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Sciences, Macro-Molecular a Santra Mantu aging cell death of and driver a is collapse Proteostasis rnia ikfco savnigae poal eas cell because “probably age, advancing diseases is 50 factor the than which risk for more principal (proteinopathies), in deposition in protein implicated decline abnormal is of the control proteostasis, the quality in to proteins protein Central the (17–20). protect proteome degrada- normally cell’s that synthesis, chaperoning protein and in tion, involved messenger systems proper quality-control of (12–16). age loss with the observed stoichiometry for protein and responsible RNA be stoi- Such may their (11). binding in changes factor transcription changes alter the and could Further, (10) levels chiometry (1). histone organization of depletion chromosomal significant modifi- of histone loss methylation, and DNA cation, include are changes genes These how how affect read. on proteins DNA-binding focusing and epigenetic, DNA are to changes theories of Other shortening Such 9). progressive (6). (8, the life telomeres and deleteri- throughout (7) mutations accumulate to include that changes importance DNA to primary changes ous attributing gene-centric, are stochastic mechanism and general the action. a take pinpoint about We a more than cell. be destruction the to longevity in biomolecule and location of aging spatial of class damage its which or Oxidative in hits limits. it nonspecific span and life can- indiscriminate gene abolish single is or Any cell. aging the reverse in failure not take system-wide we more which a mechanism, be aging to the of in question is here “top-down” gene-to-gene interest the by Our (1). or databases mutations sequence using point time— comparisons a or at knock-ins, genes knockouts, few from by comes a aging perturbing cellular by about experiments, known “bottom-up” is a what play of to Much known role. is key damage Oxidative impacts biomolecules. aging cellular because most effects from causes disentangle to difficult I afrCne o hscladQatttv ilg,SoyBokUiest,SoyBok Y11794-5252; NY Brook, Stony University, Brook Stony Biology, Quantitative and Physical for Center Laufer ihrognss el g n i yntrlprocesses. been has natural It by it? drive die that and mechanisms molecular age the are cells What organisms, higher n nte iwi htaigrslsfo elnn protein declining from results aging that is view Another theories Some (1–5). diverse are aging cell of Theories | aging a,b,1 | e .Dill A. Ken , xdtv damage oxidative htso h olwn:Lf pnshort- span Life following: the show that a,c,d,2 d | eateto hmsr,SoyBokUiest,SoyBok Y17430;and 11794-3400; NY Brook, Stony University, Brook Stony Chemistry, of Department misfolding n dmM .d Graff de R. M. Adam and , | chaperones a,e,1 1073/pnas.1906592116/-/DCSupplemental at online information supporting contains article This 2 1 ulse ne the under Published interest.y competing Negev.y no the declare and of authors University The Ben-Gurion M.S. A.B.-Z., and K.A.D., Institute; research; M.S., Weizmann U.A., and Reviewers: designed data; analyzed paper. A.M.R.d.G. the A.M.R.d.G. wrote and and A.M.R.d.G. and M.S. K.A.D., research; performed M.S., A.M.R.d.G. contributions: Author diverting in oxi- protein damaged on of conformation role modeling protein the Our of and 32). (38–40) impact (20, dizability critical studied the poorly proper- remain addresses downstream impact pro- their of and damage, understanding ties of solid upstream a properties to yield tein contributed folding have While (37). studies determining degradation these and folding principles Others between partitioning (33–35). broader or means (36) folding for the promote looked or systems 32) have chaperone (20, which activation heat-shock by of mechanism the age. (25, with oxidation declines and proteostasis temperature how any of and 31), impact how of of the biochemistry biophysics (30), cell-wide and fold the proteins on genetics but the protein, or on gene com- particular not important an focus changes is of it We set 29), ponent. broad (15, age a with of proteome one the degradation only impacting and is damage (24) protein synthesis While protein function (28). and impaired stability to their of and loss (25–27) bet- 24). to (23, lead is can damage radiation proteins DNA to by of Damage than survival oxidation as protein by resistance, predicted such ter of is measure known damage “all and key