{"paper_id":"36dfa58f-6b4e-4d66-af27-e103d0c97201","body_text":"1 \nFrom experimental clues to theoretical modeling: Evolution 2 \nassociated with the membrane-takeover at an early stage of life 3 \nWentao Ma 1*, Chunwu Yu 2  4 \n1. Hubei Key Laboratory of Cell Homeostasis, College of Life Sciences, Wuhan 5 \nUniversity, Wuhan 430072, China 6 \n2. College of Computer Sciences, Wuhan University, Wuhan 430072, China 7 \n* Correspondence to: 8 \n  Wentao Ma 9 \n  College of Life Sciences, 10 \nWuhan University,  11 \nWuhan, 430072,  12 \nP. R. China 13 \nEmail: mwt@whu.edu.cn 14 \n 15 \nAbstract: 16 \nModern cell membranes are primarily composed of phospholipids, while primitive cell 17 \nmembranes in the beginning of life are believed to have formed from simpler lipids (such as 18 \nfatty acids) synthesized in the prebiotic environment. An attractive experimental study 19 \nsuggested that the corresponding “membrane-takeover” (as an evolutionary process) is likely 20 \nto have occurred very early (e.g. in the RNA world) due to some simple physical effects, and 21 \nmight have subsequently triggered some other evolutionary processes. Here, via computer 22 \nmodeling on a system of RNA-based protocells, we convinced the plausibility of such a 23 \nscenario and elaborated on relevant mechanisms. It is shown that in protocells with a fatty-24 \nacid membrane, because of the benefit of phospholipid content (i.e., stabilizing the 25 \nmembrane), a ribozyme favoring the synthesis of phospholipids may emerge; subsequently, 26 \ndue to the reduced membrane permeability on account of the phospholipid content, two 27 \nother functional RNA species could arise: a ribozyme exploiting more fundamental materials 28 \n(thus more permeable) for nucleotide synthesis and a species favoring across-membrane 29 \ntransportation. This case exemplifies a combination of experimental and theoretical efforts 30 \nregarding early evolution, which may shed light on that notoriously complicated problem: the 31 \norigin of life. 32 \n  33 \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \nIntroduction 34 \n It is thought that the primitive cells (protocells) should have had a membrane composed 35 \nof simple, single-chain lipids, such as fatty acids and their derivatives (generally referred to as 36 \n“fatty acids” below for concise), which were present in the prebiotic environment\n1-3\n. Indeed, 37 \nthough phospholipids may also have been synthesized prebiotically\n4, 5\n, they, as more complex 38 \nmolecules, are likely to have been much less abundant – especially considering that they 39 \nshould have been made from those single-chain lipids. In the logic of “the simpler, the more 40 \nlikely to emerge de novo”, it is more plausible that the first membranes were assembled from 41 \nthe single-chain lipids, and phospholipid membranes came later, perhaps due to Darwinian 42 \nevolution. Another major reason in favor of “fatty acids first” for primordial membranes is that 43 \nphospholipid-based membranes are much less permeable, thus would seriously hinder 44 \nprotocells from obtaining crucial materials available in environments for growth and 45 \nreproduction\n1-3\n. 46 \nTraditionally, as a further argument for the scene of “fatty acids first”, it is emphasized 47 \nthat these single-chain lipids are more fluid or dynamic – thus favoring the spontaneous 48 \ngrowth and division of protocells\n1-3\n. But evidence has now accumulated to show that 49 \nphospholipid-based membranes are also sufficiently dynamic for growth and division\n4, 6-8\n. 50 \nTherefore, this argument seems now no longer valid. However, notably, if the scene of “fatty 51 \nacids first” is true, these findings actually imply that the membrane-takeover from fatty-acid 52 \nmembranes to phospholipid membranes could have occurred quite early – well before the 53 \nadvent of complex forms like modern cells, which have specific functions regarding cellular 54 \ngrowth and division. 55 \nInterestingly, via experimental studies, Szostak and coworkers found evidence in support 56 \nof such an early membrane-takeover\n9\n. It was shown that fatty acid vesicles with a portion of 57 \nphospholipid components would grow at the expense of those pure fatty acid vesicles (see 58 \nalso associated earlier work\n10, 11\n). The main reason is that the involvement of phospholipids 59 \nwould reduce the efflux of fatty acids from the membrane and ， through the 60 \nexchange equilibrium of these molecules between vesicles via the environment, eventually 61 \nresult in a net inflow of fatty acids. This means, as the authors stated, “the ability to synthesize 62 \nphospholipids from single-chain substrates would have therefore been highly advantageous 63 \nfor early cells competing for a limited supply of lipids”\n 9\n. Undoubtedly, with the emergence of 64 \nthis function in protocells, the phospholipid content of the membrane would have increased. 65 \nFurthermore, in the same work, it was demonstrated that the permeability of the 66 \nmembrane declines in proportion to the rise in phospholipid content\n9\n. The reduction of 67 \npermeability was ascribed to the decreased fluidity (i.e., increased order) in a membrane 68 \ncontain more phospholipid molecules (in the form of double-chain lipids). This “would have 69 \nled to a cascade of new selective pressures for the evolution of metabolic and transport 70 \nmachinery to overcome the reduced membrane permeability” \n9\n. In other words, as they 71 \nclarified, “cells could have evolved the ability to synthesize their own building blocks from 72 \nsimpler, more permeable substrates”, and “membrane transporters, a hallmark of modern 73 \ncells, would have emerged as a means for overcoming low membrane permeability”. 74 \nObviously, by exploring relevant physical effects, the experimental work was trying to 75 \nformulate speculations on some tendencies of Darwinian evolution in the early stage of life. 76 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \nHowever, at least up to now, such evolutionary tendencies are per se difficult to follow up in 77 \nlaboratory. On the other hand, with the rapid development of theoretical studies in the field 78 \nof the origin of life (e.g., see refs \n12-16\n), it is now well feasible to model such early evolution, i.e., 79 \nto study relevant evolutionary dynamics by computer simulation. So here we ask: can we 80 \ndemonstrate in silico the plausibility of the evolutionary events suggested by the experimental 81 \nwork? Additionally, via the modeling, it is expected that we would get a more comprehensive 82 \nunderstanding on detailed mechanisms involved in the evolution. 83 \nThe RNA world hypothesis is now widely accepted in the field of the origin of life \n17-19\n, 84 \ndue to its logical reasonability as well as accumulating evidence supporting it. In fact, the most 85 \nmeaningful point of this idea is that it tries to explain the onset of Darwinian evolution\n16, 20, 21\n – 86 \nand the subsequent process in life’s history is just a matter of Darwinian evolution. In the 87 \nscenario, RNA played both the roles of genetic material and functional molecules, as the two 88 \nfundamental requirements for the “running” of Darwinian evolution (thus evading the 89 \n“Chicken and Egg” dilemma – which came first, DNA or proteins?). Though there are still 90 \nongoing debates on it, the scenario undoubtedly offers a relatively simple platform for us to 91 \nmodel early evolutionary events like the ones we are concerned about here (actually, in the 92 \noriginal experimental work it was also implied the suggested functions associated with the 93 \nmembrane-takeover may have evolved in the RNA world\n9\n). Therefore, here we aim to model 94 \nthe emergence of a ribozyme favoring the synthesis of phospholipids in RNA-based 95 \nprotocells – due to the phospholipids’ benefit for stabilizing the membrane, and the 96 \nsubsequent arising of a ribozyme favoring the exploitation of simpler (thus more permeable) 97 \nsubstrates, or that of an RNA functional species favoring the membrane transport – owing to 98 \nthe decreased membrane permeability resulting from the increased phospholipid content. 99 \nResults 100 \nAbout the model 101 \nWe conducted the computer simulation using a Monte Carlo model similar to those used 102 \nin our previous work concerning the RNA-based protocells\n22-24\n. It is described below in general 103 \nterms (see Methods for details). The system is a two-dimensional N × N square grid (with 104 \ntoroidal topology to avoid edge effects). Molecules are distributed within the grid rooms, 105 \nincluding nucleotides, RNA, fatty acids, phosphatidic acids (here as a representative of 106 \nphospholipids) and glycerophosphates (the head-group-maker of phosphatidic acids), as 107 \nwell as some relevant precursors: nucleotide precursors, nucleotide-precursor’s precursors, 108 \nand glycerophosphate precursors. Amphiphiles (fatty acids and phospholipids) may assemble 109 \nat the boundary of a grid room and form a membrane, then the grid room is occupied by a 110 \nprotocell. In each time step, certain events may occur to molecules and protocells with defined 111 \nprobabilities (Table 1). 112 \nIn the beginning of a simulation, a certain quantity of nucleotide-precursor’s precursors, 113 \nfatty acids and glycerophosphate precursors are introduced into the system. During the 114 \nsimulation process, protocells or RNA species may be inoculated (see below for detailed 115 \ndescriptions in different cases). In the system, nucleotide-precursor’s precursors may 116 \ntransform into nucleotide precursors, which in turn form nucleotides (randomly as A, G, C, or 117 \nU). Nucleotides may assemble into RNA via random ligation. RNA may conduct template-118 \ndirected replication. Glycerophosphate precursors may transform into glycerophosphates, 119 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \nwhich in turn react with fatty acids on the membrane and produce phosphatidic acids thereon. 120 \nWith its membrane absorbing amphiphiles, a protocell may grow and after reaching a certain 121 \nsize, may divide into two – the molecules within it and the amphiphiles on its membrane 122 \nwould assort randomly into its offspring (thus reproduction). 