From experimental clues to theoretical modeling: Evolution associated with the membrane-takeover at an early stage of life

16 Modern cell membranes are primarily composed of phospholipids, while primitive cell 17 membranes in the beginning of life are believed to have formed from simpler lipids (such as 18 fatty acids) synthesized in the prebiotic environment. An attractive experimental study 19 suggested that the corresponding “membrane-takeover” (as an evolutionary process) is likely 20 to have occurred very early (e.g. in the RNA world) due to some simple physical effects, and 21 might have subsequently triggered some other evolutionary processes. Here, via computer 22 modeling on a system of RNA-based protocells, we convinced the plausibility of such a 23 scenario and elaborated on relevant mechanisms. It is shown that in protocells with a fatty-24 acid membrane, because of the benefit of phospholipid content (i.e., stabilizing the 25 membrane), a ribozyme favoring the synthesis of phospholipids may emerge; subsequently, 26 due to the reduced membrane permeability on account of the phospholipid content, two 27 other functional RNA species could arise: a ribozyme exploiting more fundamental materials 28 (thus more permeable) for nucleotide synthesis and a species favoring across-membrane 29 transportation. This case exemplifies a combination of experimental and theoretical efforts 30 regarding early evolution, which may shed light on that notoriously complicated problem: the 31 origin of life. 32 33 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint

34 It is thought that the primitive cells (protocells) should have had a membrane composed 35 of simple, single-chain lipids, such as fatty acids and their derivatives (generally referred to as 36 “fatty acids” below for concise), which were present in the prebiotic environment 1-3 . Indeed, 37 though phospholipids may also have been synthesized prebiotically 4, 5 , they, as more complex 38 molecules, are likely to have been much less abundant – especially considering that they 39 should have been made from those single-chain lipids. In the logic of “the simpler, the more 40 likely to emerge de novo”, it is more plausible that the first membranes were assembled from 41 the single-chain lipids, and phospholipid membranes came later, perhaps due to Darwinian 42 evolution. Another major reason in favor of “fatty acids first” for primordial membranes is that 43 phospholipid-based membranes are much less permeable, thus would seriously hinder 44 protocells from obtaining crucial materials available in environments for growth and 45 reproduction 1-3 . 46 Traditionally, as a further argument for the scene of “fatty acids first”, it is emphasized 47 that these single-chain lipids are more fluid or dynamic – thus favoring the spontaneous 48 growth and division of protocells 1-3 . But evidence has now accumulated to show that 49 phospholipid-based membranes are also sufficiently dynamic for growth and division 4, 6-8 . 50 Therefore, this argument seems now no longer valid. However, notably, if the scene of “fatty 51 acids first” is true, these findings actually imply that the membrane-takeover from fatty-acid 52 membranes to phospholipid membranes could have occurred quite early – well before the 53 advent of complex forms like modern cells, which have specific functions regarding cellular 54 growth and division. 55 Interestingly, via experimental studies, Szostak and coworkers found evidence in support 56 of such an early membrane-takeover 9 . It was shown that fatty acid vesicles with a portion of 57 phospholipid components would grow at the expense of those pure fatty acid vesicles (see 58 also associated earlier work 10, 11 ). The main reason is that the involvement of phospholipids 59 would reduce the efflux of fatty acids from the membrane and ， through the 60 exchange equilibrium of these molecules between vesicles via the environment, eventually 61

in a net inflow of fatty acids. This means, as the authors stated, “the ability to synthesize 62 phospholipids from single-chain substrates would have therefore been highly advantageous 63 for early cells competing for a limited supply of lipids” 9 . Undoubtedly, with the emergence of 64 this function in protocells, the phospholipid content of the membrane would have increased. 65 Furthermore, in the same work, it was demonstrated that the permeability of the 66 membrane declines in proportion to the rise in phospholipid content 9 . The reduction of 67 permeability was ascribed to the decreased fluidity (i.e., increased order) in a membrane 68 contain more phospholipid molecules (in the form of double-chain lipids). This “would have 69 led to a cascade of new selective pressures for the evolution of metabolic and transport 70 machinery to overcome the reduced membrane permeability” 9 . In other words, as they 71 clarified, “cells could have evolved the ability to synthesize their own building blocks from 72 simpler, more permeable substrates”, and “membrane transporters, a hallmark of modern 73 cells, would have emerged as a means for overcoming low membrane permeability”. 74 Obviously, by exploring relevant physical effects, the experimental work was trying to 75 formulate speculations on some tendencies of Darwinian evolution in the early stage of life. 76 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint However, at least up to now, such evolutionary tendencies are per se difficult to follow up in 77 laboratory. On the other hand, with the rapid development of theoretical studies in the field 78 of the origin of life (e.g., see refs 12-16 ), it is now well feasible to model such early evolution, i.e., 79 to study relevant evolutionary dynamics by computer simulation. So here we ask: can we 80 demonstrate in silico the plausibility of the evolutionary events suggested by the experimental 81 work? Additionally, via the modeling, it is expected that we would get a more comprehensive 82 understanding on detailed mechanisms involved in the evolution. 83 The RNA world hypothesis is now widely accepted in the field of the origin of life 17-19 , 84 due to its logical reasonability as well as accumulating evidence supporting it. In fact, the most 85 meaningful point of this idea is that it tries to explain the onset of Darwinian evolution 16, 20, 21 – 86 and the subsequent process in life’s history is just a matter of Darwinian evolution. In the 87 scenario, RNA played both the roles of genetic material and functional molecules, as the two 88 fundamental requirements for the “running” of Darwinian evolution (thus evading the 89 “Chicken and Egg” dilemma – which came first, DNA or proteins?). Though there are still 90 ongoing debates on it, the scenario undoubtedly offers a relatively simple platform for us to 91 model early evolutionary events like the ones we are concerned about here (actually, in the 92 original experimental work it was also implied the suggested functions associated with the 93 membrane-takeover may have evolved in the RNA world 9 ). Therefore, here we aim to model 94 the emergence of a ribozyme favoring the synthesis of phospholipids in RNA-based 95 protocells – due to the phospholipids’ benefit for stabilizing the membrane, and the 96 subsequent arising of a ribozyme favoring the exploitation of simpler (thus more permeable) 97 substrates, or that of an RNA functional species favoring the membrane transport – owing to 98 the decreased membrane permeability resulting from the increased phospholipid content. 99

100 About the model 101 We conducted the computer simulation using a Monte Carlo model similar to those used 102 in our previous work concerning the RNA-based protocells 22-24 . It is described below in general 103 terms (see Methods for details). The system is a two-dimensional N × N square grid (with 104 toroidal topology to avoid edge effects). Molecules are distributed within the grid rooms, 105 including nucleotides, RNA, fatty acids, phosphatidic acids (here as a representative of 106 phospholipids) and glycerophosphates (the head-group-maker of phosphatidic acids), as 107 well as some relevant precursors: nucleotide precursors, nucleotide-precursor’s precursors, 108 and glycerophosphate precursors. Amphiphiles (fatty acids and phospholipids) may assemble 109 at the boundary of a grid room and form a membrane, then the grid room is occupied by a 110 protocell. In each time step, certain events may occur to molecules and protocells with defined 111 probabilities (Table 1). 112 In the beginning of a simulation, a certain quantity of nucleotide-precursor’s precursors, 113 fatty acids and glycerophosphate precursors are introduced into the system. During the 114 simulation process, protocells or RNA species may be inoculated (see below for detailed 115 descriptions in different cases). In the system, nucleotide-precursor’s precursors may 116 transform into nucleotide precursors, which in turn form nucleotides (randomly as A, G, C, or 117 U). Nucleotides may assemble into RNA via random ligation. RNA may conduct template-118 directed replication. Glycerophosphate precursors may transform into glycerophosphates, 119 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint which in turn react with fatty acids on the membrane and produce phosphatidic acids thereon. 120 With its membrane absorbing amphiphiles, a protocell may grow and after reaching a certain 121 size, may divide into two – the molecules within it and the amphiphiles on its membrane 122 would assort randomly into its offspring (thus reproduction). 