Evolutionary Effects of Mitochondrial Segregation and Mutation in The

Evolutionary eﬀects of mitochondrial segregation and mutation in the development of complex multicellular life with germ line

Arunas Radzvilavicius CoMPLEX, University College London, Gower Street, London WC1E 6BT, United Kingdom ∗ Andrew Pomiankowski and Nick Lane (supervisors) GEE, University College London, Gower Street, London WC1E 6BT, United Kingdom

(Dated: August 20, 2013)

The emergence of multicellularity in eukaryotes transformed the mapping between germ line fitness and adult viability by introducing the effects of mutation accumulation, segregation of organelles, division of labour and differentiation. These changes can play an important role in the evolution of extra-nuclear inheritance patterns. The uniparental mode of mitochondrial transmission, traditionally believed to be responsible for the evolution of two sexes, is advantageous, but can hardly spread to fixation in the model populations of unicellular individuals. The amplification of fitness differences, associated with the emergence of multicellularity, facilitates the spread of advantageous mutations affecting extra-nuclear genomes, thus making the fixation of uniparental mode of inheritance very likely. Early germ line sequestration in multicellular species is believed to protect reproductive cell lineages from the accumulation of deleterious mutations. The existence of species without isolated germ line shows, however, that early sequestration of germ line is not universally advantageous. In this contribution we analyse the issue in the light of mitochondrial fitness and effects of multicellularity. Despite the constant accumulation of new mutations, late germ line sequestration increases mitochondrial variance between reproductive cells, possibly resulting in the improvement of population fitness. Depending on effective mutation rates, either early or late germ line sequestration can be evolutionary advantageous. The proposed model can possibly account for the correlation between mtDNA mutation rates and the evolution of germ line specification modes observed in nature.

