Solvent constraints for biopolymer folding and evolution in extraterrestrial environments

Significance

It is generally believed that life must occur in liquid solvents, as this is the regime in which relevant biochemistry can happen. For biochemistry to evolve, we propose that spontaneous molecular folding and the ability to encode function in biopolymer sequences is also required. We explore the limits to life emergence set by folding and evolution theories by relating them to the physical characteristics of different solvents that may occur in extraterrestrial environments. We find that along water, many solvents are compatible with biopolymer folding and evolution.

Abstract

We propose that spontaneous folding and molecular evolution of biopolymers are two universal aspects that must concur for life to happen. These aspects are fundamentally related to the chemical composition of biopolymers and crucially depend on the solvent in which they are embedded. We show that molecular information theory and energy landscape theory allow us to explore the limits that solvents impose on biopolymer existence. We consider 54 solvents, including water, alcohols, hydrocarbons, halogenated solvents, aromatic solvents, and low molecular weight substances made up of elements abundant in the universe, which may potentially take part in alternative biochemistries. We find that along with water, there are many solvents for which the liquid regime is compatible with biopolymer folding and evolution. We present a ranking of the solvents in terms of biopolymer compatibility. Many of these solvents have been found in molecular clouds or may be expected to occur in extrasolar planets.

Biology is based on biochemistry and biochemistry as we know it requires biopolymers. There are two fundamental characteristics that can be expected to be universal for any biopolymer: their potential for folding and evolution. It has been argued that biopolymers allow processes of folding and assembly to be detached from the required investment of free energy (1). For small molecules, by contrast, assembly and investment are directly coupled. Therefore, small molecules cannot achieve the elaborate folds and assemblies that we find on terrestrial biological relics. Spontaneous folding to specific structures is one of the fundamental aspects that come naturally to biopolymers. Specific, fast and robust folding can only occur in polymers that follow the “Principle of Minimal Frustration” (2), for which there is a fundamental correlation between similarity in structure and energetic distribution. In these polymers, the folded structure can be encoded in the sequence of monomers given an environment (3). The application of statistical mechanics to polymer models defines the parameters relevant to describe the characteristic structural transitions of these systems (4). Quantitative molecular interpretation of these theories provide the basis for the exploration of the ranges of the constraints that are expected to be found for any biological polymer.

Besides (but not independently of) folding, biopolymers must be able to change over time, they must explore new structural and functional forms that allow for biochemistry to evolve. Biopolymer evolution can be fundamentally described as explorations on the sequence space that encodes the structural forms (5). Changes in the sequences relate to changes in the structures, giving rise to genotype to phenotype mappings. For terrestrial biopolymers, this mapping is certainly complex and depends on the details of the environment in which the information is decoded. Recently, molecular information theory was conjured with energy landscape theory to find the evolutionary informational footprint in foldable polymers (6). It was found that the average information contained in the sequences of evolved terrestrial proteins is very close to the average information needed to specify a fold. Moreover, it was shown that it is possible to compute the efficiency for conversion of folding free energy into sequence information, that for terrestrial proteins is around 50%.

We propose here that spontaneous folding and molecular evolution are two universal aspects that must concur whether life is happening. These aspects are fundamentally related to the chemical composition of the biopolymers and crucially depend on the solvent in which these are embedded. It is generally accepted that life must occur in liquid solvents, as this is the phase in which relevant biochemistry can happen (7, 8). Some characteristics that are expected for possible alternative solvents are the ability to form hydrogen bonds, the presence of hydrophobic phase separation allowing for membrane systems, acid/base properties, chemical stability of known biomolecules, feasibility of a wide range of metabolic reactions, temperature range of liquid, etc. (1–3). There is a wide range of proposed life-sustaining solvents that includes water, ammonia, sulfuric acid, formamide, hydrocarbons, dihydrogen, dinitrogen, carbon dioxide, carbon disulfide, hydrazine, hydrogen cyanide, hydrogen sulfide, nitric oxide, and silicon dioxide to name some (1–3), many of which have been found in molecular clouds or may be expected to occur in extrasolar planets (8). The likelihood of the occurrence of seas of different candidate solvents in exoplanets has been evaluated as a function of stellar type (8). Here, we present a different but complementary analysis, by abstracting out the detailed chemistry of the polymer and concentrating on the solvent characteristics that constrain biopolymer folding and evolution in extraterrestrial environments.

