Exploring the nature of the translocon-assisted protein insertion

Abstract

The elucidation of the molecular nature of the translocon-assisted protein insertion is a challenging problem due to the complexity of this process. Furthermore, the limited availability of crucial structural information makes it hard to interpret the hints about the insertion mechanism provided by biochemical studies. At present, it is not practical to explore the insertion process by brute force simulation approaches due to the extremely lengthy process and very complex landscape. Thus, this work uses our previously developed coarse-grained model and explores the energetics of the membrane insertion and translocation paths. The trend in the calculated free-energy profiles is verified by evaluating the correlation between the calculated and observed effect of mutations as well as the effect of inverting the signal peptide that reflects the “positive-inside” rule. Furthermore, the effect of the tentative opening induced by the ribosome is found to reduce the kinetic barrier. Significantly, the trend of the forward and backward energy barriers provides a powerful way to analyze key energetics information. Thus, it is concluded that the insertion process is most likely a nonequilibrium process. Moreover, we provided a general formulation for the analysis of the elusive apparent membrane insertion energy, ΔG_app, and conclude that this important parameter is unlikely to correspond to the free-energy difference between the translocon and membrane. Our formulation seems to resolve the controversy about ΔG_app for Arg.

The establishment of the correct functional topology of membrane proteins is a subject of great current interest (e.g., refs. 1–3). It is known that the protein-conducting channel named translocon (TR) plays a vital role in membrane proteins biogenesis (4). Although biochemical and structural (e.g., refs. 5 and 6) studies have provided crucial information about the insertion process, the understanding of this process is still limited. The difficulties in gaining detailed understanding are also apparent from the emerging problem in fully defining the molecular meaning of the intriguing results about the apparent free energy, ΔG_app. That is, the concept of ΔG_app, introduced by Hessa et al. (7) for the assessment of inserted versus secreted helical domains (Background), appeared in recent years to be more complex than previously thought. Apparently, the most logical implication of the original descriptions of ΔG_app has been that it represents an equilibrium result of the partition between membrane and water. In fact, this was implied by the attempts to correlate ΔG_app with the water–membrane partitions. However, different works (8–10) implied that the corresponding equilibrium constant corresponds to the equilibrium between the TR and the membrane (see also Background). Unfortunately, none of these works has offered a clear physical rationale for why one has to consider such equilibrium without considering the transfer to water. We note that even the interesting discussion in ref. 10 does not provide a verifiable model (that can be rejected or accepted), because it does not provide a kinetic diagram with assumed reaction rates and activation barriers (of the type that will be given in this work). Furthermore, the fact that the insertion is driven by ATP hydrolysis or ribosome-induced vectorial process has not been related to the analysis of ΔG_app, except in our study (11), which considered a possible rationale for the nonequilibrium process. However, this was a hypothetical exercise, rather than a structure/energy-based study.

In addition to the problem in rationalizing ΔG_app, there are other key sources of yet-unresolved experimental constraints, such as the “positive-inside” rule and different mutational effects (see below) that can help in guiding the challenging task of understanding the TR effect. However, in the absence of key information about the energetics and structure of intermediates along the insertion path, one must attempt to use simulation approaches to gain a clearer understanding. In principle, one may try brute force all-atom simulations, but such efforts have not led yet to a progress in understanding the insertion barrier, which may be far too high for even millisecond simulations. Here, the insight about possible path for the beginning of the insertion (12) cannot help in telling us about the rate-determining processes. One may also try to obtain the relevant potential of mean force with an all-atom model, but the corresponding landscape is very complex and the convergence is expected to be problematic. Thus, we believe that it is crucial to use coarse-grained (CG) models in studying the insertion energetics and then to augment such studies by considering the effect of mutations on the directionality of the signal peptide (SP) insertion and on other observations.

CG models were introduced in protein modeling in 1975 (13) and have become since then very powerful tools for modeling biological systems (14, 15). In fact, a CG model has already been used by us in a study (11) of ΔG_app (Background). A very recent work (16) used a drastically simpler CG model and explored the insertion rate for SPs of variable sizes. This study probably captured effects that are determined by very coarse features. However, the model has not explored the relevant energetics, and we believe that understanding the nature of the free-energy landscape rather than dynamical features is crucial here. Thus, it seems to us that our CG model that is focused on a realistic description of the electrostatic energetics provides the optimal current strategy for this challenging task, and such a study is described here.