I. INTRODUCTION 3. The division of labour between information-storing molecules (DNA) and catalysts (proteins); 1. Multicellularity as a major evolutionary transition 4. The symbiosis of prokaryotes yielding eukaryotic The history of life on Earth is the history of gradual cells with mitochondria and/or chloroplasts; adaptations and major evolutionary transitions towards 5. The origin of sexual reproduction; systems of higher complexity. Every transition involves a shift from independently replicating units to the indivis- 6. The cooperation between unicellular organisms to ible and autonomous groups of cooperating entities. The give rise to multicellularity; concept of “individual”, as a unit of selection, must therefore be redefined after every such transition. The follow- 7. The emergence of social groups of multicellular or- ing events in the history of life are generally believed to ganisms. be major evolutionary transitions (Maynard Smith and In this work we are interested in changes induced by Szathmáry, 1995): the major transition from unicellular organisms to sta- 1. The compartmentalization of the groups of repli- ble complex multicellularity. It is widely believed, that cating molecules; throughout the history of life on Earth multicellularity has evolved independently more than 20 times (Cavalier- 2. The formation of chromosomes from independent Smith, 1991; Kaiser, 2001; Maynard Smith and Szath- replicators; máry, 1995). There is significant evidence that the transition occurred only once in metazoans and plants (King, 2004) and multiple times in algae and fungi (Baldauf, 2003; Bonner, 2000; Kaiser, 2001; Kirk, 1998). The tran- ∗[email protected] sition to the primitive form of multicellularity can be di- 2 rectly observed in laboratory conditions in the presence nor immortality, with the exception of some stem cell lin- of predators (Boraas et al., 1998). eages. This is an example of altruistic behaviour, mak- Several essential conditions had to be satisfied for the ing the multicellular individual indivisible. Germ cells, successful emergence of true multicellularity: cooperation on the other hand, are responsible for reproduction only. between lower level entities, division of labour, emergence With the spatial separation of vegetative and reproduc- of new group-fitness level and control or punishment of tive functions, separation in time is no longer necessary. selfish cells (Buss, 1987; Maynard Smith and Szathmáry, It has been proposed, that the sequestration of germ 1995; Michod and Roze, 2001). Mechanisms required for line protects lineages from origination and vertical trans- the stable multicellularity to evolve must have included mission of defector traits (Buss, 1987, 1983). As the small communication and signalling between cells, adhesion to group of cells is devoted to become the progenitors of all ensure physical stability and regulation of growth, divi- reproductive cells, mutation arising in any of the somatic sion as well as differentiation. It is currently believed that cells is not generally transmitted to the subsequent gen- the essential components of these mechanisms were in- erations. The evolution of germ line sequestration could deed present in unicellular ancestors of multicellular lin- have been an incredibly important transition, allowing eages (Abedin and King, 2010; King et al., 2003; Prochnik the development of complex, highly differentiated and et al., 2010). It is therefore very likely that simple multi- adapted organisms with massive numbers of somatic cell cellularity evolved by adopting existing molecular ma- divisions. Reproductive cell lineages are also believed chinery rather than de novo creation of new complex to experience lower nuclear mutation rates due to lower genotypes. metabolic activity (Drake et al., 1998), and accumulate The emergence of multicellularity created a new type less mutations due to lower number of cell divisions (Mi- of map between the genotype of zygote and adult phe- chod and Roze, 2001). notype, representing the new unit of selection. In the Despite seemingly obvious evolutionary advantages of realm of simple unicellular organisms, cell is an individ- having an isolated lineage of reproductive cells, many ual entity, which means that there is a direct correlation multicellular taxa do not sequester separate germ line between the viability of a cell and the fitness of the in- (Blackstone and Jasker, 2003). Multicellular organisms dividual. Selection acts on a multicellular organism as a that do not acquire an isolated germ line in the earliest whole, therefore viability of distinct cells is not equivalent stages of their development often have a population of to the fitness of the individual. The fitness of a complex pluripotent cells, e.g. cnidarian stem cells or meristem- and highly differentiated organism depends on the perfor- atic cells in plants, which can differentiate into reproduc- mance of its vegetative and reproductive tissues. Every tive cells after later epigenetic modification. It appears tissue is a collection of cells devoted to perform a specific that the possession of germ line is not a necessary re- task. The division of labour in complex multicellular life quirement for the evolution of differentiation in complex forms makes every tissue vitally important. Failure of a multicellular organisms. The question of what selective single tissue leads to a failure of the organism as a whole. forces promote early or late germ line sequestration is still The division of labour and differentiation into distinct largely unsolved (Grosberg and Strathmann, 2007). The tissues therefore have weakened the correlation between answer might not have much to do with the protection germ line genotype and organism phenotype even more. against defectors or deleterious nuclear mutations. In the present work we provide a novel analysis of the costs and benefits of sequestering a germ line from the 2. Benefits of germ line sequestration perspective of mitochondrial fitness. The transmission of mtDNA genes does not follow Mendelian laws of inher- The fitness of a biological entity can be described as itance. Furthermore, multiple copies of mtDNA within a product of two components, the ability to survive and the cell give rise to phenotypic threshold effects (Rossig- the efficiency of reproduction. Vegetative and reproduc- nol et al., 2003) and mutant segregation—phenomena, tive functions of simple unicellular organisms are coupled unique to the genetics of cytoplasmic organelles. Our at the most fundamental level of cell. The same elemen- mathematical model accounts for mutation accumulation tary entity is responsible for both components of uni- and random mtDNA segregation in somatic tissues, as cellular fitness, although the growth and multiplication well as different modes of cytoplasmic inheritance. stages are separated in time. The same is true for most We argue, that early germ line separation can be both primitive multicellular organisms without the division of beneficial and disadvantageous, depending on the con- labour across cells. The transition to true multicellular- ditions such as mtDNA mutation rates and size of mito- ity has separated vegetative and reproductive functions chondrial population. In populations with low mitochon- in spatial dimension by the means of differentiation. So- drial mutation rates, the phenomenon of random segre- matic cells perform vegetative activities, but the informa- gation results in higher variance between germ cells se- tion stored in their genomes is lost after a single genera- questered late. In those cases, despite simultaneous ac- tion. Somatic cells generally do not exhibit totipotency cumulation of deleterious mutations, high number of cell 3 divisions before generating gametes is evolutionary ben- 4. Patterns of mitochondrial inheritance eficial and stable. We propose, that the absence of early germ line sequestration in some species might be the re- Being descendants of ancient prokaryotes, mitochon- sult of fitness benefits associated with increased variation. dria cannot be synthesized de novo according to the rules Our model predicts relations between the mode of germ specified in the nuclear genome alone. It is natural then, line sequestration and mitochondrial mutation rate, copy that these organelles must originate from existing mito- number of mtDNA and mode of cytoplasmic inheritance. chondria and must be passed to the zygote through the cytoplasmic inheritance from at least one parental gamete. The strikingly common feature of eukaryotes is 3. Mitochondria in the evolution of complex eukaryotes the uniparental mode of cytoplasmic inheritance (UPI), as most eukaryotic sexual organisms receive their mito- All known eukaryotes evolved from the common chondria only from one of two parental gametes (Birky, prokaryotic ancestor only once in four billion years of 2001, 1995), while mitochondrial genes of the other ga- Earth’s history (Lane and Martin, 2010). Eukaryotic mete are lost. genome is the combination of two prokaryotic genomes— The sexual asymmetry of fusing gametes in anisoga- eubacterial and archaebacterial—suggesting that en- mous species has long been thought to be related to uni- dosymbiosis is the mechanism responsible for the evo- parental transmission of mitochondria. These species are lution of nucleated cells (Cox et al., 2008; Rivera and characterized by many small male gametes and a few Lake, 2004). In fact, all known eukaryotes possess mito- large female eggs, which potentially results in fixation of chondria or reduced and modified versions of mitochon- maternal mtDNA genes due to massive difference in mi- dria known as mitosomes and hydrogenosomes (Hjort et tochondrial population sizes (Birky, 1995). Mitochondria al., 2010). It is therefore very likely, that evolution of of non-transmitting mating type, on the other hand, can eukaryotic cell was possible only with the acquisition of be segregated out of the germ line completely (Kuroiwa mitochondria, as suggested by the hydrogen hypothesis and Uchida, 1996; Mogensen, 1996; Yu and Russel, 1992). of the first eukaryote (Martin and Muller¨ , 1998). The difference in gamete size or the number of organelles, Many eukaryotic traits are present in prokaryotes in however, cannot explain the existence of UPI in isog- their more primitive form, including large size (Schulz amous organisms, including unicellular Chlamydomonas and Jorgensen, 2001), compartmentalization (Lindsay et reinhardtii (Goodenough et al., 2007). In some cases or- al., 2001), signalling (Waters and Bassler, 2005), in- ganelle DNA