123 Significantly, the model has a “resolution” at the nucleotide level, thus inherently suitable 124 for studying the early Darwinian evolution, which relies essentially on the sequence-function 125 connection. In the model, an RNA molecule containing a characteristic sequence (domain) is 126 assumed to have a special function (i.e. as a ribozyme). The total materials (for RNA and the 127 membrane) in the system is constant, and the RNA-based protocells compete for these 128 materials. In the competition, those protocells containing functional RNA species “beneficial” 129 to protocell’s reproduction may spread (become thriving) in the system – or say, those “useful” 130 functional RNA species may spread among protocells. In practice, here the characteristic 131 sequence of a functional RNA species is arbitrarily presumed on account of our ignorance of 132 relevant cases, but this does not matter – what our modeling aims to explore is merely: if a 133 characteristic sequence bears a special function, can the sequence spread? Or more abstractly, 134 could a specific “sequence-function connection” result in a case of Darwinian evolution? 135 The spread of the ribozyme favoring phospholipid-synthesis in protocells 136 As suggested by the original experimental work 9 , the ability to synthesize phospholipids 137 would have been highly advantageous for protocells competing for a limited supply of lipids, 138 since the efflux of fatty acids would decrease with the increase of phospholipid content in the 139 membrane. As mentioned above regarding the model, we consider phosphatidic acids as a 140 representative of phospholipids here. In reality, phosphatidic acid is the simplest phospholipid 141 and was indeed likely to have been directly involved in the membrane-takeover. In the 142 potential relevant synthetic route, phosphorylation of glycerol appears to have been 143 inefficient, while the acylation of glycerophosphates by fatty acids could have been 144 productive 5, 25, 26 . In other words, the bottleneck was the formation of glycerophosphates – 145 thus, here we assume a glycerophosphate-synthetase ribozyme (GR) as a representative of 146 the supposed “ribozyme favoring phospholipid-synthesis”, and the synthesized 147 glycerophosphate molecules would reach the protocell membrane and react with fatty acids 148 therein in a non-enzymatic way. Indeed, a recent study demonstrated that the acylation 149 leading to phospholipids may well have occurred free of enzymes 4 . Figure 1 shows a scheme 150 depicting how a protocell containing GR could have grown at the expense of the one without 151 GR. With the growth of membrane, GR within the protocell may replicate; with the 152 enlargement of the protocell, it may divide into offspring protocells due to physical instability 3, 153 27 – thereby achieving “reproduction”. The protocell without GR would shrink and may 154 eventually break or fuse with other protocells. 155 First of all, we want to explore whether protocells containing GR could become thriving 156 by virtue of its function in favoring the synthesis of phospholipids. In the simulation, an “empty” 157 fatty-acid protocell is inoculated at step 1×10 3 . By absorbing fatty acids in the system, the 158 empty protocells grow and divide – eventually spreading in the system. Then, at step 1×10 4 , 159 ten empty protocells are selected (arbitrarily, the same below), each inoculated with one GR 160 molecule, while ten other empty protocells are each inoculated with one control (RNA species 161 without function) molecule. It was found that the protocells containing GR could spread, 162 whereas the ones containing the control could not (Fig. 2a, the upper panel); in other words, 163 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint the GR could spread among protocells, whereas the control could not (Fig. 2a, the lower 164 panel). 165 In order to study the underlying mechanism, we investigated the influences of several 166 key parameters. Firstly, to confirm that the spread of GR protocells (or say, the spread of GR) 167 is owing to the function of GR, we explored the influence of PGFR (the probability of glycerol-168 phosphate formation catalyzed by the ribozyme; see Table 1 for descriptions of parameters). 169 Indeed, with the stepwise turning-down of the ribozyme function, the spread of the GR 170 protocells is weakened and finally completely suppressed (Fig. 3-PGFR). 171 Next, we were interested in whether the advantage of GR protocells could be attributed 172 to the decrease of fatty acid desorption from their membranes, as suggested by the original 173 experimental work 9 . In accordance with the experimental work, the probability of a fatty acid 174 molecule leaving the membrane is here assumed to be negatively correlated with the content 175 of phospholipids in the membrane, i.e., in proportion to 1/(1+ FPL×RPM), where RPM is the 176 ratio of phospholipids in the membrane and FPL is a factor representing the degree of this 177 influence (see Methods for details). Somewhat surprisingly, the decrease of FPL does not 178 significantly affect the spread of GR protocells (Fig. 3-FPL, cyan symbols) – even when FPL is set 179 to 0 (after step 2.5×10 6 ), which indicates that phospholipids in the membrane no longer have 180 an impact on the desorption of fatty acids, the spread of GR protocells is only marginally 181 inhibited. That is to say, there should be other mechanisms that favor the GR protocells. 182 In fact, in that original paper 9 , a potential additional reason was proposed: with a fraction 183 of “insoluble” phospholipids, actually, “only the fraction of the vesicle surface area composed 184 of fatty acids can contribute to monomer efflux, whereas the entire surface area permits fatty 185 acid influx, leading to a net influx (growth)”. In other words, the formation of phospholipid 186 molecules from fatty acids on the membrane could “fasten” this portion of fatty acids. In our 187 model, the default value of the probability of a phospholipid molecule leaving the membrane 188 (PPLM=1×10 -4 ) is much lower than that for a fatty acid molecule ( PFLM=0.002). Therefore, in 189 addition to set FPL to 0, we tried to assume the same value for these two probabilities (thus 190 the “fastening effect” no longer exists) – and “witnessed” the collapse of GR protocells’ spread! 191 (Fig. 3-FPL, purple symbols, where after step 3.5×10 6 PFLM is set to 1×10 -4 ; see also Fig. S1, 192 purple symbols, where after step 3.5×10 6 PPLM is increased to 0.002). Subsequently, we 193 explored the “fasten effect” per se – indeed, the decreasing of PFLM (thus more approaching 194 to the value of PPLM) comes against the spread of GR protocells (Fig. 3-PFLM, cyan symbols). In 195 this case, even when PFLM is set to a value identical with that of PPLM (after step 2.5×10 6 ), the 196 GR protocells can still spread at a significant level, which is then completely suppressed when 197 FPL is set to 0 (after step 3.5×10 6 , purple symbols). That is to say, the two reasons mentioned 198 above, the “fastening effect” and the “anti-desorption effect”, do work together – both 199 contribute to the net influx of fatty acids, and eventually result in the spread of GR protocells. 200 The co-spread of the ribozyme favoring phospholipid-synthesis and another ribozyme 201 in protocells 202 After observing that GR may spread among protocells de novo, we asked whether this 203 phospholipid-synthesis favoring ribozyme may become thriving in protocells that already 204 contain other ribozymes. An RNA species catalyzing the template-directed synthesis (and 205 thus the RNA replication) has long been suggested to have been the first ribozyme emerging 206 in the RNA world, usually referred to as an “RNA replicase” 18, 28-31 . Another appealing 207 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint candidate is a ribozyme capable of catalyzing the synthesis of nucleotides 32-34 , namely 208 nucleotide-synthetase ribozyme (NR) – it may also favor its own replication by supplying 209 monomers (the replication could have based on non-enzymatic copying of RNA) 35, 36 . In fact, 210 both the two ribozymes, as supported by modeling work, might have spread early in the RNA 211 world 24, 35, 37-40 . Here we choose NR-containing protocells as the target protocells to see 212 whether GR could spread therein, mainly considering that in this study we will later introduce 213 a related ribozyme, i.e., a nucleotide-precursor-synthetase ribozyme (NPR) – it is attractive to 214 involve two ribozymes in the same “pathway”. 215 In the simulation, after the initial inoculation at step 1×10 3 , empty protocells spread; then, 216 at step 1×10 4 , ten of them are selected, each inoculated with one NR molecule (and control 217 molecules are inoculated into another ten empty protocells). As expected, the NR protocells 218 spread (while the protocells with the control cannot) (Fig. 2b). Subsequently, at step 3×10 5 , 219 ten NR protocells are selected, each inoculated with one GR, and another ten NR protocells 220 are each inoculated with one control. Eventually, protocells containing both NR and GR 221 spread in the system – or say, GR co-spreads with NR among protocells (while the control 222 cannot). 223 Noticeably, in his later essays, the leader of the original experimental work, Prof. Szostak 224 explicitly suggested that a ribozyme favoring phospholipid-synthesis might have emerged 225 first in the RNA world, and other beneficial ribozymes followed 36, 41 . Therefore, based on the 226 case shown in the de novo spread of GR (Fig. 2a), we investigate whether NR could follow. 227 After the spread of GR protocells, ten of them are selected, each inoculated with one NR 228 (another ten GR protocells are each inoculated with one control). Eventually, protocells 229 containing both NR and GR spread in the system (Fig. 2c). 