Results

Characteristic Temperatures of Biopolymer Folding and Evolution.

Energy landscape theory and molecular information theory deduce in an abstract manner the conditions that are necessary for the evolution of folded biopolymers. Since the deductions do not depend on the chemical nature of the biopolymer or the solvent, the results can be used to assess whether alternative biochemistries support biopolymer existence.

Energy landscape theory and molecular information theory identify at least four characteristic temperatures of biopolymer folding and evolution (6). First, the physiological temperature T_phys is the one at which the molecule functions in a biological setting. Second, the folding temperature T_f is the one at which 50% of the molecules remain folded. Empirically, on earth, T_f is on average around 15 degrees higher than T_phys (6). Given the broad temperature ranges considered in this work, we will approximate T_phys=T_f for simplicity. Relaxing this assumption to allow for a T_f that is up to 30 K higher than T_phys does not change the main conclusions of our work. Third, the glass temperature T_g is related to the thermodynamics of trapping the polymer in the configurational space. Below T_g, the system runs out of entropy and its kinetics exhibit unfoldable glass-like behavior (2). Fourth, the selection temperature T_sel is related to the strength of selection for folding stability during evolution of the biopolymer sequence in the sequence space. If T_sel is lower than T_g, a biopolymer sequence can evolve for folding.

We propose that evolved biopolymer sequences must correspond with polymers that are folded and active at the physiological temperature. From energy landscape theory considerations, the relationship between these four characteristic temperatures is (6)

$$T_{sel}<T_g<T_{phys}<T_f.$$ [1]

Eq. 1 implies that the ratios T_g/T_sel and T_f /T_g are both higher than one. Both conditions need to be met for evolution of folded biopolymers. The condition for T_g/T_sel ensures that foldable biopolymers’ sequences can evolve in a relevant timescale, while the condition for T_f /T_g ensures that evolved biopolymer structure can fold in a relevant timescale.

We can refine these theoretical limits given by Eq. 1 as follows. Energy landscape theory provides the following relationship between T_sel, T_g, and T_f (6, 9, 10):

$$\frac{2}{T_f{T}_{\mathit{sel}}}=\frac{1}{T_g^2}+\frac{1}{T_f^2}.$$ [2]

According to molecular information theory, the folded structures can be encoded in sequences of monomers, and the ratio of T_sel to T_phys defines the efficiency for the conversion of folding free energy into sequence information. This ratio has an upper limit of $ln(2)$ (6, 11):

$$Eff=\frac{T_{\mathit{sel}}}{T_{\mathit{phys}}}\simeq \frac{T_{\mathit{sel}}}{T_f}\le ln(2).$$ [3]

If we solve Eq. 2 for T_g and substitute $T_{\mathit{sel}}=Eff·T_f$, we obtain

$$\frac{T_f}{T_g}=\sqrt{\frac{(2-Eff)}{Eff}}\ge 1.373.$$ [4]

If we solve Eq. 2 for T_f and combine the solution with Eq. 3 we obtain $Eff={(T_{\mathit{sel}}/T_g)}^2/(1+\sqrt{1-{(T_{\mathit{sel}}/T_g)}^2})$. Since $Eff\le ln(2)$, it follows that

$$\frac{T_g}{T_{\mathit{sel}}}\ge 1.048.$$ [5]

Finally, putting together [4] and [5] we get

$$\frac{T_f}{T_{\mathit{sel}}}\ge 1.439.$$ [6]