123 \nSignificantly, the model has a “resolution” at the nucleotide level, thus inherently suitable 124 \nfor studying the early Darwinian evolution, which relies essentially on the sequence-function 125 \nconnection. In the model, an RNA molecule containing a characteristic sequence (domain) is 126 \nassumed to have a special function (i.e. as a ribozyme). The total materials (for RNA and the 127 \nmembrane) in the system is constant, and the RNA-based protocells compete for these 128 \nmaterials. In the competition, those protocells containing functional RNA species “beneficial” 129 \nto protocell’s reproduction may spread (become thriving) in the system – or say, those “useful” 130 \nfunctional RNA species may spread among protocells. In practice, here the characteristic 131 \nsequence of a functional RNA species is arbitrarily presumed on account of our ignorance of 132 \nrelevant cases, but this does not matter – what our modeling aims to explore is merely: if a 133 \ncharacteristic sequence bears a special function, can the sequence spread? Or more abstractly, 134 \ncould a specific “sequence-function connection” result in a case of Darwinian evolution? 135 \nThe spread of the ribozyme favoring phospholipid-synthesis in protocells 136 \nAs suggested by the original experimental work\n9\n, the ability to synthesize phospholipids 137 \nwould have been highly advantageous for protocells competing for a limited supply of lipids, 138 \nsince the efflux of fatty acids would decrease with the increase of phospholipid content in the 139 \nmembrane. As mentioned above regarding the model, we consider phosphatidic acids as a 140 \nrepresentative of phospholipids here. In reality, phosphatidic acid is the simplest phospholipid 141 \nand was indeed likely to have been directly involved in the membrane-takeover. In the 142 \npotential relevant synthetic route, phosphorylation of glycerol appears to have been 143 \ninefficient, while the acylation of glycerophosphates by fatty acids could have been 144 \nproductive\n5, 25, 26\n. In other words, the bottleneck was the formation of glycerophosphates – 145 \nthus, here we assume a glycerophosphate-synthetase ribozyme (GR) as a representative of 146 \nthe supposed “ribozyme favoring phospholipid-synthesis”, and the synthesized 147 \nglycerophosphate molecules would reach the protocell membrane and react with fatty acids 148 \ntherein in a non-enzymatic way. Indeed, a recent study demonstrated that the acylation 149 \nleading to phospholipids may well have occurred free of enzymes\n4\n. Figure 1 shows a scheme 150 \ndepicting how a protocell containing GR could have grown at the expense of the one without 151 \nGR. With the growth of membrane, GR within the protocell may replicate; with the 152 \nenlargement of the protocell, it may divide into offspring protocells due to physical instability\n3, \n153 \n27\n – thereby achieving “reproduction”. The protocell without GR would shrink and may 154 \neventually break or fuse with other protocells. 155 \n First of all, we want to explore whether protocells containing GR could become thriving 156 \nby virtue of its function in favoring the synthesis of phospholipids. In the simulation, an “empty” 157 \nfatty-acid protocell is inoculated at step 1×10\n3\n. By absorbing fatty acids in the system, the 158 \nempty protocells grow and divide – eventually spreading in the system. Then, at step 1×10\n4\n, 159 \nten empty protocells are selected (arbitrarily, the same below), each inoculated with one GR 160 \nmolecule, while ten other empty protocells are each inoculated with one control (RNA species 161 \nwithout function) molecule. It was found that the protocells containing GR could spread, 162 \nwhereas the ones containing the control could not (Fig. 2a, the upper panel); in other words, 163 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \nthe GR could spread among protocells, whereas the control could not (Fig. 2a, the lower 164 \npanel). 165 \nIn order to study the underlying mechanism, we investigated the influences of several 166 \nkey parameters. Firstly, to confirm that the spread of GR protocells (or say, the spread of GR) 167 \nis owing to the function of GR, we explored the influence of PGFR (the probability of glycerol-168 \nphosphate formation catalyzed by the ribozyme; see Table 1 for descriptions of parameters). 169 \nIndeed, with the stepwise turning-down of the ribozyme function, the spread of the GR 170 \nprotocells is weakened and finally completely suppressed (Fig. 3-PGFR).  171 \nNext, we were interested in whether the advantage of GR protocells could be attributed 172 \nto the decrease of fatty acid desorption from their membranes, as suggested by the original 173 \nexperimental work\n9\n. In accordance with the experimental work, the probability of a fatty acid 174 \nmolecule leaving the membrane is here assumed to be negatively correlated with the content 175 \nof phospholipids in the membrane, i.e., in proportion to 1/(1+ FPL×RPM), where RPM is the 176 \nratio of phospholipids in the membrane and FPL is a factor representing the degree of this 177 \ninfluence (see Methods for details). Somewhat surprisingly, the decrease of FPL does not 178 \nsignificantly affect the spread of GR protocells (Fig. 3-FPL, cyan symbols) – even when FPL is set 179 \nto 0 (after step 2.5×10\n6\n), which indicates that phospholipids in the membrane no longer have 180 \nan impact on the desorption of fatty acids, the spread of GR protocells is only marginally 181 \ninhibited. That is to say, there should be other mechanisms that favor the GR protocells.  182 \nIn fact, in that original paper\n9\n, a potential additional reason was proposed: with a fraction 183 \nof “insoluble” phospholipids, actually, “only the fraction of the vesicle surface area composed 184 \nof fatty acids can contribute to monomer efflux, whereas the entire surface area permits fatty 185 \nacid influx, leading to a net influx (growth)”. In other words, the formation of phospholipid 186 \nmolecules from fatty acids on the membrane could “fasten” this portion of fatty acids. In our 187 \nmodel, the default value of the probability of a phospholipid molecule leaving the membrane 188 \n(PPLM=1×10\n-4\n) is much lower than that for a fatty acid molecule ( PFLM=0.002). Therefore, in 189 \naddition to set FPL to 0, we tried to assume the same value for these two probabilities (thus 190 \nthe “fastening effect” no longer exists) – and “witnessed” the collapse of GR protocells’ spread! 191 \n(Fig. 3-FPL, purple symbols, where after step 3.5×10\n6\n PFLM is set to 1×10\n-4\n; see also Fig. S1, 192 \npurple symbols, where after step 3.5×10\n6\n PPLM is increased to 0.002). Subsequently, we 193 \nexplored the “fasten effect” per se – indeed, the decreasing of PFLM (thus more approaching 194 \nto the value of PPLM) comes against the spread of GR protocells (Fig. 3-PFLM, cyan symbols). In 195 \nthis case, even when PFLM is set to a value identical with that of PPLM (after step 2.5×10\n6\n), the 196 \nGR protocells can still spread at a significant level, which is then completely suppressed when 197 \nFPL is set to 0 (after step 3.5×10\n6\n, purple symbols). That is to say, the two reasons mentioned 198 \nabove, the “fastening effect” and the “anti-desorption effect”, do work together – both 199 \ncontribute to the net influx of fatty acids, and eventually result in the spread of GR protocells. 200 \nThe co-spread of the ribozyme favoring phospholipid-synthesis and another ribozyme 201 \nin protocells 202 \n After observing that GR may spread among protocells de novo, we asked whether this 203 \nphospholipid-synthesis favoring ribozyme may become thriving in protocells that already 204 \ncontain other ribozymes. An RNA species catalyzing the template-directed synthesis (and 205 \nthus the RNA replication) has long been suggested to have been the first ribozyme emerging 206 \nin the RNA world, usually referred to as an “RNA replicase”\n 18, 28-31\n. Another appealing 207 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \ncandidate is a ribozyme capable of catalyzing the synthesis of nucleotides\n32-34\n, namely 208 \nnucleotide-synthetase ribozyme (NR) – it may also favor its own replication by supplying 209 \nmonomers (the replication could have based on non-enzymatic copying of RNA)\n35, 36\n. In fact, 210 \nboth the two ribozymes, as supported by modeling work, might have spread early in the RNA 211 \nworld\n24, 35, 37-40\n. Here we choose NR-containing protocells as the target protocells to see 212 \nwhether GR could spread therein, mainly considering that in this study we will later introduce 213 \na related ribozyme, i.e., a nucleotide-precursor-synthetase ribozyme (NPR) – it is attractive to 214 \ninvolve two ribozymes in the same “pathway”. 215 \nIn the simulation, after the initial inoculation at step 1×10\n3\n, empty protocells spread; then, 216 \nat step 1×10\n4\n, ten of them are selected, each inoculated with one NR molecule (and control 217 \nmolecules are inoculated into another ten empty protocells). As expected, the NR protocells 218 \nspread (while the protocells with the control cannot) (Fig. 2b). Subsequently, at step 3×10\n5\n, 219 \nten NR protocells are selected, each inoculated with one GR, and another ten NR protocells 220 \nare each inoculated with one control. Eventually, protocells containing both NR and GR 221 \nspread in the system – or say, GR co-spreads with NR among protocells (while the control 222 \ncannot). 223 \nNoticeably, in his later essays, the leader of the original experimental work, Prof. Szostak 224 \nexplicitly suggested that a ribozyme favoring phospholipid-synthesis might have emerged 225 \nfirst in the RNA world, and other beneficial ribozymes followed\n36, 41\n. Therefore, based on the 226 \ncase shown in the de novo spread of GR (Fig. 2a), we investigate whether NR could follow. 227 \nAfter the spread of GR protocells, ten of them are selected, each inoculated with one NR 228 \n(another ten GR protocells are each inoculated with one control). Eventually, protocells 229 \ncontaining both NR and GR spread in the system (Fig. 2c). 