Dynamics of translation can determine the spatial organization of membrane-bound proteins and their mRNA Elgin Korkmazhana, Hamid Teimourib,c, Neil Petermanb,c, and Erel Levineb,c,1

aHarvard College, Harvard University, Cambridge, MA 02138; bDepartment of Physics, Harvard University, Cambridge, MA 02138; and cFAS Center for Systems Biology, Harvard University, Cambridge, MA 02138

Edited by William Bialek, Princeton University, Princeton, NJ, and approved October 17, 2017 (received for review January 17, 2017) Unlike most macromolecules that are homogeneously distributed these patterns are determined by the organization of the cod- in the bacterial cell, mRNAs that encode inner-membrane proteins ing sequence, the presence of slow codons, the rate of transla- can be concentrated near the inner membrane. Cotranslational tion initiation, and the availability of auxiliary proteins required insertion of the nascent peptide into the membrane brings the for membrane targeting (referred to as the secretory machinery). translating ribosome and the mRNA close to the membrane. This By calculating the distribution of the number of proteins placed suggests that kinetic properties of translation can determine the together in the membrane, we suggest implications of mRNA spatial organization of these mRNAs and proteins, which can be localization on the organization of proteins on the membrane. modulated through posttranscriptional regulation. Here we use a We thus propose a mechanism for the formation of protein clus- simple stochastic model of translation to characterize the effect of ters in the membrane and investigate its implications on the reg- mRNA properties on the dynamics and statistics of its spatial distri- ulation of their size distribution. bution. We show that a combination of the rate of translation ini- tiation, the availability of secretory apparatuses, and the composi- Model tion of the coding region determines the abundance of mRNAs near We model an mRNA molecule as a one-dimensional lattice with the membrane, as well as their residence time. We propose that the L sites and open boundaries (Fig. 1A). Each site can be occu- spatiotemporal dynamics of mRNAs can give rise to protein clusters pied by at most one ribosome. A ribosome enters the first site on the membrane and determine their size distribution. of the lattice at a rate α if that site is empty. Once in the lattice, they move unidirectionally, hopping from one lattice site to the translation | spatial organization | membrane proteins | protein clusters next at a rate γ when it is empty. Ribosomes at the very last site exit the lattice at a rate β. This model, known as the TASEP, is ecent imaging techniques reveal the subcelllular locations a canonical model of nonequilibrium statistical mechanics and Rof macromolecules in bacteria (1, 2). In contrast with the has been used—among many other things—to study aspects of prevailing view of the bacterial cell as a spatially homogeneous translation (14–17). reactor, these studies reveal an unexpected degree of subcellu- In the cell, the translation initiation rate α depends on the con- lar organization. In particular, some mRNAs have been shown centration of free ribosomes, which varies with the growth rate to exhibit distinct localization patterns (3, 4). Large-scale assays and stress level of the bacteria. The initiation rate of individ- demonstrate that mRNAs that code for inner-membrane bind- ual mRNAs depends on the affinity of ribosomes to their RBS, ing proteins are highly enriched near the membrane (5). This as well as their folding structure, which may interfere with ribo- is believed to be the result of cotranslational insertion, whereby some binding (18). In addition, the rate of translation initiation a nascent peptide is inserted into the membrane as soon as a membrane-targeting signal or domain has been translated, bring- Significance ing the translating ribosome and the entire polysome to the vicinity of the membrane (6, 7). Mechanisms of cotranslational insertion are under intense research due to their importance Unlike their eukaryotic counterparts, bacterial cells are com- and universality (8, 9). Membrane association of mRNAs has posed of a single compartment. This allows many rapidly also been suggested to affect the organization of the bacterial diffusing macromolecules, such as proteins and mRNAs, to chromosome through “transertion,” the mechanism by which be evenly distributed in the cell. Important exceptions are cotranslational insertion and transcription occur simultaneously proteins embedded in the cell membrane, which transport (7, 10, 11). material and information across the membrane. Often these In bacteria, messenger RNAs are translated in the cytoplasm proteins