Extreme accumulation of nucleotides in simulated hydrothermal pore systems

Abstract

We simulate molecular transport in elongated hydrothermal pore systems influenced by a thermal gradient. We find extreme accumulation of molecules in a wide variety of plugged pores. The mechanism is able to provide highly concentrated single nucleotides, suitable for operations of an RNA world at the origin of life. It is driven solely by the thermal gradient across a pore. On the one hand, the fluid is shuttled by thermal convection along the pore, whereas on the other hand, the molecules drift across the pore, driven by thermodiffusion. As a result, millimeter-sized pores accumulate even single nucleotides more than 10(8)-fold into micrometer-sized regions. The enhanced concentration of molecules is found in the bulk water near the closed bottom end of the pore. Because the accumulation depends exponentially on the pore length and temperature difference, it is considerably robust with respect to changes in the cleft geometry and the molecular dimensions. Whereas thin pores can concentrate only long polynucleotides, thicker pores accumulate short and long polynucleotides equally well and allow various molecular compositions. This setting also provides a temperature oscillation, shown previously to exponentially replicate DNA in the protein-assisted PCR. Our results indicate that, for life to evolve, complicated active membrane transport is not required for the initial steps. We find that interlinked mineral pores in a thermal gradient provide a compelling high-concentration starting point for the molecular evolution of life.

Fig. 1.

Heat-driven molecular accumulation in hydrothermal pores. (a) Section through aragonite (CaCO₃) from the submarine hydrothermal vent field at Lost City (kindly provided by D. Kelley; ref. 20). (b) Simulation of a part of the pore system. If subjected to a horizontal thermal gradient of 30 K, a 1,200-fold accumulation of single nucleotides is expected (logarithmic concentration color scale). A concatenation of three of these pore sections leads to a 10⁹-fold accumulation. (c) The mechanism of accumulation is driven by heat in a twofold way. Thermal convection shuttles the molecules vertically up and down and thermophoresis pushes the molecules horizontally to the right. The result is a strong molecular accumulation from the top to the bottom (linear concentration color scale).

Fig. 2.

Predicted effects of the molecule size and pore length on the accumulation level. The simulation results are based on the experimentally measured Soret coefficients and diffusion coefficients for DNA and RNA (see Table 1). (a) The accumulation increases exponentially with the size of the molecule. Whereas single nucleotides are accumulated 7-fold in a short cleft of aspect ratio 10:1, double-stranded DNA comprising 1,000 base pairs accumulates 10¹⁵-fold. The equilibration takes 9 min for single nucleotides and 14 min for single stranded RNA comprising 22 bases. For DNA polynucleotides of 100 and 1,000 bp it takes 18 or 33 min, respectively. (b) Elongation of the cleft exponentially increases the accumulation. For example, the accumulation of single nucleotides is raised to a 10¹⁰-fold level in a pore with an aspect ratio of 125:1. A linear concentration scale is used in both plots, scaled to the respective maximal concentration. The time to reach steady state is 9 min for r = 10, 4 h for r = 50 and 23 h for r = 125.

Fig. 3.

Exponential accumulation. The accumulation depends exponentially on the aspect ratio r and the temperature difference ΔT, according to the analytical theory (Eq. 1). Even for single nucleotides, it is remarkably easy to reach exceedingly large molecular accumulations. The accumulation is calculated for ΔT = 30 K.

Fig. 4.

Robustness of the accumulation. (a) Equally efficient accumulation is found for a large variety of geometries. Regions of reduced accumulation are bridged vertically by mass diffusion. Strongly inclined pores accumulate molecules equally well. A linear concentration scale is used in both plots. (b) Likewise, a wide range of pore cross-sections yields identical accumulations. As for two dimensional clefts, optimal accumulation is achieved if the convection speed balances the diffusion time across the pore.

Fig. 5.

Pore width and equilibration time. (a) The optimal cleft width depends moderately on the molecular size and temperature difference. The optimal cleft width is proportional to D^1/3 and ΔT^−1/3 with the diffusion coefficient D and temperature difference ΔT. As a result, much longer nucleotides require only slightly narrower pores. (b) Accumulation drops considerably for pores with a nonoptimal width. Nucleotides are selectively accumulated in particularly narrow chambers. For a wider pore width d ≈ 150 μm, the accumulation of molecules with different sizes reaches comparable levels. (c) The equilibration toward a 10⁸-fold accumulation takes 14 h for single nucleotides and 25 h for single-stranded RNA comprising 22 bases. For DNA polynucleotides of 100 and 1,000 bp. it takes 70 or 8 min, respectively. This might be counterintuitive, but larger molecules accumulate faster because a considerably shorter cleft is sufficient to achieve the same level of accumulation.

Fig. 6.

Reduction of the accumulation by diffusive leakage and upflow. (a) A diffusive leak is introduced at the bottom of the pore over 1/5 of the pore width. The numbers beneath indicate the reduction of accumulation relative to the nonleaking pore in Fig. 2a. (b) Upflow is introduced into the cleft shown on the left side. For longer polynucleotides, the accumulation drops considerably faster with increasing upflow. Short molecules are less affected. The drop in accumulation for both diffusive leaks and upflow drift is readily compensated by a slight elongation of the pore.