230 \nIn the three cases mentioned above, to avoid the influence of random events such as 231 \nRNA degradation, we investigated the plausibility of the spread of GR or the co-spread of GR 232 \nand NR through selecting ten protocells and inoculating each with one molecule of relevant 233 \nRNA species. The observed spread or co-spread, in fact, already reflects a full sense of 234 \n“Darwinian evolutionary dynamics”, meaning that in reality, once the RNA species appeared, 235 \nthey may have become thriving among protocells. As an example, in Fig. 2d, we showed an 236 \ninstance of evolution without any inoculation of ribozyme. Firstly, NR emerges naturally in 237 \nempty protocells, and then GR emerges naturally in NR protocells (see Fig. 4 for snapshots 238 \non the spatial distribution during the evolution). In this case, to “facilitate” the natural 239 \nappearance of a ribozyme, the probability of random ligation of RNA (PRL) is augmented from 240 \nits default value 1×10\n-6\n to 5×10\n-6\n; and to “promote” the natural appearance of the other 241 \nribozyme in protocells contained the first ribozyme, their characteristic sequences are 242 \nassumed as different from each other with only two residues (see the figure’s legends for 243 \ndetails).   244 \nAbout the membrane takeover and the influence of decreased permeability 245 \n Then we were concerned about the change of membrane contents resulting from the 246 \nspread of the ribozyme favoring phospholipid-synthesis. Fig. 5a shows the membrane change 247 \ncoming with the spread of GR in empty protocells (the case is just the one shown in Fig. 2a; 248 \nbut here in order to demonstrate the transition clearly, the horizontal axis adopts a smaller 249 \nscale). Fig. 5b shows the membrane change coming with the spread of GR in NR protocells 250 \n(the case is just the one shown in Fig. 2b). In both cases, we can see a rising of the ratio of 251 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \nphospholipids in the membrane (RPM, the lower panel) for the protocells with GR (i.e., Cgr in 252 \nFig. 5a and Cnrgr in Fig. 5b). Note that the RPM for those protocells without GR (i.e., C in Fig. 253 \n5a and Cnr in Fig. 5b) also increases a bit, which may be attributed to phospholipids’ exchange 254 \nbetween protocells.  255 \nNo matter how, we can see that in both cases, RPM only rises to a limited level after the 256 \nemergence of GR. We reasoned that this should be on account of the relatively low efficient 257 \nnon-enzymatic reaction of glycerophosphates with fatty acids on the membrane. That is, 258 \nwhile glycerophosphates are plenty due to the function of GR, the subsequent reaction of 259 \nphospholipids’ formation becomes the bottle neck. Indeed, when we assume a high rate for 260 \nthe non-enzymatic formation of phospholipids (i.e. PPF) in the midway, the ratio of 261 \nphospholipids rises to a rather high level immediately (Fig. S2). This result implies that in reality, 262 \nit should be the later emergence of a ribozyme or enzyme favoring this bottle-neck reaction 263 \nthat may have ultimately taken the membrane-takeover towards a more thorough degree. 264 \nRemarkably, merely via inducing such a “limited membrane takeover” (i.e. with a low level of 265 \nphospholipid content in the membrane), GR is capable of thriving.  266 \nSince the phospholipid content in the membrane would reduce the membrane 267 \npermeability\n9\n and thus the availability of raw material for protocells, the GR’s advantage might 268 \nbe weakened. It was then attractive to see how the GR protocells’ spread would be affected. 269 \nSomewhat surprisingly, we found that when the factor regarding the influence of 270 \nphospholipid content on the membrane permeability for nucleotides and nucleotide 271 \nprecursors (FPP) is turned up – even in a dramatic way, i.e. from its default value of 20 to 200, 272 \n2000, and 2×10\n4\n, there is nearly no influence on the spread of GR (Fig. 3-FPP, orange symbols). 273 \nIn the model, according to the rule revealed in the original experimental work\n9\n, the membrane 274 \npermeability is assumed to be negatively related to phospholipid content in the membrane – 275 \nin proportion to 1/(1+FPP×RPM) (see Methods for details). Therefore, a possible cause for the 276 \nlittle influence of FPP on GR’s spread is concerning the “limited membrane-takeover” (i.e. with 277 \na low RPM). Indeed, if PPF is turned up to achieve a higher RPM (as mentioned above, refer to 278 \nFig. S2), we can see some effects (Fig. S3, the purple line) – but still rather limited. Finally, we 279 \nturned to the weak version of FPP, i.e. FPPW. This factor is regarding the influence of phospholipid 280 \ncontents on the membrane permeability for precursors of nucleotide precursors and 281 \nprecursors of glycerophosphates – we increased it from its default value of 3 to a value of 282 \n3000 (in reality, this factor could not be very large because for such precursors, which should 283 \nbe quite small in molecular size, the permeability difference between the fatty acid membrane 284 \nand phospholipid membrane could not be that large\n2, 42\n), and see a more obvious decline in 285 \nGR molecules (Fig. 3- FPP, the purple line). But the GR protocells still only decline marginally 286 \n(Fig. 3-FPP, purple circles), which means that there are fewer GR molecules in each GR protocell. 287 \nNotably, for this case, RPM also declines for GR protocells (Fig. S4), which should result from 288 \nthe decrease of GR, as well as the less availability of its substrates – precursors of 289 \nglycerophosphates. No matter how, the effect concerning FPPW means, an important reason 290 \nwhy a quite high value of FPP alone would not obviously inhibit the spread of GR may be 291 \nattributed to the remained availability of raw materials with a smaller size (thus with a greater 292 \npermeability), as alternative resources. 293 \nThe subsequent spread of the ribozyme using more fundamental materials and the RNA 294 \nspecies favoring the membrane transport 295 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \nIndeed, when original raw materials for chemical synthesis in protocells are blocked by 296 \nthe membrane, more fundamental and permeable raw materials might have acted as 297 \nalternative resources. However, as demonstrated above, the “initial membrane-takeover”, 298 \nwhich may have been caused by the emergence of one ribozyme (e.g. GR here) functioning 299 \nin the pathway of phospholipid synthesis, should have been at a “low level”. Then, the 300 \nquestion becomes attractive whether such a “low level membrane-takeover” (thus with a 301 \nrelatively small influence on the membrane permeability) at the early stage, could, as 302 \nsupposed in the original experimental work\n9\n, have driven the evolution concerning the arising 303 \nof function for exploiting the more fundamental and permeable raw materials.  304 \nThe answer is positive (see Fig. 6a). In the simulation, at step 1×10\n4\n, ten empty protocells 305 \nare selected, each of which is inoculated with one NR molecule, one GR molecule, and one 306 \ncontrol molecule. Then the NR-GR protocells spread (the control does not spread). The solid 307 \ncircles and solid lines represent the case in which no influence of phospholipid content on the 308 \nmembrane’s permeability is considered (i.e. FPP and FPPW are set to 0) throughout the whole 309 \nsimulation process, while the empty circles and dotted lines represent the case in which the 310 \n“negative” influence of phospholipid content is turned on at step 3×10\n5\n (thereafter we can 311 \nobserve a little decrease of the NR-GR protocells and that of NR and GR molecules). For both 312 \ncases, at step 6×10\n5\n, ten NR-GR protocells are selected, each of which is inoculated with a 313 \nmolecule of nucleotide-precursor-synthetase ribozyme (NPR). The ribozyme is assumed to 314 \nbe able to catalyze the formation of nucleotide precursors from precursors of nucleotide 315 \nprecursors, which is more permeable. In the first case (i.e., without the negative influence of 316 \nthe phospholipid content), NPR cannot spread, whereas in the second case (i.e., with that 317 \nnegative influence), the NPR spreads (the black dotted line) – or say, the NR-GR-NPR 318 \nprotocells spread (the black empty circles). For snapshots of spatial distribution, see Fig. S5a 319 \n(notably, after the spread of NPR, its substrates, i.e. precursors of nucleotide precursors, are 320 \nrepresented by the background yellow, are almost been exhausted – in the panel of step 321 \n2,000,000). In other words, the negative influence of phospholipid content on the membrane’s 322 \npermeability could indeed cause the thriving of the functional species exploiting more 323 \nfundamental (thus more permeable) raw materials. To confirm that the spread of NPR is 324 \nattributed to its function of exploiting precursors of nucleotide precursors, we turned off this 325 \nfunction at step 1.4×10\n6\n. As expected, we saw the vanishing of this species (Fig. S6a). 326 \nSimilar to the situation for exploring the spread of GR, to avoid the influence of 327 \nunexpected random events of RNA degradation, here we selected ten NR-GR protocells and 328 \ninoculated each with one molecule of NPR. The subsequent spread of NPR, in fact, already 329 \nmeans that this RNA species may have emerged and become thriving in protocells. In reality, 330 \nthough it is impossible for NPR to have appeared simultaneously in so many protocells, it may 331 \nhave had chances to appear in protocells repeatedly especially considering the long time 332 \nscale concerning the origin of life. For example, Fig. S7a shows a modeling case that one NPR 333 \nmolecule is inoculated into one NR-GR protocell every 1×10\n5\n step, and NPR eventually 334 \nspreads in the system. 