can be degraded during or after fertilization, ternal membranes (Pinevich, 1997) and recombination or segregated into extra-embryonic tissues during early (Smith et al., 1993). However, despite their high en- cleavages (Birky, 1995; Kaneda et al., 1995; Shitara et ergetic and reproductive efficiency bacteria have never al., 1998). evolved the level of cellular complexity observed only in A broad variety of mechanisms ensuring uniparental mitochondrion-bearing eukaryotes and have never led to mitochondrial inheritance suggests that UPI could have true multicellularity. evolved multiple times and independently in different eu- The answer to this puzzle is undoubtedly related to karyotic species. It has been proposed that the asymme- incredibly high amounts of energy needed to evolve and try of mating types and uniparental inheritance evolved maintain cellular complexity (Lane and Martin, 2010). to minimize the selfish conflict between cytoplasmic While the amount of energy produced can be increased genes and spread of deleterious mitochondrial mutations by internalization and invagination of energy-generating (Hoekstra, 2000; Hurst and Hamilton, 1992; Law and membranes (Pinevich, 1997), only small local copies of HUtson, 1992). Uniparental transmission of mitochon- mitochondrial DNA allow for instant response by gene ex- dria decreases mtDNA variation within cell’s mitochon- pression to changes in membrane potential (Allen, 1993, drial population, but increases variation between cells 2003; Lane and Martin, 2010). The majority of mito- and organisms, thus purging deleterious mutations (Roze chondrial genes were either lost or transferred to the nu- et al., 2005). Finally, it has been recently proposed cleus, leaving only genes coding for some essential parts of that UPI might improve mitochondrial-nuclear adapta- respiratory machinery. The small size of mtDNA there- tion (Hadjivasiliou et al., 2012), since oxidative phospho- fore allows to maintain hundreds and thousands of copies rylation is dependent on proteins and RNA’s encoded in every cell. Large mitochondrial populations provide by both nuclear and mitochondrial genomes, requiring energetic support for the single copy of nuclear genome effective cooperation and adaptation (Blier et al., 2001; allowing it to grow in size and complexity, invent new Burton and Barreto, 2012; Lane, 2011). genes and pathways, evolve novel proteins, leading to Despite the obvious fitness advantages of populations higher complexity of the cell and, eventually, true multi- with UPI, it is not clear whether uniparentally organelles cellularity. transmitting mutants can spread and overtake the population with biparental mode of organelle transmission. In fact, it has been demonstrated that the spread of uni- 4 parental mode of inheritance in primitive unicellular pop- of mitochondria M, which in the simplest version of the ulations can be very limited due to the leakage of fitness model is the same as the number of mtDNA molecules, benefits to the wild-type part of the population (Had- that is, a single mitochondrion contains only one copy jivasiliou et al., 2013). It is also not completely clear of mtDNA. We consider only two mitochondrial states, whether the evolution of sexual dimorphism is related wild-type or mutant with respect to a certain allele. Fit- to the need to ensure uniparental transmission of mito- ness of the cell depends only on the fraction of mutant chondrial DNA, as might be the case with anisogamous mitochondria m/M. species (Hurst and Hamilton, 1992). Another possibility Every mitotic division in somatic cell line is coupled is that two mating types with isogametes were already with a random mitochondrial mutation event with the present for unrelated reasons, and only later became as- rate µS. This mutation rate represents copying errors sociated with the specific pattern of mitochondrial inher- associated with the replication of mtDNA before every itance (Hoekstra, 2000; Perrin, 2012). Recent modelling mitotic division. During the process of cell division, or- shows that UPI is likely to fix in unicellular populations ganelles are randomly assigned to two daughter cells, giv- with pre-existing mating types only under conditions of ing rise to the effects of mitochondrial segregation—one high mutational load (Hadjivasiliou et al., 2012). of the major interests of the present work. After γG cell The fitness advantage of UPI mutants alone might divisions a single randomly chosen undifferentiated cell is not be enough to drive uniparental organelle transmis- cloned to become the germ cell. We assume, that germ sion mode to fixation and the evolution of two sexes in line separation is followed by a single mutation event with primitive populations of unicellular organisms. Evolu- the mutation rate µG. This mutation probability is asso- tionary transition to multicellularity completely reshapes ciated with all the mutation events that are independent the mapping between germ line genotype and adult phe- of the number of divisions in soma: mutations caused notype, since individual cell does not longer serve as an by high mitochondrial activity, mitochondrial fissions in- elementary unit of selection. Division of labour between side of the germ cell and long term environmental effects. cells and tissues introduces even more non-linearities. It Back mutations are ignored, as their rate is assumed to is very likely, that due to mitochondrial segregation and be extremely low. mutation accumulation, the map between germ line fit- ° ness and adult viability is both stochastic and convex, i.e. °T divisions S divisions small differences in germ line fitness result in significant °G divisions changes of adult viability. The effect, which we call “the amplification of fitness differences”, possibly increases the ¹S ¹S ¹S efficiency of selection and allows even slightly advantageous strategies to spread and fix. In this work we show, that the amplification of fitness differences in complex multicellular organisms makes the fixation of UPI not ¹G just possible, but practically unavoidable. The size of mi- º =2° T tissues tochondrial population, level of multicellularity and dif- Fusion, T 2° S cells in each ferentiation all play an important role, as together with meiosis somatic mitochondrial mutation rate they determine the Figure 1 Schematic representation of a single haploid life cy- shape of mapping between germ line and adult fitness. cle. Starting from the initial cell, the organism undergoes Similar mechanisms might be responsible for a very fast γG mitotic divisions, after which a single cell is cloned to be- spread of advantageous, complexity-increasing mutations come the germ line. Somatic cell lineage then goes through after the transition to multicellularity. another γT −γS divisions before differentiation into vitally important tissues. Each cell after the 2γT -cell stage undergoes another γS mitotic divisions and gives rise to its own tissue. II. MATHEMATICAL MODEL AND COMPUTATIONAL The fitness of an organism is determined by the distribution APPROACH of mitochondrial mutations in the adult stage, but it is only reproductive cell that gets selected and transmits its genetic The mathematical model developed in this work is material to the future generations. based on the finite population of haploid multicellular individuals, following the simple life cycle illustrated in Differentiation into tissues begins when the embryo Figure1 with mathematical descriptions provided in Ap- reaches νT-cell stage, i.e. after γT cell divisions. Ev- pendicesA andB. Each generation starts with a single ery individual cell at this stage becomes the founder of cell subsequently undergoing a number of mitotic divi- a new tissue, which means that the viability of a certain sions, separating germ line and differentiating into tis- tissue depends largely on the state of the founder cell be- sues. Model parameters control the timing of these major fore differentiation. We consider each tissue to be vitally developmental events. Each cell contains a fixed number important, therefore the fitness of an organism depends mostly on the fitness of the worst tissue. The number of 5 cell divisions in tissues γS is generally considered to be tion and mutation processes during the population life high, i.e. up to γS = 50. cycle are provided in AppendixA. Random numbers in The maturation of individuals is followed by the se- the C++ implementation of the model are generated by lection and random fusions of gametes. Probability for employing“Mersenne Twister”random number generator the organism to be selected for reproduction is propor- from GNU Scientific Library (Matsumoto and Nishimura, tional to its fitness, which in turn depends on the distri- 1998). bution of mitochondrial mutants in cells and tissues as The number of cells in every organism increases ex- well as shapes of fitness (viability) functions for a sin- ponentially with the number of mitotic divisions. With gle cell, tissue and organism. The viability of a single large population sizes, numerical calculations become too cell should be a decreasing function of the number of computationally expensive after reaching 10 cell divi- detrimental mitochondrial mutations m. Low numbers sions. This makes the stochastic simulations of largely of mutants in general should not largely affect the fit- multicellular tissues virtually impossible. However, since ness of a cell with large M. Phenotypic threshold effects our model defines fitness of a single tissue as the average associated with mitochondrial diseases, however, suggest value of cellular fitness values, we can easily approximate that fitness of the cell should decline rapidly as m gets stochastic fitness distribution function by its determinis- closer to M (Rossignol et al., 2003). Some experimental tic version for large numbers of cell divisions. Such an studies estimate that respiratory deficiency and associ- approximation results in the deterministic mapping be- ated decline in cellular viability might appear after more tween the fitness of the founder cell and viability of the than 80% of the mitochondrial population acquires the resulting tissue (AppendixB). Although this“mean field” deleterious mutation (Inoue et al., 2007; Nakada et al., approximation is valid in the limit of large numbers of cell 2004, 2006). Building upon the previous research (Had- divisions, numerical simulations showed that it does not jivasiliou et al., 2012, 2013), we model cellular fitness as result in large errors even for the population as small as a concave quadratic function 220 cells.