230 In the three cases mentioned above, to avoid the influence of random events such as 231 RNA degradation, we investigated the plausibility of the spread of GR or the co-spread of GR 232 and NR through selecting ten protocells and inoculating each with one molecule of relevant 233 RNA species. The observed spread or co-spread, in fact, already reflects a full sense of 234 “Darwinian evolutionary dynamics”, meaning that in reality, once the RNA species appeared, 235 they may have become thriving among protocells. As an example, in Fig. 2d, we showed an 236 instance of evolution without any inoculation of ribozyme. Firstly, NR emerges naturally in 237 empty protocells, and then GR emerges naturally in NR protocells (see Fig. 4 for snapshots 238 on the spatial distribution during the evolution). In this case, to “facilitate” the natural 239 appearance of a ribozyme, the probability of random ligation of RNA (PRL) is augmented from 240 its default value 1×10 -6 to 5×10 -6 ; and to “promote” the natural appearance of the other 241 ribozyme in protocells contained the first ribozyme, their characteristic sequences are 242 assumed as different from each other with only two residues (see the figure’s legends for 243 details). 244 About the membrane takeover and the influence of decreased permeability 245 Then we were concerned about the change of membrane contents resulting from the 246 spread of the ribozyme favoring phospholipid-synthesis. Fig. 5a shows the membrane change 247 coming with the spread of GR in empty protocells (the case is just the one shown in Fig. 2a; 248 but here in order to demonstrate the transition clearly, the horizontal axis adopts a smaller 249 scale). Fig. 5b shows the membrane change coming with the spread of GR in NR protocells 250 (the case is just the one shown in Fig. 2b). In both cases, we can see a rising of the ratio of 251 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint phospholipids in the membrane (RPM, the lower panel) for the protocells with GR (i.e., Cgr in 252 Fig. 5a and Cnrgr in Fig. 5b). Note that the RPM for those protocells without GR (i.e., C in Fig. 253 5a and Cnr in Fig. 5b) also increases a bit, which may be attributed to phospholipids’ exchange 254 between protocells. 255 No matter how, we can see that in both cases, RPM only rises to a limited level after the 256 emergence of GR. We reasoned that this should be on account of the relatively low efficient 257 non-enzymatic reaction of glycerophosphates with fatty acids on the membrane. That is, 258 while glycerophosphates are plenty due to the function of GR, the subsequent reaction of 259 phospholipids’ formation becomes the bottle neck. Indeed, when we assume a high rate for 260 the non-enzymatic formation of phospholipids (i.e. PPF) in the midway, the ratio of 261 phospholipids rises to a rather high level immediately (Fig. S2). This result implies that in reality, 262 it should be the later emergence of a ribozyme or enzyme favoring this bottle-neck reaction 263 that may have ultimately taken the membrane-takeover towards a more thorough degree. 264 Remarkably, merely via inducing such a “limited membrane takeover” (i.e. with a low level of 265 phospholipid content in the membrane), GR is capable of thriving. 266 Since the phospholipid content in the membrane would reduce the membrane 267 permeability 9 and thus the availability of raw material for protocells, the GR’s advantage might 268 be weakened. It was then attractive to see how the GR protocells’ spread would be affected. 269 Somewhat surprisingly, we found that when the factor regarding the influence of 270 phospholipid content on the membrane permeability for nucleotides and nucleotide 271 precursors (FPP) is turned up – even in a dramatic way, i.e. from its default value of 20 to 200, 272 2000, and 2×10 4 , there is nearly no influence on the spread of GR (Fig. 3-FPP, orange symbols). 273 In the model, according to the rule revealed in the original experimental work 9 , the membrane 274 permeability is assumed to be negatively related to phospholipid content in the membrane – 275 in proportion to 1/(1+FPP×RPM) (see Methods for details). Therefore, a possible cause for the 276 little influence of FPP on GR’s spread is concerning the “limited membrane-takeover” (i.e. with 277 a low RPM). Indeed, if PPF is turned up to achieve a higher RPM (as mentioned above, refer to 278 Fig. S2), we can see some effects (Fig. S3, the purple line) – but still rather limited. Finally, we 279 turned to the weak version of FPP, i.e. FPPW. This factor is regarding the influence of phospholipid 280 contents on the membrane permeability for precursors of nucleotide precursors and 281 precursors of glycerophosphates – we increased it from its default value of 3 to a value of 282 3000 (in reality, this factor could not be very large because for such precursors, which should 283 be quite small in molecular size, the permeability difference between the fatty acid membrane 284 and phospholipid membrane could not be that large 2, 42 ), and see a more obvious decline in 285 GR molecules (Fig. 3- FPP, the purple line). But the GR protocells still only decline marginally 286 (Fig. 3-FPP, purple circles), which means that there are fewer GR molecules in each GR protocell. 287 Notably, for this case, RPM also declines for GR protocells (Fig. S4), which should result from 288 the decrease of GR, as well as the less availability of its substrates – precursors of 289 glycerophosphates. No matter how, the effect concerning FPPW means, an important reason 290 why a quite high value of FPP alone would not obviously inhibit the spread of GR may be 291 attributed to the remained availability of raw materials with a smaller size (thus with a greater 292 permeability), as alternative resources. 293 The subsequent spread of the ribozyme using more fundamental materials and the RNA 294 species favoring the membrane transport 295 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint Indeed, when original raw materials for chemical synthesis in protocells are blocked by 296 the membrane, more fundamental and permeable raw materials might have acted as 297 alternative resources. However, as demonstrated above, the “initial membrane-takeover”, 298 which may have been caused by the emergence of one ribozyme (e.g. GR here) functioning 299 in the pathway of phospholipid synthesis, should have been at a “low level”. Then, the 300 question becomes attractive whether such a “low level membrane-takeover” (thus with a 301 relatively small influence on the membrane permeability) at the early stage, could, as 302 supposed in the original experimental work 9 , have driven the evolution concerning the arising 303 of function for exploiting the more fundamental and permeable raw materials. 304 The answer is positive (see Fig. 6a). In the simulation, at step 1×10 4 , ten empty protocells 305 are selected, each of which is inoculated with one NR molecule, one GR molecule, and one 306 control molecule. Then the NR-GR protocells spread (the control does not spread). The solid 307 circles and solid lines represent the case in which no influence of phospholipid content on the 308 membrane’s permeability is considered (i.e. FPP and FPPW are set to 0) throughout the whole 309 simulation process, while the empty circles and dotted lines represent the case in which the 310 “negative” influence of phospholipid content is turned on at step 3×10 5 (thereafter we can 311 observe a little decrease of the NR-GR protocells and that of NR and GR molecules). For both 312 cases, at step 6×10 5 , ten NR-GR protocells are selected, each of which is inoculated with a 313 molecule of nucleotide-precursor-synthetase ribozyme (NPR). The ribozyme is assumed to 314 be able to catalyze the formation of nucleotide precursors from precursors of nucleotide 315 precursors, which is more permeable. In the first case (i.e., without the negative influence of 316 the phospholipid content), NPR cannot spread, whereas in the second case (i.e., with that 317 negative influence), the NPR spreads (the black dotted line) – or say, the NR-GR-NPR 318 protocells spread (the black empty circles). For snapshots of spatial distribution, see Fig. S5a 319 (notably, after the spread of NPR, its substrates, i.e. precursors of nucleotide precursors, are 320 represented by the background yellow, are almost been exhausted – in the panel of step 321 2,000,000). In other words, the negative influence of phospholipid content on the membrane’s 322 permeability could indeed cause the thriving of the functional species exploiting more 323 fundamental (thus more permeable) raw materials. To confirm that the spread of NPR is 324 attributed to its function of exploiting precursors of nucleotide precursors, we turned off this 325 function at step 1.4×10 6 . As expected, we saw the vanishing of this species (Fig. S6a). 326 Similar to the situation for exploring the spread of GR, to avoid the influence of 327 unexpected random events of RNA degradation, here we selected ten NR-GR protocells and 328 inoculated each with one molecule of NPR. The subsequent spread of NPR, in fact, already 329 means that this RNA species may have emerged and become thriving in protocells. In reality, 330 though it is impossible for NPR to have appeared simultaneously in so many protocells, it may 331 have had chances to appear in protocells repeatedly especially considering the long time 332 scale concerning the origin of life. For example, Fig. S7a shows a modeling case that one NPR 333 molecule is inoculated into one NR-GR protocell every 1×10 5 step, and NPR eventually 334 spreads in the system. 335 Next, we turned to the plausibility of the emergence of a functional species that favors 336 the membrane transport – as another strategy for “adapting to” the decreased membrane 337 permeability, which was also proposed in the original experimental study 9 . An RNA species, 338 named TR here, is assumed to be capable of favoring the membrane transport (see Discussion 339 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint for a comment on this RNA species in a chemical context). As mentioned above, the 340 permeable possibility of nucleotide precursors, i.e. the substrates of NR, has been assumed 341 to be in proportion to 1/(1+ FPP×RPM). Here, with the introduction of another factor, FTR, the 342 expression is changed to 1/[1+ FPP×RPM/(1+t×FTR)], where t refers to the number of TR 343 molecules in the protocell. That is, the more TR molecules there are in the protocell, the more 344 permeable the membrane is. Notably, the increased permeability is here assumed to be in 345 regard of both directions (inwards and outwards), in consideration that active transport 346 should not yet have been achievable in such an early stage. The simulation showed that due 347 to the negative influence of phospholipid content on the membrane’s permeability, TR can 348 spread in protocells (Fig. 6b; for snapshots of spatial distribution, see Fig. S5b), and when its 349 function is turned off, it decreases and eventually vanishes (Fig. S6b). Fig. S7b shows a case in 350 which one TR molecule is inoculated into one NR-GR protocell intermittently (every 1×10 4 351 step) and TR eventually becomes thriving in protocells. 352