Since Eq. 2 comes from a simplified random energy model for the energetics of folding and evolution, the precise values obtained should be considered as first-order approximations. The combination of energy landscape theory with molecular information theory provides theoretical limits for the ratios between T_sel, T_g, and T_f. An evolved, coded, biopolymer able to fold into a specific conformation should fulfill conditions [4]–[6]. A general diagram of these relations is presented in Fig. 1. The T_f /T_g ratio indicates the funneling of the folding energy landscape, which directly relates to the foldability of the biopolymer (4). The T_g/T_sel ratio is related to the selection strength of the sequences, as the ratio increases the possibility of finding codable sequences by mere chance decreases, as the sequence entropy of the foldable ensemble must decrease as T_sel lowers. Notice that there is a fundamental compromise between foldability and evolvability: The better the folding, the more difficult it is to find sequences that will code for it (12). This result is independent of the chemistry of the polymer and the physics of the solvent, and we propose that this is a universal characteristic expected to occur in biological polymers in any extraterrestrial environment.

Fig. 1.

Relationship between the characteristic temperatures for folding and evolution of biopolymers. The T_f/T_g ratio indicates the funneling of the folding energy landscape, which directly relates to the foldability of a biopolymer. The T_g/T_sel ratio relates to the selection strength of the sequences that code for a biopolymer. The limits imposed by energy landscape theory are shown in brown and the limits set by molecular information theory in blue.

Biopolymer Folding in Water.

In this section, we examine the properties of water to provide values for the T_f and T_g of biopolymers. As a starting point, we focus on a pressure of 1 atm. The potential influence of changes in environmental pressure is discussed in a latter section. Under these conditions, water is a liquid from 273.15 to 373.13 K. Since terrestrial life mainly exists in liquid water, we assume that T_f may take values in this range of temperatures.

First, we consider the value of the glass temperature T_g for water. Water is a complex substance presenting multiple transitions (13) (Fig. 2, Left). Liquid water can be superheated to about 553 K, and small droplets with 1 to 10 microns in diameter can be supercooled to about 231 K (13). Water, like any other liquid, can be vitrified when cooled fast enough to avoid crystallization. Most experimental observations report that rapidly cooled water at atmospheric pressure has a glass transition temperature of about 136 K (13). The dynamic and transport properties of supercooled water show critical behavior as a function of temperature, as indicated by various techniques such as viscosity, dielectric relaxation and NMR measurements, neutron and light scattering spectroscopies and molecular dynamics simulations (13–15). The estimated values for the critical temperature of supercooled water range from 212 to 228 K, with an average of 220 ± 7 K (Fig. 1, red horizontal line).

Fig. 2.

Temperature domains of water and terrestrial biopolymers at atmospheric pressure. Left: temperature domains of stability and metastability for liquid and glassy water (black) and dynamic transition (red) (13–15). Equilibrium transitions are shown as full lines, kinetically controlled transitions as dashed lines. Right: temperature domains and glass transition for folding of terrestrial biopolymers (blue). Circles indicate proteins (16–20), squares indicate RNA (17, 21–23), and triangles indicate DNA (24–27). Above the glass transition temperature (dashed line), a biopolymer can search for its folded form in an efficient manner. Below the biopolymer glass transition temperature a biopolymer is trapped in a rough energy landscape and will not fold in a biologically relevant timescale. The theoretical limits for T_sel and T_f calculated from the average glass transition temperature and Eqs. 4–6 are shown as continuous lines. Adapted from ref. 13.

Second, we consider the glass transition of three terrestrial biopolymers undergoing structural transitions in aqueous media: proteins, RNA and DNA, which were studied using molecular dynamics simulations and neutron scattering (Fig. 2, Right). The glass transition of model proteins takes place between 180 and 210 K, with an average value of 196 ± 14 K (16–20) (Fig. 2, blue circles). The glass transition of different RNA samples takes place between 190 and 230 K, with an average value of 212 ± 17 K (17, 21–23) (Fig. 2, blue squares). Finally, the glass transition of different DNA samples was observed at temperatures between 205 and 223 K, with an average value of 215 ± 9 K (24–27) (Fig. 2, blue triangles). In sum, three terrestrial biopolymers present a glass transition at an average temperature close to 207 ± 16 K (Fig. 2, blue horizontal line).

The glass transition temperature of terrestrial biopolymers at 207 ± 16 K is very close to the critical temperature of supercooled water at approximately 220 ± 7 K (Fig. 2, red horizontal line). This result is in line with the general idea that biopolymer folding and solvent dynamics are intimately linked. Large-scale protein motions do follow the solvent fluctuations but can be slower by a large factor. Slowing takes place because large-scale motions consist of many small steps, each determined by the rate constant for solvent fluctuations. This phenomenon is called slaving (28) and suggests that the glass transition of biopolymers may be coupled to a water transition. As discussed above, this temperature may be 136 K or close to 220 K, depending on which solvent transition is most relevant for folding. From the comparison of the Left and Right sides of Fig. 2, we propose that the limiting factor for the T_g of a biopolymer in any liquid can be approximated as the critical temperature of the supercooled liquid.

This empirical result is supported by the views of polymer evolution stemming from energy landscape theory (2, 12). Foldability of a polymer can be characterized by the ratio T_f /T_g and may be expected to increase during evolution. T_f is linked to the temperature at which the biopolymer functions, T_phys (6). Increasing T_f beyond the typical value of T_phys + 15 would generally compromise polymer function due excessive stability and damping of function-related dynamics (3). We thus expect the T_g of a polymer to decrease during evolution toward the lower bound dictated by solvent motions, namely the temperature for the dynamical transition of the solvent. In sum, a well-evolved biopolymer can be expected to present solvent slaving and a T_g corresponding to the dynamical transition of the solvent. Relaxing this assumption to allow for a glass transition temperature for the polymer that is up to 20 K higher than that of the solvent does not change the main conclusions of our work.

We can put together Eqs. 4–6 relating T_f, T_g, and T_sel for biopolymer folding with our empirical estimation for the glass transition temperature at 207 K. This yields an upper limit for the selection temperature T_sel at approximately 197 K (Fig. 2, Right). This upper limit is compatible with previous estimates of T_sel close to 108 K (10). It also yields a lower limit for the folding temperature T_f close to 284 K (Fig. 2, Right). The T_f of most proteins from psychrophilic organisms being above 298 K (29), is compatible with the lower limit of 284 K. Further, experimental and/or theoretical estimation of the characteristic temperatures T_f , T_g, and T_sel for multiple biomolecules yields values for the T_f /T_g ratio higher than the lower theoretical limits of Eqs. 4 and 6 in 25 out of 28 cases (6, 10, 16–18, 20, 21, 26, 30–36). We conclude that these theoretical limits for T_f, T_g, and T_sel in water are in reasonable agreement with the available empirical data and can therefore be used as a starting point to analyze biopolymer folding in nonaqueous solvents.

Characteristic Temperatures of Solvents Linked to Alternative Biochemistries.

We include in this study a total of 56 solvents from four broad categories (SI Appendix, Table S1). The first category is water and other solvents for which the dynamic transition temperature has been characterized. The second category is hydrocarbons, which have been linked to alternative biochemistries (37, 38). The third category is low molecular weight (up to approximately 100 Da) substances made out of elements abundant in the universe such as H, C, N, O, and S (39), which may potentially partake in alternative biochemistries. The fourth category is other substances for which we know the melting point, boiling point, and the glass transition temperature, such as halogenated substances and aromatic substances. These are included in order to explore a wide range of solvent physical properties.