Although the current CG study cannot provide fully quantitative insertion free-energy profile, combining the profile with systematic analysis of the effect of SP and TR mutations and using it to identify energetics constraint, sheds an interesting light on the TR insertion process. This includes reproducing several key observations and highlighting the role of the kinetic control by the barrier for the insertion process. Furthermore, the CG analysis appears to provide a very powerful way of analyzing the origin of ΔG_app.

Background

In analyzing the TR-assisted insertion process, it is important to address the key experimental observations. Here, we start with the elegant experiments of von Heijne, White, and their coworkers (7) in which they determined a scale that reflects the apparent energetic of inserting a transmembrane (TM) helix into a membrane in biological conditions. These workers generated a construct with two TM helixes of this protein (TM1 and TM2) and an additional helix (the H helix), flanked by two acceptor sites for N-linked glycosylation. The degree of membrane integration of the H helix was then determined by the number of glycosylated sites and the apparent equilibrium constant, K_app = f_1g/f_2g (where f_1g and f_2g are the fractions of singly and doubly glycosylated proteins, respectively). This value was then converted to the relevant apparent free energy, ΔG_app = −RT lnK_app, which was then decomposed to the contribution from each of the 20 naturally occurring amino acids placed in the middle of the H helix.

The basic question in exploring the molecular meaning of ΔG_app and the TR-mediated insertion process is the nature of the relevant energetics and insertion paths. The original implication has been that the translocon effect is relatively small and that the experimental findings are related to the energetics of the specific amino acid in the center of the membrane. This issue is important in view of attempts to point out the possibility that the experiments have not established that the controversial low ΔG_app for a positively charged Arg corresponds to Arg in the center of the membrane, since we have an obvious possibility that the Arg side chain is tilted toward the membrane surface and that this explains the low ΔG_app (9, 10, 17). We point out in this respect that one can use a more trivial suggestion, just saying that the center of the helix can move and place the central charge closer to the membrane surface. However, it seems to be clear from the heated arguments in the field that the insertion is related to the Arg energy when it is in the center of the membrane. In fact, once it is asserted that ΔG_app corresponds to the water membrane partition, then this must be related to the energy of being at the center of the membrane. This issue is further addressed in the SI Text.

We would also like to clarify that our CG finding about the importance of helix–helix interaction in reducing the ΔG_app for Arg cannot be overlooked by arguing that the experiment by Meindl-Beinker et al. (18) shows very little effect of mutating the helixes (SI Text).

At any rate, the difficulties of reproducing the assumed energetic of Arg at the center of the membrane led to the implication that the observed energy corresponds to the motion from the TR to the membrane (8–10). Unfortunately, as stated above, we are not aware of a clear justification for this assumption. Thus, the relatively clearly defined issue of the energetic of charges in the center of the membrane forces one to move to the far more challenging issue of the energetics of the whole insertion process.

The pioneering studies of von Heijne (e.g., ref. 19) have established the positive-inside rule, which identified the retention of the positively charged N terminus on the intracellular part of the membrane. However, the exact structure-based origin of this effect remains an open question.

In both prokaryotic and eukaryotic cells, proteins are allowed entry into the secretory pathway only if they are endowed with a specific targeting signal—a SP (20). Goder and Spiess (1) performed systematic and elegant studies of the in/out ratio in the insertion of SPs with a helical segment and a tail of different length and provided intriguing information about the insertion process. In particular (Fig. S1), it has been found that increasing the positive charge in the N-terminal increases the percentage of the C-translocated peptides (N_in), whereas increasing the length of the helix decreases this percentage. Furthermore, the fraction of C-translocated peptides increases upon moving from short tails to longer tails, until reaching a fixed fraction (SI Text). Reproducing and rationalizing these experimental trends is clearly a worthwhile challenge.

Results

Our analysis starts with a focus on the SP sequences studies by Goder and Spiess (1). These SPs generated mixed topologies in experiment where the partitioning depended on the flanking charges and the signal hydrophobicity. In our modeling, we truncated the C-terminal to four residues and used the sequences shown in Fig. S2 (we also performed calculations that considered the tail).