stress Protein that a (22). cell to noted stress” the to been response resistance has of confer of It gerontogenes repairers natural (10). line genome primary front the a the of a sustainers are is is proteins Proteostasis it because because and (21). aging age” in culprit with compromised increas- becomes ingly disposal and production protein and regulation owo orsodnemyb drse.Eal [email protected] Email: addressed. be may correspondence whom work.y To this to equally contributed A.M.R.d.G. and M.S. iepeitoso h iesa fteworm the of span life elegans. the quantita- negative several of the makes predictions when model tive happens The the death positive. in the to proteins overwhelms point tipping aggregated The and leading cell. misfolded proteins, damaged accumulating irreversibly to fold to trying dis- tracted are chaperones garbage The overfilled exceeded. is and—like synthe- capacity down, cans—chaperone healthy slow proteins, degradation cell’s and sis the in damage randomly Oxidative increase: accumulates processes negative age, with folded). 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BIOPHYSICS AND COMPUTATIONAL BIOLOGY the limited chaperone resources away from the folding of their Synthesis undamaged counterparts (40, 41). Premises of the Proteostasis Collapse Model Here is our model of proteostasis collapse with age. The mathe- matical details, parameters, and justifications are given in Mate- Undamaged rials and Methods and SI Appendix. First, each protein in the N proteins cell has a rate of folding, unfolding, misfolding, and aggrega- tion. Many of these rates are known (33, 43, 44). Here, we considered a single type of average protein—namely, ones that U are clients of the HSP70 chaperone system, because of exper- iments (45) and theory (40) showing that these proteins are the dominant targets of protein oxidation. Second, we modeled M the trafficking of proteins on and off of chaperones. Many of Oxidative these rates, too, are known (46–49). Third, whereas these first 2 damage aspects—folding and chaperone trafficking—describe only nor- A mal proteostasis in young healthy cells, we included also a slow, cumulative oxidative-damage component that is known for cell growth and protein degradation (50, 51). Some of this damage will be irreversible, leading to proteins that cannot reach their functional native structures and thus are biased toward misfold- ing and aggregation. Of necessity, we leave out many details, such as the folding of membrane proteins, the mitochondrial gener- Damaged ation of energy, and regulatory processes. It is not our goal to proteins model everything. Here are the premises:

1) Each protein in a cell has an intrinsic propensity to fold or Uox misfold. Most proteins carry out their function only when in their properly folded, native conformation (17–19). Here, we Mox model the folding process of an average HSP70 chaperone- dependent protein as it transitions between 4 conformational states: its folded, functional native state (N), unfolded state A (U), misfolded state (M), and aggregated state (A) (Fig. 1). ox The interconversion processes are modeled by using cou- pled Ordinary Differential Equations (ODEs) (Materials and Methods and SI Appendix). The transition rates and equilibria Fig. 1. Proteostasis model of cell aging. In the model, proteins convert between these states were previously determined (33, 40, 42), between native (N), unfolded (U), misfolded (M), and aggregated (A) as well as their dependencies on temperature (SI Appendix). states (upper plane) with rates estimated from experimental data (33, 42). 2) Each protein sustains damage at a rate determined by its Chaperone-dependent folding of newly synthesized or thermally unfolded foldedness. A principal cause of proteome aging is oxidative proteins compete with the processes of protein oxidation, aggregation, and damage (27, 52). Both experimental (38, 39) and theoretical degradation, collectively defining the quality of the proteome and pro- teostasis at a given age. The lower plane describes the interconversion of (40) studies support the idea that nonnative conformations oxidatively damaged unfolded (Uox ), misfolded (Mox ), and aggregated (Aox ) are the major target of oxidative damage. As in previous work states. Chaperones are represented by yellow disks. (40), the flux of damage Jdam = kdam[U ], where kdam is the rate constant of damage, scaling proportionately to reactive