The present approach requires knowledge of the melting point, boiling point, and dynamic transition temperature of each solvent. The values for the melting point and boiling point are taken from the literature. Since the dynamic transition temperature of most relevant solvents remains uncharacterized, we calculate the dynamic transition temperature for the remaining solvents from literature values for the glass transition temperature and the empirical linear relationships shown in SI Appendix, Fig. S1. We restrict ourselves to substances with a known glass transition temperature in the range of 40 to 400 K to avoid large extrapolations in the calculations. These requirements leave out of consideration liquids without a documented glass transition temperature in the 40 to 400 K range, such as ammonia, formamide, hydrogen sulfide, dinitrogen, and dihydrogen. Last, we exclude supercritical fluids, where applicability of the theory is unclear since their properties lie somewhere between a liquid and a gas.

Biopolymer Folding in Alternative Solvents.

We use Eqs. 3 and 4 and SI Appendix, Eq. S2 to calculate the T_f /T_g ratio, the efficiency for conversion of free energy into information, and the T_g/T_sel ratio as a function of T_f , for 54 solvents, for the temperature range in which each substance is a liquid at 1 atm. The results are shown in Fig. 3. Water is shown as a thick black line, hydrocarbons as green lines, small substances from C, H, O, N, and S as magenta lines, and the remaining solvents in SI Appendix, Table S1 as thin black lines. The horizontal lines highlight the theoretical limits for each parameter, with those from energy landscape theory shown in brown and those from molecular information theory in blue.

Fig. 3.

Temperature dependence of parameters relevant to biopolymer foldability, codability, and evolvability, for 54 solvents at 1 atm. Water is shown as a thick black line, hydrocarbons as green lines, small substances from C, H, O, N, and S as magenta lines and the remaining solvents in SI Appendix, Table S1 as gray lines. The horizontal lines highlight the theoretical limits for each parameter, with those from energy landscape theory shown as blue lines and those from molecular information theory in brown lines. (A) T_f/T_g ratio. (B) Efficiency for conversion of folding free energy into sequence information. (C) T_g/T_sel ratio.

The ratio T_f /T_g increases linearly with T_f , the efficiency decreases monotonically with T_f and the ratio T_g/T_sel increases monotonically with T_f in the biologically relevant range (Fig. 3). The values of T_f for which the T_f /T_g ratio and the efficiency cross their theoretical limits of approximately 1.373 and 0.69 are the same in all panels due to the linkage between Eqs. 2 and 3 and coincide with the highest value of T_f for which the T_g/T_sel ratio crosses its theoretical limit of 1.048. Above this value of T_f , foldable biopolymer sequences can be coded and evolve in a relevant timescale, and evolved biopolymer sequences can fold in a relevant timescale. All solvents considered have T_f /T_g and T_g/T_sel ratios above the theoretical minima and an efficiency below the theoretical maximum for at least a fraction of the temperature range in which they are liquid (Fig. 3). Thus, all substances considered here are in principle compatible with the existence of some biopolymer at 1 atm.

Is Water Particularly Well-Suited for Biopolymer Folding?

We present a quantitative comparison between the substances in SI Appendix, Table S1 with regard to their support for biopolymer folding and evolution, with particular attention to water. Fig. 3 shows that all solvents considered have values of T_f, T_g, T_sel, and efficiency compatible with biopolymer folding and evolution for at least a fraction of the temperature range in which they are liquid (Fig. 3). Here, we would like to focus on the following question: “If solvent X is present in the liquid state in a given celestial body, how likely is it to support biopolymer folding and evolution?”. We propose a Biopolymer Solvent score (BSscore) for each solvent that addresses this question by evaluating the geometric average of two contributions:

$$\text{BSscore}=\sqrt{\frac{\text{Biopolymer} \mathrm{range}}{\text{Liquid} \mathrm{range}}·\frac{\text{Average} \mathrm{efficiency}}{\text{Maximal} \text{efficiency}}}.$$ [7]