The TR was modeled by using as a starting point the SecY structure of the SecA-bound form (5) (Protein Data Bank ID code 3DIN). The SP structure was created in PyMOL (21) from an arbitrary helix of 30 residues by mutating the amino acids to the required sequence. The generated SP was inserted into the TR by first placing it in the lateral gate [according to the recent electron cryomicroscopy data (22, 23)] and then relaxing the system, applying torsion and hydrogen bond constraints on the helical part of the SP (22 oligo-leucine) to prevent it from unfolding. The resulting model is depicted in Fig. 1.

Fig. 1.

The CG model of the RR SP inside the TR (at X = 0). The SP is shown in purple, the TR in orange with the TM 2b and 7 forming lateral gate in green, and the membrane in gray. Part of the membrane is removed for better protein visibility.

To explore the origin of the observed (1) dependence of the in/out ratio on the flanking charges of the SP, we calculated the barriers for the SP insertion into the TR for three SPs, which are named here RR, PR, and PH (Fig. S2). We started with a targeted molecular dynamics (TMD) treatment in which we pulled the SP from inside the TR to the cytoplasm (to reflect the reversed TR insertion process), to the membrane and to the exoplasm (to reflect the translocation process). All of the TMD runs constrained the helical region of the SP to prevent it from unwinding. At any rate, after obtaining the SP insertion path we evaluated the CG energies along this path (see justification in SI Text) and also used a specialized treatment to obtain stable results for mutational studies (see SI Text). In imposing the helical constraint, we considered the fact that exploring the insertion of a nonhelical system will drastically reduce the reliability of the calculations. Thus, we focused on the helical system whose energetics provides a qualitative limit to the energetics of other insertion processes (Fig. S3). We also note that a recent work (24) concluded, by length estimates, that the inserted system in related cases is at least partially helical. It was also found that the energetics of a helical construct and a construct in which the helix is perturbed by a central proline residue is quite similar, indicating that nonhelical and helical insertion should have similar barriers.

The reaction coordinate (X) for the TR insertion and translocation was taken as the rms of the first and last amino acid of the SP, respectively, and as the rms of the first and last residues of the helical part of the SP for the membrane insertion. Zero reaction coordinate corresponds to the SP positioned inside the lateral gate of the TR, X_ins/transl < 0 – SP inside the cytoplasm, X_ins > 0 – SP inside membrane, and X_transl > 0 – SP in the extracellular part.

Although the insertion process is complicated and is driven by a vectorial process (e.g., the ribosome), we started examining the energetics of the insertion without the ribosome and then explored some aspect of the ribosome-assisted insertion and the effect of the tail. Furthermore, we focused on the ΔΔG, namely the difference between the effects of mutations on each of SP helical configurations (rather than on the difference between the energies of the relaxed configuration of each mutant).

Energetics of the Translocon-Assisted Membrane Insertion and Translocation.

The calculated profile for translocon-assisted membrane insertion and translocation of RR SP is shown in Fig. 2, where the data points are plotted relative to the ΔG_tot(A_in) of the corresponding SP in the N_in orientation. It should be noted that ΔG_tot(A_out) appears to be shifted up for RR SP, although the free energy of the system where the SP is fully positioned in water should be the same independently of the SP orientation. The shift is due to the electrostatic interaction of the SP with the overall field from the TR. This effect decreases when the charge of the SP is reduced. Overall, we find that two positive charges on the N terminus side of the RR SP contribute to the highest barrier for the insertion into the TR. We can also see the reduction in the free energy of the SP positioned inside the TR (state B) when the charges are eliminated (Supporting Information).

Fig. 2.

The CG free-energy profiles for insertion into the TR (blue lines), into the membrane (red lines) and translocation (green lines) for the RR SP in the N_in (solid line) and N_out (dashed line) orientations. All profiles are plotted relative to the free energy of the N_in SP in water (at the very negative X). The data points were obtained from the calculations for the SP without the tail. The effect of the tail is discussed in the text. Note that the difference between the energy of C_(in) and C_(out) is an artifact due to the fluctuations in the distance between the SP and the TR as well as due to the limited membrane spacing. The energy in the membrane is most probably too negative as discussed in SI Text and indicated by the tentative gray lines.