oxygen species (ROS) levels, and [U] is the concentration of unfolded protein (see SI Appendix, Table S1 for parameter hence ROS) has been shown to significantly amplify the heat- values). Once oxidized, proteins are assumed to be unable to shock response during the periods of high mistranslation, a fold, as shown in Fig. 1, consistent with experiments (45). process evoked when chaperones become titrated (45). Due 3) Chaperones modulate the foldedness and damage levels of to the inability of irreversibly damaged proteins to fold, their repeated binding to chaperones creates a futile cycle that can their client proteins. Chaperones are proteins that help other only be terminated by their degradation or aggregation. proteins (their clients) fold. By binding to nonnative con- 5) Proteome health also depends on the rates of synthesis and formations and giving them a fast route to folding, ATP- degradation of proteins. To complete the model, we there- dependent chaperones are responsible for maintaining a high fore need to know how the rates of cell growth kgr (t) and degree of foldedness (53). The collective effect of these chap- degradation k (t) change with age, t. Given the highly regu- erones, called foldases, is modeled by taking the kinetics and deg lated nature of these processes, it is outside the scope of the concentrations of their dominant member, the HSP70 chaper- current model to predict them from first principles. Instead, ones (12) (SI Appendix). Given that nonnative conformations since both have been measured experimentally (12, 50) (SI are thought to be the major target of oxidation, chaperones Appendix, Fig. S1), we take them as inputs to the model, play a key role in controlling damage levels (40, 45). o −λgr t 4) Chaperones can become preoccupied handling damaged pro- approximating the data using exponential fits: kgr = kgr e o −λdegt o o teins that are unable to fold, preventing them from helping and kdeg = kdege , where kgr and kdeg are the initial values. their undamaged client proteins that are either newly syn- The decay constants are determined from fitting the exper- ◦ −1 thesized or spontaneously unfolded (54–56). Experimental imental data, giving values at 20 C of λgr = 0.4 d and −1 support for this assumption includes the increased chaper- λdeg = 0.14 d , respectively. These rates are assumed to one binding observed for proteins with disease-causing point scale with temperature following Arrhenius kinetics, doubling mutations, which mirror the destabilizing effects of side-chain roughly every 8 ◦C, as observed for enzymatic processes (SI oxidation (25, 57, 58). Further, the presence of oxygen (and Appendix, Eq. S4 and Table S1).

2 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1906592116 Santra et al. 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Fig. atae al. et Santra C AB IAppendix (SI ODEs the solving By anradtselegans Caenorhabditis ncl gn,oiaiedmg ed oicesdmsodn and misfolding increased to leads damage oxidative aging, cell In at µ T = = D −d T 20 = (lnS ◦ 20.1 .Tevria ahdln shows line dashed vertical The C. )/dt ◦ and rdsmos.Teblack The symbols). (red C eciigtedeath the describing aeil n Meth- and Materials S (t ) t A reflecting h cor- the ; i.2A Fig. and Age- ) B). lp qa oteatvto nryo h rcs.However, process. the of energy activation 3C the Fig. to equal the 1/T vs. slope of living) a plot of rate a a so is (which reactions, (T span these life inverse of the of speed aging logarithm of the rate to the theory, proportional that is In 65). acceleration (64, reactions temperature-dependent Arrhe- biochemical of the of chemistry dictating physical the kinetics metabolism, from nius faster expected of is turn, because in temperatures which, sup- higher span to at life appear shorter that (63)—namely, is observations Hypothesis such Rate-of-Living Qualitatively, the port (61). d 10 only ss iesa a eakbeadsrn eedneon dependence elegans strong example, tis For considerably. and shortens span organ- remarkable life temperatures, ismal higher a at Maintained 61). has (51, temperature span life Temperature. 