attach to the membrane before their translation is by diffusible ribosomes. Ribosomes bind the mRNA at a ded- complete, anchoring their mRNAs to the vicinity of the mem- icated ribosomal binding site (RBS) at the upstream (5’) end brane. This coupling between translation and localization sug- and translate the coding region until they reach a stop codon, gests that the dynamics of translation may shape the spa- where they release the newly synthesized protein and the mRNA. tial organization. In this paper, we use a canonical model of This suggests that translation can be localized near the mem- nonequilibrium statistical physics to characterize this connec- brane as long as one of the translating ribosomes is attached tion and show how tunable kinetic properties allow the cell to to a membrane-bound nascent protein. The rate of translation initiation varies widely among different genes and is influenced regulate the spatial organization of both mRNAs and proteins. by physiological and environmental cues. Elongation rate is less Author contributions: E.K., N.P., and E.L. designed research; E.K. performed research; H.T. sensitive, but rare codons may stall the elongating ribosome and and N.P. contributed new reagents/analytic tools; E.K. and E.L. analyzed data; and E.K. slow down translation. and E.L. wrote the paper. Here we use a simple model, based on the totally asym- The authors declare no conflict of interest. metric exclusion process (TASEP) (12, 13), to investigate how the dynamics of translation determines the spatial pattern of This article is a PNAS Direct Submission. membrane-bound proteins and their mRNAs. We find that This is an open access article distributed under the PNAS license. within the range of parameters typical to model bacteria, the spa- 1To whom correspondence should be addressed. Email: [email protected]. tial organization of mRNAs can range from a homogeneous dis- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. tribution to a strong bias toward the membrane. We show how 1073/pnas.1700941114/-/DCSupplemental.

13424–13429 | PNAS | December 19, 2017 | vol. 114 | no. 51 www.pnas.org/cgi/doi/10.1073/pnas.1700941114 Downloaded by guest on September 29, 2021 Downloaded by guest on September 29, 2021 fsite if 25). site 24, (20, different significantly not that typically assume are we they convenience, as For 23). 22, (20, that 0.2 cor- means model This for this codons. values in typical 10 site about a here use that to we understand results, responds and exact known TASEP of simple simplicity use the make the to maintain and To model TASEP. the simple of quali- exclusion the are the to that of similar results length tatively yields the generalization This extending (14). by interaction account have models into Previous this codons. 10 taken about to extends footprint their paper. the of We end substantial. the be While toward can possibility impact (21). this their structure explore rare, are mRNA codons” unfavorable “slow or such competition slow tRNAs include locally scarce some that that for However, mechanisms codons through variation. adjacent elongation such or down ignore individual genes mostly harbor individual we mRNAs in and controlled 20), readily (10, be cannot and conditions okahne al. et Korkmazhan < (α/γ tran- phase nonequilibrium With exhibits sitions. model this lattice infinite an Information. Supporting occupancy the studying on therefore is focus Our gene. of effect to gene from and the Thus, (19)]. RNAs posttranscriptional rate regulatory for small cell through the [e.g., by regulation controlled dynamically be can membrane. the from away diffuses mRNA vicinity the mRNA, the membrane from detaches the and to (iv PSR mRNA the in somes the brings and (iii protein nascent bound translat- (ii completed SRR has the ribosome translating ing no (i as long vicinity as membrane cell the the in to diffusing mRNA an of Localization (B) region first recognition the signal The comprises boundaries. (SRR) open with TASEP the of view matic 1. 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Fig. of γ PSR ) g ftersdnetime residence the of +1 )γ (γ ` ` i.S2A). Fig. 0.Tefollowing The ∼100. Φ(t (γ Φ(t ftePR(i.2 (Fig. PSR the of + | + s ) ) o.114 vol. h ieo h PSR, the of size the α, ) steeoetedistri- the therefore is s −(g n t einare median its and ) −` +1) Φ(s ˜ | ) , ii u rttask first Our o 51 no. numerically. fFg 1B). Fig. of t pn by spent α | C ` Φ(t (Fig. 13425 sites and [1] ),

BIOPHYSICS AND PHYSICS COMPUTATIONAL BIOLOGY AB somes rather insensitive to the precise value of α. Irrespective of the details of the waiting time distribution, the mean time spent away from the membrane is given by 1/α for α . 0.5, where it saturates at approximately 2/γ (Fig. 3B, Inset).