m 2 ω = 1 − . (1) M III. SIMULATION RESULTS

The viability of a tissue is calculated by averaging cel- A. Evolution of uniparental mode of cytoplasmic lular fitness values, while the fitness of an organism is inheritance in multicellular eukaryotes considered to be equal to the viability of the worst tissue. 1. Unicellular limit of the model In this work we assume that the distinction between two mating types is already present—gamete of type “1” By setting γT = γG = γS = 0 we reduce our model to can only fuse with the type “2” gamete—and the ratio of the simplest case of unicellular life form, sharing many sexes is 1:1. The mode of mitochondrial inheritance is similarities with the case studied before by Hadjivasil- controlled by a single nuclear locus, closely linked to the iou et al. (2013). The gamete is cloned from the initial mating type, as it is the case in several model organisms cell, therefore there is a complete correlation between fit- (Yan et al., 2004). Fusions of gametes with a1 and a2 ness of the initial cell and viability of the adult organ- alleles result in biparental inheritance of mitochondria ism. Hadjivasiliou et al. (2013) found, that the spread of (BPI). Mitochondria are inherited only from the mating UPI mutant allele linked with a mating type in the an- type “1” in the case of fusion between gametes carrying cestral population of unicellular individuals with BPI is alleles A1 and a2 (subscript here denotes mating type). favoured by high numbers of mtDNA’s and heavy muta- Part of the present work treats germ line sequestration tional loads. Despite a few slight differences between the age γG as an evolvable trait. We assume, that germ line two models, including the population size, we expected specification mode is controlled by the nuclear locus with the same trends to be reflected in our results. alleles G (high γG, late germ line separation) and g (early Our stochastic model allowed us to investigate the germ line separation), which might be independent or spread of allele A1 in the populations of up to 50 000 linked to the mating type locus. We model the invasion individuals with ancestral genotypes a1 and a2. Starting of a certain mutant allele by inserting it at the frequency from a random fitness distribution across the population, of 5% into the ancestral wild-type population in the state we allowed the system to reach equilibrium (for at least of mutation-selection equilibrium. 100 generations, depending on the system size) before The high complexity of the model prevents us from inserting allele A1 at low frequency, which was typically finding exact mathematical descriptions even in the sim- chosen to be 5%. The time evolution of allele A1 fre- plified case of infinite populations. We therefore are quency was then tracked for at least 5 000 generations. forced to rely on stochastic simulations with population Due to stochastic nature of the system, we chose to de- sizes up to 50 000 individuals. Definitions of probabil- scribe the spread of UPI mutants by the mean equilib- ity density functions, corresponding to random segrega- 6 rium frequency of allele A1 after the transitional stage, set to zero, the germ line is separated by cloning the ini- i.e. after first 500 generations. The standard deviation tial cell and there is no differentiation. The fitness of an of frequency values was used to represent the magnitude organism, however, is measured only when the number of random fluctuations around the equilibrium. of somatic cells reaches 2γS . Two consequences of mul- The results of our simulations in the unicellular limit ticellularity contribute to the destruction of the correla- are in perfect agreement with the previous findings (Had- tion: the accumulation of deleterious mutations and the jivasiliou et al., 2013), which confirms that finiteness of decrease of fitness due to random segregation of extra- the population and probabilistic nature of the model nuclear DNA. does not prevent it from capturing the key behaviour Every mitotic cell division is followed by the mito- of spreading allele A1. The dependence of equilibrium chondrial mutation event with the corresponding muta- frequency of UPI mutant allele pA1 on the mitochondrial tion rate µS, resulting in the accumulation of mtDNA mutation rate µG is illustrated in Figure2, where sym- mutations. Secondly, due to random segregation of or- bols depict average values and error bars correspond to ganelles during the somatic growth stage, variation of the standard deviation of frequency pA1 . High mutation mutant numbers between cells increases, i.e. the proba- rates µG > 0.05 result in complete fixation of the uni- bility distribution function for the number of mutant mi- parental mode of inheritance with pA1 = 0.5 for M > 50. tochondria m becomes broader. Since the cellular fitness Mutant allele of the cytoplasmic inheritance locus A1 re- function is concave, the broadening generates more indi- places ancestral allele a1 easier in populations with higher viduals with lower fitness than those with higher fitness, number of mitochondria. As an example, complete fixa- resulting in additional decrease of organism viability. tion of UPI allele was observed already at µG = 0.03 for In Figure3 we demonstrate the two consequences of M = 200 in contrast to µG = 0.06 for M = 50. High simple multicellularity by plotting adult fitness as a func- mutation rate and large number of mitochondria both tion of the viability of an initial cell ϕA = Φ(ϕU). Note result in the decrease of population fitness, e.g. the fit- that due to high number of cell divisions in a single tissue, ness distribution is shifted towards lower viabilities. As in this case only the “mean field” approach is used (Ap- a result, relative advantage of uniparental mode of cyto- pendixB), which results in a completely deterministic plasmic inheritance increases, while leakage of fitness to relations between organism fitness in different stages of the sub-population of a1 and a2 becomes less efficient. development. Unicellular limit of the model with γS = 0 corresponds to the linear function ϕA = ϕU (solid line in Figure3). Increased number of divisions γS results in the 0.6 convex function ϕA = Φ(ϕU), lying below the unicellular baseline. Due to the reasons mentioned before, deviations 0.5 from the linear function become stronger as the number of divisions γS and mutation rate µS grows. The effect 0.4 of mitochondrial segregation plays a major role when the number of mitochondria is relatively small (e.g. M = 20 1