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Span Environmental Life on Depend Span Life Does How rate mortality the modeled of and probability discussion survival 62) For (61, (62). experimentally elsewhere seen mortality in slowing Gom- 2 survival observed associated (Fig. the and probability rate with The mortality consistent (12). time-dependent plateau qualitatively pertzian, a also misfolding appears reaching is that protein before aggregation model (60) increased of dam- exponentially onset 2) in grow rapid 27); the to rise 3) (25, finally, exponential and, 2B) an (59); (Fig. 1) levels find: age which experiments, with iepoensnhss hw t1 ,ad3do dlho bu,gen and green, (blue, adulthood processes of d enzymatic 3 than and respectively). 2, lines, faster 1, red increases at shown line) synthesis, (black protein unfold- like proteins average effectively of the and rate temperature, bind increasing ing to With allowed (D) represents not chaperones. curve are deplete proteins cyan high damaged The at if line). experimentally prediction orange prediction observed the S2, the rate Fig. is growth Appendix, line slowed (SI green the temperatures The of model. absence current the the repre- in line of blue prediction The the in behavior. sents regions life-span distinct dominate shows processes temperature (C different absolute (61). which inverse al. of et function a Stroustrup as in span reported 20 those are orange, brackets to the black from are, (30 Stroustrup temperatures tem- from The different data (symbols). (20.1 Ward at experimental (61) and mortality with al. Voorhies of compared et Van rates lines) and Predicted (solid circles) (B) peratures (red triangles). (61) (orange al. (51) et experimental Stroustrup with life from compared of line), data decay (black Predicted temperature (A) increasing proteins. with of span properties fundamental the by tated 3. Fig. C AB ◦ steaslt eprtr)sol ieasrih iewith line straight a give should temperature) absolute the is ) 30 C), ◦ ) 22.1 C), eprtr eedneo uvvlpoaiiyadlf pni dic- is span life and probability survival of dependence Temperature hw htlf pnflosamr ope behavior complex more a follows span life that shows ◦ rw at grown (30.9 C ◦ (23.7 C ◦ ) 31.3 C), 20 S C ◦ (t ) 25.5 C), ◦ and see ), ie bu 2d e at yet d, 22 about lives C ◦ (31.3 C ,atog tde aklate-life lack does it although D), IAppendix. 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BIOPHYSICS AND COMPUTATIONAL BIOLOGY ABdangerous feedback loop that may explain why the heat-shock response is highly sensitive to the presence of damaging free radicals (41). The increasing diversion of chaperones away from the folding of newly synthesized proteins may also be why, above 28 ◦C, an additional behavior is observed experimentally: Growth begins to slow (SI Appendix, Fig. S2). In this extreme heat, slowing growth may be one of the few mechanisms the cell has to dimin- ish the folding burden and delay proteostasis collapse. To test this, we modeled aging with (blue) and without (green) slowed Fig. 4. Effect of oxidative damage on survival probability and life span. growth (Fig. 3C). The difference between the 2 curves suggests (A) The predicted dependence of life span on the concentration of exter- that slower synthesis provides a modest benefit to life span, pre- ◦ nal oxidant, tBuOOH (black solid line), compared with experimental data dicted to make a 2-fold difference by T = 35 C. It reiterates [red circles; Stroustrup et al. (61)]. Beyond a critical concentration (0.5 mM), a key result observed throughout our modeling—namely, that life span drops sharply in an approximately power-law fashion. (B) The proteostasis capacity is tightly coupled to the rate of protein age-dependent rise in protein damage is shown for 3 concentrations of synthesis. tBuOOH (indicated by vertical dashed lines in A). The vertical dashed lines In short, while our model does show a component of life span in B indicate the average life span. that is attributable to the rate-of-living via metabolic speed-up, it also shows an additional component based on cell stresses. As the cell is stressed by heat, proteins unfold, misfold, and aggregate. than the Rate-of-Living Hypothesis would predict. Our model Chaperones are recruited, but with age, the synthesis of “good gives the following interpretation. protein” and the chaperoning of those spontaneously unfold- Heating at normal temperatures between 15 ◦C and 24 ◦C ing ultimately succumb to damage levels, at which bad protein increases metabolism. Across the proteome, and across species, becomes overwhelming. enzymatic rates are known to roughly double for every 8 ◦C rise in temperature, following Arrhenius kinetics (SI Appendix, Life Span Shortens with Added Oxidant Concentration. Since oxi- Eq. S4). Around