353 In the present study, following the clues suggested by an experimental study from 354 Szostak and coworkers 9 , we examined, through computer modeling, an evolution of 355 protocells’ membrane from the one composed of only single-chain amphiphiles like fatty 356 acids towards the one containing double-chain amphiphiles like phospholipids, induced by 357 simple physical effects. The former has been deemed to be the membrane of earliest 358 protocells 1-3 , whereas the latter is a membrane more approaching that of modern cells, which 359 is more stable but less permeable. The simulation showed that such a membrane-takeover, 360 though limited initially, could indeed occur on account of “stabilizing effects” caused by the 361 increasing phospholipid content in the membrane 9 , which is brought about by the emergence 362 of a functional species favoring phospholipid synthesis in protocells (Fig. 2). Subsequently, the 363 reduced membrane permeability could trigger the emergence of an additional functional 364 species which makes use of more fundamental (thus more permeable) raw materials, or a 365 species facilitating the membrane transport (Fig. 6) – both valid as supposed in the original 366 experimental study 9 . 367 In the modeling, as for the functional species favoring the synthesis of phospholipid, we 368 adopted a ribozyme catalyzing the formation of glycerophosphates (GR), which appears to 369 have been the bottle-neck reaction, and the resulting glycerophosphates is assumed to be 370 able to reach the membrane and react with fatty acids there in situ, which seems to have been 371 efficient even in a non-enzymatic way 4, 5, 25, 26 . Another reason why we did not adopt a ribozyme 372 catalyzing the latter reaction is that RNA is likely difficult to cope with reactions occurring on 373 the membrane because of its polar skeleton – in reality, this function may have emerged after 374 the advent of proteins. Similarly, functions favoring the membrane transport seems also to 375 have been implemented by proteins coming later. But there is also some evidence supporting 376 RNA’s potential role on membrane transport, e.g. see refs 43, 44 . No matter how, at least to 377 avoid a more complicated modeling involving proteins and amino acids, here we assumed an 378 RNA species functioning this way (TR). 379 Our modeling study revealed some details regarding the membrane-takeover and 380 relevant evolution. For instance, in the original experimental paper, as for the advantages of 381 containing phospholipids in the membrane, it was pointed out that apart from phospholipids’ 382 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint effect of preventing the desorption of fatty acids, an additional mechanism is concerning “a 383 decrease in the net efflux from the membrane due to the reduced fraction of the membrane 384 surface area occupied by fatty acids” 9 . In other words, the fatty acids that have reacted to 385 form phospholipids are “anchored” and would not participate in the desorption. Here we have 386 figured out that this “fastening effect” is not absolute because phospholipids may also leave 387 the membrane though much more difficult (PPLM<<PFLM). By parameter analysis (Fig. 3-FPL and 388 -PFLM; see also Fig. S1), we demonstrated how the two effects work together to support the 389 thriving of the ribozyme favoring phospholipid-synthesis (GR). 390 As another detail, the initial membrane-takeover, most likely involving only one catalytic 391 function in the pathway of phospholipid synthesis (e.g., GR here), should have been quite 392 limited – i.e. with merely a low level of phospholipid content (Fig. 5). A more thorough 393 takeover is supposed to have occurred with the advent of other functions within the pathway 394 (Fig. S2). However, interestingly, the GR, only via inducing such a limited membrane-takeover, 395 can enjoy the benefit of phospholipids (i.e., stabilizing the membrane) and thrive in the system. 396 Surprisingly as well, such a low level of phospholipid content, via its limited negative influence 397 on the membrane permeability, is sufficient to trigger the emergence of the function for 398 exploiting more fundamental and permeable raw materials (NPR) and that of the function for 399 membrane transport (TR). 400 Remarkably, the series of evolutionary events associated with the membrane-takeover 401 at an early stage of life, as demonstrated by the present modeling, exemplifies the scenario 402 concerning the onset of Darwinian evolution, in which simple physical or chemical effects (e.g., 403 here the decreasing efflux of fatty acids due to increasing phospholipid content in the 404 membrane and the subsequent reduction of membrane permeability) may have driven the 405 emergence of relevant functions. Additionally, as we have seen, albeit the degree of the 406 effects might have been quite limited, new “inventions” could have still been induced – the 407 power of Darwinian evolution is here clearly “witnessed”. 408 In fact, such early evolutionary events of life belong to the field of biogenesis. This field, 409 or named “the origin of life”, is to a degree a problem of chemistry, which mainly addresses 410 the environments and chemical mechanisms involved in the process 45-47 (generally referred to 411 as prebiotic chemistry). On the other hand, however, it is undoubtedly also a problem of 412 evolution, which involves the rules of the so-called “chemical evolution” and the subsequent 413 early Darwinian evolution 48-50 . While experimental exploration has covered nearly the entire 414 aspect regarding chemistry, it seems to be seriously constrained in the aspect of evolution. 415 For instance, here, the clues for an early membrane-takeover came from an elegant 416 experimental work of Szostak and coworkers 9 , which detected relevant simple physical 417 mechanisms which might have led to the corresponding evolutionary events. However, it is 418 at least up-to-now difficult for experimental researchers to follow up on those events (lab 419 work’s limitation in this respect could usually be attributed to the potential long time scale 420 required in the evolution, as well as the complicated nature of these evolutionary events 16 ). In 421 contrast, theoretical modeling and associated computer simulation is apt at such exploration, 422 i.e. on the plausibility of the suggested evolution and those underlying mechanisms 12-16, 51 . It is 423 expected that the combination of experimental and theoretical efforts like the one 424 demonstrated in the present study would significantly enhance our understanding on those 425 complex processes involved in the origin of life. 426 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint

427 The events occurring in the model system 428 In each time step (i.e. Monte Carlo step), certain events may occur to molecules and 429 protocells with defined probabilities (see Fig. 7 for a schematic; refer to Table 1 for 430 descriptions of the probabilities and other parameters). Only molecules within the same grid 431 room can interact with each other. A molecule may move to an adjacent room (the related 432 probability: PMV) if there is no membrane in that direction (see below for the situation of 433 encountering a membrane). A protocell may also move to an adjacent room ( PMC) (while 434 pushing away molecules in that room). 435 Nucleotide-precursor’s precursors may form nucleotide precursors in a non-enzymatic 436 way (PNPF) or catalyzed by NPR (PNPFR). Nucleotide precursors may form nucleotides (randomly 437 as A, G, C, or U) in a non-enzymatic way ( PNF) or catalyzed by NR ( PNFR), Glycerophosphate 438 precursors may form glycerophosphates in a non-enzymatic way ( PGF) or catalyzed by GR 439 (PGFR). Nucleotide precursors, nucleotides, and glycerophosphates may also decay into their 440 precursors (PNPD, PND, and PGD respectively). 441 Nucleotides may join to form RNA via random ligation (PRL). An RNA molecule may attract 442 substrates (nucleotides or oligomers) ( PAT) via base-pairing with some error rate ( PFP), and 443 substrates aligned on the template may be ligated ( PTL) – that is, the template-directed 444 synthesis. The substrates or the full complementary chain may separate from the template 445 (PSP). Phosphodiester bonds within an RNA chain may break (PBB) and thus the RNA molecule 446 turns into two fragments. A nucleotide residue at the end of an RNA chain may decay into a 447 nucleotide precursor (PNDE). 