335 \nNext, we turned to the plausibility of the emergence of a functional species that favors 336 \nthe membrane transport – as another strategy for “adapting to” the decreased membrane 337 \npermeability, which was also proposed in the original experimental study\n9\n. An RNA species, 338 \nnamed TR here, is assumed to be capable of favoring the membrane transport (see Discussion 339 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \nfor a comment on this RNA species in a chemical context). As mentioned above, the 340 \npermeable possibility of nucleotide precursors, i.e. the substrates of NR, has been assumed 341 \nto be in proportion to 1/(1+ FPP×RPM). Here, with the introduction of another factor, FTR, the 342 \nexpression is changed to 1/[1+ FPP×RPM/(1+t×FTR)], where t refers to the number of TR 343 \nmolecules in the protocell. That is, the more TR molecules there are in the protocell, the more 344 \npermeable the membrane is. Notably, the increased permeability is here assumed to be in 345 \nregard of both directions (inwards and outwards), in consideration that active transport 346 \nshould not yet have been achievable in such an early stage. The simulation showed that due 347 \nto the negative influence of phospholipid content on the membrane’s permeability, TR can 348 \nspread in protocells (Fig. 6b; for snapshots of spatial distribution, see Fig. S5b), and when its 349 \nfunction is turned off, it decreases and eventually vanishes (Fig. S6b). Fig. S7b shows a case in 350 \nwhich one TR molecule is inoculated into one NR-GR protocell intermittently (every 1×10\n4\n 351 \nstep) and TR eventually becomes thriving in protocells. 352 \nDiscussion 353 \nIn the present study, following the clues suggested by an experimental study from 354 \nSzostak and coworkers\n9\n, we examined, through computer modeling, an evolution of 355 \nprotocells’ membrane from the one composed of only single-chain amphiphiles like fatty 356 \nacids towards the one containing double-chain amphiphiles like phospholipids, induced by 357 \nsimple physical effects. The former has been deemed to be the membrane of earliest 358 \nprotocells\n1-3\n, whereas the latter is a membrane more approaching that of modern cells, which 359 \nis more stable but less permeable. The simulation showed that such a membrane-takeover, 360 \nthough limited initially, could indeed occur on account of “stabilizing effects” caused by the 361 \nincreasing phospholipid content in the membrane\n9\n, which is brought about by the emergence 362 \nof a functional species favoring phospholipid synthesis in protocells (Fig. 2). Subsequently, the 363 \nreduced membrane permeability could trigger the emergence of an additional functional 364 \nspecies which makes use of more fundamental (thus more permeable) raw materials, or a 365 \nspecies facilitating the membrane transport (Fig. 6) – both valid as supposed in the original 366 \nexperimental study\n9\n. 367 \nIn the modeling, as for the functional species favoring the synthesis of phospholipid, we 368 \nadopted a ribozyme catalyzing the formation of glycerophosphates (GR), which appears to 369 \nhave been the bottle-neck reaction, and the resulting glycerophosphates is assumed to be 370 \nable to reach the membrane and react with fatty acids there in situ, which seems to have been 371 \nefficient even in a non-enzymatic way\n4, 5, 25, 26\n. Another reason why we did not adopt a ribozyme 372 \ncatalyzing the latter reaction is that RNA is likely difficult to cope with reactions occurring on 373 \nthe membrane because of its polar skeleton – in reality, this function may have emerged after 374 \nthe advent of proteins. Similarly, functions favoring the membrane transport seems also to 375 \nhave been implemented by proteins coming later. But there is also some evidence supporting 376 \nRNA’s potential role on membrane transport, e.g. see refs\n 43, 44\n. No matter how, at least to 377 \navoid a more complicated modeling involving proteins and amino acids, here we assumed an 378 \nRNA species functioning this way (TR). 379 \n Our modeling study revealed some details regarding the membrane-takeover and 380 \nrelevant evolution. For instance, in the original experimental paper, as for the advantages of 381 \ncontaining phospholipids in the membrane, it was pointed out that apart from phospholipids’ 382 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \neffect of preventing the desorption of fatty acids, an additional mechanism is concerning “a 383 \ndecrease in the net efflux from the membrane due to the reduced fraction of the membrane 384 \nsurface area occupied by fatty acids”\n 9\n. In other words, the fatty acids that have reacted to 385 \nform phospholipids are “anchored” and would not participate in the desorption. Here we have 386 \nfigured out that this “fastening effect” is not absolute because phospholipids may also leave 387 \nthe membrane though much more difficult (PPLM<<PFLM). By parameter analysis (Fig. 3-FPL and 388 \n-PFLM; see also Fig. S1), we demonstrated how the two effects work together to support the 389 \nthriving of the ribozyme favoring phospholipid-synthesis (GR). 390 \nAs another detail, the initial membrane-takeover, most likely involving only one catalytic 391 \nfunction in the pathway of phospholipid synthesis (e.g., GR here), should have been quite 392 \nlimited – i.e. with merely a low level of phospholipid content (Fig. 5). A more thorough 393 \ntakeover is supposed to have occurred with the advent of other functions within the pathway 394 \n(Fig. S2). However, interestingly, the GR, only via inducing such a limited membrane-takeover, 395 \ncan enjoy the benefit of phospholipids (i.e., stabilizing the membrane) and thrive in the system. 396 \nSurprisingly as well, such a low level of phospholipid content, via its limited negative influence 397 \non the membrane permeability, is sufficient to trigger the emergence of the function for 398 \nexploiting more fundamental and permeable raw materials (NPR) and that of the function for 399 \nmembrane transport (TR). 400 \nRemarkably, the series of evolutionary events associated with the membrane-takeover 401 \nat an early stage of life, as demonstrated by the present modeling, exemplifies the scenario 402 \nconcerning the onset of Darwinian evolution, in which simple physical or chemical effects (e.g., 403 \nhere the decreasing efflux of fatty acids due to increasing phospholipid content in the 404 \nmembrane and the subsequent reduction of membrane permeability) may have driven the 405 \nemergence of relevant functions. Additionally, as we have seen, albeit the degree of the 406 \neffects might have been quite limited, new “inventions” could have still been induced – the 407 \npower of Darwinian evolution is here clearly “witnessed”.  408 \nIn fact, such early evolutionary events of life belong to the field of biogenesis. This field, 409 \nor named “the origin of life”, is to a degree a problem of chemistry, which mainly addresses 410 \nthe environments and chemical mechanisms involved in the process\n45-47\n (generally referred to 411 \nas prebiotic chemistry). On the other hand, however, it is undoubtedly also a problem of 412 \nevolution, which involves the rules of the so-called “chemical evolution” and the subsequent 413 \nearly Darwinian evolution\n48-50\n. While experimental exploration has covered nearly the entire 414 \naspect regarding chemistry, it seems to be seriously constrained in the aspect of evolution. 415 \nFor instance, here, the clues for an early membrane-takeover came from an elegant 416 \nexperimental work of Szostak and coworkers\n9\n, which detected relevant  simple physical 417 \nmechanisms which might have led to the corresponding evolutionary events. However, it is 418 \nat least up-to-now difficult for experimental researchers to follow up on those events (lab 419 \nwork’s limitation in this respect could usually be attributed to the potential long time scale 420 \nrequired in the evolution, as well as the complicated nature of these evolutionary events\n16\n). In 421 \ncontrast, theoretical modeling and associated computer simulation is apt at such exploration, 422 \ni.e. on the plausibility of the suggested evolution and those underlying mechanisms\n12-16, 51\n. It is 423 \nexpected that the combination of experimental and theoretical efforts like the one 424 \ndemonstrated in the present study would significantly enhance our understanding on those 425 \ncomplex processes involved in the origin of life.  426 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \nMethods 427 \nThe events occurring in the model system 428 \nIn each time step (i.e. Monte Carlo step), certain events may occur to molecules and 429 \nprotocells with defined probabilities (see Fig. 7 for a schematic; refer to Table 1 for 430 \ndescriptions of the probabilities and other parameters). Only molecules within the same grid 431 \nroom can interact with each other. A molecule may move to an adjacent room (the related 432 \nprobability: PMV) if there is no membrane in that direction (see below for the situation of 433 \nencountering a membrane). A protocell may also move to an adjacent room ( PMC) (while 434 \npushing away molecules in that room). 435 \n Nucleotide-precursor’s precursors may form nucleotide precursors in a non-enzymatic 436 \nway (PNPF) or catalyzed by NPR (PNPFR). Nucleotide precursors may form nucleotides (randomly 437 \nas A, G, C, or U) in a non-enzymatic way ( PNF) or catalyzed by NR ( PNFR), Glycerophosphate 438 \nprecursors may form glycerophosphates in a non-enzymatic way ( PGF) or catalyzed by GR 439 \n(PGFR). Nucleotide precursors, nucleotides, and glycerophosphates may also decay into their 440 \nprecursors (PNPD, PND, and PGD respectively). 441 \nNucleotides may join to form RNA via random ligation (PRL). An RNA molecule may attract 442 \nsubstrates (nucleotides or oligomers) ( PAT) via base-pairing with some error rate ( PFP), and 443 \nsubstrates aligned on the template may be ligated ( PTL) – that is, the template-directed 444 \nsynthesis. The substrates or the full complementary chain may separate from the template 445 \n(PSP). Phosphodiester bonds within an RNA chain may break (PBB) and thus the RNA molecule 446 \nturns into two fragments. A nucleotide residue at the end of an RNA chain may decay into a 447 \nnucleotide precursor (PNDE).  