room temperature, the dominant proteosta- dation is a well-known aging agent, adding an oxidant to cells sis processes—synthesis, folding, degradation, and their rates of should decrease their life span, as shown in recent experiments decay—all scale similarly with temperature, causing life span (61). To explore the behavior predicted from the proteosta- to scale inversely with metabolic rate. Thus, over this nar- sis model, we assumed that damage to the proteome occurs in row temperature range, life span scales consistently with the linear proportion to the amount of oxidant, consisting of the Rate-of-Living Hypothesis (63). basal level of ROS made by the cell as well as that from the At Temperatures from 24 ◦C to 28 ◦C, Protein Unfolding Rates added oxidant tert-butyl hydroperoxide (tBuOOH). The dam- Begin to Exceed Synthesis Rates. Protein unfolding rates have age rate can be expressed as k = k o (1 + [tBuOOH ] ), where dam dam co a steeper temperature dependence than other proteostasis pro- o k is the rate of damage in the absence of tBuOOH and co is 4 ◦ dam cesses, roughly doubling every C (66, 67). By using kinetics a constant with units of concentration, determined by the best inferred previously for HSP70 clients (33), unfolding rates are fit to experimental data. Fig. 4A shows that the predicted life predicted to catch up to the rates of protein synthesis in early span (black curve) agrees well with the experimental measure- adulthood within this temperature range (Fig. 3D). This rapid ments [red points; Stroustrup et al. (61)]. Life span changes acceleration of spontaneous unfolding of proteins is a central very little at low levels of tBuOOH, as it makes only a small reason why greater chaperone levels are beneficial at higher contribution to the overall damage rate. However, beyond a crit- temperatures, regulated through the heat-shock response (68). ical value, life span drops sharply. The age-dependent rise in Yet, oddly, this stress response is turned off very early in protein damage is shown in Fig. 4B for 3 values of [tBuOOH] C. elegans adulthood (69). Other stress-response pathways such (shown by vertical dashed lines in Fig. 4A). Consistent with as the mitochondrial unfolded protein response and the endo- the experimental observation, the extent of damage at death plasmic reticulum unfolded protein response are also strongly (Fig. 4B, vertical dashed lines) increases with shortening life down-regulated (59) by a mechanism that can be modulated by span (74, 75). gonadal signaling (70–72) and dietary restriction (73). Given that a single temperature was used to raise the worms (61), our model therefore uses a single, constant chaperone level for all adult temperature conditions and ages (12). A B Heating at Temperatures Above 28 ◦C Rapidly Fills Available Chaperone Capacity, Forcing Protein Synthesis to Slow. Life span is predicted to shorten much more rapidly at temperatures above 28 ◦C, as unfolding loads begin to overshadow synthesis (SI Appendix, Effective Parameters). The temperature dependence of the total unfolding burden faced by the cell thus transitions from a synthesis-dominated regime, where the burden doubles every 8 ◦C, to an unfolding-dominated regime, where the burden dou- bles every 4 ◦C. At such high unfolding loads, we hypothesized that life span might be particularly sensitive to the burden from Fig. 5. Increased chaperone capacity extends life span. (A) Chaperone dependence of relative (rel.) life span (τ/τo, where τo is the life span with damaged proteins. To test this, we modeled aging with (blue) ◦ ◦ and without (cyan) the ability for damaged proteins to bind wild-type [WT] chaperone level) at T = 20 C (blue line), T = 25 C (orange line), and T = 30 ◦C (red line). The predicted increase of life span (orange chaperones. Consistent with our hypothesis, chaperone distrac- line) quantitatively captures the experimentally observed life span exten- tion by damaged proteins begins decreasing life span between sion at = 25 ◦C (black triangles) (77). ( ) The temperature dependence of ◦ ◦ T B T = 28 C and 31 C (Fig. 3C). This sensitivity is further com- life-span extension due to a 2-fold increase in chaperone level with (solid pounded by the rising levels of unfolded, oxidation-prone pro- line) and without (dashed line) the ability of chaperones to bind, and thus teins at these temperatures. Together, these processes provide a be titrated by, damaged protein.