448 Amphiphiles with a sufficient number (LAM; in quotient of tails, i.e., a fatty acid counts one 449 whereas a phospholipid counts two) may accumulate at the boundary of a grid room and 450 form a membrane ( PMF), thus “creating” a protocell. Fatty acids may join or leave the 451 membrane ( PFJM and PFLM respectively), and phospholipids may also join or leave the 452 membrane ( PPJM and PPLM respectively). Nucleotide-precursor’s precursors, nucleotide 453 precursors, nucleotides and glycerophosphate precursors may permeate through the 454 membrane (PNPPP, PNPP, PNP and PGPP respectively). Glycerophosphates may enter a membrane 455 and react with fatty acids thereon in situ to form phosphatidic acids, i.e., phospholipids (PPF). 456 Phospholipids may decay into fatty acids and glycerophosphates, either within the membrane 457 or out of the membrane ( PPDM and PPD respectively). A protocell may fuse with another 458 protocell in an adjacent grid room ( PCF), divide (with an offspring protocell occupying an 459 adjacent grid room while pushing away molecules in that room) (PCD), or break (PCB) – resulting 460 in the disassembly of its membrane components. 461 Notably, similar to our previous modeling work concerning the evolution of the RNA 462 world, the energy problem is here not considered explicitly. For example, nucleotides and 463 oligonucleotides are implicitly assumed to be activated – in particular, when they form from 464 the degradation of RNA, they are assumed to be activated again immediately to be able to 465 be reused in the further synthesis of RNA. Interestingly, such in situ activation within protocells 466 has recently been shown possible by lab work 52, 53 . In history, the energy source may have 467 involved chemical energy in the hatchery of the primordial life, such as hydrothermal vents at 468 the sea bottom 54-56 or hydrothermal fields on land 57, 58 , as supposed. Since the substrates are 469 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint here assumed to be always “activated”, the protocells in the model system are competing for 470

but not energy – as mentioned already, the total materials in the system, including 471 those related to RNA and the membrane of protocells are assumed to be limited (that is, TNPPB, 472 TFB, and TGPB, plus those material introduced by the rare events of inoculation). Certainly, in 473 reality, competitions for materials and energy are both possible in Darwinian evolution. 474 The setting of parameters 475 The parameters should be set according to some rules. For example, reactions catalyzed 476 by ribozymes should be much more efficient than corresponding non-enzymatic reactions, 477 so PNFR >> PNF, PGFR >> PGF, and PNPFR >> PNPF. Template-directed ligation should be much more 478 efficient than “random ligation”, so PTL >> PRL. The nucleotide residues within the chain are 479 assumed to be protected from decay, whereas those at the end of the chain are only partially 480 protected – i.e. may decay but at a rate lower than that of free nucleotides, i.e., PNDE PNPP >> PNP 2, 42 . Because of the 482 self-assembly feature of the membrane, PMF >> PCB, PFJM >> PFLM, and PPJM >> PPLM. 483 Phospholipids should more difficult to leave the membrane than fatty acids, so PPLM < PFLM. 484 Phospholipids should be more difficult to decay within the membrane, so PPDM PMC. Nucleotides and RNA 486 should be easier to degrade outside protocells (due to the higher water activity), so FDO > 1; 487 the influence of phospholipid content on the permeability of smaller molecules should be 488 weaker than that of larger molecules, so Fppw < Fpp 2, 42 . 489 Obviously, the rules mentioned above are far from justifying the setting of that many 490 parameters used here (Table 1). In fact, owing to our limited knowledge concerning prebiotic 491 environments and chemistry, it is usually difficult to justify the parameter setting in the 492 modeling studies concerning the origin of life. However, the evolution during the origin of life 493 is remarkably characterized by the tendency from simplicity to complexity, which is a special, 494 rare phenomenon nature 48-50, 59 . Therefore, any relevant hypothetic scene in the area (e.g., here, 495 the speculation concerning the evolution of the protocell membrane), if supported by 496 modeling, merits our attention. In this consideration, exploring parameter-setting in favor of 497 the scene is valuable, which we called “parameter-exploration” in a way of “reverse modeling” 498 (see ref 15 for a detailed discussion). In practice, here most parameters have been explored 499 and adopted based on our experience in previous modeling studies concerning RNA-based 500 protocells 22-24 . When manual testing was difficult, a machine learning-like approach was used 501 to automatically explore the parameter space 15 . 502 The default values listed in Table 1 were adopted to shape the cases for demonstrating 503 our results. Actually, though the outcomes of the simulations may be influenced by the 504 change of those “key parameters” (e.g. for GR‘s spreading, see Fig. 3) and some of the other 505 parameters (see Figs. S8-1 and S8-2, as explained in Box S1), in general, they have turned out 506 to be fairly robust against “moderate adjustments” of most of the parameters. 507 To avoid cumbersome computation, total materials ( TNPPB, TFB, and TGPB), “the lower limit 508 number of amphiphiles to form a membrane” ( LAM), and the length of the characteristic 509 domain for a functional RNA species ( LCDR) are set obviously smaller in scale than the 510 corresponding situations in reality. Such simplifications are believed to be not in conflict with 511 the fundamental mechanisms reflected in the modeling. 512 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint Some detailed mechanisms concerning the implementation of the model 513 When the breaking site of an RNA chain is at a single-chain region, the breaking 514 probability is PBB. When the breaking site is within a double-chain region, the two parallel 515 bonds may break simultaneously – but with a smaller probability, i.e. PBB 3/2 (note that a 516 probability has a value between 0 and 1). However, for the case of outside protocells, a factor, 517 FDO, is involved to consider the corresponding higher water activity ( FDO > 1): the breaking 518 probability for a single-chain is PBB ×FDO, while that for a double-chain is (PBB ×FDO) 3/2 . The factor 519 FDO also works in the situation of nucleotide decaying and nucleotide residue decaying at the 520 end of RNA, i.e., PND×FDO and PNDE ×FDO respectively for the case of outside protocells. 521 The probability of the separation of the two strands of a duplex RNA is assumed to be 522 PSP r , where r = n 1/2 and n is the number of base pairs in the duplex. When n = 1, the probability 523 would be PSP. When n increases, the separation of the two strands would be more difficult. 524 The introduction of 1/2 corresponds to the consideration that the self-folding of single chains 525 may aid the dissociation of the duplex. 526 The probability of membrane formation is assumed to be 1-(1-PMF) x , where x= a-LAM + 1 527 and a is the number of amphiphiles (in quotient of tails, i.e., a fatty acid counts one whereas 528 a phospholipid counts two, the same below) in the grid room. When a is equal to LAM (the 529 lower limit of the number of amphiphiles to form a protocell membrane), the probability of 530 membrane formation is equal to PMF. This assumption concerns the consideration that the 531 more amphiphiles in a grid room, the more probable they would assemble to form a vesicle. 532 The probability of a fatty acid leaving the membrane is assumed to be PFLM / (y × z), where 533 y = 1 + i /(b/2) 3/2 and z = 1 + FPL×RPM. The item y represents the consideration for the 534 “osmotic pressure effect”: a higher concentration of the inner impermeable ions would cause 535 the protocell to be more swollen, and thus amphiphiles on the membrane are less likely to 536 leave, as suggested by experimental work 60 . Wherein, i is the quantity of inner impermeable 537 ions, i.e. RNAs (measured by the number of nucleotide residues, the same below), and b is 538 the quantity of amphiphiles within the membrane. Then, b/2 (there are two layers in the 539 membrane) is a “scale” representation of the surface area of the membrane and ( b/2) 3/2 is a 540 scale representation of the cellular space. Thus, i/(b/2) 3/2 is a representation of the 541 concentration of the ions. The item z represents the consideration for the phospholipid 542 content’s effect on preventing fatty acids from desorbing the membrane 9 , wherein RPM refers 543 to the ratio of phospholipids in the membrane (see the legend of Fig. 5 for an explanation), 544 and FPL is the factor representing the strength of this effect. Similarly, the probability of a 545 phospholipid leaving the membrane is assumed to be PPLM / ( y ×z), in which y and z are 546 explained the same way. In other words, with the increase of phospholipid content, the 547 membrane would be more stable, and any membrane components (including phospholipids 548 themselves) would be less likely to leave the membrane 9, 61 . 