The difference between the highest and the lowest temperature for which the theoretical conditions are met is the liquid range that is compatible with folding. The upper limit of this range is the boiling point for all solvents considered here, while the lower limit depends on the specific solvent (SI Appendix, Table S1). In principle, solvents for which the temperature compatible with folding and evolution matches with the liquid range are more likely to yield a positive answer to the question above. We evaluate this using a normalized measure, the fraction of the temperature range for the liquid state that is compatible with folding, (Biopolymer range)/(Liquid range). This measure takes values from 0.14 to 1 for the solvents in our database. We also reason that solvents with a higher average efficiency in the liquid range that is compatible with folding are more likely to yield a positive answer to our question. We thus consider the efficiency for conversion of folding free energy into sequence information, averaged over the liquid range that is compatible with folding and evolution and normalized by its theoretical maximum $ln(2)$. This measure takes values from 0.36 to 1 for the solvents in our database. As indicated by Eq. 7, the BSscore for each solvent is the geometric average of the fraction of the liquid range that is compatible with folding and evolution and the normalized average efficiency.

Fig. 4, Left panel, shows the relationship between the two variables for 54 substances in SI Appendix, Table S1 at 1 atm. Water is shown as a black circle, hydrocarbons as green circles, small substances from C, H, O, N, and S as magenta circles and the remaining solvents in SI Appendix, Table S1 as gray circles. The gray lines indicate constant values of the BSscore. Since Fig. 2 shows considerable uncertainty in the dynamic transition temperature of water, with values ranging from 180 to 230 K, we recalculated the BSscore for water using values within this range. This yields the black line in Fig. 4, Left panel, with BSscore values from 0.71 to 0.89 (average 0.82 ± 0.06), confirming that water belongs to the group of solvents with both a high average efficiency for conversion of folding free energy into sequence information and a large fraction of the liquid range compatible with folding. As suspected, water appears to be an exceptionally good solvent to support biopolymer folding and evolution. The remaining solvents can be ranked by the BSscore and the distribution is shown in Fig. 4, Right panel.

Fig. 4.

Biopolymer solvent scoring. (Left) Relationship between the fraction of the biopolymer compatible range and the liquid range of solvents and the average fractional efficiency for conversion of folding free energy to sequence information, for 54 solvents at 1 atm. Large black circle: water. Green circles: hydrocarbons. Magenta circles: small substances from C, H, O, N, and S. Gray circles: other solvents in SI Appendix, Table S1. Black line: range for water calculated from the uncertainty in the dynamic transition temperature presented in Fig. 2 (values range from 180 to 230 K). The gray lines indicate constant values of the BSscore (Eq. 7). (Right) Ranking of the solvents according to the BSscore.

Role of Pressure.

The presented results suggest that all 54 solvents analyzed may support biopolymer folding and evolution at 1 atm, at least in some range of temperatures. However, solvents may be subject to very different pressures in extraterrestrial environments. For example, the atmospheric pressures in the solar system may range from tens of microbars to nearly 100 bar (40). Liquid water can exist in a large fraction of this pressure range, from approximately 6 × 10⁻³ to 220 bar. It seems relevant to ask how the results presented in Figs. 3 and 4 change at different pressures. The temperatures for the dynamic transition of water and for its melting point vary little with pressure (15, 41). On the other hand, the boiling point of water increases sharply with increasing pressure (41). We expect other solvents to behave similarly due to the small changes in molar volume associated with the glass transition and melting, relative to the change in molar volume upon boiling (42).