To explore the consistency of the different models, we compared the difference in the barrier heights for the TR insertion [ΔΔg^‡(A`<sub>out</sub>→A`_in)] and the difference in the free energies inside the TR [ΔΔG(B_out→B_in)] of the SPs in the N_in and N_out orientations with the corresponding experimental values [ΔΔG_exp(N_out→N_in)] (Fig. 3A and Supporting Information). Both sets have a reasonable correlation with the experiment. However, the calculated effects are significantly larger than the corresponding observed effect. This trend is due in part to the missing compensating contributions associated with the use of a fixed helix and an identical path for N_in and N_out [note that the apparent dielectric effect reflects factors that are not explicitly included in the simulations (25)], as well as to the missing effect of the tail, which will be considered below.

Fig. 3.

Examining the correlation between different calculated and observed effects. ΔΔg^‡(N_out→N_in) is the difference in the TR insertion barrier heights for the N_in and N_out orientations of the SP, and ΔΔG(N_out→N_in) is the difference in the free energy of the SP positioned inside the TR in N_in and N_out orientations. In addition, ΔΔG_exp(N_out→N_in) is the experimental estimate of the difference between the free energies of the two orientations. (A) The correlation plots for the insertion of the different SPs. (B) The correlation plots for the insertion of the 60[H1](+1) SP . The data points are obtained for the wild-type SecY TR and the R74E, Q93R, Q234R, and K264E mutants. (C) The correlation plots for the insertion of the 40Leu16(+5) SP. The data points are for the wild-type and four mutant SecY structures (R74E, Q93R, Q234R, and K264E) as well as for the mutations of the SP (D6R and K37E).

To explore the qualitative effect of the tail residues, we added 21 residues to the C terminus of RR, PR, and PH SPs, using the sequence of the H1ΔLeu22 protein (1) with a limited relaxation. Here, we considered first the effect of a short tail case (Fig. S1) in which we used the actual sequence of the 21-residue tail with its ionizable groups. In this case, we reproduced the observed trend of Fig. S1 and rationalized its origin (see SI Text and concluding discussion). For the long tail limit, we have not performed any simulations, but it is reasonable to assume that the longer tail will increase the hydrophobicity effect in the N_in insertion. The consideration of the tail also helped to rationalize the overestimate of ΔΔg^‡(A`<sub>in</sub>→A`_out) obtained for an isolated helix, since the tail charges destabilize N_in (SI Text).

Effect of Mutations on the Energetics of the TR-Assisted SP Insertion.

Next, we calculated the effect of TR mutations on the energetics of the SP insertion, considering the experimental data from refs. 6 and 26. The SP models were derived from 60[H1](+1) and 40[Leu16](+5) peptides, while truncating the N- and C-terminals of the SPs (Fig. S2). The peptide models were built in a way similar to that described above. The experimental results for the TR mutations were taken from studies of the yeast Saccharomyces cerevisiae Sec61 TR (6, 26). To check the effect of similar mutations in the Thermotoga maritima SecY system, we also used the sequence alignment data from ref. 27, considering data from conserved residues in both organisms. The calculated results are summarized in the Supporting Information and the correlations of ΔΔg^‡(A`<sub>out</sub>→A`_in) and ΔΔG(B_out→B_in) with ΔΔG_exp(N_out→N_in) depicted in Fig. 3 B and C. As can be seen from Fig. 3B, ΔΔg^‡(A`<sub>out</sub>→A`_in) of the 60[H1](+1) SP has better correlation with the experiments than ΔΔG(B_out→B_in). Moreover, for the 40[Leu16](+5)CPY, ΔΔG(B_out→B_in) is uncorrelated with ΔΔG_exp(N_out→N_in) (see discussion below). Finally, we found that the effect of the TR mutations that change the in/out ratio is independent from the tail effect.

Effect of the Ribosome on the Energetics of the TR-Assisted SP Insertion.