549 The probability of a nucleotide permeating into a protocell is assumed to be PNP × s / 550 (u×v), where s = b /LAM, u = 1 + FDE × i / (b/2) 3/2 , and v = 1 + FPP × RPM (wherein, i, b and RPM 551 are explained in the same way as above). The item s represents the consideration of the 552 constraining effect of the cellular space on the influx of nucleotides. That is, when b increases, 553 meaning that the cellular space increases correspondingly, the probability of a nucleotide 554 permeating into the protocell would become greater. The introduction of the item u 555 represents the consideration of the effect of Donnan’s equilibrium 62 , wherein FDE means the 556 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint degree of this effect; simply put, RNAs, which are charged and impermeable, may suppress 557 the incoming of permeable materials with the same charge, i.e., nucleotides here (see ref 22 558 for a detailed explanation). The introduction of the item v represents the consideration of 559 suppressing effect of phospholipid content on the permeability of the membrane, wherein FPP 560 means the degree of this effect; that is, the permeation of nucleotides would decrease with 561 the increase of phospholipid content 9 . Likewise, the probability of a nucleotide precursor 562 permeating into a protocell is assumed to be PNPP × s / ( u×v). With a little difference, the 563 probability of a nucleotide-precursor’s precursor permeating into a protocell is assumed to 564 be PNPPP × s / ( u×v’), where v’ = 1 + FPPW × RPM and Fppw is a weak version of FPP – in 565 consideration that the permeation of such small molecules should be suppressed with a less 566 extent 2, 42 . The glycerophosphate precursor, i.e., glycerol here, is uncharged (thus no Donnan’s 567 equilibrium effect is considered) and small in molecular size (thus Fppw is adopted), so the 568 corresponding permeating probability is PGPP × s /v’. Additionally, for the version of model 569 involving the function of TR, the probability of a nucleotide precursor permeating into a 570 protocell is assumed to be PNPP × s / (u×v’’), where v’’ = 1 + FPP × RPM / (1+t×FTR) and t is the 571 number of TR molecules in the protocell. That is, the increase of TR molecules would enhance 572 the membrane transportation of nucleotide precursors. Note that for the situations of 573 permeating out from a protocell, the item of s (concerning the cellular space) and u 574 (concerning Donnan’s equilibrium) is not considered, e.g., for a nucleotide in a protocell, the 575 probability of permeating outwards is simply PNP / v. 576 The probability of protocell division is assumed to be PCD × (1 – 2 × LAM/b), where b is the 577 quantity of amphiphiles within the membrane. When b is no more than twice that of LAM, the 578 probability is no larger than 0, i.e., the protocell cannot divide. This assumption considers the 579 fact that the larger the protocell, the more probable it would divide, on account of the physical 580 instability. 581 The probability of the movement of an RNA molecule is assumed to be PMV/m 1/2 , where 582 m is the mass of the RNA, relative to a nucleotide. This assumption represents the 583 consideration of the effect of the molecular size on the molecular movement. The square root 584 was adopted here according to the Zimm model, concerning the diffusion coefficient of the 585 polymer molecules in the solution 63 . 586 (Note: Source codes of the simulation program can be obtained from GitHub—see Code 587 availability statement. Besides the role of evidencing the reproducibility of the present study, 588 the source codes present more details about the implementation of the model and may help 589 readers to understand the simulation better). 590 591 Code availability. The C source codes implementing the models are available from: 592 https://github.com/mwt2001gh/membrane-takeover/blob/main/Fig-gr-final-1.cpp 593 (corresponding to the case shown in Fig. 2a) and 594 https://github.com/mwt2001gh/membrane-takeover/blob/main/Fig-npr-final-1.cpp 595 (corresponding to the case shown in Fig. 6a). 596 Data availability. The authors declare that the data supporting the findings of this 597 study are available within the paper and its Supplementary Information files. 598

599 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint W.T.M. is supported by the National Natural Science Foundation of China (No. 31571367) 600 (http://www.nsfc.gov.cn) and Natural Science Foundation of Hubei Province (CN) (No. 601 2019CFB685) (http://kjt.hubei.gov.cn). 602 Author contributions. W.T.M.. conceived the study, designed, implemented and analyzed 603 the model, and wrote the paper. C.W.Y. participated in the design and implementation of the 604 model. 605 Competing interests. The authors declare no competing interests. 606 607

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Science 302, 618-622 (2003) 728 729 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint Table 1. Parameters used in the computer simulation 730 Probabilities Descriptions Default Values PAT An RNA template attracting a substrate (by base-pairing) 0.9 PBB A phosphodiester bond breaking within an RNA chain 1×10 -5 PCB A protocell breaking 1×10 -4 PCD A protocell dividing 0.1 PCF Two adjacent protocells fusing with each other 0.001 PFJM A fatty acid joining the membrane 0.9 PFLM A fatty acid leaving the membrane 0.002 PFP The false base-pairing when a template attracts a substrate 0.001 PGD A glycerophosphate decaying into its precursor 0.1 PGF A glycerophosphate forming from its precursor (non-enzymatic) 0.002 PGFR A glycerophosphate forming from its precursor catalyzed by GR 0.9 PGPP A glycerophosphate precursor permeating through the membrane 0.9 PMC A protocell moving 0.1 PMF A membrane forming 0.1 PMV A nucleotide/fatty acid/phospholipid (or relevant precursors) moving 0.9 PND A nucleotide decaying into its precursor 0.02 PNDE A nucleotide residue decaying at RNA’s chain end 0.001 PNF A nucleotide forming from its precursor (non-enzymatic) 0.005 PNFR A nucleotide forming from its precursor catalyzed by NR 0.2 PNP A nucleotide permeating through the membrane 5×10 -5 PNPD A nucleotide precursor decaying into its precursor 0.005 PNPF A nucleotide precursor forming from its precursor (non-enzymatic) 0.002 PNPFR A nucleotide precursor forming from its precursor catalyzed by NPR 0.3 PNPP A nucleotide precursor permeating through the membrane 0.05 PNPPP A nucleotide-precursor’s precursor permeating through the membrane 0.5 PPD A phospholipid decaying (into fatty acid and glycerophosphate) 0.1 PPDM A phospholipid decaying within the membrane 0.01 PPF A phospholipid forming (on the membrane) 0.02 PPJM A phospholipid joining the membrane 0.9 PPLM A phospholipid leaving the membrane 1×10 -4 PRL The random ligation of nucleotides and RNA 1×10 -6 PSP The separation of a base pair 0.5 PTL The template-directed ligation of RNA 0..02 Others Descriptions Default Values N The system is defined as an N × N grid 30 TNPPB Total nucleotide-precursor’s precursors introduced in the beginning 80000 TFB Total fatty acids introduced in the beginning 50000 TGPB Total glycerophosphate precursors introduced in the beginning 50000 FDE Factor of the Donnan’s equilibrium effect 1 FDO Factor of molecular degradation outside protocells 10 FPL Factor of phospholipids' influence on amphiphiles leaving the membrane 5 FPP Factor of phospholipids on permeability (for nucleotides or their precursors) 20 FPPW F PP for nucleotide-precursor’s precursors or glycerophosphate precursors 3 FTR Factor for the RNA species functioning in membrane transport (TR) 100 LAM The lower limit number of amphiphiles to form a membrane 200 LCDR The length of the characteristic domain of a functional RNA species 7 Note: The probabilities are listed with names in alphabetical order. The simulation cases shown in this 731 paper adopt the default values, unless being stated explicitly to be different. The default characteristic 732 sequence for GR is “UUGAGCG”, for NR is “GCACGUA”, for NPR is “UCACGAG”, for TR is “CUGCUAG”, and 733 for the control is “GGCUACU”. See Methods for details on the principle of setting parameter values. 734 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint 735 736 Fig. 1 Protocells would benefit from a ribozyme favoring the synthesis of phospholipids in the 737 competition. Legends: FA—fatty acid; PL—phospholipid, i.e. phosphatidic acid here; G—738 glycerophosphate; Gp—glycerophosphate precursor (e.g., glycerol); GR—glycerophosphate-739 synthetase ribozyme (here representing the ribozyme favoring the synthesis of phospholipids). 740 The glycerophosphates produced through the catalysis of GR may reach the membrane and 741 non-enzymatically react with fatty acids therein to form phosphatidic acids (the phospholipid 742 molecules synthesized on the inner layer of the membrane may flip to the outer layer). The 743 formation of phospholipids on the membrane would prevent fatty acids from leaving the 744 membrane to a certain extent, which results in a net inflow of fatty acids in the lipid 745 competition. With the growth of the membrane, the number of GR within the protocell may 746 increase as a result of RNA replication. 747 748 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint 749 Fig. 2 The spread of the glycerophosphate-synthetase ribozyme (GR) and its co-spread with 750 the nucleotide-synthetase ribozyme (NR) in RNA-based protocells. Legends: Cgr—protocells 751 containing GR; Cnr—protocells containing NR; Cnrgr—protocells containing NR and GR; 752 Cctl—protocells containing the control RNA species; gr—GR; nr—NR; ctl—the control RNA 753 species (the legends apply to all the subfigures). Note that the lower panel of a subfigure 754 demonstrates the trend of the total molecule number of relevant RNA species in the system. 