We may now reconsider our calculations with T_g and the melting point as constants and a boiling point that increases with pressure. The main effect would then be an increase of the liquid range from the right extreme of all lines in Fig. 3. The effect of this would be twofold: the average efficiency for conversion of folding free energy into sequence information would decrease and the fraction of the liquid range where folding is possible would increase. The outcome in terms of BSscore would depend on the interplay between these two factors. In the case of water, Fig. 5 shows the pressure dependence of the BSscore (black), the normalized average efficiency (blue) and the fraction of the liquid range where folding is possible (orange). In this case, the efficiency is maximal at lower pressures, the fraction of the liquid range where folding is possible is maximal at higher pressures and the BSscore varies within a relatively narrow range (0.45 to 0.86), is above 0.7 for pressures above 0.04 atm, and is close to the maximum value (0.85) at 1 atm. Overall, the influence of pressure on the ability of water to support biopolymer folding is modest. Since the overall shape of the phase diagram is expected to be the same for other substances, we propose that this conclusion holds for the other solvents considered here.

Fig. 5.

Pressure dependence for biopolymer folding and evolution in water. Pressure dependence of the BSscore (black), the normalized average efficiency (blue), and the fraction of the liquid range where folding and evolution are possible for water (orange).

Discussion

We are still uncertain whether Life happens in other parts of the universe besides our beloved planet Earth. Much research and lots of speculations are being put forward yet few consensus on how Life may look like, and thus how to detect it have been reached (43). At the molecular level, is life the same everywhere? Are there alternative biochemistries? To gain insight into these questions, we propose to abstract out the many known details of terrestrial biochemistry and ask: What are physicochemical characteristics of the solvents that may sustain life that constrain biopolymer folding and evolution?

Energy landscape and molecular information theories allow one to put the fundamentals of biopolymer folding, coding, and evolution under scrutiny given the assumption that these must happen in liquid solvents and some sequence space. We have shown that the physical characteristics of solvents constrain the ranges where folding and evolution are possible. Folding is constrained by the characteristic temperatures of the solvents, and coding is constrained by the efficiency of the energy-to-information conversion. We believe that both must play a significant role in determining the emergence of biopolymers, regardless of their detailed chemical composition.

The ability of most nonaqueous solvents to support biopolymer folding in general is in line with previous experimental results with specific terrestrial biopolymers. For example, several DNA duplexes maintain their structure in glycerol and ethylene glycol (44), and the proteins subtilisin and lysozyme remain folded in glycerol, dioxane, and acetonitrile (32, 45–47). Lysozyme can undergo reversible folding in glycerol (48). Moreover, many enzymes retain their catalytic activities in nonaqueous organic solvents (49, 50). It seems likely that most mixtures of the solvents considered here also support biopolymer folding. This opens the door to considering the existence of life in mixed solvents.

We can speculate on whether terrestrial biopolymers (proteins, RNA, and DNA) can evolve, fold, and function in any nonaqueous solvent. Our results suggest that the solvent requirements of evolvability and foldability can be fulfilled in most cases. However, it should also be kept in mind that biopolymer folding and function also require that the folded state is more stable than the unfolded state and soluble in the new solvent (51). Terrestrial proteins are likely to be less stable in polar solvents such as ethanol, and markedly insoluble in nonpolar solvents such as cyclohexane. This is clearly due to the physicochemical properties of the genetically coded terrestrial amino acids in relation to the properties of the solvent (51). Thus, it seems unlikely that the current set of terrestrial amino acids can support life in solvents other than water (51).