In the absence of direct estimate of the time for the insertion process, we took the estimate (2) of a translation rate of ∼5 aa per second. We note, however, that this estimate does not tell us what exactly the actual barrier in the TR is and that it is taken in the absence of alternative information. At any rate, this time constant can be converted to an activation barrier of 20 kcal/mol based on transition state theory (see SI Text for clarifications). This barrier is most probably much lower than the barrier without the external help of activating systems such as the ribosome. The ribosome can act just by its direct electrostatic effect or by changing the structure of the TR and thus reducing the barrier. To explore these options, we examined first how the ribosome charges may affect the barrier for the SP insertion. This was done by adding 16 negative charges 5 Å away from the membrane surface in a position similar to rRNA H59 helix of the ribosome using the data from the cryo-EM structure of the ribosome–SecY complex (22). The addition of the negative charges reduces the barriers for RR TR insertion in N_in and N_out orientations by ∼2 kcal/mol. Next, we explored the possible indirect effect of the ribosome-induced TR structural changes on the SP insertion. For this purpose, we used the cryo-EM structure of the SecY. Now (Fig. 4) we obtained very significant reduction in the barrier heights for the RR SP insertion into the ribosome-bound TR: Δg^‡(A`<sub>in</sub>) = 6.3 kcal/mol and Δg<sup>‡</sup>(A`_out) = 9.3 kcal/mol. Although the high-resolution structure of the ribosome–TR complex is not available and our modeling does not involve the simulation of a protein chain growing inside the ribosome, we believe that we captured the trend in the real effect. We also note that despite the fact that the X-ray structure with SecA does not show the large structural change used here it may also have an activated open structure (5). However, it is very likely that the movement from the SecA-bound to the ribosome-bound TR structure presents a significant overestimate of the actual opening. Thus, we considered in Fig. 4 (and in the subsequent discussion) a profile that takes 55% of the SecA-bound and 45% of the ribosome-bound TR insertion profiles to reproduce the rough estimate of Δg^‡(A`_in) (20 kcal/mol) of the barrier of the insertion process. The idea is that in this way we capture the some of the tentative effect of the ribosome while still having a reasonable barrier. We are also well aware that the role of SecA includes an active ATP-driven process (see figure S2 of ref. 11). However, in the present case, we only consider this effect implicitly.

Fig. 4.

Estimating the trend in the effect of the ribosome on the TR insertion profile. RR SP was inserted into the SecA-bound SecY TR (solid line) and ribosome-bound Sec61 TR (dotted line) in N_out orientation. The profiles are plotted with the respect to the system structure with the SP in water (X ∼ −74 Å). The intermediate profile was generated by scaling the TR-bound and the ribosome-bound profiles by 0.55 and 0.45, respectively, to obtain the estimate of Δg^‡ = 20 kcal/mol (dashed line).

Conceptual Analysis

Although the present CG profile does not provide a quantitative tool of estimating the activation barriers for the insertion process, there are elements of the calculations that are quite reliable and robust, at least in establishing the relative trends. The current work allows us to use an energy-based formulation in relating the insertion problem to the available experiments. This can be done by considering the energy diagrams of Fig. 5 and the more complete description in Figs. S4 and S5, in which we provide estimates of the barriers for the different feasible paths. Here, we used the scaled results mentioned above with Δg^‡(A`_out) set at 20 kcal/mol. Furthermore, the energy values in the membrane were treated as discussed in SI Text, leading to the second set of energies used in Fig. S5.

Fig. 5.

A qualitative free-energy diagram for the retention model. The profiles for the SP insertion in the N_in (solid line) and N_out (dashed line) orientations consist of TR insertion (in blue), membrane insertion (in red), and translocation (in green) parts. State A corresponds to the SP in the cytoplasm, state B to the SP inside the TR, state C to the SP inserted into the membrane, and state D to the SP in the exoplasm. Note that we have not considered the barrier for the exit of the tail in the N_in case.

In considering Figs. S4 and S5, we can reach several tentative conclusions. The first is that the insertion is most probably irreversible because the barrier for going back from the membrane to the initial state is too high. That is, the forward barrier in the ribosome-assisted process can be estimated to be ∼20 kcal/mol, whereas the stabilization by the membrane is most probably >10 kcal/mol. Thus, the back reaction is at the range of 30 kcal/mol, which is not accessible at biological times. Note that we define here a limiting barrier , which correspond to the time of the experiment or the time when competing processes stop the insertion. Our conclusion about the irreversibility is supported by the analysis of the mutation experiments where we found much better correlation between the calculated and observed results for the forward activation barrier that for the equilibrium free energy (e.g., Fig. 3C).

