk (which needs \(b>c\)) fails. What is an equilibrium is a mixed strategy — play hawk with some probability \(p^\ast\). Setting the expected payoff of hawk equal to the expected payoff of dove against a population playing hawk with probability \(p\), $\(p\cdot\frac{b-c}{2} + (1-p)\, b \;=\; (1-p)\cdot\frac{b}{2},\)$ and solving gives $\(p^\ast = \frac{b}{c}.\)$ A bigger benefit pushes the equilibrium frequency of hawks up; a bigger cost of fighting pushes it down — matching the intuition that fighting becomes more attractive exactly when it's more rewarding and less costly.
This is negative frequency-dependent selection: whichever strategy is currently rare does better than whichever is currently common. A lone hawk among doves does great; a lone dove among hawks does great (it just avoids every fight). That pressure pushes the population toward the equilibrium mix and holds it there — and the mix can be implemented either as two coexisting genotypes (pure hawks and pure doves, at frequencies \(p^\ast\) and \(1-p^\ast\)) or as one genotype that plays hawk with probability \(p^\ast\) on each encounter. Either way, it looks like phenotypic heterogeneity in the population.
Rock–paper–scissors is the sharpest illustration of what a Nash equilibrium does and doesn't mean. The equilibrium of that game is to play each of the three moves with probability \(1/3\) — at that mixture, no one has an incentive to deviate, given everyone else is playing it. But that equilibrium is emphatically not the best response to any particular opponent: if you know your opponent always plays rock, the best response is always paper, not \(1/3\)-\(1/3\)-\(1/3\). A Nash equilibrium is a description of stability under mutual best response, not a claim that the equilibrium strategy is optimal against a given fixed strategy.
A foraging-game reading of yeast on mixed sugars. Yeast grown in a mix of glucose and galactose show a bimodal response in the GAL genes (needed to metabolize galactose): measuring galactose- pathway expression across single cells, some cells switch it on strongly and others don't switch it on at all — a clonal population splitting into two visibly different phenotypes. One reading of this, offered as work from the lecturer's own group, treats it as a foraging game: imagine a population choosing between two food sources (blueberries and red berries, say). If everyone else is eating blueberries, it pays you to switch to red berries — you don't have to share. If everyone else switches to red berries, blueberries become the better choice. That is exactly the negative frequency dependence of Hawk–Dove, transplanted to resource choice, and it again predicts coexistence of the two phenotypes as the equilibrium — implementable either by two genotypes or by one genotype expressing both phenotypes with some probability.
One thing this equilibrium does not do is maximize the population's total fitness. In Hawk–Dove, a population that was entirely doves would do strictly better in aggregate than the mixed equilibrium \(p^\ast\) — but that all-dove state isn't stable, so it never gets there. The lesson generalizes: a mixed-strategy explanation for heterogeneity is a claim about individual-level stability under negative frequency dependence, not a claim that the observed mixture is good for the population as a whole.
Altruism and division of labor: colicin¶
The third explanation gives up individual payoff altogether. Many gram-negative bacteria, including E. coli, carry plasmids encoding colicins — toxins — and the only way a cell releases its colicin is by lysing: bursting open and dying. The same plasmid also encodes an immunity protein, so a cell that lyses kills competing bacteria that lack the plasmid, while other cells that do carry the plasmid (and are therefore protected by the immunity protein) are unharmed. This is kin selection in a strict, mechanistic sense: "relatedness" here means sharing that particular plasmid, not genealogical kinship in the usual sense.
For the plasmid to spread, lysis has to be stochastic and rare — that's a strict requirement, not an incidental detail. If every plasmid-carrying cell always lysed, the plasmid would simply extinguish itself; it can never propagate. But if only a small fraction of the carriers — a lecture's example is around 1% — lyse and release colicin at any given time, that fraction kills off competing, non-carrying bacteria while the surviving majority of carriers, protected by the immunity protein, benefits from the reduced competition. The plasmid spreads through the population even though a minority of its own carriers dies to make that happen: altruistic self-sacrifice, with the beneficiaries being the individual's genetic relatives in the relevant sense — other carriers of the same toxin/immunity plasmid.
Three explanations, one observation¶
Put together, phenotypic heterogeneity in a clonal population can arise from at least three distinct evolutionary logics, and they are not interchangeable even though they can look similar under a microscope:
- Bet hedging is a response to an unpredictable environment: it maximizes the long-run geometric growth rate of a single lineage and requires no interaction between individuals at all.
- Mixed strategies arise from a game among individuals in the same population: the equilibrium is set by negative frequency-dependent selection, and it need not maximize the population's total fitness.
- Altruistic self-sacrifice trades an individual's fitness for the fitness of its genetic relatives, via a mechanism (like a toxin/immunity plasmid) that only works if the sacrifice is rare.
Each makes different, falsifiable, experimentally distinguishable predictions — about who benefits, about whether the observed mixture maximizes population growth or only individual payoff, about whether the effect depends on environmental fluctuation at all. The lecture's parting point is a methodological one: seeing heterogeneity and reaching immediately for "bet hedging" is a common reflex in the field, but the other two explanations are, as far as anyone can tell, just as general and just as common — which means the heterogeneity itself is never enough evidence on its own, and distinguishing between the three requires designing the measurement, not just making the observation.
Sources¶
Recording bjxcf6pfrha (MIT 8.591J Systems Biology, Fall 2014). Transcript only — nothing
written on the board was captured, so the direct-sensing / symmetric / asymmetric diagram above is
reconstructed from the spoken description of the arrows between \(S_1, S_2, R_1, R_2\).
- Anticipatory regulation, the Pavlovian frame, direct sensing vs. symmetric vs. asymmetric regulation, the Tagkopoulos and Mitchell papers, and the note on figure design: 00:00–46:50.
- Referred to but not contained in this transcript: Kussell & Leibler, Science (2005) — the formal, information-theoretic treatment of switching among \(n\) phenotypes and environments that this lecture treats as backdrop (named repeatedly, e.g. 01:09, 56:44); Tagkopoulos et al., Science (2008), on symmetric anticipatory regulation of temperature/oxygen response (10:10– 17:18); Mitchell et al., Nature (2009), the paper this half of the lecture works through (02:13–46:50), including a follow-up PNAS paper by Amir Mitchell developing its timing model in more detail (23:53); Bang Wong's series of articles in Nature Methods on figure and color design (42:25); the second half of the Mitchell et al. paper, on a parallel cross-protection story in yeast during fermentation, which the lecturer explicitly skipped (44:34).
- Phenotypic heterogeneity, its three evolutionary explanations, bet hedging, seed germination, the geometric mean, and persister cells: 47:54–1:04:30.
- Mixed strategies, Hawk–Dove, negative frequency-dependent selection, rock–paper–scissors, and the glucose/galactose foraging-game reading: 1:04:30–1:14:34.
- Builds on an earlier class session on game theory ("about two weeks" prior) not included in this transcript; the glucose/galactose interpretation is attributed to the lecturer's own (unpublished, as presented here) group work (1:12:21).
- Altruism, division of labor, and colicin production: 1:14:34–1:17:56.
- Flagged as a topic with a dedicated future reading not included here ("we're going to read more about this later," 1:15:47).
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