448 \nAmphiphiles with a sufficient number (LAM; in quotient of tails, i.e., a fatty acid counts one 449 \nwhereas a phospholipid counts two) may accumulate at the boundary of a grid room and 450 \nform a membrane ( PMF), thus “creating” a protocell. Fatty acids may join or leave the 451 \nmembrane ( PFJM and PFLM respectively), and phospholipids may also join or leave the 452 \nmembrane ( PPJM and PPLM respectively). Nucleotide-precursor’s precursors, nucleotide 453 \nprecursors, nucleotides and glycerophosphate precursors may permeate through the 454 \nmembrane (PNPPP, PNPP, PNP and PGPP respectively). Glycerophosphates may enter a membrane 455 \nand react with fatty acids thereon in situ to form phosphatidic acids, i.e., phospholipids (PPF). 456 \nPhospholipids may decay into fatty acids and glycerophosphates, either within the membrane 457 \nor out of the membrane ( PPDM and PPD respectively). A protocell may fuse with another 458 \nprotocell in an adjacent grid room ( PCF), divide (with an offspring protocell occupying an 459 \nadjacent grid room while pushing away molecules in that room) (PCD), or break (PCB) – resulting 460 \nin the disassembly of its membrane components. 461 \n Notably, similar to our previous modeling work concerning the evolution of the RNA 462 \nworld, the energy problem is here not considered explicitly. For example, nucleotides and 463 \noligonucleotides are implicitly assumed to be activated – in particular, when they form from 464 \nthe degradation of RNA, they are assumed to be activated again immediately to be able to 465 \nbe reused in the further synthesis of RNA. Interestingly, such in situ activation within protocells 466 \nhas recently been shown possible by lab work\n52, 53\n. In history, the energy source may have 467 \ninvolved chemical energy in the hatchery of the primordial life, such as hydrothermal vents at 468 \nthe sea bottom\n54-56\n or hydrothermal fields on land\n57, 58\n, as supposed. Since the substrates are 469 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \nhere assumed to be always “activated”, the protocells in the model system are competing for 470 \nmaterials but not energy – as mentioned already, the total materials in the system, including 471 \nthose related to RNA and the membrane of protocells are assumed to be limited (that is, TNPPB, 472 \nTFB, and TGPB, plus those material introduced by the rare events of inoculation). Certainly, in 473 \nreality, competitions for materials and energy are both possible in Darwinian evolution. 474 \nThe setting of parameters 475 \nThe parameters should be set according to some rules. For example, reactions catalyzed 476 \nby ribozymes should be much more efficient than corresponding non-enzymatic reactions, 477 \nso PNFR >> PNF, PGFR >> PGF, and PNPFR >> PNPF. Template-directed ligation should be much more 478 \nefficient than “random ligation”, so PTL >> PRL. The nucleotide residues within the chain are 479 \nassumed to be protected from decay, whereas those at the end of the chain are only partially 480 \nprotected – i.e. may decay but at a rate lower than that of free nucleotides, i.e., PNDE < PND. 481 \nConsidering experimental evidence on permeability, PNPPP > PNPP >> PNP \n2, 42\n. Because of the 482 \nself-assembly feature of the membrane, PMF >> PCB, PFJM >> PFLM, and PPJM >> PPLM. 483 \nPhospholipids should more difficult to leave the membrane than fatty acids, so PPLM < PFLM. 484 \nPhospholipids should be more difficult to decay within the membrane, so PPDM < PPD. The 485 \nmovement of molecules should be easier than protocells, so PMV > PMC. Nucleotides and RNA 486 \nshould be easier to degrade outside protocells (due to the higher water activity), so FDO > 1; 487 \nthe influence of phospholipid content on the permeability of smaller molecules should be 488 \nweaker than that of larger molecules, so Fppw < Fpp \n2, 42\n.  489 \nObviously, the rules mentioned above are far from justifying the setting of that many 490 \nparameters used here (Table 1). In fact, owing to our limited knowledge concerning prebiotic 491 \nenvironments and chemistry, it is usually difficult to justify the parameter setting in the 492 \nmodeling studies concerning the origin of life. However, the evolution during the origin of life 493 \nis remarkably characterized by the tendency from simplicity to complexity, which is a special, 494 \nrare phenomenon nature\n48-50, 59\n. Therefore, any relevant hypothetic scene in the area (e.g., here, 495 \nthe speculation concerning the evolution of the protocell membrane), if supported by 496 \nmodeling, merits our attention. In this consideration, exploring parameter-setting in favor of 497 \nthe scene is valuable, which we called “parameter-exploration” in a way of “reverse modeling” 498 \n(see ref \n15\n for a detailed discussion). In practice, here most parameters have been explored 499 \nand adopted based on our experience in previous modeling studies concerning RNA-based 500 \nprotocells\n22-24\n. When manual testing was difficult, a machine learning-like approach was used 501 \nto automatically explore the parameter space\n15\n.  502 \nThe default values listed in Table 1 were adopted to shape the cases for demonstrating 503 \nour results. Actually, though the outcomes of the simulations may be influenced by the 504 \nchange of those “key parameters” (e.g. for GR‘s spreading, see Fig. 3) and some of the other 505 \nparameters (see Figs. S8-1 and S8-2, as explained in Box S1), in general, they have turned out 506 \nto be fairly robust against “moderate adjustments” of most of the parameters. 507 \nTo avoid cumbersome computation, total materials ( TNPPB, TFB, and TGPB), “the lower limit 508 \nnumber of amphiphiles to form a membrane” ( LAM), and the length of the characteristic 509 \ndomain for a functional RNA species ( LCDR) are set obviously smaller in scale than the 510 \ncorresponding situations in reality. Such simplifications are believed to be not in conflict with 511 \nthe fundamental mechanisms reflected in the modeling. 512 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \nSome detailed mechanisms concerning the implementation of the model 513 \nWhen the breaking site of an RNA chain is at a single-chain region, the breaking 514 \nprobability is PBB. When the breaking site is within a double-chain region, the two parallel 515 \nbonds may break simultaneously – but with a smaller probability, i.e. PBB\n3/2 \n(note that a 516 \nprobability has a value between 0 and 1). However, for the case of outside protocells, a factor, 517 \nFDO, is involved to consider the corresponding higher water activity ( FDO > 1): the breaking 518 \nprobability for a single-chain is PBB ×FDO, while that for a double-chain is (PBB ×FDO)\n3/2\n. The factor 519 \nFDO also works in the situation of nucleotide decaying and nucleotide residue decaying at the 520 \nend of RNA, i.e., PND×FDO and PNDE ×FDO respectively for the case of outside protocells. 521 \nThe probability of the separation of the two strands of a duplex RNA is assumed to be 522 \nPSP\n r\n, where r = n\n1/2\n and n is the number of base pairs in the duplex. When n = 1, the probability 523 \nwould be PSP. When n increases, the separation of the two strands would be more difficult. 524 \nThe introduction of 1/2 corresponds to the consideration that the self-folding of single chains 525 \nmay aid the dissociation of the duplex. 526 \nThe probability of membrane formation is assumed to be 1-(1-PMF)\nx\n, where x= a-LAM + 1 527 \nand a is the number of amphiphiles (in quotient of tails, i.e., a fatty acid counts one whereas 528 \na phospholipid counts two, the same below) in the grid room. When a is equal to LAM (the 529 \nlower limit of the number of amphiphiles to form a protocell membrane), the probability of 530 \nmembrane formation is equal to PMF. This assumption concerns the consideration that the 531 \nmore amphiphiles in a grid room, the more probable they would assemble to form a vesicle. 532 \nThe probability of a fatty acid leaving the membrane is assumed to be PFLM / (y × z), where 533 \ny = 1 + i /(b/2)\n3/2\n and z = 1 + FPL×RPM. The item y represents the consideration for the 534 \n“osmotic pressure effect”: a higher concentration of the inner impermeable ions would cause 535 \nthe protocell to be more swollen, and thus amphiphiles on the membrane are less likely to 536 \nleave, as suggested by experimental work\n60\n. Wherein, i is the quantity of inner impermeable 537 \nions, i.e. RNAs (measured by the number of nucleotide residues, the same below), and b is 538 \nthe quantity of amphiphiles within the membrane. Then, b/2 (there are two layers in the 539 \nmembrane) is a “scale” representation of the surface area of the membrane and ( b/2)\n3/2\n is a 540 \nscale representation of the cellular space. Thus, i/(b/2)\n3/2\n is a representation of the 541 \nconcentration of the ions. The item z represents the consideration for the phospholipid 542 \ncontent’s effect on preventing fatty acids from desorbing the membrane\n9\n, wherein RPM refers 543 \nto the ratio of phospholipids in the membrane (see the legend of Fig. 5 for an explanation), 544 \nand FPL is the factor representing the strength of this effect. Similarly, the probability of a 545 \nphospholipid leaving the membrane is assumed to be PPLM / ( y ×z), in which y and z are 546 \nexplained the same way. In other words, with the increase of phospholipid content, the 547 \nmembrane would be more stable, and any membrane components (including phospholipids 548 \nthemselves) would be less likely to leave the membrane\n9, 61\n. 549 \nThe probability of a nucleotide permeating into a protocell is assumed to be PNP × s / 550 \n(u×v), where s = b /LAM, u = 1 + FDE × i / (b/2)\n3/2\n, and v = 1 + FPP × RPM (wherein, i, b and RPM 551 \nare explained in the same way as above). The item s represents the consideration of the 552 \nconstraining effect of the cellular space on the influx of nucleotides. That is, when b increases, 553 \nmeaning that the cellular space increases correspondingly, the probability of a nucleotide 554 \npermeating into the protocell would become greater. The introduction of the item u 555 \nrepresents the consideration of the effect of Donnan’s equilibrium\n62\n, wherein FDE means the 556 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \ndegree of this effect; simply put, RNAs, which are charged and impermeable, may suppress 557 \nthe incoming of permeable materials with the same charge, i.e., nucleotides here (see ref \n22\n 558 \nfor a detailed explanation). The introduction of the item v represents the consideration of 559 \nsuppressing effect of phospholipid content on the permeability of the membrane, wherein FPP 560 \nmeans the degree of this effect; that is, the permeation of nucleotides would decrease with 561 \nthe increase of phospholipid content\n9\n. Likewise, the probability of a nucleotide precursor 562 \npermeating into a protocell is assumed to be PNPP × s / ( u×v). With a little difference, the 563 \nprobability of a nucleotide-precursor’s precursor permeating into a protocell is assumed to 564 \nbe PNPPP × s / ( u×v’), where v’ = 1 + FPPW × RPM and Fppw is a weak version of FPP  – in 565 \nconsideration that the permeation of such small molecules should be suppressed with a less 566 \nextent\n2, 42\n. The glycerophosphate precursor, i.e., glycerol here, is uncharged (thus no Donnan’s 567 \nequilibrium effect is considered) and small in molecular size (thus Fppw is adopted), so the 568 \ncorresponding permeating probability is PGPP × s /v’. Additionally, for the version of model 569 \ninvolving the function of TR, the probability of a nucleotide precursor permeating into a 570 \nprotocell is assumed to be PNPP × s / (u×v’’), where v’’ = 1 + FPP × RPM / (1+t×FTR) and t is the 571 \nnumber of TR molecules in the protocell. That is, the increase of TR molecules would enhance 572 \nthe membrane transportation of nucleotide precursors. Note that for the situations of 573 \npermeating out from a protocell, the item of s (concerning the cellular space) and u 574 \n(concerning Donnan’s equilibrium) is not considered, e.g., for a nucleotide in a protocell, the 575 \nprobability of permeating outwards is simply PNP / v.  576 \nThe probability of protocell division is assumed to be PCD × (1 – 2 × LAM/b), where b is the 577 \nquantity of amphiphiles within the membrane. When b is no more than twice that of LAM, the 578 \nprobability is no larger than 0, i.e., the protocell cannot divide. This assumption considers the 579 \nfact that the larger the protocell, the more probable it would divide, on account of the physical 580 \ninstability. 581 \nThe probability of the movement of an RNA molecule is assumed to be PMV/m\n1/2\n, where 582 \nm is the mass of the RNA, relative to a nucleotide. This assumption represents the 583 \nconsideration of the effect of the molecular size on the molecular movement. The square root 584 \nwas adopted here according to the Zimm model, concerning the diffusion coefficient of the 585 \npolymer molecules in the solution\n63\n. 586 \n(Note: Source codes of the simulation program can be obtained from GitHub—see Code 587 \navailability statement. Besides the role of evidencing the reproducibility of the present study, 588 \nthe source codes present more details about the implementation of the model and may help 589 \nreaders to understand the simulation better). 590 \n 591 \nCode availability. The C source codes implementing the models are available from: 592 \nhttps://github.com/mwt2001gh/membrane-takeover/blob/main/Fig-gr-final-1.cpp 593 \n(corresponding to the case shown in Fig. 2a) and 594 \nhttps://github.com/mwt2001gh/membrane-takeover/blob/main/Fig-npr-final-1.cpp 595 \n(corresponding to the case shown in Fig. 6a). 596 \nData availability. The authors declare that the data supporting the findings of this 597 \nstudy are available within the paper and its Supplementary Information files. 598 \nAcknowledgements 599 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \nW.T.M. is supported by the National Natural Science Foundation of China (No. 31571367) 600 \n(http://www.nsfc.gov.cn) and Natural Science Foundation of Hubei Province (CN) (No. 601 \n2019CFB685) (http://kjt.hubei.gov.cn). 602 \nAuthor contributions. W.T.M.. conceived the study, designed, implemented and analyzed 603 \nthe model, and wrote the paper. C.W.Y. participated in the design and implementation of the 604 \nmodel. 605 \nCompeting interests. 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Dynamics of polymer molecules in dilute solution: viscoelasticity, flow birefringence 725 \nand dielectric loss. J. Chem. Phys. 24, 269-278 (2012). 726 \n64. Hanczyc, M. M., Fujikawa, S. M. & Szostak, J. W. Experimental models of primitive cellular 727 \ncompartments: Encapsulation, growth, and division. Science 302, 618-622 (2003) 728 \n  729 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \nTable 1. Parameters used in the computer simulation 730 \nProbabilities Descriptions Default Values \nPAT An RNA template attracting a substrate (by base-pairing) 0.9 \nPBB A phosphodiester bond breaking within an RNA chain 1×10\n-5\n \nPCB A protocell breaking 1×10\n-4\n \nPCD A protocell dividing 0.1 \nPCF Two adjacent protocells fusing with each other 0.001 \nPFJM A fatty acid joining the membrane 0.9 \nPFLM A fatty acid leaving the membrane 0.002 \nPFP The false base-pairing when a template attracts a substrate 0.001 \nPGD A glycerophosphate decaying into its precursor 0.1 \nPGF A glycerophosphate forming from its precursor (non-enzymatic) 0.002 \nPGFR A glycerophosphate forming from its precursor catalyzed by GR 0.9 \nPGPP A glycerophosphate precursor permeating through the membrane 0.9 \nPMC A protocell moving 0.1 \nPMF A membrane forming 0.1 \nPMV A nucleotide/fatty acid/phospholipid (or relevant precursors) moving 0.9 \nPND A nucleotide decaying into its precursor 0.02 \nPNDE A nucleotide residue decaying at RNA’s chain end 0.001 \nPNF A nucleotide forming from its precursor (non-enzymatic) 0.005 \nPNFR A nucleotide forming from its precursor catalyzed by NR 0.2 \nPNP A nucleotide permeating through the membrane 5×10\n-5\n \nPNPD A nucleotide precursor decaying into its precursor 0.005 \nPNPF A nucleotide precursor forming from its precursor (non-enzymatic) 0.002 \nPNPFR A nucleotide precursor forming from its precursor catalyzed by NPR 0.3 \nPNPP A nucleotide precursor permeating through the membrane 0.05 \nPNPPP A nucleotide-precursor’s precursor permeating through the membrane 0.5 \nPPD A phospholipid decaying (into fatty acid and glycerophosphate) 0.1 \nPPDM A phospholipid decaying within the membrane 0.01 \nPPF A phospholipid forming (on the membrane) 0.02 \nPPJM A phospholipid joining the membrane 0.9 \nPPLM A phospholipid leaving the membrane 1×10\n-4\n \nPRL The random ligation of nucleotides and RNA 1×10\n-6\n \nPSP The separation of a base pair 0.5 \nPTL The template-directed ligation of RNA 0..02 \nOthers Descriptions Default Values \nN The system is defined as an N × N grid 30 \nTNPPB Total nucleotide-precursor’s precursors introduced in the beginning 80000 \nTFB Total fatty acids introduced in the beginning 50000 \nTGPB Total glycerophosphate precursors introduced in the beginning 50000 \nFDE Factor of the Donnan’s equilibrium effect 1 \nFDO Factor of molecular degradation outside protocells 10 \nFPL Factor of phospholipids' influence on amphiphiles leaving the membrane 5 \nFPP Factor of phospholipids on permeability (for nucleotides or their precursors) 20 \nFPPW F PP for nucleotide-precursor’s precursors or glycerophosphate precursors 3 \nFTR Factor for the RNA species functioning in membrane transport (TR) 100 \nLAM The lower limit number of amphiphiles to form a membrane 200 \nLCDR The length of the characteristic domain of a functional RNA species 7 \nNote: The probabilities are listed with names in alphabetical order. The simulation cases shown in this 731 \npaper adopt the default values, unless being stated explicitly to be different. The default characteristic 732 \nsequence for GR is “UUGAGCG”, for NR is “GCACGUA”, for NPR is “UCACGAG”, for TR is “CUGCUAG”, and 733 \nfor the control is “GGCUACU”. See Methods for details on the principle of setting parameter values. 734 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \n 735 \n 736 \nFig. 1 Protocells would benefit from a ribozyme favoring the synthesis of phospholipids in the 737 \ncompetition. Legends: FA—fatty acid; PL—phospholipid, i.e. phosphatidic acid here; G—738 \nglycerophosphate; Gp—glycerophosphate precursor (e.g., glycerol); GR—glycerophosphate-739 \nsynthetase ribozyme (here representing the ribozyme favoring the synthesis of phospholipids). 740 \nThe glycerophosphates produced through the catalysis of GR may reach the membrane and 741 \nnon-enzymatically react with fatty acids therein to form phosphatidic acids (the phospholipid 742 \nmolecules synthesized on the inner layer of the membrane may flip to the outer layer). The 743 \nformation of phospholipids on the membrane would prevent fatty acids from leaving the 744 \nmembrane to a certain extent, which results in a net inflow of fatty acids in the lipid 745 \ncompetition. With the growth of the membrane, the number of GR within the protocell may 746 \nincrease as a result of RNA replication. 747 \n 748 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \n 749 \nFig. 2 The spread of the glycerophosphate-synthetase ribozyme (GR) and its co-spread with 750 \nthe nucleotide-synthetase ribozyme (NR) in RNA-based protocells. Legends: Cgr—protocells 751 \ncontaining GR; Cnr—protocells containing NR; Cnrgr—protocells containing NR and GR; 752 \nCctl—protocells containing the control RNA species; gr—GR; nr—NR; ctl—the control RNA 753 \nspecies (the legends apply to all the subfigures). Note that the lower panel of a subfigure 754 \ndemonstrates the trend of the total molecule number of relevant RNA species in the system. 