755 For all the cases, an “empty” fatty-acid protocell is inoculated at step 1×10 3 . (a) The de novo 756 spread of GR among protocells. Wherein, at step 1×10 4 , ten empty protocells are selected 757 (arbitrarily, the same below), each inoculated with one GR molecule, and another ten empty 758 protocells are selected, each inoculated with one control molecule. ( b) The spread of GR in 759 protocells containing NR. Wherein, at step 1×10 4 , ten empty protocells are selected, each 760 inoculated with one NR, and another ten empty protocells are selected, each inoculated with 761 one control; at step 3×10 5 , ten NR protocells are selected, each inoculated with one GR, and 762 another ten NR protocells are selected, each inoculated with one control. ( c) The spread of 763 NR in protocells containing GR, Wherein, at step 1×10 4 , ten empty protocells are selected, 764 each inoculated with one GR, and another ten empty protocells are selected, each inoculated 765 with one control; at step 3×10 5 , ten GR protocells are selected, each inoculated with one NR, 766 and another ten GR protocells are selected, each inoculated with one control. ( d) An 767 evolutionary case without inoculation of the RNA species – first, NR occurs naturally in empty 768 protocells, and then GR occurs naturally in NR protocells. PRL = 5×10 -6 . The characteristic 769 sequence of GR is “CCAUGUA” – only two nucleotides different from that of NR (default 770 sequence: “GCACGUA”, see the footnotes of Table 1); the control species adopts a 771 characteristic sequence of “UCAGGUA”, two nucleotides different from either of the two 772 ribozymes. 773 774 775 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint 776 Fig. 3 The influence of several key parameters on the spread of the protocells containing GR. 777 Legends: Cgr—GR protocells, with default parameter values; Cgr-para-up—GR protocells, for 778 increasing the parameter; Cgr-para-down—GR protocells, for decreasing the parameter; gr—779 GR, with default parameter values; gr-para-up—GR, for increasing the parameter; gr-para-780 down—GR, for decreasing the parameter (the legends apply to all the subfigures). The red 781 arrows indicate the steps where the parameter adjustments are conducted. For ( PGFR), the 782 default value 0.9 is turned up to 0.95, 0.98 and 0.99 at these points of change, respectively, 783 or turned down to 0.1, 0.05 and 0.02 at these points. For (FPL), the default value 5 is turned up 784 to 10, 20 and 50 at the first three points of change, respectively, or turned down to 2, 1 and 785 0 at these points; additionally, at the fourth change point of the turning-down case, PFLM is 786 changed from its default value 0.002 to 1×10 -4 (the legends Cgr* and gr* refer to this change). 787 For (PFLM), the default value 0.002 is turned up to 0.005, 0.01 and 0.02 at the first three points 788 of change, respectively, or turned down to 5×10 -4 , 2×10 -4 and 1×10 -4 at these points; 789 additionally, at the fourth change point of the turning-down case, FPL is changed from its 790 default value 5 to 0 (the legends Cgr* and gr* refer to this change). For (FPP), the default value 791 20 is turned down to 10, 5 and 2 at the first three change points, respectively, or turned up 792 to 200, 2000 and 2×10 4 at these points; additionally, at the fourth change point of the turning-793 up case, FPPW is changed from its default value 3 to 3000 (the legends Cgr* and gr* refer to 794 this change). 795 796 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint 797 Fig. 4 The snapshots on spatial distribution of a case exemplifying the natural spread of NR 798 and GR among protocells. The evolutionary dynamics of the case is shown in Fig. 2d. The 799 color-depth of yellow in the background represents the concentration of the raw materials 800 for forming nucleotides in the system (i.e. precursors of nucleotide precursors). The grey 801 squares denote the membranes of protocells, and the corresponding color-depth is in 802 proportion to the phospholipid content in the membrane. The red dots denote NR, and the 803 blue dots denote GR. An empty protocell is inoculated at step 1000 (the grey arrow), and then 804 empty protocells spread in the system (in reality, the first empty protocell might have formed 805 due to the inducing of mineral particles 64 or the concentration effect during dry-wet circles 57, 806 58 ). The red arrow indicates the first NR emerging naturally in an empty protocell. The blue 807 arrow indicates the first GR emerging naturally in an NR protocell. 808 809 810 811 812 813 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint 814 Fig. 5 The alteration of membrane contents with the rising of a ribozyme favoring 815 phospholipid-synthesis (i.e. GR). Legends: C—empty protocells; Cgr—protocells containing 816 GR; Cnr—protocells containing NR; Cnrgr—protocells containing NR and GR. For a certain 817 kind of protocells (C, Cgr, Cnr, or Cnrgr), The ratio of phospholipids in the membrane (RPM) 818 of a protocell is calculated as 2* pnum/(2*pnum+fnum), where pnum and fnum denote the number of 819 phospholipids and that of fatty acids respectively (note that a phospholipid molecule has two 820 non-polar tails whereas a fatty acid has one). Here the vertical axis represents the average 821 RPM of the corresponding protocells, and it is set to 0 ad hoc at the points where that kind 822 of protocells does not exist. (a) The change of membrane contents during the spread of GR 823 in empty protocells (the case is the same as the one shown in Fig. 2a, but the horizontal axis 824 adopts a smaller scale). (b) The change of membrane contents during the spread of GR in NR 825 protocells (the case is the same as the one shown in Fig. 2b). 826 827 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint 828 Fig. 6 The decreased permeability caused by phospholipid content in the membrane could 829 drive the emergence of other functions in the protocells. The legends identical to those 830 included in Fig. 2 have the same meaning; additional ones: Cnrgrnpr – protocells containing 831 NR, GR and NPR, Cnrgrtr – protocells containing NR, GR and TR, npr – NPR, and tr – TR. At 832 step 1×10 3 , an empty fatty-acid protocell is inoculated. At step 1×10 4 , ten empty protocells 833 are selected (arbitrarily, the same below), each of which is inoculated with one NR molecule, 834 one GR molecule, and one control molecule. (a) NPR, i.e. a ribozyme using more fundamental 835 raw materials, would not spread if the influence of phospholipid content on membrane 836 permeability is not assumed (solid circles and solid lines; FPP and FPPW are set to 0 throughout 837 the simulation), but would spread when this influence is considered (empty circles and dotted 838 lines; at step 3×10 5 , FPP and FPPW are turned up to 30 and 3 respectively). In both cases, at step 839 6×10 5 , ten NR-GR protocells are selected, each of which is inoculated with one NPR molecule. 840 (b) TR, an RNA species favoring the membrane transport, would not spread if the influence 841 of phospholipid content on membrane permeability is not assumed (solid circles and solid 842 lines; FPP and FPPW are set to 0 throughout the simulation), but would spread when this influence 843 is considered (empty circles and dotted lines; at step 3×10 5 , FPP and FPPW are turned up to 30 844 and 3 respectively). In both cases, at step 6×10 5 , ten NR-GR protocells are selected, each of 845 which is inoculated with one TR molecule. PNP=5×10 -6 . 846 847 848 849 850 851 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint 852 853 Fig. 7 Events occurring in the model system and associated parameters. Solid arrows denote 854 chemical reactions and dashed arrows represent other events. Legends: Npp—nucleotide-855 precursor’s precursor; Np—nucleotide precursor; Nt—nucleotide; FA—fatty acid; Gp—856 glycerophosphate precursor; G—glycerophosphate; PL—phospholipid, i.e. phosphatidic acid 857 here; NPR—nucleotide-precursor-synthetase ribozyme; NR—nucleotide-synthetase 858 ribozyme; GR—glycerophosphate-synthetase ribozyme. The events occurring within a 859 protocell are shown in ( a), and the events concerning the behaviors of the protocells are 860 depicted in (b), which adopts a smaller scale. For a naked room, there would be no membrane 861 and associated events. Note that TR, i.e., the functional RNA species involved in the 862 membrane transport, which functions in an abstract way in the model, is not depicted here; 863 and there are a few parameters unsuitable or difficult to represent here (see text for detailed 864 explanations). 865 866 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint Supplementary Information 867 868 869 Fig. S1 The influence of FPL and PPLM on the spread of the protocells containing GR. The 870 situation is the same as that shown in Fig. 3-FPL, except that at the fourth change point of the 871 turning-down case (cyan symbols, where FPL equals to 0), instead of changing PFLM, PPLM is 872 changed from its default value 1×10 -4 to 0.002 (the legends Cgr* and gr* refer to this change). 873 874 875 876 Fig. S2 The influence of PPF on the content of membrane components. The legends are the 877 same as those in Fig. 5. (a) Based on the case of Fig. 5a, at step 7×10 5 , PPF is changed from its 878 default value 0.02 to a value of 0.2. ( b) Based on the case of Fig. 5b, at step 7×10 6 , PPF is 879 changed from its default value 0.02 to a value of 0.2. With the increase of RPM for those 880 protocells with GR (i.e., Cgr in a and Cnrgr in b), the RPM for the protocells without GR (i.e., C 881 in a and Cnr in b) also increases, which should be attributed to phospholipids’ exchange 882 between protocells. 883 884 885 886 887 888 889 890 891 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint 892 893 Fig. S3 The influence of FPP and PPF on the spread of the protocells containing GR. The situation 894 is the same as that shown in Fig. 3-FPP, except that at the fourth change point of the turning-895 down case (orange symbols, where FPP=2×10 4 ), it is PPF (instead of FPPW) that is changed – from 896 its default value 0.02 to 0.2 (the legends Cgr* and gr* refer to this change). 