A 0.3 in Figure3), and becomes less significant as M grows, p bringing the correlation function closer to the unicellular 0.2 M=50 baseline. M=100 The growing number of cell divisions in a tissue γS M=200 0.1 results in higher germ line fitness and increase of equilibrium frequency of allele A1 (Figure4). We suspect, 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 that the reason behind this is the amplification of fitness ¹G differences, associated with the part of correlation func- ∂ϕ tion where A > 1 and increased selection strength. Figure 2 Equilibrium frequency of UPI mutant allele A1 in ∂ϕU the population of unicellular haploid individuals as a function As we have already seen in the unicellular case, for small of mutation rate µG. γS higher number of mitochondria results in larger pA1 . However, as the number of cell divisions γS increases and passes a certain critical value, segregation and mutation accumulation within a single growth cycle become more 2. Reducing the correlation between germ line and adult fitness important, surpassing the effect of background mutations between generations (µG). In those cases, UPI spreads By increasing the number of cell divisions in a tissue easier in populations with relatively small numbers of γS 6= 0 we arrive at the most primitive multicellular case mitochondria, where amplification of fitness differences of the model, where completely linear correlation between is stronger. As an example, consider the population with the fitness of the initial cell and viability of the adult in- µG = 0.015 and µS = 0.001 (Figure4). Consistent dividual is violated. Note that both γG and γT are still 7

1 0.55 °S=0 °S=40, M=20, ¹S=0.001 0.5 0.8 °S=40, M=100, ¹S=0.001 M=50, ¹ =0.001 ° =40, M=100, ¹ =0.003 S S S 0.45 M=100, ¹S=0.001 M=50, ¹S=0.003 0.4 M=100, ¹ =0.003 0.6 S

A 0.35

' °S, ¹S increasing 0.4 0.3

0.25 0.2 M increasing 0.2

0 0.15 0 0.2 0.4 0.6 0.8 1 70 0 10 20 30 40 50 60 70 'U °S

Figure 3 Correlation between the fitness of an organism in Figure 4 Equilibrium frequency of UPI mutant allele A1 in the one-cell stage of development and adult fitness of the the population of primitive haploid individuals with γT = same individual ϕA = Φ(ϕU ) in the simplest deterministic γG = 0 as a function of number of cell divisions γS under four case of a single tissue and high number of divisions after germ different conditions. Mutation rate in germ line is constant line separation γS . Mitochondrial segregation and mutation and set to µG = 0.015. accumulation—consequences of multicellularity—result in the loss of correlation between the fitness of a zygote and viability of an adult. Deviations from linear correlation function and segregation (AppendixA), every value of fitness ϕU become more evident as the number of divisions γS and so- corresponding to a certain state of the initial cell, results matic mitochondrial mutation rate µS increases. The effect in several values of adult viability ϕ . Note, however, of random mitochondrial segregation becomes weaker as M A that symbols in Figure5 represent only the most likely grows. transitions, as the computational procedure was repeated only 100 times for every possible state of the initial cell. Nevertheless, we can safely state that differentiation to- with the results of the unicellular case, mutant allele A1 spreads easier in the population of multicellular individ- gether with high number of cell divisions in tissues ampli- fies the effects of multicellularity by pushing the mapping uals with γS < 20 if the number of mitochondria in each cell is large, M = 100. However, increased number of mi- between ϕU and ϕA further away from the unicellular tochondria has the opposite effect and limits the spread of baseline ϕA = ϕU (Figure5). As we have already seen UPI mutant allele in populations of highly multicellular before, increasing number of mitochondria M lowers the significance of segregational effects. organisms with γS > 30, where segregation and amplification are stronger with small mitochondrial populations The effect of differentiation into multiple vital tissues (M = 50). on the spread of mutant allele A1 is illustrated in Figure 6. Data points corresponding to eight tissues show a significant increase of equilibrium UPI mutant frequencies 3. Differentiation into tissues strengthens the effects of as compared to the case of a single tissue. We argue, that multicellularity differentiation into vitally important tissues strengthens the selection by amplifying and exposing small fitness dif- We further increase the complexity of the model or- ferences in the germ line. Once again, high M facilitates ganisms by setting γT > 0, which results in differenti- the spread of A1 only for small tissues, that is low values ation into more than one tissue. In our model, every of γS. High number of cells in tissues increases the signif- somatic tissue is considered to be vital and therefore fit- icance of the amplification of fitness differences, which is ness of the organism is determined by the viability of less effective in large mitochondrial populations. There- the worst tissue. Due to strictly finite number of tissues fore, UPI spread in populations of highly multicellular (νT = 1 ... 256), the “mean field” approach is inappro- individuals with large γS might be favoured by relatively priate. We therefore are forced to rely on computation- small mitochondrial populations. ally intensive stochastic simulations of finite multicellular populations (up to 50 000 individuals). The stochastic version of the mapping between founder 4. The effect of germ line separation age γG cell fitness and adult viability can be constructed by run- ning the simulation repeatedly (Figure5). As a conse- The number of cell divisions before the separation of quence of probabilistic nature of mitochondrial mutation germ line does not affect the shape of correlation func- 8

creases with γG (Figure7). The accumulation of mtDNA 1 mutations shifts the fitness distribution within popula- ºT=1, M=50 tion towards lower reproductive rates, which means that 6 ºT=2 , M=50 γ has the effect similar to M in the unicellular case. 0.8 º =26, M=100 G T Similarly, if µ is significantly higher than µ , germ line ° =40 G S S fitness can increase with γ due to low rate of mutation ¹ =0.001 G 0.6 S accumulation and increased variation induced by mito- A chondrial segregation. This results in lower mutational ' 0.4 load and lower frequency of mutants with UPI allele A1 at equilibrium (Figure8).

0.2 0.5

0.45 0 0 0.2 0.4 ' 0.6 0.8 1 U 0.4

Figure 5 Correlation between the ﬁtness of an organism in a 1 =2

A º one-cell stage of development and adult fitness of the same 0.35 T p ºT=4 individual ϕA = Φ(ϕU ) in the population of multicellular in- ºT=8 dividuals with νT tissues and 40 cell divisions in each tissue. 0.3 Symbols depict the combinations of initial and adult fitness ¹G=0.005 values found in a single generation throughout 100 simulation ¹ =0.005 0.25 S runs for each starting configuration. The stochastic nature of M=130 the model results in several adult fitness values corresponding to a single initial fitness ϕ . 0.2 U 0 1 2 3 °G Figure 7 Equilibrium frequency of UPI mutant allele A in 0.55 1 the population of haploid individuals as a function of number =0.001 0.5 ¹S of cell divisions before germ line sequestration γG. Organisms ¹G=0.01 differentiate into 2, 4 or 8 tissues ( γ = 1, γ = 2 and γ = 3 0.45 T T T correspondingly). The number of mitochondria in each cell 0.4 is M = 130, while µG = 0.005, µS = 0.005 and γS = 20. Error bars represent standard deviation of frequency values

1 0.35

A ﬂuctuating around the mean value (symbols) throughout the p 0.3 course of 5 000 generations.