Subcellular mRNA Organization. In previous sections we calculated the residence time of an mRNA near and away from the mem- brane. We now explore the implications of cotranslational mem- brane insertion on the subcellular organization of both mRNAs and the proteins they encode. When an mRNA is not kept near the membrane by a ribosome that synthesizes an already-bound nascent protein, it is free to CD diffuse in the cytoplasm. Once one of the translating ribosomes clears the SRR, this free diffusion can bring the nascent peptide to the membrane, where it will be inserted. Diffusion of polysomes in the bacterial cell is very fast (31), such that an mRNA in the middle of a cell is expected to reach the membrane in 0.5 to 4 s. Compared with the translation rate of ∼ 15 codons per sec- ond, we take transport to the membrane to be instantaneous and simply describe mRNA localization in terms of one of two states: cytoplasmic and membrane-localized (20, 29). We assume that different events in which an mRNA becomes localized occur at independent positions on the membrane. Fig. 2. Distribution of residence times near the membrane. (A) The effect In Fig. 4A we show the steady-state ratio between the proba- of translation initiation rate α on the probability density for a PSR of size bilities of the two states. With short- and medium-length PSRs, a ` = 10. (Inset) Mean residence time increases with the ratio α/γ between population of mRNAs can be significantly represented both near translation initiation and elongation. (B) Same, for a PSR of size ` = 30. (C) the membrane and in the free-diffusion state, as long as its trans- The effect of length ` of the PSR on the probability density for α = 0.05γ. lational activity is not very high. Importantly, in these cases, the (D) Same, for α = 0.2γ. subcellular localization of these mRNAs can be modulated sig- nificantly by posttranscriptional regulation of translation initia- tion. This can be done, for example, by small regulatory RNAs, D). As expected, for small values of α the distribution is well- as in the case of shiA, whose translation is activated by the small approximated by a Gamma distribution that is dominated by the RNA RyhB (28). time it takes a ribosome to walk through the PSR (on average The situation is different if a protein presents a membrane- `/γ). For a very short PSR, the median residence time near the targeted domain early in its coding sequence. This, for exam- membrane exceeds the typical lifetime of a bacterial mRNA (a ple, is the case for proteins whose N terminus sequence is rec- few minutes) when α take values at the higher end of the typi- ognized by the SRP. Unless the translation of such an mRNA cal range. With a larger PSR, this is also true for more moderate is extremely inefficient, our model predicts that such mRNAs values of α. However, our results suggest a very broad distribu- spend their entire lifetime in the vicinity of the membrane. This tion of residence times near the membrane, suggesting frequent is also true for mRNAs that have shorter PSR but are translated events in which an mRNA leaves the membrane after a short with high efficiency. However, as discussed below, these conclu- stay, even under the condition where the mean residence time is sions are revised if the secretory machinery (such as the SRP) is very long. scarce or rate-limiting. Many RNA nucleases are found on or near the membrane, Distribution of Residence Times Away from the Membrane. We now possibly accelerating mRNA turnover there (5). In this case, consider the probability distribution for the residence time away transcripts that are more biased toward the membrane have a from the membrane, which we denote by Θ(t). Periods spent shorter lifetime and are expected to produce fewer proteins (Fig. away from the membrane correspond to time intervals in which S4). Notably, if degradation occurs through a multistep pro- no ribosome on the mRNA is attached to a nascent peptide that cess (e.g., through recruitment of small RNAs), this modulation is targeted to the membrane; namely, no ribosome resides in the PSR. In Supporting Information we obtain an exact expression for Θ(t) in terms of the particle gap distribution, which is known AB exactly for the TASEP. This expression can be evaluated more easily using a mean-field approximation of this distribution, and we verified the validity of this approximation using Monte-Carlo simulations (Fig. S2B). Fig. 3 shows the distributions of residence time away from the membrane for different lengths of the SRR and for different val- ues of α. The length of the SRR has only a minor effect on this distribution. When the SRR is long, it is likely that at the time when the PSR is emptied one or more ribosomes are present in the SRR. The distribution Θ(t) is then dominated in these cases by the waiting time for the arrival of the most forward ribosome to the PSR and is given approximately by αe−αt . When the SRR is short, however, it is possible that the departing ribosome leaves the mRNA completely unbound. We note that the length of the Fig. 3. Distribution of residence times away from the membrane. (A) The PSR itself is not expected to have any significant effect on these effect of translation initiation rate α on the probability density for an SRR of results (Fig. S3), due to the absence of long-range correlations at size m = 80 and a PSR of size ` = 20. (B) Same, for a SRR of size m = 40 and low α. a PSR of size ` = 20. (Inset) Mean residence time decreases with the ratio The waiting time distribution saturates at α ' 0.5. This is the α/γ between translation initiation and elongation. The line 1/α is shown effect of the maximal current phase, which makes the flux of ribo- for comparison.