897 898 899 900 Fig. S4 The corresponding decline of GR protocells’ phospholipid content in the membrane 901 (RPM) with the turning up of FPPW. The cases are the same as those shown in Fig. 3- FPP 902 (concerning orange and purple symbols). Legends: “default” represents the case without the 903 change of FPPW (i.e. with a default value of 3), while “ FPPW-up” represents the case that FPPW is 904 changed from its default value to 3000 at step 3.5×10 6 . 905 906 907 908 909 910 911 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint 912 913 Fig. S5 The snapshots on spatial distribution of the cases showing the spread of new 914 functional RNA species in NR-GR protocells due to the decreased membrane permeability. 915 The evolutionary dynamics of the two cases are shown in Fig. 6. In addition to the symbols 916 that are explained the same way as those included in Fig. 4, here black dots are introduced 917 to denote new functional RNA species. ( a) The black dots denote NPR molecules. The left 918 subfigure (step 500,000) represents the stage before the spread of NPR (that is, only NR and 919 GR exist), whereas the right subfigure (step 2,000,000) represents the stage after the spread 920 of NPR. Notably, after the spread of NPR, its substrates, i.e. precursors of nucleotide 921 precursors, which are represented by color-depth of the background yellow, are almost 922 exhausted. ( b) The black dots denote TR molecules. The left subfigure (step 500,000) 923 represents the stage before the spread of TR, whereas the right subfigure (step 2,000,000) 924 represents the stage after the spread of TR. The phenomenon of the precursors of nucleotide 925 precursors’ exhaustion is not observed – because the function of TR is to facilitate the across-926 membrane transport of nucleotide precursors rather than to exploit precursors of nucleotide 927 precursors. 928 929 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint 930 931 Fig. S6 The spread of the ribozyme exploiting more fundamental raw materials (NPR) and 932 that of the RNA species favoring membrane transport (TR) are attributed to their function. 933 The figure is explained the same way as Fig. 6, except that the cases denoted by solid circles 934 and solid lines in Fig. 6, which represent the situation without consideration of negative 935 influence of phospholipid content on the membrane’s permeability, are not shown – here, 936 instead, solid circles and solid lines denote the cases in which the relevant function is turned 937 off after 1.4×10 6 . (a) The function of NPR is turned off by setting PNPFR to 0. ( b) The function 938 of TR is turned off by setting FTR to 0. 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint 954 955 Fig. S7 The simulation cases modeling the emergence of NPR and TR in reality. The legends 956 are the same as those in Fig. 6. The modeling situations are the same as those in the cases of 957 Fig. 6, except the details explained in the following. At step 1×10 4 , only one empty protocell 958 is selected and inoculated with one molecule of NR, GR and the control species – note that 959 since the raw materials in the system are initially abundant, such an inoculation (to achieve 960 the spread of NR-GR protocells) need not be conducted repeatedly (that is, unlike the ones 961 mentioned below). (a) After step 6×10 5 , one molecule of NPR is inoculated into one NR-GR 962 protocell every 1×10 5 steps. PBB=5×10 -5 , PNFR=0.9 and PNPFR=0.5. (b) For the case in which the 963 influence of phospholipid content on membrane permeability is considered (empty circles 964 and dotted lines), FPP and FPPW are turned up (to 30 and 3 respectively) at step 2×10 5 . After 965 step 2.5×10 5 , one molecule of TR is inoculated into one NR-GR protocell every 1×10 4 steps. 966 PBB=5×10 -5 and PNFR=0.9. 967 968 969 970 971 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint 972 Fig. S8-1. The influence of other parameters (in addition to those shown in Fig. 3) on the 973 spread of GR protocells (part 1). The representations are the same as those in Fig. 3. The 974 values adopted at the three critical change points (red arrowheads) are listed in Table S1. See 975 Box S1 for a comment on the influence. 976 977 Fig. S8-2. The influence of other parameters (in addition to those shown in Fig. 3) on the 978 spread of GR protocells (part 2). The representations are the same as those in Fig. 3. The 979 values adopted at the three critical change points (red arrowheads) are listed in Table S1. See 980 Box S1 for a comment on the influence. 981 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint Table S1. The values adopted in the parameter analysis (Figs. S8-1 and S8-2) 982 Note: The upper portion of the parameters (above the dashed line) is for Fig. S8-1 and the 983 lower portion is for Fig. S8-2. “v0” means the default value; “Up-v1”, “Up-v2” and “Up-v3” 984 means the values adopted at the three change points (one after another; see red arrowheads 985 in the figures) for the case of parameter-turning-up; “Down-v1”, “Down-v2” and “Down-v3” 986 means the values adopted at the three change points for the case of parameter-turning-987 down. 988 Up-v3 Up-v2 Up-v1 v0 Down-v1 Down-v2 Down-v3 0.2 0.05 0.01 PGF=0.002 0.001 5×10 -4 2×10 -4 0.05 0.02 0.01 PNF=0.005 0.002 0.001 5×10 -4 0.02 0.01 0.005 PNPF=0.002 0.001 5×10 -4 2×10 -4 0.2 0.1 0.05 PPF=0.02 0.01 0.005 0.002 0.2 0.1 0.05 PND=0.02 0.01 0.005 0.002 0.01 0.005 0.002 PNDE=0.001 5×10 -4 2×10 -4 1×10 -4 0.05 0.02 0.01 PNPD=0.005 0.002 0.001 5×10 -4 0.9 0.5 0.2 PGD=0.1 0.05 0.02 0.01 0.9 0.5 0.2 PPD=0.1 0.05 0.02 0.01 0.1 0.05 0.02 PPDM=0.01 0.005 0.002 0.001 1×10 -5 5×10 -6 2×10 -6 PRL=1×10 -6 5×10 -7 2×10 -7 1×10 -7 1×10 -4 5×10 -5 2×10 -5 PBB=1×10 -5 5×10 -6 2×10 -6 1×10 -6 100 50 20 FDO=10 5 2 1 0.99 0.98 0.95 PAT=0.9 0.5 0.2 0.1 0.01 0.005 0.002 PFP=0.001 5×10 -4 2×10 -4 1×10 -4 0.9 0.5 0.2 PMF=0.1 0.05 0.02 0.01 0.001 5×10 -4 2×10 -4 PPLM=1×10 -4 5×10 -5 2×10 -5 1×10 -5 0.2 0.1 0.05 PTL=0.02 0.01 0.005 0.002 0.95 0.9 0.8 PSP=0.5 0.2 0.1 0.05 0.99 0.98 0.95 PMV=0.9 0.5 0.2 0.1 0.99 0.98 0.95 PFJM=0.9 0.5 0.2 0.1 0.99 0.98 0.95 PPJM=0.9 0.5 0.2 0.1 20 10 5 FPPW=3 1 0.5 0.2 10 5 2 FDE=1 0.5 0.2 0.1 5×10 -4 2×10 -4 1×10 -4 PNP=5×10 -5 2×10 -5 1×10 -5 5×10 -6 0.5 0.2 0.1 PNPP=0.05 0.02 0.01 0.005 0.95 0.9 0.8 PNPPP=0.5 0.2 0.1 0.05 0.99 0.98 0.95 PGPP=0.9 0.5 0.2 0.1 0.001 5×10 -4 2×10 -4 PCB=1×10 -4 5×10 -5 2×10 -5 1×10 -5 0.01 0.005 0.002 PCF=0.001 5×10 -4 2×10 -4 1×10 -4 0.9 0.5 0.2 PCD=0.1 0.05 0.02 0.01 0.9 0.5 0.2 PMC=0.1 0.05 0.02 0.01 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint 989 Box S1. On the influence of parameters (for Figs. S8-1 and S8-2) 990 Firstly, we note that the default values of the parameters we adopted are almost the best for the spread of protocells containing GR (blue solid circles) – that is, the change of parameter values, either upwards or downwards, could barely improve the level of GR protocells (orange empty circles for “upwards” and cyan empty circles for “downwards”) and seldom improve the level of GR molecules (orange dotted lines for “upwards” and cyan dotted lines for “downwards”). This means our initial parameter- exploration is quite successful (see text for the meaning of “parameter-exploration”). Secondly, we see that the spread of GR protocells is robust to the “moderate” change of most parameter values. In the analysis, when turning up or down a parameter, typically a scale of 2 or 2.5 times was adopted, unless the probability might be larger than 1 (see Table S1 for details). In most cases, the apparent influence on the spread of GR protocells comes only at the third change point, or even never occurs within the changing scope. Thirdly, we comment briefly below on the cases in which the parameter change brings about obvious effects. (1) For the cases shown in Fig. S8-1. A high probability of non-enzymatic production of glycerophosphates ( PGF) is unfavorable because GR’s advantage would be weakened. A low probability of nucleotide formation (PNF), which brings about the shortage of the building blocks of RNA, is disadvantageous; likewise, a low probability of nucleotide precursor formation (PNPF) is disadvantageous. On the other side of the coin, a higher probability concerning decay of nucleotides (PND) and that of nucleotide precursors (PNPD) would also result in the scarceness of RNA’s building blocks. A too high probability of RNA’s end-decaying (PNDE) may shorten the life span of GR to an extent that the ribozyme cannot sustain in the system through replication. A small factor of degradation outsides protocells (FDO) means the synthesis of RNA within protocells would be short of raw materials. A low probability for an RNA template to attract substrates (PAT) means the template-directed replication of GR would become difficult. A high error rate in the replication of RNA (PFP) is disadvantageous because the heredity of GR is weakened. (2) For the cases shown in Fig. S8-2. A low probability for substrates aligned on an RNA template to ligate ( PTL) is unfavorable because it would also slow down the template-directed replication. A low probability for the separation of a base pair (PSP) is unfavorable because of the difficulty of strand separation in the RNA replication (note that the spread of GR is depressed at the first down-turning point, which means it is quite sensitive to the decline of this parameter). A high probability of protocell-breaking ( PCB) is unfavorable because the existence of protocells becomes problematic. A high probability of protocell-fusing (PCF) is disadvantageous because the protocells without GR tend to fuse with those containing GR and thus the GR is “parasitized”. Related to this point, a high moving rate of protocells (PMC) is unfavorable because this would tend to bring the protocells without GR adjacent to GR protocells and enhance the likelihood of the cell-fusion. 991 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint