Memory in microbes: quantifying history-dependent behavior in a bacterium

The transient behavior (first 11 hours) of the SpoIIE (sporulation) reporter clusters into five distinct classes of behavior (different onset times and sigmoidal vs. more pulsatile expression), whereas the transient behavior of the AprE (degradative enzyme synthesis) reporter clusters into three classes (different onset times and different expression levels) and the growth reporter into just two classes (some vs. almost no growth) (see left panels of Fig. 6a,b,c). The mutual information between the resulting clustering vectors and the cell history vector captures how well the different behavioral classes of each observable correspond to different cell histories. Performing this calculation, we estimate Itrans(spo) = 1.96 bits of short-term memory in the sporulation reporter; Itrans(AprE) = 1.4855 bits of short-term memory in the degradative enzyme synthesis reporter, and Itrans(OD) = 1 bit of short-term memory in the growth dynamics reporter OD600. Thus, all three observables exhibit short-term memory of the cell histories tested, with the sporulation reporter exhibiting the most memory and growth dynamics the least.

Dividing these absolute bit counts by the entropy of the cell history space, we estimate the short-term memory fidelities of sporulation initiation, degradative enzyme synthesis, and growth dynamics to be Ptrans(spo) = Itrans(spo)/H(M) = 1.96/3.3219 = 0.59, Ptrans(AprE) = Itrans(AprE)/H(M) = 1.48/3.3219 = 0.45, and Ptrans(OD) = Itrans(OD)/H(M) = 1/3.32≈0.3, respectively. This means that if one were to observe all 30 short-term responses of one of the three reporters after t0 but not told which history corresponds to which trajectory, 59% of the uncertainty about cell history prior to time t0 could be reduced by observation of the transient sporulation reporter dynamics after time t0, 45% of this uncertainty about the past could be reduced by observation of the degradative enzyme synthesis reporter dynamics after t0, and only 30% of this uncertainty could be reduced by observation of the growth dynamics after t0. More intuitively, one could say that 59%, 45% and 30% of the cell histories tested are ‘remembered’ by the short-term dynamics of the sporulation, degradative enzyme synthesis, and growth reporters, respectively (see Fig. 7 and Table S1).

Though short term memory can be important—because even short term behavioral differences may have fitness consequences [59], especially if they are on the order of environmental fluctuations [28], [60]—long term memory is generally the first thing that comes to mind when memory is discussed [61]–[64]. One might expect long term memory in B. subtilis stress responses-sporulation control especially-because of the feedback topologies in their regulatory circuitry and reportedly bistable behaviors [10], [36]–[39].

To estimate the long term memory in each individual pathway we first clustered the final segment of the 30 time series of each reporter (from 21 to 24 hours after t0) to estimate the number of distinct long-term behaviors for each of the three pathway reporters (results = 2 unequal-sized clusters for each reporter, as shown in Fig. 6, though the cluster sizes and associated cell histories differ across reporters). We then calculated the mutual information between the clustering results and the cell history vector to arrive at lower bound estimates of Iasym(spo) = 0.8813 bits, Iasym(AprE) = 0.72 bits, and Iasym(OD) = 0.97 bits of long-term memory in the networks controlling sporulation initiation, AprE synthesis and growth dynamics, respectively. Thus, like a switch, there appear to be two, stable, long term behaviors for each pathway reporter, though the probability of converging to each is not equal or the same across reporters, as is reflected by distinct bit counts of less than 1 (if half the past histories lead to one attractor and the other half of the histories lead to the other, there would be 1 bit of asymptotic memory).

Dividing these absolute numbers by the entropy of the cell history space, we estimate the long-term memory fidelities of sporulation initiation, degradative enzyme synthesis, and growth to be Pasym(spo) = Iasym(spo)/H(M) = 0.8813/3.3219 = 0.265, Pasym(AprE) = 0.22, and Pasym(OD) = 0.29, respectively. Thus, approximately 25% of the uncertainty about cell history prior to the onset of starvation is reduced by knowledge of any one of the three long-term reporter dynamics in the starvation environment. To summarize, all three observables exhibit around 1 bit of long-term memory of the histories tested, though of different aspects of cell history as will be shown below. One bit is a significant amount but much less than the nearly 2 bits of memory seen in the most retentive short-term response.

The above memory estimates are in a sense high-level, because each of the 10 distinct cell histories is treated identically. By drilling down a level of resolution to the component parts of the cell histories–initial nutrient composition of the media and cell density reached in that media (which can also feasibly affect both the nutritional composition of the medium and cell state while in log phase)–we can investigate which aspects of cell history are remembered by the observables and for how long.

In the short term, all three observables have a perfect memory of whether they were grown in LB or GM, and only a partial memory of their density in this medium. Put more formally, if we consider growth medium in isolation and calculate the mutual information between growth medium prior to time t0 and transient response of the three reporters to starvation after time t0, we see that a history of growth in LB can be distinguished from a history of growth in GM with 100% memory fidelity (Ptrans(Spo)(Medium1;Y;ttran s = 11 hrs) = Ptrans(AprE)(Medium1;Y;ttran s = 11 hrs) = Ptrans(OD)(Medium1;Y; ttran s = 11 hrs) = 1, where Medium1 is a random variable representing growth medium prior to time t0, and can take on the values GM or LB). In contrast, the ability of the pathways to remember the population density reached prior to t0 (and any changes in cell state these differences in cell density create) is less simple. With a history of growth in GM, the cell density prior to the onset of starvation at t0 is not ‘remembered’ by the short-term B. subtilis sporulation, degradative enzyme synthesis, or growth dynamics responses, even transiently (0% memory fidelity), as all responses are indistinguishable within noise (Itrans(Density1/Medium1 = GM;Y; ttran s = 11hrs) = 0). However, when grown in LB, the cell density prior to t0 is remembered with 80% memory fidelity by the transient sporulation dynamics and with 60% memory fidelity by the transient AprE dynamics (Ptrans(Spo)(Density1/Medium1 = LB;Y; ttran s = 11 hrs) = 0.8; Ptrans(AprE)(Density1/Medium1 = LB;Y; ttran s = 11 hrs) = 0.6).

In the long term, all three observables have only a partial memory of which medium they were grown in, and to what density. Like in the transient memory case, past growth medium is remembered better than past cell density, but unlike in the transient memory case, there is no perfectly clean dividing line separating out the long-term responses to the two growth media histories. For example, given observations of the long-term behavior of the sporulation reporter, a history of growth in LB can be distinguished from a history of growth in GM with only 39% memory fidelity (Iasym(spo)(Medium1;Y)/H(Medium1) = 0.39), whereas cell densities (grouped into five classes, (D,-1,-2,-3 and -4)) prior to t0 are remembered even less well, with only 12.1% memory fidelity (Iasym(spo)(Density1;Y)/H(Density1) = 0.121). A similar pattern can be seen in the long-term memories of the other two reporters. Interestingly, though each reporter exhibits two possible long-term behaviors, the clusters are different sizes and the histories that correspond to each behavioral cluster are different for different pathways. As will be shown in the next section, these differences lead to the possibility of an increased memory capacity in the higher dimensional space defined by the combined activities of multiple pathways.

Interestingly, analysis of the transient memory of the pairs of pathway readouts (Spo, AprE), (Spo, OD600), and (AprE, OD600)) shows no increase in memory in the higher dimensional space than is found in the most retentive pathway in the dyad (see Figure 7). For example, we estimate the transient memory found in the pair (AprE, OD600) to be 1.4855 bits, which is the same bit count found in AprE alone (Memorth(trans)(M;(AprE, OD600)) = (1.4855-1.4855)/(1.4855) = 0). Likewise, the three-dimensional readout (Spo, AprE, OD600) shows no more transient memory than is found in the sporulation pathway (1.96 bits), its most retentive member.

However, the same conclusion does not follow for asymptotic memory. Every pair of pathway readouts contains more asymptotic memory than either constituent signal, and the triple pathway readout contains more asymptotic memory (at 1.57 bits) than any of the constituent pairs (see Figure 7). This implies that the long term behavior of our three observables occupies a relatively high dimensional space, with each subsystem responding differently to aspects of past conditions. For example, though the AprE pathway is estimated to have only 0.7219 bits of asymptotic memory and the growth measure OD600 has only 0.971 bits of asymptotic memory, the pair (AprE, OD600) has 1.371 bits of asymptotic memory (Memorth(asym)(M;(AprE, OD600)) = (1.371-0.971)/(0.7219) = 0.554, or 55.4% of the maximum). Put more concretely, the asymptotic behavior of the AprE signal alone ‘remembers’ two classes of cell history: the first a history of growth in rich medium to higher densities and the second all other histories in the compendium. Whereas observations of the asymptotic behavior of the growth signal allow distinction between two different classes of cell history; the first growth in rich medium to all densities greater than the lowest tested (-4), and the second all other histories in the compendium. Viewed together as a combined vector in a higher dimensional space, the asymptotes of the pair (AprE, OD600) permit distinction between three classes of cell history: growth in rich medium to higher cell densities, growth in rich medium to low (but not lowest) and intermediate cell densities, and, finally, growth in rich medium to the lowest density or growth in poorer medium to any density. Adding the sporulation signal increases the information storage yet again, by adding another discernable class, leading to a total long-term combinatorial storage of 1.57 bits.

Thus, because the different cellular systems in B. subtilis remember different aspects of prior history, the combined activity of multiple pathways is able to combinatorially store more information about the past than can any individual pathway. However, the total asymptotic memory is still somewhat less than the total transient memory (1.57 vs. 1.96 bits). (For a complete accounting of cell history memory over all signal combinations, and for the mutual information between all pairs of signals, including the transient and asymptotic responses of each signal, see Figure 7 and Table S1.)

Though evidence that bacterial cells are able to remember their histories and use these memories to alter their behavior in a fitness enhancing manner would not raise expectations that bacteria could recite π or write music, it would enrich the motifs-modules-games view of bacterial regulation [12] by adding game strategies with memory to the repertoire of microbes. This exploratory paper does not provide evidence that B. subtilis, or any other microbe, is intelligent or is playing an evolved, fitness-enhancing memory strategy. Rather, in this work we propose that the familiar phenomenon of history-dependent behavior in microbes reflects a form of memory worth studying systematically and quantifying, and that doing so sets the foundation for understanding both the mechanisms and function of memory in cell behavior and fitness. To this end we formulated a conceptual information-theory based framework for measuring microbial memory, thereby introducing tools that begin to observe and quantify the relationship between past cell history and future cell behavior from a new angle. This method produces a phenomenological measure of cellular memory without regard to the specific cellular mechanisms encoding it.

We then applied these tools to a simple set of medium-shift experiments on B. subtilis, in the process demonstrating that B. subtilis does ‘remember’, both in the short and long term, aspects of its cell history, and that this memory is distributed differently among the observables. More short term than long term memory was evident, with short-term sporulation dynamics exhibiting the most memory and long-term degradative enzyme AprE synthesis dynamics the least. As expected, some but not all of the history-dependence between the sporulation and AprE reporters is shared (AprE has 75% of the short-term and 80% of the long-term memory estimated for sporulation). We also illustrated how to quantify memory in multiple combined variables, in the process showing that because the different cellular systems in B. subtilis remember different aspects of prior history to different degrees, the combined activity of multiple pathways is able to combinatorially store more information about the past than can any individual pathway. Of the two components of cell history varied in our compendium–past growth medium and the cell density reached in this medium, which can alter cell state even in log phase–growth medium appeared to be better remembered by B. subtilis, with past density remembered best when originally grown in the medium richest with nutrients, LB. Admittedly we do not yet know whether the memory we have observed is fitness enhancing and evolved or just incidental, or what molecular mechanisms or artifacts are responsible for the observed pattern of memory storage. Rather, these simple experiments and the surrounding analysis and framework demonstrate what could be the beginning of a larger memory program, and indicate that memory in cellular behaviors may be a rich area for further exploration.