4 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1906592116 Santra et al. 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Life an Extend Can Properties? Overexpression Cellular Chaperone on Depend Span Life Does How model the is line diversion. dashed chaperone capacity The of degradation absence line). the increased (solid in of prediction temperature benefit on at The highly (B) data depends type. experimental wild temper- are WT, different symbols at relative; span black life The increase to atures. predicted is capacity degradation 6. Fig. on—iia ocaeoe—htlf pncnb extended we be model, can span the life in chaperones—that dam- capacity to protein degradation found—similar of proteins up-regulating regulatory cell of By the levels on the (83). ridding controlling span by directly indirectly by and life shown age span cellular been life has extend of overexpression to dependence Proteasome the rates. degradation predicts Span. also Life Extends model Machinery Degradation the Overexpressing high at synthesis up- decreasing 5B by strongly temperatures. capacity Fig. be chaperone (69), up cannot freeing worms of chaperones adult As in we line). regulated disappeared behavior, chaperones. dashed largely bind model 5B, behavior to nonlinear (Fig. this strong proteins the damaged in did, of we role When ability central dam- the if off a test turned synthesis play To protein S2). proteins of Fig. aged Appendix , inhibition (SI the experimentally and observed diversion chaperone in AB .C oi .Ceml,Aigadmlclrchaperones. molecular and Aging Csermely, P. Soti, defective C. of interactions 4. aging. The ageing: of of theory network science A Kirkwood, odd T. Kowald, of A. the hallmarks 3. The Understanding Kroemer, G. Kirkwood, Serrano, M. T. Partridge, 2. L. Blasco, M. Lopez-Otin, C. 1. u (2003). process. ageing the in scavengers Res. and Mutat. radicals free proteins, aberrant mitochondria, (2005). aging. ≈ 0.4 28 Increasing (A) span. life extends capacity degradation Increased Cell d ◦ −1 1411 (2013). 1194–1217 153, oi ie,cicdn ihtesaprise sharp the with coincident line), solid 5B, (Fig. C 0–3 (1996). 209–236 316, .elegans C. T at 25 = T 20 = ◦ ,a 0 nraei hprn ee can level chaperone in increase 80% an C, 5.Ti si uniaieagreement quantitative in is This ≈45%. 7,7) ri is(0,admc (81). mice and (80), flies fruit 79), (78, ◦ al S1 Table Appendix, (SI C hw h importance the shows x.Gerontol. Exp. T h oe gives model The = Cell 20 .T explore To ). ◦ 1037–1040 38, 437–447 120, .(3.rel., (83). C. The r aiaBobr o sitnewt grs n h eiwr o their for reviewers work; the this and initiate figures; helped with comments. helpful assistance that for insight Bromberg valuable thank Sarina We her Dr. PHY1205881. for Grant Dong NSF Meng-Qiu by Dr. and Biology Quantitative and Physical ACKNOWLEDGMENTS. 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(Fig. (83) significantly otlt ae easmdta twspootoa otedmg level damage the the to predict To proportional aging. was of it relation: the that biomarker following assumed a we as rate, considered mortality generally is level age as time this defined we (61), al. et Stroustrup in param- associated eters the changing dam- by level) oxidative proteasome or (temperature, level, interest chaperone age, of stress the imposed the 20 we to day, at this corresponding fixed of change end simulation temperature the keeping After The stress. d, oxidative S1). external 1 of Table further absence a Appendix, for (SI out carried degradation was and growth of decay corresponding of point point, proteins, starting this the of to At concentrations complexes. of chaperone-bound independence and time chaperones, the by indicated as state, (t age to system T the allowing to Prior .E lcbr,C rie,J zsa,Tlmrsadtlmrs:Tept rmmaize, from path The telomerase: and Telomeres Szostak, J. Greider, C. Blackburn, E. 8. Bahar R. cancer. and 7. aging, damage, DNA Hoeijmakers, J. 6. laryn- palatal, with difficulty Respiratory Chawda, S. Simonds, A. Taylor, R. McAuley, J. 5. deg gr = h urn oe rdcsdmg ee ihicesn g.Tedam- The age. increasing with level damage predicts model current The Tetrahymena heart. (2009). eladrsiaoymsl rmri dl-ne lxne’ disease. Alexander’s (2017). adult-onset 10.1136/bcr-2016-218484 in tremor muscle respiratory and geal a ntaie t20 at initialized was (t ◦ 20 ,yticesdlf pnb 5 t25 at 25% by span life increased yet C, ,wee[P where ), ◦ o ogeog 1 )t aesr httesse ece steady reached system the that sure make to d) (10 enough long for C (t olwn h xeietlcneto of convention experimental the Following S1 . Table Appendix, SI Nature ] rwh[k growth )], nrae elt-elvraini eeepeso naen mouse ageing in expression gene in variation cell-to-cell Increased al., et h oe xlis2rmral exper- remarkable 2 explains model The elegans. 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