755 \nFor all the cases, an “empty” fatty-acid protocell is inoculated at step 1×10\n3\n. (a) The de novo 756 \nspread of GR among protocells. Wherein, at step 1×10\n4\n, ten empty protocells are selected 757 \n(arbitrarily, the same below), each inoculated with one GR molecule, and another ten empty 758 \nprotocells are selected, each inoculated with one control molecule. ( b) The spread of GR in 759 \nprotocells containing NR. Wherein, at step 1×10\n4\n, ten empty protocells are selected, each 760 \ninoculated with one NR, and another ten empty protocells are selected, each inoculated with 761 \none control; at step 3×10\n5\n, ten NR protocells are selected, each inoculated with one GR, and 762 \nanother ten NR protocells are selected, each inoculated with one control. ( c) The spread of 763 \nNR in protocells containing GR, Wherein, at step 1×10\n4\n, ten empty protocells are selected, 764 \neach inoculated with one GR, and another ten empty protocells are selected, each inoculated 765 \nwith one control; at step 3×10\n5\n, ten GR protocells are selected, each inoculated with one NR, 766 \nand another ten GR protocells are selected, each inoculated with one control. ( d) An 767 \nevolutionary case without inoculation of the RNA species – first, NR occurs naturally in empty 768 \nprotocells, and then GR occurs naturally in NR protocells. PRL = 5×10\n-6\n. The characteristic 769 \nsequence of GR is “CCAUGUA” – only two nucleotides different from that of NR (default 770 \nsequence: “GCACGUA”, see the footnotes of Table 1); the control species adopts a 771 \ncharacteristic sequence of “UCAGGUA”, two nucleotides different from either of the two 772 \nribozymes. 773 \n   774 \n 775 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \n776 \nFig. 3 The influence of several key parameters on the spread of the protocells containing GR. 777 \nLegends: Cgr—GR protocells, with default parameter values; Cgr-para-up—GR protocells, for 778 \nincreasing the parameter; Cgr-para-down—GR protocells, for decreasing the parameter; gr—779 \nGR, with default parameter values; gr-para-up—GR, for increasing the parameter; gr-para-780 \ndown—GR, for decreasing the parameter (the legends apply to all the subfigures). The red 781 \narrows indicate the steps where the parameter adjustments are conducted. For ( PGFR), the 782 \ndefault value 0.9 is turned up to 0.95, 0.98 and 0.99 at these points of change, respectively, 783 \nor turned down to 0.1, 0.05 and 0.02 at these points. For (FPL), the default value 5 is turned up 784 \nto 10, 20 and 50 at the first three points of change, respectively, or turned down to 2, 1 and 785 \n0 at these points; additionally, at the fourth change point of the turning-down case, PFLM is 786 \nchanged from its default value 0.002 to 1×10\n-4\n (the legends Cgr* and gr* refer to this change). 787 \nFor (PFLM), the default value 0.002 is turned up to 0.005, 0.01 and 0.02 at the first three points 788 \nof change, respectively, or turned down to 5×10\n-4\n, 2×10\n-4\n and 1×10\n-4\n at these points; 789 \nadditionally, at the fourth change point of the turning-down case, FPL is changed from its 790 \ndefault value 5 to 0 (the legends Cgr* and gr* refer to this change). For (FPP), the default value 791 \n20 is turned down to 10, 5 and 2 at the first three change points, respectively, or turned up 792 \nto 200, 2000 and 2×10\n4\n at these points; additionally, at the fourth change point of the turning-793 \nup case, FPPW is changed from its default value 3 to 3000 (the legends Cgr* and gr* refer to 794 \nthis change). 795 \n 796 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \n 797 \nFig. 4 The snapshots on spatial distribution of a case exemplifying the natural spread of NR 798 \nand GR among protocells. The evolutionary dynamics of the case is shown in Fig. 2d. The 799 \ncolor-depth of yellow in the background represents the concentration of the raw materials 800 \nfor forming nucleotides in the system (i.e. precursors of nucleotide precursors). The grey 801 \nsquares denote the membranes of protocells, and the corresponding color-depth is in 802 \nproportion to the phospholipid content in the membrane. The red dots denote NR, and the 803 \nblue dots denote GR. An empty protocell is inoculated at step 1000 (the grey arrow), and then 804 \nempty protocells spread in the system (in reality, the first empty protocell might have formed 805 \ndue to the inducing of mineral particles\n64\n or the concentration effect during dry-wet circles\n57, \n806 \n58\n). The red arrow indicates the first NR emerging naturally in an empty protocell. The blue 807 \narrow indicates the first GR emerging naturally in an NR protocell.   808 \n 809 \n 810 \n 811 \n 812 \n 813 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \n 814 \nFig. 5 The alteration of membrane contents with the rising of a ribozyme favoring 815 \nphospholipid-synthesis (i.e. GR). Legends: C—empty protocells; Cgr—protocells containing 816 \nGR; Cnr—protocells containing NR; Cnrgr—protocells containing NR and GR. For a certain 817 \nkind of protocells (C, Cgr, Cnr, or Cnrgr), The ratio of phospholipids in the membrane (RPM) 818 \nof a protocell is calculated as 2* pnum/(2*pnum+fnum), where pnum and fnum denote the number of 819 \nphospholipids and that of fatty acids respectively (note that a phospholipid molecule has two 820 \nnon-polar tails whereas a fatty acid has one). Here the vertical axis represents the average 821 \nRPM of the corresponding protocells, and it is set to 0 ad hoc at the points where that kind 822 \nof protocells does not exist. (a) The change of membrane contents during the spread of GR 823 \nin empty protocells (the case is the same as the one shown in Fig. 2a, but the horizontal axis 824 \nadopts a smaller scale). (b) The change of membrane contents during the spread of GR in NR 825 \nprotocells (the case is the same as the one shown in Fig. 2b). 826 \n 827 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \n 828 \nFig. 6 The decreased permeability caused by phospholipid content in the membrane could 829 \ndrive the emergence of other functions in the protocells. The legends identical to those 830 \nincluded in Fig. 2 have the same meaning; additional ones: Cnrgrnpr – protocells containing 831 \nNR, GR and NPR, Cnrgrtr – protocells containing NR, GR and TR, npr – NPR, and tr – TR. At 832 \nstep 1×10\n3\n, an empty fatty-acid protocell is inoculated. At step 1×10\n4\n, ten empty protocells 833 \nare selected (arbitrarily, the same below), each of which is inoculated with one NR molecule, 834 \none GR molecule, and one control molecule. (a) NPR, i.e. a ribozyme using more fundamental 835 \nraw materials, would not spread if the influence of phospholipid content on membrane 836 \npermeability is not assumed (solid circles and solid lines; FPP and FPPW are set to 0 throughout 837 \nthe simulation), but would spread when this influence is considered (empty circles and dotted 838 \nlines; at step 3×10\n5\n, FPP and FPPW are turned up to 30 and 3 respectively). In both cases, at step 839 \n6×10\n5\n, ten NR-GR protocells are selected, each of which is inoculated with one NPR molecule. 840 \n(b) TR, an RNA species favoring the membrane transport, would not spread if the influence 841 \nof phospholipid content on membrane permeability is not assumed (solid circles and solid 842 \nlines; FPP and FPPW are set to 0 throughout the simulation), but would spread when this influence 843 \nis considered (empty circles and dotted lines; at step 3×10\n5\n, FPP and FPPW are turned up to 30 844 \nand 3 respectively). In both cases, at step 6×10\n5\n, ten NR-GR protocells are selected, each of 845 \nwhich is inoculated with one TR molecule. PNP=5×10\n-6\n. 846 \n 847 \n 848 \n 849 \n 850 \n 851 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \n 852 \n 853 \nFig. 7 Events occurring in the model system and associated parameters. Solid arrows denote 854 \nchemical reactions and dashed arrows represent other events. Legends: Npp—nucleotide-855 \nprecursor’s precursor; Np—nucleotide precursor; Nt—nucleotide; FA—fatty acid; Gp—856 \nglycerophosphate precursor; G—glycerophosphate; PL—phospholipid, i.e. phosphatidic acid 857 \nhere; NPR—nucleotide-precursor-synthetase ribozyme; NR—nucleotide-synthetase 858 \nribozyme; GR—glycerophosphate-synthetase ribozyme. The events occurring within a 859 \nprotocell are shown in ( a), and the events concerning the behaviors of the protocells are 860 \ndepicted in (b), which adopts a smaller scale. For a naked room, there would be no membrane 861 \nand associated events. Note that TR, i.e., the functional RNA species involved in the 862 \nmembrane transport, which functions in an abstract way in the model, is not depicted here; 863 \nand there are a few parameters unsuitable or difficult to represent here (see text for detailed 864 \nexplanations). 865 \n 866 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \nSupplementary Information 867 \n 868 \n 869 \nFig. S1 The influence of FPL and PPLM on the spread of the protocells containing GR. The 870 \nsituation is the same as that shown in Fig. 3-FPL, except that at the fourth change point of the 871 \nturning-down case (cyan symbols, where FPL equals to 0), instead of changing PFLM, PPLM is 872 \nchanged from its default value 1×10\n-4\n to 0.002 (the legends Cgr* and gr* refer to this change). 873 \n 874 \n 875 \n 876 \nFig. S2 The influence of PPF on the content of membrane components. The legends are the 877 \nsame as those in Fig. 5. (a) Based on the case of Fig. 5a, at step 7×10\n5\n, PPF is changed from its 878 \ndefault value 0.02 to a value of 0.2. ( b) Based on the case of Fig. 5b, at step 7×10\n6\n, PPF is 879 \nchanged from its default value 0.02 to a value of 0.2. With the increase of RPM for those 880 \nprotocells with GR (i.e., Cgr in a and Cnrgr in b), the RPM for the protocells without GR (i.e., C 881 \nin a and Cnr in b) also increases, which should be attributed to phospholipids’ exchange 882 \nbetween protocells. 883 \n 884 \n 885 \n 886 \n 887 \n 888 \n 889 \n 890 \n 891 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \n 892 \n 893 \nFig. S3 The influence of FPP and PPF on the spread of the protocells containing GR. The situation 894 \nis the same as that shown in Fig. 3-FPP, except that at the fourth change point of the turning-895 \ndown case (orange symbols, where FPP=2×10\n4\n), it is PPF (instead of FPPW) that is changed – from 896 \nits default value 0.02 to 0.2 (the legends Cgr* and gr* refer to this change). 897 \n 898 \n 899 \n 900 \nFig. S4 The corresponding decline of GR protocells’ phospholipid content in the membrane 901 \n(RPM) with the turning up of FPPW. The cases are the same as those shown in Fig. 3- FPP 902 \n(concerning orange and purple symbols). Legends: “default” represents the case without the 903 \nchange of FPPW (i.e. with a default value of 3), while “ FPPW-up” represents the case that FPPW is 904 \nchanged from its default value to 3000 at step 3.5×10\n6\n. 905 \n 906 \n 907 \n 908 \n 909 \n 910 \n 911 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \n 912 \n 913 \nFig. S5 The snapshots on spatial distribution of the cases showing the spread of new 914 \nfunctional RNA species in NR-GR protocells due to the decreased membrane permeability. 