A more complete program for investigating memory in bacteria would encompass at least three lines of inquiry, essentially the ‘what’, ‘how’, and ‘why’ of bacterial memory. The first line of inquiry (what), for which this study is an example, is the quantification of environmental memory in a microbe. This study could be extended by resolving the population-averaged behavior analyzed in this paper into single-cell measurements and memory classification and quantification. Given that sporulation is thought to be a stochastically triggered bistable developmental process [10], [36]–[39], one might expect the population-averaged measurements (Figure 5.b) to resolve into bimodal distributions of high and low GFP-expressing cells. And since AprE synthesis control is believed to be more deterministic and analog, one might expect more monomodal distributions. Preliminary data from flow cytometry analysis support this expectation, at least for some histories and time points (see Figure S1 in Supplemental Information), but further work is needed to determine for what conditions and pathways memory at the single-cell level can be classified as stochastic, and the form and quantification of this stochasticity. An exploration of the memory characteristics of other cellular players active in these and interacting networks, and the space of their environmental sensitivity, with the goal of estimating the ‘true’ memory capacity of the system, are other possible extensions of this work.

A second line of inquiry (how) would build upon the first by elucidating the causal basis for any observed environmental memory. Though many genetic and epigenetic bacterial switching mechanisms have been elucidated [8], [10], [16], still unclear is exactly how different types of environmental and intercellular signals might be encoded and remembered within cellular circuitry for varying lengths of time, a question addressable through mutant studies and modeling. On the ‘meta’ level one could ask whether memory is stored within single cells, population distributions, or in the larger state space defined by the cell-environment interaction through distributions of nutrients, waste products, enzymes, signaling molecules, biofilm generating conditions, and so on. A third line of inquiry could focus on the ‘why’s' of environmental memory. Is environmental memory, if it exists, controlled or incidental: evolutionarily advantageous, deleterious, or neutral? Is there evidence that memory-modulation of phenotype expression control does not provide a fitness advantage in the present but rather in a future implicitly anticipated from past experiences, thus implying an internal model of environmental dynamics (in analogy to the internal model principle in control [65])? We suspect that answers to these ‘why’ questions could be key to whether the others are worth deeply pursuing.

Though we do not yet know whether the memory we have observed is fitness enhancing and evolved, or merely incidental, we can speculate. Looking qualitatively at the three behavioral observables together, we notice that when cells are grown to low density in the less rich GM medium prior to the onset of starvation conditions, they on average grow very fast after resuspension in starvation media, and after a brief lag start turning on their degradative enzyme synthesis and their probabilistic sporulation machinery, even as the population continues to grow. Whereas when cells are grown in richer, nutrient filled LB medium to the same low density prior to the onset of starvation conditions, they take a quite different approach. In this case, cells seem to adopt a wait-and-see strategy, forgoing growth and delaying sporulation and AprE synthesis for many hours.

A game strategy with memory?: The most tempting speculation is that B. subtilis is playing a memory strategy in an evolutionary game. From a game perspective, one could take these observations as a sign that after transitioning from a less rich medium to starvation, B. subtilis uses its memory of past nutrient-limited growth in the context of an implicit internal model of environmental dynamics to ‘predict’ how long starvation conditions will last. If the cells expect starvation to last a long time, a rational course of action might be to create as many spores as possible, as fast as possible, to maximize the spore count that will lie dormant until the next period of nutritional plenty. On the other hand, if growth in a rich environment prior to starvation in the context of this internal model produces a prediction of a short period of starvation, the rational action might be to delay sporulation, thereby decreasing the chances of having committed irreversibly to an unnecessary, costly 8 hour developmental program during which conditions could improve and the cells could be growing. Viewed in this way, B. subtilis's cell-history dependent behavior might constitute an evolved probabilistic memory strategy in its game of survival. Such a strategy would trump diversification strategies without memory [28]–[30], [35], [66], [67], and be analogous to adaptive model-based bet hedging over a diversified portfolio in the stock market [28].