Now, despite the above conclusion, we still have to ask whether the equilibration between the in and out configurations may involve state B as an intermediate. To explore this issue, we note that the barrier for moving to the membrane [B_(in) → C_(in) or B_(out) → C_(out)] is relatively small [in agreement with other calculations (8)]. Thus, the retention model (Fig. 5) leads to the conclusion that state C_(out) can move to state D. In fact, the model also allows for movement from D to C_(in) through B_(in). However, this is inconsistent with the fact that the in/out equilibrium is not determined by the final states [C_(out) and C_(in)] because these states are likely to have very similar energies (unless somehow the SP inserted to the membrane stays near the TR or the ribosome). It is also likely that we underestimate the D to B barrier (this possibility is discussed in SI Text and also indicated in the figure), but it would not change our conclusions. Considering the alternative inversion model (Fig. S4B), we can also see the same problem (equilibration between the two inserted configurations). Interestingly, the second inversion model (Fig. S4C) seems to be inconsistent with the observed in/out partition, because the barrier for A to B (or A`) is identical for the in and out paths and this should lead to 50% ratio, which is not observed experimentally in most cases. However, it may be possible that the second barrier becomes higher than the first barrier in the case of a short tail. In such a case, we will have a very small in/out ratio for a short tail and a ratio of 50% (which is the result of having the same rate limiting barrier) only for a longer tail. However, because we did not observe exactly 50%, this would mean that such a scenario is only possible if the path of Fig. S4C is not the only path. At any rate, the crucial point is that all models are consistent with a kinetic control by Δg<sup>‡</sup>(A`_in) and none seems to reflect the equilibrium between the TR and membrane (see also concluding discussion).

The analysis of Fig. S4 is not directly related to the experiment that determined ΔG_app (which used a different system). Thus, we consider in Figs. 6 and 7 the process that corresponds to the measurements of ΔG_app. In generating this figure, we took into account the fact that both state H and G are likely to have similar values to within a few kilocalories per mole, because otherwise (with the exception discussed below) the population in water would not be observed experimentally. Thus, we considered the limit of the second set of the membrane water energies (see above and SI Text) but also kept in mind the actual CG results. Using these two limits, we can reach the following conclusions (Fig. 7): (i) If ΔΔG(H→G) is small and if the back barriers from H to F () or G to F () are lower than the limiting barrier, , we come back to the original idea that ΔG_app reflects equilibrium between the membrane and the water systems (Fig. 7A) . In this case, the equilibration is independent of the energy of state F so it is not an equilibration between the TR and the membrane. (ii) If ΔΔG(H→G) is large and and are higher than the , then we have a kinetic control, where we might have a linear free-energy relationship (LFER), where the product distribution is correlated with the activation barriers (SI Text and Fig. S6), so that the forward rates are correlated with ΔG_app (Fig. 7B). (iii) In the less likely case that the ΔG's of H and G are very different [|ΔΔG(H→G)| > 4 kcal/mol], the forward barriers from F must determine the populations of G and F (otherwise one of them will not be observed) and in this case ΔG_app must be determine by LFER. The seemingly alternative option that |ΔΔG(H→G)| > 4 kcal/mol and that the barriers and are lower than would lead to the finding of all of the population in G (which is inconsistent with the experimental finding) (Fig. 7C). (iv) Finally, in the case when the barriers are sufficiently small, we can just focus on the equilibrium problem with K₁ = W/TR and K₂ = M/TR (where M, W, and TR correspond to G, H, and F, respectively), assuming that the experiment cannot determine whether the H helix is in the membrane or in the TR region, so that K_app = (TR + M)/W. Now we can show (SI Text) that K_app = (1 + K₂)/K₁ and thus when K₁ and K₂ are much larger than 1, we have K_app = K₂/K₁ = M/W, and when K₂ << 1, we have K_app = 1/K₁ = TR/W. Overall, none of the considered options is consistent with the currently popular assumption that ΔG_app is determined by the equilibrium between the TR and membrane.

Fig. 6.

A kinetic scheme for the analysis of ΔG_app. The reported values are taken from the CG calculations of the H helix with a central arginine. The values in bracket present an estimate that is within the limits considered in Fig. 7A. However, the energies of H and G might be significantly less negative. The numbers on the paths and at each state represent the activation barriers and relative free energies, respectively, and are given in kilocalories per mole. The figure also provides the rate constants for the key steps discussed in the text.