0.25 ºT=1, M=50 0.2 ºT=1, M=100 ºT=8, M=50 0.15 B. Evolution of germ line sequestration in multicellular ºT=8, M=100 eukaryotes 0.1 0 10 20 30 40 50 60 70 °S Many complex eukaryotes store their reproductive cells in a separate lineage, frequently associated with low Figure 6 Equilibrium frequency of UPI mutant allele A1 in metabolic rate and low number of mitotic divisions. It the population of haploid individuals as a function of a num- is widely believed, that the possession of a separate ber of cell divisions in tissues γS in organisms with 1 and 8 germ line protects the organism from the accumulation tissues. The values of m utation rates are set to µ = 0.01 G of deleterious mutations in both nuclear and cytoplasmic and µ = 0.001. Germline is separated at the beginning of a S genomes. In a broad variety of species, however, germ new generation (γG = 0). line is absent, as reproductive cells are separated from other cell lineages, even after high numbers of mitotic di- tion ϕA = Φ(ϕU), however it still affects the position of visions. In some metazoans germ line can be regenerated mutation-selection equilibrium. As we show in the next from so called primordial germ cells. A broad variety of section, late germ line sequestration can either be evo- germ cell specification mechanisms leads to the conclu- lutionary beneficial or harmful, depending on the values sion that the evolutionary advantage of clear distinction of mutation rates µS and µG. In cases of relatively high between germ line and soma is not universal. In this sec- somatic mutation rate µS, late germ line separation re- tion we use the results of our computational modelling to describe the costs and advantages of germ line specifica- sults in lower population fitness, ans subsequently pA1 in- tion early or late in the development cycle of the organism 9

to separate a germ cell with more mitochondrial muta- 0.48 tions, which leads to the decline in population fitness (tri- angles and squares in Figure9). Somatic mutation rate 0.46 lowered by an order of magnitude makes a big difference: sufficiently low µS makes later germ line separation bene- 0.44 ficial, as population fitness increases with γG (circles and diamonds in Figure9). 1

A 0.42 =2 p ºT ºT=4 0.4 ºT=8 1.02 ¹ =0.02 ° =6, ° =40, M=50 G 1 T S 0.38 ¹S=0.001 M=100 0.98 0.36 0.96 0 1 2 3 °G 0.94 avg ' Figure 8 Equilibrium frequency of UPI mutant allele A1 in 0.92 the population of haploid individuals as a function of number 0.9 of cell divisions before germ line separation γG. Organisms differentiate into 2, 4 or 8 tissues ( γ = 1, γ = 2 and γ = 3 0.88 BPI T T T =0.001, =0.02 correspondingly). The number of mitochondria in each cell ¹S ¹G UPI 0.86 BPI is M = 100, while µG = 0.02, µS = 0.001 and γS = 20. ¹S=0.01, ¹G=0.001 UPI Error bars represent standard deviation of frequency values 0.84 fluctuating around the mean value (symbols) throughout the 0 1 2 3 4 5 6 7 course of 5000 generations. Conditions are advantageous for °G later germ line separation. Figure 9 Average population fitness at the equilibrium as a function of germ line separation age γG for two conditions and two modes of mitochondrial inheritance. and define the conditions, under which different modes of germ line sequestration are likely to evolve. The accumulation of mtDNA mutants is not the only force responsible for the position of mutation-selection equilibrium, that is, steady sate fitness of the popula- 1. Benefits of specifying the germ line early or late tion. Every mitotic cell division is followed by random In our model, germ line separation age is controlled by partitioning of cytoplasmic organelles. According to the definitions of our model, parental cell with q mutant mi- the parameter γG, which represents the number of cell divisions before germ cells are cloned from the main cell tochondria gives birth to the daughter cell with m mutants according to the hypergeometric probability distri- lineage. High values of γG lead to the accumulation of mtDNA mutations as well as stronger effect of random bution (see AppendixA). This means that some daugh- mitochondrial segregation during every mitotic division. ter cells are likely to have m > q and lower fitness, while others will have m < q and will be fitter. Generally, Two mitochondrial mutation rates—µG and µS—affect the fitness of germ cells and adult individuals. Mutation besides shifting due to mutation accumulation, the probability distribution function for the number of mitochon- rate µG controls the baseline fitness, and represents the effect of mtDNA mutations independent of the number drial mutants m or cellular fitness ϕC gets broader with every cell division due to random partitioning and segre- of somatic cell divisions. Parameter µS, on the other hand, is associated with fission of mitochondria before gation. In cases with low µS later germ line separation every mitotic division and thus is responsible for the rate increases variance between germ cells, which gives access of mutation accumulation during the development of so- to fitter daughter cells. Natural selection then leads to matic tissues. the higher population fitness. In this section we assume that entire population uses a Whether late germ line separation is beneficial or not single mode of mitochondrial inheritance, that is, either depends on the set of parameters used. More mutations BPI or complete UPI. Our results show, that the effect of are accumulated in populations of organisms with high mutation rates µS as well as large M. Segregation ef- increasing γG can be either beneficial of disadvantageous, depending on the selected conditions, i.e. values of mu- fects, on the other hand, are strongest in multicellular organisms with small mitochondrial populations M. To tation rates µG and µS (Figure9). As one would expect, investigate the effect of model parameters on the fitness high somatic mutation rate µS results in the build-up of mtDNA mutations with every replication and cell divi- advantages of a certain mode of germ line specification, we further analyse in detail a specific complex multicellu- sion. Because of this, higher γG increases the probability 10