If the above scenario is true, one would expect sporulation initiation delay to be a likely feature of the sporulation regulation strategy of B. subtilis to exhibit memory. Within our experimental compendium, the delay in turning on the sporulation machinery, as estimated by the amount of time it takes for GFP to start being noticeably expressed from the SpoIIE promoter by a population (normalized GFP intensity >0.035, after which GFP rapidly increases), ranges from a relatively short 1.5 hours to a much longer nearly 8 or more hours after the onset of starvation (Figs. 5b and S2 in Supplemental Information). Calculating the mutual information between GFP expression delays and cell history, we see that most (86%) of the short-term memory in the sporulation reporter can be recapitulated by reducing the trajectories to this single number (I(M; Initiation Delay)/Itrans(M;Y;ttrans = 11hrs) = 1.685/1.96 ≈ 0.86). This calculation does not prove that the history-dependence we have observed is an evolved and fitness enhancing memory strategy in a game, but it is suggestive.

…or an artifact of metabolism?: Then again, the explanation could have little to do with evolutionary games. It could be that differences in metabolic stores, housekeeping apparatus, or metabolic state induced by the different media and different biomass of the culture simply represent initial conditions from which entry into sporulation and other stress responses is more or less easy [1]. For example there might be more ribosomes after growth in LB than there are after growth in GM, forcing cells coming from the latter to stop growth and initiate sporulation sooner. Or it could be that growth in GM, a medium that while not nutrient-limited is lacking the excess of simple carbon and nitrogen sources and readily available amino acids found in LB, activates metabolic pathways that can facilitate growth and spore formation in stress conditions. Then, when transferred to starvation conditions, cells might be able to use this metabolic machinery (and perhaps some form of intracellular nutrient storage) to scavenge whatever scarce nutrients are to be found in the new medium in order to grow and turn on their sporulation and degradative enzyme pathways nearly immediately. Whereas with a history of growth in rich, complex LB medium, cells might enter starvation conditions of SM without enzymatic or other reserves necessary for a near-immediate response to severely limited conditions, and thus require a delay while the cells construct the necessary metabolic machinery to acclimate to their environment.

These possibilities are not mutually exclusive; history-dependent behaviors could stem from some combination of evolved diversification game strategy and artifactual adaptive metabolic processes. Experiments comparing the fitness of wildtype bacteria to mutants with disrupted memory mechanisms coupled to a game theoretic analysis will be necessary to distinguish among the possibilities, and would identify the mechanistic source of memory behaviors in the process. In any case, we hope that this conceptual framework and analytical approach to quantifying memory in cellular behaviors will be a useful point of departure for studying a new set of questions about cellular regulation and evolutionary strategy in microbes.

Bacillus subtilis 168 trpC (Bacillus Genetic Stock center) was used as the wild-type strain. Escherichia coli strain DH5α was used for all plasmid amplifications and isolations. Escherichia coli was grown at 37°C in LB supplemented, when necessary, with ampicillin at a final concentration of 100 µg/ml. B. subtilis was cultured at 37°C in either LB, growth medium (GM) or sporulation medium (SM). GM and SM media are commonly used in the ‘induction of sporulation by resuspension protocol’ described by Harwood and Cutting [58] and were supplemented with 50 µg/ml and 20 µg/ml L-tryptophan respectively. Antibiotics were added, with the following final concentrations: chloramphenicol, 5 µg/ml; spectinomycin, 100 µg/ml.