Fig. 7.

Analysis of the interplay between the limiting energetics and the corresponding consequences in the final partition. () and () represent, respectively, the activation barrier for moving back from water (or membrane) to the TR and to the cytosol. is the limiting barrier that corresponds to the length of the time in of the experimental measurements. ΔΔG is the actual free-energy difference between the water and membrane. The barriers are related to the corresponding rate constant by transition state theory. In case A, ΔG_app can represent water/membrane equilibrium. In case B, we can only account for the observed ΔG_app by assuming LFER, whereas in case C, we have a situation where all of the H segments will be inserted into the membrane, which is not observed experimentally. Additional options are considered in the text. The energies of H and G might be significantly less negative then the calculated values (SI Text).

Concluding Remarks

The present study focused on the qualitative CG exploration of the insertion free-energy landscape using the hints provided by biochemical studies. The relative heights and positions of the calculated CG barriers were found to be consistent with key mutational information and with the positive-inside rule. Furthermore, the tentative effect of the TR opening induced by the ribosome is found to reduce the kinetic barrier. Equally important is the fact that our systematic analysis indicated that the mutation studies of the insertion process are much better correlated with ΔΔg^‡ that ΔΔG, indicating that we have a kinetic control.

Our finding can be explained in rather clear qualitative terms, starting from our view that the knowledge of the energetics of the system should provide the clearest way of describing the kinetics and the partition results. For example, it must be obvious that the positive-inside rule is related to the interaction of the charge of the SP with some regions of the overall system, but elucidating the relevant energy contributions is crucial for a concrete understanding. Here, the seemingly obvious suggestion would be the interaction of positive charges with the negative ribosome charges that stabilizes the barrier for the N_in path. However, this cannot explain why mutations of the TR change the in/out ratio. In this case, our calculations established that the TR electrostatic potential stabilizes a positive SP charge near the top of the free-energy profile [the TS at A`_(out) of Fig. 5]. Thus, the most likely possibility is that the electric potential of the TR, at X of approximately −40 Å, is responsible to the positive-inside rule. Now, if this is true, then the insertion is controlled by the height of the barrier, which is a nonequilibrium kinetic control (SI Text). Furthermore, our study seems to indicate that the effect of the mutations that change the in/out distribution is independent on the ribosome effect.

This work reproduced the opposing trends in the effect of the hydrophobicity and polarity on the in/out ratio. That is, the increase in positive charge increases the barrier for insertion of the positive head and thus reduces the N_out fraction. However, increasing the hydrophobicity of the SP helix reduces the barriers for both the N_out and N_in, but does it to a lesser extent in the case of N_in, where the tail must also pass near the inserted helix. This opposing trend is indicated in Fig. S1 and also discussed in SI Text. Finally, we may also speculate on the possible reason for the increase of the in/out ratio for long tails (2) (without performing actual simulations). That is, with a long tail we probably have an increase in hydrophobicity in the N_in case, and this is likely to lead to a decrease of the N_in barrier and an increased in/out ratio.

The most important advance in the present work is not so much in providing qualitative free-energy profiles but in forcing us to look at the alternative kinetic options in a well-defined energy-based logical way and to be able to incorporate experimental and conceptual constraints in the overall analysis. In particular, the trend of the forward and backward energy barriers provide a powerful way of analyzing key energetics information such as the apparent membrane insertion energy ΔG_app. It is concluded that ΔG_app is unlikely to correspond to the difference between the free energies of the protein inside the translocon and the membrane, but in most limiting cases to the equilibrium between the membrane and water or the equilibrium between the TR and water. The use of our formulation seems to resolve the controversy about ΔG_app of Arg (SI Text)_.

Interestingly, our calculated profile seems to provide a rationale to the results found in the recent exciting experiment of ref. 24.

Overall, we view the present study as a demonstration of the need of a clear mechanistic formulation in the study of the translocon-mediated insertion and of the ability of CG modeling to augment available experimental information and to provide further constraints on the kinetic analysis.

Methods

The present work uses a CG model that describes the main chains by an explicit model and represents the side chains by a simplified united atom model. The model has a unique treatment of the electrostatic energy that increases its reliability. The details of the model are given elsewhere (28) and in SI Text.