13426 | www.pnas.org/cgi/doi/10.1073/pnas.1700941114 Korkmazhan et al. 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BIOPHYSICS AND PHYSICS COMPUTATIONAL BIOLOGY AB heterogeneous membrane and the thermodynamics of interac- tions between proteins in the cluster (48). However, how proteins of the same species find each other in the crowded membrane is not well understood. Our model suggests a mechanism for nucleation of such clus- ters as well as an opportunity for the cell to control their ini- tial sizes. In this mechanism, cluster formation is facilitated by a burst of proteins translated from a single mRNA anchored to the membrane. Such a cluster can be heterogeneous if the mRNA is polycistronic and encodes multiple membrane bind- ing proteins, such as different components of a transporter or receptor. These proteins can stay together through interactions that occur cotranslationally or by embedding in a lipid raft that Fig. 6. Effect of a slow codon on mRNA localization. (A) The effect of a limits diffusion (34). Interestingly, in some cases, operons that slow codon on the distribution of residence times near the membrane, for encode inner-membrane proteins also encode outer-membrane α = 0.1γ and m = 90, ` = 10. (B) The effect of a slow codon on the distribu- proteins that are not inserted cotranslationally (such as fecA tion of the number of proteins synthesized at a single location. Parameters of E. coli, which encodes an outer-membrane porin and shares are as in A, with the case α = 0.05γ included. a transcript with genes that encode the ferric dicitrate ABC transporter). In this case, our model would suggest that long Conclusions and Discussion residence times of such polycistronic mRNAs near the mem- brane can facilitate translocation of these proteins to the outer Recent large-scale superresolution microscopy experiments con- membrane. firmed that mRNAs of membrane–protein coding genes are Together, our analysis predicts several possible effects of the enriched in the vicinity of the membrane (5) and that some mem- translation initiation rate α and the structure of the mRNA on brane proteins tend to cluster on the membrane (32, 33). In the spatial distribution of mRNAs and membrane-bound pro- this work, we study a model for the effect of translation dynam- teins as well as on localization-dependent lifetime of the mRNA. ics on the subcellular organization of membrane proteins and These predictions can be tested experimentally by measuring their mRNAs. We show that this internal organization has a the effects of perturbations to the initiation rate or the struc- strong impact on the enrichment of transcripts near the mem- ture of polycistronic mRNAs using smFISH and superresolution brane. When the PSR is short, the mRNA distribution is highly microscopy. Perturbation to the initiation rate can be done by dependent on the rate of translation initiation and can range introducing mutations to the RBS or by controlling the abun- from an (almost) homogeneous distribution at low initiation dance of a small regulatory RNAs (see Supporting Information rates to a highly skewed distribution toward the membrane at for details). high rates. Transcripts with long PSRs, on the other hand, are Previously it has been proposed that coupling between inser- effectively trapped near the membrane even when the trans- tion, translation, and transcription (known as transertion) may lation rate is not particularly high and the associated secre- facilitate formation of membrane domains (49). In this model, tory machinery (if any) is nonlimiting. This is also the case for it is assumed that the locus on the chromosome where these polycistronic mRNAs that code for multiple membrane bind- proteins are encoded is fixed in space and is held close to the ing proteins. Having limited secretory machinery, on the other membrane through a chain of DNA–RNA polymerase–mRNA– hand, may recover variability in membrane enrichment of such ribosome–proteins–membrane. This model, however, does not transcripts. consider what happens to proteins that are translated after the The rate of translation initiation of specific genes can be con- transcription of the mRNA is complete. Our