Life in nonaqueous solvents would likely be supported by biopolymers that are chemically different from the terrestrial ones (52). There are three main points relevant to the suitability of a protein-like biopolymer to evolve, fold, and sustain life in a given solvent. We can first consider that biopolymer sequences must evolve to the point in which they contain enough information to specify a given fold (6). This minimal amount of information is determined by the configurational entropy change upon folding of the biopolymer in a given solvent (6). The evolutionary choice of a given biopolymer–solvent pair poses an informational requirement for folding. Second, the folding of a biopolymer in a given solvent is associated with a favorable change in the free energy of the system. At the atomic scale, folding involves breaking a myriad of molecular interactions between solvent molecules and between solvent and biopolymer and forming precise intramolecular interactions in the biopolymer. The free energy balance associated with this process is also dictated by the properties of the solvent–biopolymer pair (51). Third, the properties of the solvent determine the efficiency for the conversion of free energy into sequence information. Interestingly, the efficiency expected for different solvents is predicted to be at least half of the maximal one in most solvents examined (Fig. 4). The maximal amount of information that is gained by a biopolymer by folding in a solvent is dictated by the properties of both solvent and biopolymer. If a biopolymer is to evolve and fold in a certain solvent, the amount of information gained by conversion of folding free energy should match the amount of information required to specify its folded conformation (6). Both of these quantities are determined by physicochemical properties of the solvent-biopolymer pair. We speculate that biopolymers associated with alternative solvents must be chemically different from those found in water-based terrestrial life. Alternative chemical structures previously suggested for biopolymers include polyelectrolytes in general (53), protein-like polyesters (54, 55), peptides made from beta- and gamma-amino acids (56), and polymers originating in the opening of common cyclic prebiotic chemicals (57).

The theory presented here is universal for biopolymers that fold and function in regular fluids, those for which we can estimate the dynamic transition temperature from the glass transition temperature. In its present form, the theory can not address several solvents that have been linked to extraterrestrial life. For example, solvents such as ammonia (37) do not have a known dynamic or glass transition in the 40 to 400 K range. Supercritical fluids such as carbon dioxide (58) and biopolymer folding in vacuo (59) also fall out of the scope of the theory. Some naturally occurring biopolymers also challenge the theory because they do not fold in a conventional manner but follow downhill folding (60) because they function through liquid–liquid phase separation (61) or because they are intrinsically disordered (62). Nevertheless, the foldable and evolved biopolymers considered here seem to be highly relevant to Life.

All solvents considered here support biopolymer folding under some conditions, with efficiencies for the conversion of free energy into information in the same order of magnitude (Fig. 3B). This result can be traced back to the correlations between the characteristic temperatures of these substances (SI Appendix, Fig. S1), which can be explained by the law of corresponding states. This law recasts the properties of fluids in terms of their critical points. In this scenario, the properties that vary among fluids determine their critical temperature and pressure. The degree to which all fluids deviate from ideal gas behavior is the same at the same reduced temperature and pressure, which in turn leads to the correlations between the characteristic temperatures (63). The law of corresponding states assumes that intermolecular interactions in the fluid are a function only of the ratio between the intermolecular distance R and a characteristic distance R₀ (64). This assumption is accurate for large values of R where the intermolecular potential energy is proportional to R⁻⁶. To a point, our results can then be traced back to the existence of Van der Waals interactions, which is undoubtedly a universal phenomenon. Substances which are not spherically symmetrical and for which other intermolecular forces are relevant deviate to varying degrees from the law of corresponding states, leading to deviations from the correlations between characteristic temperatures and to the diversity of behaviors shown in Fig. 3. Thus, the differences in efficiency and in the range of liquid temperatures where a solvent supports folding and evolution are fundamentally related to the rotational asymmetry and polarity of its constituent molecules. We have shown here how to derive the basic characteristics expected for biopolymers from these fundamental principles.

Materials and Methods

In estimating T_f/T_g, T_g/T_sel, and efficiency for biopolymer folding in nonaqueous solvents, we utilized known solvent melting and boiling points from literature sources, presented in SI Appendix, Table S1 and SI Text. T_g values were obtained from literature or calculated using established empirical relationships between solvent characteristic temperatures. Additionally, we estimated the dynamic transition temperature for nonaqueous solvents by leveraging linear relationships between glass transition temperatures and characteristic temperatures of various substances, as detailed in SI Appendix, SI Text. T_f values were set within the liquid state temperature range. To assess efficiency, we applied Eq. 3, assuming T_f ~ T_phys as detailed in SI Appendix, SI Text.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

All study data are included in the article and/or SI Appendix.