915 \nThe evolutionary dynamics of the two cases are shown in Fig. 6. In addition to the symbols 916 \nthat are explained the same way as those included in Fig. 4, here black dots are introduced 917 \nto denote new functional RNA species. ( a) The black dots denote NPR molecules. The left 918 \nsubfigure (step 500,000) represents the stage before the spread of NPR (that is, only NR and 919 \nGR exist), whereas the right subfigure (step 2,000,000) represents the stage after the spread 920 \nof NPR. Notably, after the spread of NPR, its substrates, i.e. precursors of nucleotide 921 \nprecursors, which are represented by color-depth of the background yellow, are almost 922 \nexhausted. ( b) The black dots denote TR molecules. The left subfigure (step 500,000) 923 \nrepresents the stage before the spread of TR, whereas the right subfigure (step 2,000,000) 924 \nrepresents the stage after the spread of TR. The phenomenon of the precursors of nucleotide 925 \nprecursors’ exhaustion is not observed – because the function of TR is to facilitate the across-926 \nmembrane transport of nucleotide precursors rather than to exploit precursors of nucleotide 927 \nprecursors. 928 \n 929 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \n 930 \n 931 \nFig. S6 The spread of the ribozyme exploiting more fundamental raw materials (NPR) and 932 \nthat of the RNA species favoring membrane transport (TR) are attributed to their function. 933 \nThe figure is explained the same way as Fig. 6, except that the cases denoted by solid circles 934 \nand solid lines in Fig. 6, which represent the situation without consideration of negative 935 \ninfluence of phospholipid content on the membrane’s permeability, are not shown – here, 936 \ninstead, solid circles and solid lines denote the cases in which the relevant function is turned 937 \noff after 1.4×10\n6\n. (a) The function of NPR is turned off by setting PNPFR to 0.  ( b) The function 938 \nof TR is turned off by setting FTR to 0. 939 \n 940 \n 941 \n 942 \n 943 \n 944 \n 945 \n 946 \n 947 \n 948 \n 949 \n 950 \n 951 \n 952 \n 953 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \n 954 \n 955 \nFig. S7 The simulation cases modeling the emergence of NPR and TR in reality. The legends 956 \nare the same as those in Fig. 6. The modeling situations are the same as those in the cases of 957 \nFig. 6, except the details explained in the following. At step 1×10\n4\n, only one empty protocell 958 \nis selected and inoculated with one molecule of NR, GR and the control species – note that 959 \nsince the raw materials in the system are initially abundant, such an inoculation (to achieve 960 \nthe spread of NR-GR protocells) need not be conducted repeatedly (that is, unlike the ones 961 \nmentioned below). (a) After step 6×10\n5\n, one molecule of NPR is inoculated into one NR-GR 962 \nprotocell every 1×10\n5 \nsteps. PBB=5×10\n-5\n, PNFR=0.9 and PNPFR=0.5. (b) For the case in which the 963 \ninfluence of phospholipid content on membrane permeability is considered (empty circles 964 \nand dotted lines), FPP and FPPW are turned up (to 30 and 3 respectively) at step 2×10\n5\n. After 965 \nstep 2.5×10\n5\n, one molecule of TR is inoculated into one NR-GR protocell every 1×10\n4\n steps. 966 \nPBB=5×10\n-5\n and PNFR=0.9. 967 \n 968 \n 969 \n 970 \n 971 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \n 972 \nFig. S8-1. The influence of other parameters (in addition to those shown in Fig. 3) on the 973 \nspread of GR protocells (part 1). The representations are the same as those in Fig. 3. The 974 \nvalues adopted at the three critical change points (red arrowheads) are listed in Table S1. See 975 \nBox S1 for a comment on the influence. 976 \n 977 \nFig. S8-2. The influence of other parameters (in addition to those shown in Fig. 3) on the 978 \nspread of GR protocells (part 2). The representations are the same as those in Fig. 3. The 979 \nvalues adopted at the three critical change points (red arrowheads) are listed in Table S1. See 980 \nBox S1 for a comment on the influence. 981 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \nTable S1. The values adopted in the parameter analysis (Figs. S8-1 and S8-2) 982 \nNote: The upper portion of the parameters (above the dashed line) is for Fig. S8-1 and the 983 \nlower portion is for Fig. S8-2. “v0” means the default value; “Up-v1”, “Up-v2” and “Up-v3” 984 \nmeans the values adopted at the three change points (one after another; see red arrowheads 985 \nin the figures) for the case of parameter-turning-up; “Down-v1”, “Down-v2” and “Down-v3” 986 \nmeans the values adopted at the three change points for the case of parameter-turning-987 \ndown. 988 \nUp-v3 Up-v2 Up-v1 v0 Down-v1  Down-v2 Down-v3 \n0.2 0.05 0.01 PGF=0.002 0.001 5×10\n-4\n 2×10\n-4\n \n0.05 0.02 0.01 PNF=0.005 0.002 0.001 5×10\n-4\n \n0.02 0.01 0.005 PNPF=0.002 0.001 5×10\n-4\n 2×10\n-4\n \n0.2 0.1 0.05 PPF=0.02 0.01 0.005 0.002 \n0.2 0.1 0.05 PND=0.02 0.01 0.005 0.002 \n0.01 0.005 0.002 PNDE=0.001 5×10\n-4\n 2×10\n-4\n 1×10\n-4\n \n0.05 0.02 0.01 PNPD=0.005 0.002 0.001 5×10\n-4\n \n0.9 0.5 0.2 PGD=0.1 0.05 0.02 0.01 \n0.9 0.5 0.2 PPD=0.1 0.05 0.02 0.01 \n0.1 0.05 0.02 PPDM=0.01 0.005 0.002 0.001 \n1×10\n-5\n 5×10\n-6\n 2×10\n-6\n PRL=1×10\n-6\n 5×10\n-7\n 2×10\n-7\n 1×10\n-7\n \n1×10\n-4\n 5×10\n-5\n 2×10\n-5\n PBB=1×10\n-5\n 5×10\n-6\n 2×10\n-6\n 1×10\n-6\n \n100 50 20 FDO=10 5 2 1 \n0.99 0.98 0.95 PAT=0.9 0.5 0.2 0.1 \n0.01 0.005 0.002 PFP=0.001 5×10\n-4\n 2×10\n-4\n 1×10\n-4\n \n0.9 0.5 0.2 PMF=0.1 0.05 0.02 0.01 \n0.001 5×10\n-4\n 2×10\n-4\n PPLM=1×10\n-4\n 5×10\n-5\n 2×10\n-5\n 1×10\n-5\n \n0.2 0.1 0.05 PTL=0.02 0.01 0.005 0.002 \n0.95 0.9 0.8 PSP=0.5 0.2 0.1 0.05 \n0.99 0.98 0.95 PMV=0.9 0.5 0.2 0.1 \n0.99 0.98 0.95 PFJM=0.9 0.5 0.2 0.1 \n0.99 0.98 0.95 PPJM=0.9 0.5 0.2 0.1 \n20 10 5 FPPW=3 1 0.5 0.2 \n10 5 2 FDE=1 0.5 0.2 0.1 \n5×10\n-4\n 2×10\n-4\n 1×10\n-4\n PNP=5×10\n-5\n 2×10\n-5\n 1×10\n-5\n 5×10\n-6\n \n0.5 0.2 0.1 PNPP=0.05 0.02 0.01 0.005 \n0.95 0.9 0.8 PNPPP=0.5 0.2 0.1 0.05 \n0.99 0.98 0.95 PGPP=0.9 0.5 0.2 0.1 \n0.001 5×10\n-4\n 2×10\n-4\n PCB=1×10\n-4\n 5×10\n-5\n 2×10\n-5\n 1×10\n-5\n \n0.01 0.005 0.002 PCF=0.001 5×10\n-4\n 2×10\n-4\n 1×10\n-4\n \n0.9 0.5 0.2 PCD=0.1 0.05 0.02 0.01 \n0.9 0.5 0.2 PMC=0.1 0.05 0.02 0.01 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint \n\n \n 989 \nBox S1. On the influence of parameters (for Figs. S8-1 and S8-2) 990 \nFirstly, we note that the default values of the parameters we adopted are almost \nthe best for the spread of protocells containing GR (blue solid circles) – that is, the \nchange of parameter values, either upwards or downwards, could barely improve the \nlevel of GR protocells (orange empty circles for “upwards” and cyan empty circles for \n“downwards”) and seldom improve the level of GR molecules (orange dotted lines for \n“upwards” and cyan dotted lines for “downwards”). This means our initial parameter-\nexploration is quite successful (see text for the meaning of “parameter-exploration”). \nSecondly, we see that the spread of GR protocells is robust to the “moderate” change \nof most parameter values. In the analysis, when turning up or down a parameter, \ntypically a scale of 2 or 2.5 times was adopted, unless the probability might be larger \nthan 1 (see Table S1 for details). In most cases, the apparent influence on the spread \nof GR protocells comes only at the third change point, or even never occurs within the \nchanging scope. Thirdly, we comment briefly below on the cases in which the \nparameter change brings about obvious effects.  \n(1) For the cases shown in Fig. S8-1.  \nA high probability of non-enzymatic production of glycerophosphates ( PGF) is \nunfavorable because GR’s advantage would be weakened. A low probability of \nnucleotide formation (PNF), which brings about the shortage of the building blocks of \nRNA, is disadvantageous; likewise, a low probability of nucleotide precursor formation \n(PNPF) is disadvantageous. On the other side of the coin, a higher probability concerning \ndecay of nucleotides (PND) and that of nucleotide precursors (PNPD) would also result in \nthe scarceness of RNA’s building blocks. A too high probability of RNA’s end-decaying \n(PNDE) may shorten the life span of GR to an extent that the ribozyme cannot sustain in \nthe system through replication. A small factor of degradation outsides protocells (FDO) \nmeans the synthesis of RNA within protocells would be short of raw materials. A low \nprobability for an RNA template to attract substrates (PAT) means the template-directed \nreplication of GR would become difficult. A high error rate in the replication of RNA \n(PFP) is disadvantageous because the heredity of GR is weakened.  \n(2) For the cases shown in Fig. S8-2.  \nA low probability for substrates aligned on an RNA template to ligate ( PTL) is \nunfavorable because it would also slow down the template-directed replication. A low \nprobability for the separation of a base pair (PSP) is unfavorable because of the difficulty \nof strand separation in the RNA replication (note that the spread of GR is depressed at \nthe first down-turning point, which means it is quite sensitive to the decline of this \nparameter). A high probability of protocell-breaking ( PCB) is unfavorable because the \nexistence of protocells becomes problematic. A high probability of protocell-fusing \n(PCF) is disadvantageous because the protocells without GR tend to fuse with those \ncontaining GR and thus the GR is “parasitized”. Related to this point, a high moving \nrate of protocells (PMC) is unfavorable because this would tend to bring the protocells \nwithout GR adjacent to GR protocells and enhance the likelihood of the cell-fusion. \n 991 \n.CC-BY 4.0 International licensemade available under a \n(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 \nThe copyright holder for this preprintthis version posted January 2, 2025. ; https://doi.org/10.1101/2025.01.02.631057doi: bioRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}