model suggests that trolled posttranscriptionally in response to environmental and these mRNAs may remain anchored to the membrane and syn- physiological cues by small regulatory RNAs (19), riboswitches thesize a burst of proteins at the same location. (42), and more. Our results indicate that in some cases a by- Transertion is also presumed to have an impact on the struc- product of this regulation can be a shift in the spatial distribution ture of the chromosome itself (7, 10, 11). Our model, which sug- of the target mRNAs. gests that some mRNAs can reside continuously near the mem- Together with recent experimental results, our model suggests brane, supports the idea that mRNAs may stably anchor the that the bias of mRNAs toward the membrane can be graded and chromosome to the membrane. Thus, the residence time distri- dynamically controlled. It is therefore important to ask whether bution we calculate here can be used for future modeling of chro- this spatial organization may have an intended function and mosome dynamics in vivo. whether it has implications on other cellular functions. It has been suggested that enrichment of an mRNA species near the membrane may increase its degradation rate, due to the mem- brane localization of key ribonucleases (5). Since ribosomes are known to be biased away from the nucleoid, mRNAs that reside near the membrane may be more efficiently translated (43). The combination of these two phenomena may imply that membrane- enriched mRNAs are more susceptible to sRNA regulation (27, 44). In addition, localization of mRNAs to the vicinity of the membrane by the first translated protein guarantees that sub- sequent proteins are already synthesized near the membrane. This prevents translational stalling that is caused by synthesiz- ing hydrophobic domains in the aqueous environment inside the cell (10). Here we propose that in addition, mRNA localization to the membrane may impact the spatial organization of proteins in the membrane. Recent imaging data suggest that many protein fami- lies tend to form clusters on the membrane (45, 46). Clustering is Fig. 7. The effect of having different levels of secretory machinery for believed to play important roles, for example, in the sensitivity of α = 0.05γ, L = 100, and PSR sizes of ` = 10 and ` = 95. It is seen that the extracellular receptors (47). The prevalent models for the forma- distribution of protein cluster size can vary greatly depending on the avail- tion and dynamics of these clusters rely on slow diffusion in the ability of secretory machinery.

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Sci- Harvard of in Division at ported FAS Group the Computing by supported Research work cluster ence, this Odyssey in the computations on The performed discussions. were for Stavans Joel and are Arbel-Goren mRNAs ACKNOWLEDGMENTS. coding 51). membrane–protein (50, codons of slow for PSRs enriched that shown abPrpc Biol Perspect Harb USA boundaries. open with process Gen exclusion simple asymmetric totally cells. coli Escherichia live in 38. polymerase RNA and ribosomes biol oeuesniiiyi igecells. single in sensitivity molecule Biol Perspect rnlto lnainrtsadpoenfligefficiencies. folding protein and rates elongation translation mutations. synonymous of effects life. of availability. tRNA fluctuating 8033. to genome coli Escherichia bacteria. in choice codon and pausing tional coli. escherichia in codons ouae h euaino eeepeso ysalRA nbacteria. cluster. in RNAs small by expression gene 14:056001. of regulation the modulates translation. and transcription decay. mRNA Biol ehEng Meth microscopy. light super-resolution with imaged work sensitivity. control to rnlto nsalRAefiayrvasanvlmd finteraction. of mode novel a reveals Res efficacy RNA small on translation vivo. in SRP by 21:1100–1105. recognition nascent-chain promotes codons timal recogni- molecular co-translational in involvement an events. tion suggests clusters codon heterogeneity.rare membrane in principle organizing an Microbiol as Transertion brane: sDt nii ul synthesis. curli inhibit to CsgD 42:12200–12211. 23:247–256. 44:86–92. 44:175203. 101:11310–11315. 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