Conceived and designed the experiments: AZ SDT TJT BTC MPR MOM. Performed the experiments: AZ SDT TJT BTC MPR MOM. Analyzed the data: AZ SDT TJT BTC MPR MOM. Contributed reagents/materials/analysis tools: AZ SDT TJT BTC MPR MOM. Wrote the paper: AZ SDT TJT BTC MPR MOM.
The authors have declared that no competing interests exist.
The functioning of living cells requires efficient and selective transport of materials into and out of the cell, and between different cellular compartments. Much of this transport occurs through nano-scale channels that do not require large scale molecular re-arrangements (such as transition from a ‘closed’ to an ‘open’ state) and do not require a direct input of metabolic energy during transport. Nevertheless, these ‘always open’ channels are highly selective and pass only their cognate molecules, while efficiently excluding all others; indeed, these channels can efficiently transport specific molecules even in the presence of a vast excess of non-specific molecules. Such biological transporters have inspired the creation of artificial nano-channels. These channels can be used as nano-molecular sorters, and can also serve as testbeds for examining modes of biological transport. In this paper, we propose a simple kinetic mechanism that explains how the selectivity of such ‘always open’ channels can be based on the exclusion of non-specific molecules by specific ones, due to the competition for limited space inside the channel. The predictions of the theory account for the behavior of the nuclear pore complex and of artificial nanopores that mimic its function. This theory provides the basis for future work aimed at understanding the selectivity of various biological transport phenomena.
Various channels and transporters shuttle molecules into and out of the cell, as well as between different cell compartments. Such channels have be selective, i.e. to pass only certain molecular species in a given direction, while efficiently blocking the passage of all others. Transport properties of some channels (e.g. ion channels), have been extensively studied. However, the mechanisms of channels that conduct larger molecules, such as the nuclear pore complex, which gates all transport between the cell nucleus and the cytoplasm, are less understood. In particular, it is still not clear how such channels can efficiently transport their specific molecules even in the presence of a vast excess of non-specific molecules that potentially could clog the channel. Understanding how such channels work is also important for technological applications, such as design of artificial nano-filters. In this paper, we propose a mechanism of selectivity of such channels in the presence of vast amounts of background molecular noise. The predictions of the theory account for the behavior of the nuclear pore complex and of artificial nanochannels that mimic its function. The theory provides the basis for future work aimed at understanding the selectivity of transport through various biological and artificial channels.
Living cells require the efficient and selective trafficking of molecules through various transport channels
Despite their variety, such natural and artificial transporters appear to share common mechanisms of transport selectivity and efficiency. They commonly include a channel or a passageway, through which molecules translocate by diffusion
However, in nature (and in order to be useful in many technological applications such as molecular sorters) the selected molecules have to be transported through a channel in a vast background of other molecules, many of which can interact weakly and non-specifically with the transport channel. Thus, transport channels have to be able to constantly select their cognate molecules from such a background. It is still not clear precisely how biological and artificial channels can perform selective transport under such conditions, but any useful theoretical description must take into account this non- specific competition. It is likely that various mechanisms can contribute to selectivity. For instance, in some cases, the selectivity arises from the presense of a physical or energetic barrier for the entrance of non-specific molecules into the channel
In this paper we focus on the universal selectivity properties of channels, which do not depend on the specific molecular details pertinent to each specific transporter. We show that highly selective transport is possible in the presence of non-specific competition even when the non-specific molecules are free to interact with and enter into the channel. We study the case of a mixture of two molecular species of different trapping strenghts attempting to traverse the channel. Our model relies on only two essential ingredients: transient trapping of the molecules in the channel and inter-molecular competition for the limited space inside the channel. Analysis of the model reveals a novel kinetic mechanism of the enhancement of transport selectivity through narrow channels, which relies on the sequential exclusion of weakly trapped (low affinity) non-specific molecules from the channel due to competition with strongly trapped (high affinity) cognate molecules that spend a longer time in the channel. Comparison of the theoretical predictions with experimental data shows that the predicted mechanism accounts for the transport selectivity observed in an artificial nano-channel that mimics the NPC. Due to its generality, the proposed mechanism of selectivity is expected to play a role in various biological and artificial nano-channels.
We model transport through a narrow channel in the framework of a general kinetic theory
Let us first consider a ‘one-site’ channel model (
We define the
From eq. (2), in the absence of competition, when particles of only one type are present (say
Thus, the transport efficiency of the particles of each type through a single-site channel is not influenced by the presence of particles of the other type. As we show below this is not so for channels that can accommodate more than one particle.
Selectivity conditions change when one considers transport in a mixture of two different species of molecules in longer channels, where the molecules can interfere with each other's passage through the channel. The main result is that in the presence of more strongly trapped species, the transport of more weakly trapped species is strongly inhibited, compared to the case when they are present alone.