γS 40 12 lar system with νT = 64 tissues and 2 = 2 ≈ 1.1·10 fixation probability of neutral mutants π0. We call the cells in every tissue of an adult. Allele G corresponds invader allele evolutionary advantageous if its fixation to late germ line separation after γG = 6 mitotic divi- probability π is higher than π0. Similarly, the allele is sions, while allele g codes for germ line specification after in disadvantage if π < π0. As in neutral case the genetic γG = 1 division. drift is the only evolutionary force in operation, popula- The equilibrium fitness of the population composed of tion after an infinite number of generations will consist of allele G is compared to the fitness of g population in the ancestors of a single individual. Fixation probability Figure 10, where colour codes for the fitness difference of the neutral mutant therefore corresponds to its initial ∆ϕ = ϕG − ϕg and dashed lines represent zero crossings. frequency, which in our case is π0 = 0.05. With the link- We immediately see, that low somatic mutation rate µS is age between germ line specification mode and one of the necessary to prevent the fast accumulation of mutations mating type alleles, only half of the population can be and allow for late germ line separation to be advanta- overtaken by the invader. Fixation probability in these geous. Secondly, higher background mutation rate µG cases increases to π0 = 0.1. results in the stronger advantage of allele G. With low The size of the population plays an important role in µS, population can simple become too fit for any segre- the spread of mutant alleles. In small populations, fixa- gation effects to generate enough variance (or to be more tion probability of advantageous allele might not be very precise, fitter individuals). Heavy background mutation high due to strong effect of genetic drift. Highest fix- load µG shifts fitness distribution function away from sat- ation probability observed in our numerical simulations uration, where segregation coupled with selection is again of the population with N = 100 individuals was close beneficial. For analogous reasons, parameter range where to 0.7. In general, fixation probabilities of advantageous ϕG > ϕg expands with increased M, and is wider in less germ line specification time allele increases with system fit populations with the biparental mode of mitochondrial size (data not shown here). Precise evaluation of fixa- inheritance. tion probability requires many repeated simulation runs, which becomes impractical for large population sizes due to the limitations of computing resources. 2. Spread and fixation of germ line specification mode mutants As we demonstrate in Figures 11 and 12, under G and g favourable conditions (as can bee seen in Figure 10), the fixation probability of allele G (g) invading the ances- As we have already demonstrated, due to the effects of tral population of g (G) is indeed much higher than fix- mutation accumulation and segregation, either of allelic ation probability of neutral mutants. Despite the strong variants G or g at the germ line specification mode lo- leakage of fit mitochondria into the ancestral part of the cus can have fitness advantage in the uniform population, population, invaders are in advantage even in the case depending on background and somatic mutation rates as of linkage with mating type alleles (Figures 11 and 12, well as the mode of cytoplasmic inheritance. This, how- right). Under constant somatic mutation rate µS, the ever does not necessarily mean that a given mode will frequency of fixation events for allele G invading g in- be evolutionary stable and invade in finite polymorphic creases with µG. This is as expected, since according populations. In this section we investigate the ability of to Figure 10 fitness advantage of late germ line specifica- either G or g allele to spread and overtake the ancestral tion grows as µG becomes higher. Due to similar reasons, population of the opposite mode of germ line sequestra- fixation probability of g invading G becomes lower with tion. increasing background mutation rate (Figure 12). Due to computational limitations, we were forced to According to Figure 11 in cases without genetic linkage reduce the population size to N = 100 individuals. Af- the selective advantage of allele G is higher in population ter the equilibration in the ancestral population, invader with complete BPI, as compared to UPI. As we demon- mutant allele was inserted at the frequency of 0.05. The strated in Figure 10, BPI increases the selective advan- simulation was stopped as soon as frequency of mutant tage of late germ line sequestration. Secondly, in the case allele reached 0 (extinction) or 1 (fixation). The compu- of uniparental inheritance, allele G is distributed among tational cycle was repeated 5 000 times to calculate the the sub-populations of both active and inactive mating fixation probability of invader allele π. We assumed that types, which means that there is always a part of fitness population is composed of individuals with alleles a1 and advantages lost with mitochondria not transmitted to the a2 or A1 and a2, with mating type ratio 1:1, that is, zygote, thus limiting the spread of allele G. The opposite the whole population uses only one mode of cytoplasmic is true for invasion of allele g (early germ line separation, inheritance. We tested a few possible invasion scenar- Figure 12). In this case, however, the difference between ios with or without the linkage of germ line specification fixation probabilities in UPI and BPI populations is not locus to the mating type and inheritance mode loci. significant, as the two effects oppose each other: UPI in- The case of invaders without any fitness advantages creases the advantage of early germ line sequestration, or disadvantages is of special interest, as it defines the but only in BPI populations selection acts on the full 11

¢' 0.04 0.04 =50, BPI M=50, UPI M 0.1 0.03 0.03 S

¹ 0.02 0.02 0.0 0.01 0.01

0 0.02 0.04 0.06 0.08 0.10 0 0.02 0.04 0.06 0.08 0.10 -0.1 0.04 M=100, UPI 0.04 M=100, BPI 0.03 0.03 S -0.2 ¹ 0.02 0.02 0.01 0.01 -0.3 0 0.02 0.04 0.06 0.08 0.10 0 0.02 0.04 0.06 0.08 0.10 ¹G ¹G

Figure 10 Fitness gain with late germ separation (γG = 6) over early separation (γG = 1), as a function of mutation rates for M = 50 (top row) and M = 100 with two modes of mitochondrial inheritance, UPI (left column) and BPI. Parameter range, where later germ line separation results in higher population ﬁtness expands with more mitochondria and biparental mode of 6 organelle inheritance. γS = 40, ∆ϕ = ϕG − ϕg, the number of tissues is 2 .

0.18 0.35 G→g 0.16 g→g, BPI UPI, G l.t. a2 0.3 G→g, BPI UPI, G l.t. A1 0.14 G→g, UPI BPI, G l.t. a1 No linkage 0.25 0.12

0.1 0.2

0.08 0.15 0.06 Fixation probability ¼ 0.1 0.04

0.02 0.05 0 0.02 0.04 0.06 0.08 0.1 0.12 0 0.02 0.04 0.06 0.08 0.1 0.12 ¹G ¹G

G g Figure 11 Fixation probability of the independent invader allele associated with germ line separation after γG = 6 or γG = 1 cell g divisions in the ancestral population of g allele, corresponding to early germ line separation, γG = 1 as a function of mitochondrial mutation rate µG (left). Fixation probability of invader allele G linked to (l.t.) mating type locus (right). Somatic mitochondrial mutation rate is µS = 0.001, M = 50, mitochondrial inheritance is purely biparental or purely uniparental, population size is 6 N = 100 individuals, the number of divisions after diﬀerentiation is γS = 40, while the number of tissues is νT = 2 . Mutant allele is injected with the starting frequency of f0 = 0.05. In case of genetic linkage invader allele is initially introduced only into the sub-population of one mating type, therefore it is considered ﬁxed when its global frequency reaches 0.5.

population of advantageous allele g. allele a2 in the population composed of A1 and a2 (com- The situation is somewhat changed by the introduc- plete UPI). Individuals with allele a2 do not pass their tion of genetic linkage between germ line specification mitochondria during the fusion of gametes, therefore mu- mode allele (G or g) and mating type locus (right parts tations affecting mitochondrial fitness do not experience of Figures 11 and 12). We assume, that invasion begins selective pressure and propagate under the effect of ge- with the mutant allele inserted into the sub-population netic drift alone. Advantageous germ line separation time of a single mating type at the frequency of 0.05. As a mutations linked to mating type “1” spread easier in UPI result, complete fixation is reached when the frequency population, where only mitochondria from gametes A1 of invaders reaches 0.5. Invader allele behaves as a neu- are inherited. In the case of pure UPI, there is no mixing tral mutation when inserted into the sub-population of of mitochondria between the two sub-populations, which 12

0.6 0.8

0.7 0.5 0.6 0.4 0.5 G→G, BPI g→G, BPI 0.3 0.4 g→G, UPI g→G No linkage UPI, g l.t. a2 0.3 0.2 UPI, g l.t. A1 BPI, g l.t. a1 0.2 Fixation probability ¼ 0.1 0.1

0 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0 0.02 0.04 0.06 0.08 0.1 0.12 ¹G ¹G

Figure 12 Fixation probability of the independent allele g (early separation) or G (late separation) invading the ancestral population of G allele as a function of mitochondrial mutation rate µG (left). Fixation probability of invader allele g linked to (l.t.) mating type locus (right). Somatic mitochondrial mutation rate is high, µS = 0.05, other parameters are the same as in Figure 11. Mutant allele is injected with the starting frequency of f0 = 0.05. means that the importance of accumulated ﬁtness bene- case. The spread of UPI is favoured by strong dif- ﬁts is not lowered with every fusion event. ferentiation and division of labour (large numbers of vital tissues). Depending on the mtDNA mutation rate either early or late germ line sequestration IV. CONCLUSIONS can favour the spread of UPI.