Total genomic DNA from B. subtilis 168 was isolated with DNeasy Blood & Tissue Kit (Qiagen) following manufacturer's protocol for Gram positive bacteria. Plasmid DNA was extracted from E. coli with the QIAprep kit (Qiagen). DNA restriction and cloning were performed according to standard procedures [68]. Restriction enzymes and T4 DNA ligase were obtained from New England BioLabs and used according to the manufacturer's instructions. DNA fragments were purified from agarose gels with the QIAquick gel purification kit (Qiagen). Vent DNA polymerase (New England Biolabs) was used for PCRs.

Strains and plasmids are listed in Table S2 in Supplemental Information. To integrate the fluorescent reporter fusions in the B. subtilis genome the pLFKEE integration vector was constructed as followed. The GFP variant GFPmut2 [69] was excised from pMF19 [70] by digestion with BamHI/EcoRI enzymes and ligated into pEA18 (a gift from Antje Hofmeister) digested with the same enzymes, to give pLF22. The plasmid pEA18 (cmp, spc) is a vector [71] allowing integration by double cross-over at the amyE locus, with a chloramphenicol selection. The spoIIE promoter (PspoIIE) was amplified by PCR from B. subtilis 168 genomic DNA using primers PspoIIE-D/EcoRI (atcacggaattcaaatcggtttctcttgcagaagccg) and PspoIIEM-R/HindIII (atacaaagcttttatattcgttgcctgtcattatagcg), and digested with EcoRI and HindIII, then ligated 5′ of gfpmut2 on pLF22 that had been digested with the same enzymes to give pLF25 (PspoIIE-gfp, cmp). The transcriptional profile of the spoIIE gene was verified by total RNA dot blot before and after induction of sporulation to confirm its early and specific expression induction at the onset of sporulation (see Figure S3).

To obtain the PaprE-dsred fusion, the dsredexpress coding sequence was amplified by PCR from pDsRed-Express (Clontech) using primers DsRed-D/FseI (tacggccggcctaaggaggaactacaaatggcgagcagtgaggacatcatcaagg) and DsRed-X/EcoRV (agatatcgatcagatctacaggaacaggtggtggcg). The PCR fragment obtained was digested with FseI and EcoRV. A modified version of the aprE promoter (PaprE) (developed and tested in [72]) was amplified by PCR from pSG-TTGACA [72] using primers PaprESG-D/AgeI (tgaaccggttgtcaaacatgagaattcagcg) and PaprE-R/FseI (caaggccggccaaattcagagtagacttacttaaaagac). The resulting PCR fragment was digested with AgeI and FseI and ligated with FseI/EcoRV-digested dsredexpress into AgeI/EcoRV-digested pLF25 in a three-point ligation to give pLFKEE (PspoIIE-gfp, PaprE-dsred, cmp spc). Selection of plasmid constructions in E. coli clones was done by adding ampicillin as described above and correct fusions were verified by sequencing.

To construct B. subtilis KEE, pLFKEE was transformed into B. subtilis 168 competent cells as previously described [58] and selected on LB solid medium supplemented with chloramphenicol. Integration clones were screened for their amyE phenotype on LB+1% starch solid medium [58]. The inability of the clones obtained to grow on spectinomycin was checked to eliminate single cross-over plasmid integration events. Correct integration of the fusion at the amyE locus was verified by PCR analysis.