Analogous to a single-site channel, a longer channel that may contain several particles simultaneously can be represented by a sequence of
Here, we show the results for the kinetic landscape shown in
We first review the selectivity conditions when only one species is present (say only
Transport efficiency (black line) and translocation probability (dotted line) for single species (say,
In the biological context, non-specific molecules interact only weakly with channels whereas specific cognate molecules interact strongly. Predictions of the model for the case when two species directly compete for the space inside the channel, are summarized in
The left panels describe the transport of a weakly trapped species in a titrated mixture with the strongly trapped species, relative to the case when only a weakly trapped species is present. The right panels describe the transport of a strongly trapped species in the same mixture relative to the case when only a strongly trapped species is present. In all panels the total combined flux of the particles is
Why does competition between different particle species enhance the selectivity of the transport? As mentioned above, the overall transport efficiency is influenced by two factors: 1) the ability of a particle to enter the channel in the first place (the entrance site might be temporarily occupied which prevents the entrance of new particles) and 2) the probability of a particle to translocate through the channel,
These results are summarized in
Ratio of the transport of the weakly trapped species to that of the strongly trapped species with competition, normalized by the ratio of the single-species efficiencies; black line: equal mixture (
The heuristic explanation for this phenomenon is that the particles that are strongly trapped in the channel block translocation through it. If, during the time when the channel is blocked by a strongly trapped particle present somewhere inside, a weakly trapped particle enters the channel, the latter will with a high probability quickly exit the channel on the left side. If, on the other hand, a strongly trapped particle comes in when the passage to the right side is blocked by another such particle, then, with high probability, it will stay in the pore long enough for the particle that blocks it to pass through.
The inhibition of transport of the more weakly trapped species persists beyond single file transport, when the channel can accommodate several particles at each site as shown in red lines in
Ratio of the transport selectivity of a weakly trapped species to that of a strongly trapped species, as a function of the channel length,
The effect of the presence of the weakly trapped (non-specific) species on the transport of the more strongly trapped (specific) one can also be examined from a different angle. Namely, instead of
Relative transport efficiency
The enhancement of transport of the more strongly trapped species by addition of more weakly trapped competitors is somewhat counter-intuitive, as one might expect that increasing the concentration of the non-specific competitors would clog the channel and decrease the flux of the specific particles. In particular, the theory predicts that this enhancement is present only for a certain range of trapping strength of the weakly trapped competitors.
The heuristic explanation of this effect is as follows. When the trapping strength of the non-specific competitors is close to that of the specific molecules, they block the entry and interfere with the entrance of the strongly trapped particles. On the other end, the very weakly trapped (or non-trapped) particles essentially do not penetrate the channel, and the flux of the strongly trapped ones is unaffected by their presence. However, in a certain range of intermediate trapping strengths, the non-specific competitors, although mostly filtered out, still penetrate the channel to a certain degree, accumulating near the entrance (see inset in
We note that the inhibition of transport of the weakly trapped non-specific particles by competiton with the specific ones persists even when there are more than two particle species (data not shown). Such non-linear mutual effects of the particles of different species on each other might shed light on opimization of transport by co-transport factors, commonly encountered in biology and also suggest the possibility of creation of artificial ‘nano-valves’ with nonlinear flux rectification properties
We note that the effect described here is a very general mechanism of selectivity of transport through narrow channels and is not limited to a particular fortuitous choice of the kinetic rate constants, being observed for various choices of channel kinetic profiles. Analytical results shown in the
We now turn to comparison of the theoretical predictions with recent experiments on transport through artificial nano-channels that mimic NPC function
Panel
Jovanovic-Talisman
In nature, transport channels have to select for their cognate cargoes over a vast background of other species that might interact with the channel non-specifically. How can they maintain selective transport in such conditions? It is likely that many different mechanisms of selectivity may be operational in such channels
This selectivity enhancement is a purely kinetic, non-equilibrium mechanism. Notably, it does not require input of metabolic energy
Predictions of our theory are in agreement with recent experiments on transport through artificial nano-channels that mimic the nuclear pore complex function
The analytical calculations were perfromed by pencil and paper with the help of Mathematica 5.2 package. Simulations were implemented in C language and run on a cluster of opteron processors under UNIX. The simulation code is presented in
Supporting information text and figure captions.
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Kinetic diagram of transport of particles of two different species through a two-site channel.
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Selectivity enhancement in a mixture of two species: two site channel.
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Selectivity enhancement in a mixture of two species: long channel. In all panels the exit rate of the strongly trapped species is kept fixed
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Sensitivity to the choice of the kinetic profile. Ratios of the transport efficiency of the weakly trapped species to the transport efficiency of the strongly trapped species for the different kinetic profiles shown in the insets to each panel for different values of the exit rate of the strongly trapped species. See text in Section 3 of
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Dependence of the selectivity on the concentration. Panel
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The authors thank G. Bel, A. Berezhkovskii, S. Bezrukov, C. Connaughton, I. Nemenman, J. Pearson, A. Perelson, R. Peters, Y. Rabin, J. Tetenbaum-Novatt, N. Sinitsyn, Z. Schuss, D. Yang for stimulating discussions and the anonymous reviewers for insightful comments.