In this section we provide the summary of most impor- 6. Due to increased variance between reproductive tant findings described in the paper. cells, late germ line sequestration is favoured by low somatic mutation rate, relatively high “back- 1. High mutation rate and large mitochondrial pop- ground” mutation rate and biparental mtDNA ulations drive the spread of uniparental mode of transmission. High somatic mutation rates and inheritance in simple unicellular populations. UPI lead to the evolutionary advantage of early germ line separation. 2. Multicellularity and differentiation leads to the effects of segregation, amplification of fitness differ- 7. The invasion and spread of advantageous germ line ences and loss of correlation between germ line fit- separation mode (early or late) is facilitated by ness and viability of adult individuals. Large num- linkage with active mating type (female) in UPI bers of mitochondria limit the effects of segregation. populations. The spread of early germ line sequestration allele under advantageous mutation rates is 3. In the deterministic case of primitive multicellular- strongly favoured by BPI in the case of unlinked ity with one tissue, correlation between germ line loci. fitness and adult viability is partially lost. Due to the segregation of mitochondria and amplification of fitness differences, the spread of UPI is facilitated V. DISCUSSION by high numbers of cell divisions, fast accumulation of somatic mutations and small mitochondrial pop- The emergence of multicellularity—one of the major ulations. evolutionary transitions—reshaped the living world by transforming the mapping between zygotic genotype and 4. The non-deterministic case of differentiation into adult phenotype. Together with the earlier emergence several vitally important tissues enhances the effect of complex cell it opened the door for the evolution of of organelle segregation. Low numbers of mitochon- strikingly vast variety of phenotypes and adaptations dria lead to strong segregation and amplification. observed in nature today. In this work we employed 5. Complex multicellularity with differentiation leads stochastic numerical simulations of finite populations to to the fixation of UPI with mutation rates orders analyse the consequences of the transition to multicellu- of magnitude lower than needed in the unicellular larity in the light of mitochondrial fitness, mtDNA mu- 13 tations and random segregation effects. where µG acts only on germ line cells immediately after Multicellularity introduced the new level of selection their sequestration, it can be successfully applied to all— acting on a group of co-existing entities with the division somatic and germ line—cells without significant changes of labour and differentiation, possibly amplifying the ad- in the outcome, as long as the number of accumulated vantages of traits responsible for the improved mitochon- mutations does not depend on the number of mitotic cell drial fitness. Previous work has shown that uniparental divisions. We therefore can interpret µG as “background” mode of mitochondrial inheritance (UPI) increases fitness mutation rate, possibly related to environmental factors, in unicellular populations, but cannot spread to fixation divisions during meiosis, effects of mitochondrial activ- under the conditions of low mutation rates (Hadjivasiliou ity or mitochondrial fission events in reproductive cells. et al., 2012, 2013). In this work we demonstrated, that Indeed the copy number of mtDNA can be increased to multicellularity can facilitate the invasion and spread of hundreds of thousands in mammalian oocytes (Michaels UPI in finite, but large haploid populations, making the et al., 1982), possibly leading to the accumulation of mu- fixation of the trait possible even under low mutation tations. rates—orders of magnitude lower than required in the Distinction between germ line and soma can be advan- unicellular case. tageous, since it protects reproductive cells from the ac- The equilibrium frequency of UPI mutant allele in- cumulation of deleterious nuclear or mtDNA mutations, creased with growing somatic mtDNA mutation rate µS while still allowing for the development of complex mul- and“background”mutation rate µG, as well as with grow- ticellular somatic phenotypes. The advantage, however, ing number of tissues and cell divisions. We hypothe- is not universal since there is a broad variety of species sized, that the amplification of fitness differences is re- lacking the germ line sequestered early. The results of our sponsible for the observed effects. The only requirement numerical simulations indicate that there are conditions for the amplification to be observed was the specific shape where either early or late germ line sequestration is evo- of the function mapping germ line fitness to adult viabil- lutionary advantageous. High somatic mutation rate µS ity. Large mitochondrial populations in complex multi- leads to fast mutation accumulation, which means that cellular organisms decrease germ line fitness, but at the only early germ line specification can evolve. In con- same time reduce the significance of mitochondrial seg- trast, if “background” mutation rate, not related to mi- regation and fitness amplification. Increased number of totic cell divisions, µG is more significant factor, while mitochondria in highly multicellular organisms resulted µS is low, late germ line segregation is advantageous and in decreasing frequency of advantageous UPI allele, thus will spread. The reason behind these observations is in- confirming our hypothesis. We were able to find condi- creased variance between reproductive cells separated af- tions where either late or early germ line sequestration ter the large number of cellular divisions, which coupled can result in broader spread of UPI. with selection might be more important than the build- Multiple cases of both uniparental and biparental up of deleterious mtDNA mutations. Furthermore, we modes of mitochondrial transmission are know to exist showed that the advantageous mode of germ line spec- in unicellular eukaryotes, as well as the mixtures of the ification (early/late) is more likely to spread and fix if inheritance strategies and paternal leakage in multicellu- the trait locus is linked to the allele forcing uniparental lar species (e.g. Birky, 1995; Perlman and Birky, 1974; transmission of mitochondria. Xu, 2005). At this point it is therefore hard to conclude Since the two mutation rates (µS and µG) are responsi- whether the evolution of multicellularity and differentia- ble for two different processes, their numerical values can tion has promoted the spread of UPI in natural popula- not be directly compared. However, with the definitions tions. of the model proposed in this work, late germ line seques- The dynamics of mutation accumulation in extra- tration was found to be evolutionary advantageous only nuclear genomes might differ significantly from the simi- when the contribution of µG was largely significant, while lar processes in nucleus. The definitions of two processes µS was low. Larger mitochondrial populations and the leading to mtDNA mutations and two related parame- biparental mode of organelle inheritance made the spread ters are essential for the validity of our model. Muta- of early germ line separation more likely. As expected, tion rate µS, which we called “somatic mutation rate” early germ line sequestration evolved in populations with throughout the paper, describes the probability to ac- high somatic mutation rates µS. These observations lead quire a specific mutation during a single mitotic division to predications about possible relations between mtDNA event. Mitochondrial population of a specific cell has to mutation rate, inheritance mode and germ line specifica- be doubled before every somatic division, therefore we as- tion age in natural populations: frequent somatic muta- sumed that µS corresponds mostly to the copying errors tions of mtDNA should lead to early germ line sequestra- during mtDNA replication. tion, while low µS (and µG > µS in our model) together Second mutation rate µG corresponds to random mu- with BPI should lead to the complete absence of the germ tations not related to the process of mitotic divisions. line being advantageous due to increased variation. While the results presented here correspond to the model It is well known, that the uniparental inheritance of 14 extra-nuclear genomes decreases genetic variance among It has been suggested, that present day bilaterian mtDNA copies in the same cell, but increases variance metazoans originated from the ancestor specifying its between cells and organisms (Bergstrom and Pritchard, germ line by epigenesis in the post-embryonic stages of 1998; Roze et al., 2005). We showed, that late germ line development (Extavour, 2007; Funayama, 2010), since sequestration under certain conditions increases variance this mode of germ line specification dominates among between reproductive cells, and under low somatic mu- the basal metazoans (Agata et al., 2006; Extavour, 2007). tation rates is evolutionary advantageous. Therefore in Sponges, cnidarians and even Acoelomorpha all use sim- some sense late germ line sequestration and UPI share the ilar strategies of late germ line generation from the pop- common function of ensuring sufficient variation between ulation of endodermally derived pluripotent stem cells, organisms, thus avoiding the accumulation of deleteri- capable of giving origin to both somatic and reproductive ous mutations throughout multiple generations (Muller’s cells (see Agata et al., 2006, for a review). Similarly, we ratchet, as described by Muller(1964) and Felsenstein might suspect that the late sequestration of reproductive (1974)). According to our results, the two processes cells (e.g. from lower epithelium) takes place in prim- seem to complement each other: UPI spreads easier with itive metazoan Trichoplax adhaerens (Eitel et al., 2011; late germ line sequestration when variation between sepa- Grell, 1972; Grell and Benwitz, 1981), and was present in rated germ cells is not sufficient to keep population fitness possibly related Ediacaran taxa (vendobionts) before the high, and vice versa. Cambrian explosion (Buss and Seilacher, 1994; Seilacher, Plant mtDNA in known to have an anomalously slow 1992; Sperling and Vinther, 2010). In addition, extra- mutation rate (Wolfe et al., 1987), with only rare ex- nuclear genomes of primitive non-bilaterian metazoans ceptions, such as Plantago (Cho et al., 2004). Addition- with late germ line separation (phyla Placozoa, Cnidaria, ally, there are multiple cases of heteroplasmy caused by Porifera and possibly Ediacaran fauna) share features not varying levels of BPI reported in the plant kingdom (Mc- found in complex present day metazoans, including large Cauley et al., 2005; Mogensen, 1996; Nagata et al., 1999; mtDNA sizes, the presence of introns, additional protein- Zhang et al., 2003). Angiosperms generate their gametes coding genes, bacteria-like ribosomal and transfer RNA from the meristematic cell lineages, which might have un- genes, minimally modified genetic code. dergone extremely large numbers of divisions giving birth In the light of our findings, it is tempting to state that not only to gametes, but also to the broad variety of so- the rate of mitochondrial evolution and mutation was matic tissues (Fleming, 2006; Traas and Bohn-Courseau, rather slow in the populations of early non-bilaterian 2005). According to our results, low mtDNA mutation metazoans, and increased during subsequent evolution rate and the biparental mode of organelle transmission towards more complex and more adapted individuals. are conditions favouring late germ line sequestration. Al- One of the reasons might be increased energetic require- ternatively, late germ separation together with rare so- ments, requiring higher mitochondrial activity. Another matic mutations limit the spread of UPI (Figure8). We possibility is that mutation rate might have increased for can conclude, that various levels of heteroplasmy due to the reasons unrelated to the evolution of complex fea- partial BPI (paternal leakage of mtDNA) observed in the tures, e.g. due to changing environmental conditions. plant kingdom (Barr, 2005; Birky, 1995; McCauley et al., Faster mutation rate drove the development of early germ 2005) support our findings. line sequestration, which opened the door for the further In contrast, majority of animal mtDNA has been found evolution of complex and highly differentiated soma with to evolve rapidly (Crawfors, 2003; Gilbert, 2000; Shearer large numbers of cell divisions. The emergence of com- et al., 2002, and references therein), with synonymous plex cell and, eventually, true multicellularity, became substitution rate being 50-100 times higher in mammals possible only after the symbiotic acquisition of mitochon- than in angiosperms. Consistent with the predictions of dria (Lane and Martin, 2010). Similarly, the emergence our model, bilaterian animals define their germ cell lin- of early separated germ line (most likely at the dawn eages early (Extavour, 2007; McLaren, 2001). On the of the Cambrian explosion) might have been a crucial other hand, extremely low mtDNA evolution rate has transition towards the evolution of complex, highly dif- been detected in cnidarians and sponges, with at least ferentiated multicellular metazoans. 10-20 times lower evolution tempo than in vertebrates While the present work accounts for several impor- (Duran et al., 2004; Hellberg, 2006; Shearer et al., 2002) tant consequences of multicellularity and differentiation, and some types of mutation events up to 10 times rarer many related questions still remain to be answered in than in their nuclear DNA (Fukami et al., 2000). These our future work. The role of the uniparental inheri- and related classes of primitive metazoans are usually tance of plastids, which can be inherited either together characterized by relatively late germ line sequestration, with mitochondria or from the opposite mating type, as signified by Nanos and Piwi expression patterns (Fu- needs to be examined within our theoretical framework. nayama, 2010; Juliano et al., 2010; Paulus, 1989; Tor- Similarly, mtDNA recombination frequently occurring in ras et al., 2004; Torras and González-Crespo, 2005), once species with late germ line specification must be consid- again in agreement with our model. ered, as it might be related to genetic variation keep- 15 ing the population fit. We hope that our present con- mitochondria follows hypergeometric distribution tribution together with the future work will result in a ? ? ? complete theory accounting for the role of extra-nuclear m M − m k M ?/2 − k genomes in evolutionary transitions following the emer- p (k; m?,M ?) = . (A2) gence of complex cell and multicellularity, explaining the me M ? origin of anisogamy, germ line-soma distinction, differ- M ?/2 entiation, the division of labour and patterns of cellular ? ? ageing. Variables M and m here represent total numbers of mitochondria before the division, that is M ? = 2M and m? = 2m for first meiotic subdivision, while M ? = M Appendix A: Stochastic mitochondrial processes in the and m? = m for second subdivision. Two out of four development of multicellular populations resulting haploid cells are randomly destroyed to keep the size of the population constant. Stochastic part of our model is implemented by representing mitochondrial segregation and mutation events as random processes, following hypergeometric or bino- c. Mutation mial probability distributions. Random numbers from relevant probability density functions are generated by In the present work we are only concerned with detri- employing“Mersenne Twister”random number generator mental mutations of mtDNA at the specific locus. Back- from GNU Scientific Library (Matsumoto and Nishimura, mutations can be safely ignored, as the rate of these 1998). events is assumed to be extremely low. Given the mutation rate µ and mitochondrial state of a cell m, probability for the cell with M − m wild-type mitochondria a. Mitosis to accumulate l new mutants in a single mutation event follows the binomial probability distribution Following the descriptions of random processes described by Hadjivasiliou et al. (2012) we implement mi- M − m p (l; m, M) = µl(1 − µ)M−m−l. (A3) tosis in somatic cells by first duplicating nuclear and mi- mut l tochondrial genomes, and then segregating mitochondria into two daughter cells according to simple random sampling without replacement. The probability to give birth d. Selection to a daughter cell with k ∈ {0, 1, . . . , m} mutant mitochondria starting with the cell in mitochondrial state m After the vegetative growth stage the population con- is therefore given by sists of N mature organisms. Probability for a given individual to be selected for reproduction is proportional to 2m 2(M − m) its fitness ϕ, which in turns depends on the number and k M − k distribution of mitochondrial mutations in tissues and p (k; m, M) = . (A1) mi 2M cells, as well as shapes of viability functions for a single M cell ω = f(m), tissue v = f(ω¯) and organism ϕ = f(¯v), where ω¯ and ¯v are collections of cell and tissue fitness Both resultant cells inherit an identical copy of nuclear values. genome. Selection is implemented by a simple weighted sampling with replacement. Probability to select an individual i in the selection event can therefore be expressed b. Meiosis as ϕ In the population of haploid individuals, meiosis occurs p (i) = i . (A4) sel PN after the fusion of haploid gametes. Diploid zygote first j=1 ϕj duplicates its mitochondrial and nuclear genomes, and subsequently undergoes two subdivisions to form a new generation of haploid individuals. Divisions are imple- e. Fusions mented by sampling without replacement, that is, prob- The population of selected individuals releases haploid ability to end up with a daughter cell with k mutant gametes into a common pool, where they fuse randomly (but still following the rules of mating types). Depending on the mitochondrial inheritance allele, mtDNA is inherited from both parental gametes (a1 × a2 fusions) or only from the carrier of A1 allele (A1 ×a2 fusions). In the case 16 of uniparental inheritance of organelles, 2M mitochon- ACKNOWLEDGMENTS dria are selected from the active (A1) gamete carrying M mitochondria via simple sampling with replacement. The author thanks his advisers N. Lane, A. Pomi- Mitochondria of the passive gamete are discarded. The ankowski and Z. Hadjivasiliou for inspiring weekly dis- number of mutant mitochondria k in the diploid zygote, cussions, ideas and interpretations of the findings in the assuming that A1 carrier is in mitochondrial state m, fol- light of natural systems and real evolutionary events. We lows binomial probability density function acknowledge the extensive use of computational resources at UCL’s CoMPLEX for our demanding numerical cal- 2M m k M − m2M−k culations. p (k; m, M) = . (A5) inh k M M

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