Before each experiment, cells were streaked from −80°C glycerol stocks on LB plates with chloramphenicol and grown overnight. One colony was picked and inoculated in 5 ml liquid LB medium with chloramphenicol in a series of dilution tubes and grown overnight at 37°C. The culture the closest to OD600 of 1.0 was used to inoculate 60 ml of LB or GM in 250-ml flasks to a final OD600 of 0.05 (flask D) after elimination of the culture medium by centrifugation of the cells (6,000×g, 3 min). The culture was split in two, and successive dilutions of 1:2 were performed to a total of 5 flasks of 30 ml culture (flask D and dilution flasks: -1, -2, -3, -4). Cells in all four flasks were grown simultaneously at 37°C, 200 rpm, until the most concentrated culture grew to an OD600 of 1.0 (Flask D). Then, 25 ml of each culture were harvested by centrifugation (8,000×g, 5 min) and resuspended in a pre-warmed SM medium volume calculated to obtain a final OD of 0.5 (medium density). Three aliquots of 200 μl from each flask were transferred to a sterile Costar 96-well black plate with flat clear bottom (Corning). Cells in the plate were grown in a Tecan Safire microplate spectrophotometer at 37°C medium linear shaking setting (395 rpm). Culture turbidity (OD600) and fluorescence were measured at 15 minutes intervals for a total time of 24 hours. GFPmut2 was read at wavelengths of 481 nm (excitation) and 507 nm (emission), and DsRedexpress was read at 557 nm (excitation) and 579 nm (emission).

There are a number of ways to translate the memory quantification definitions in Appendix S1 into an analysis algorithm. We took a simple fixed-interval, clustering-based approach executed as a five-step algorithm implemented the MATLAB© (http://www.mathworks.com/) analysis environment, as follows (see Supplemental Information Section S2 for schematic):

(step 0–select time intervals): The first step in analyzing the data is to select time intervals to analyze. We parsed the time series data (30 trajectories measured over 24 hours for each of three observables) into a ‘short-term’ set taken well before steady-state is reached (first 11 hours after t0, the onset of starvation–though we could have taken any endpoint between 8 and 19 hours and obtained the same result (see panel (b) in Section S3)) and an ‘long-term’ set. For our purposes, we take as our ‘proxy’ for long-term, asymptotic behavior the last three hours of our measurements, from 21 to 24 hours after t0, because by then all signals have remained flat for several hours. Experiments run for longer periods of time indicate that these signals remain flat for as long as we have measured them (36 hours, data not shown). However, we view this long-term data set as only a proxy for asymptotic behavior because though these signals remain constant for at least 36 hours, cells are forming spores and might be physiologically changing in other respects during this period and beyond.

(step 1–cluster data): We used the Matlab script in S2.2 to hierarchically cluster the 30 short-term and 30 long-term trajectories of each observable (10 cell histories×3 replicates) and to select ‘optimal’ clustering partitions for each. The assumption here is that the behavior of the observable (e.g., GFP intensity) falls into distinct classes, for example, increasing or decreasing. This script a) constructs a Euclidean distance matrix with the Matlab function pdist.m, b) constructs dendrograms using ward and average linkage with the function dendrogram.m, c) performs silhouette analysis on all tree cuts of both trees from (b) with the Matlab function silhouette.m [73], and d) ‘optimizes’ data clustering by selecting the partition that maximizes the mean silhouette, a measure of the compactness and separation of the clusters in the partition [73]. This step produced six 30×1 cluster vectors, one short-term and one long-term cluster vector for each of the three observables (i.e., ClustSPO_short, ClustSPO_long, ClustAprE_short, ClustAprE_long, ClustOD_short, ClustOD_short).

(step 2–estimate memory): Next we estimated the short-term and long-term memory in bits of each individual observable with the Matlab program Entropy_MutualInfo.m in S2.1. This program accepts two input vectors, A and B, and calculates from them individual informational entropies H(A) and H(B), the entropy of the pair H(A,B), and the mutual information between A and B, I(A;B) = H(A)+H(B)-H(A,B). H(X) is defined in Supplementary Information (Appendix S1), and H(X,Y) is calculated by first calculating the joint probability distribution over (X,Y) and then calculating the entropy H over this joint distribution. Thus, memory is estimated to be the mutual information between cell history and cell behavior and calculated by calling Entropy_MutualInfo.m with input vectors A = M = [1 1 1 2 2 2 …10 10 10], the cell history vector , and B equal to one of the six cluster vectors from step 1. To calculate memory fidelities, we normalized these memory estimates by dividing by H(M) = 3.32, the entropy of the cell history space.