Evolution in (Brownian) space:

a model for the origin of the bacterial flagellum

By Nicholas Joseph Matzke

(Draft article subject to further modification)

E-mail address: nickmatzkeATyahoo.com
(note obvious anti-spam modification)

Abstract: The bacterial flagellum is an example of a complex molecular system with multiple components required for proper function. The origin of such systems is sometimes puzzling, because it is difficult to see how selection could preserve only a subset of required components. Previous work (Thornhill and Ussery, 2000, A classification of possible routes of Darwinian evolution. J Theor Biol. 203 (2), 111-116) has outlined the general pathways by which Darwinian mechanisms can produce such systems. However, published attempts to explain flagellar origins suffer from vagueness and are inconsistent with recent discoveries and the constraints imposed by Brownian motion. A new model is proposed based on two major arguments. First, analysis of dispersal at low Reynolds numbers indicates that even very crude motility can be beneficial for large bacteria. Second, homologies between flagellar and nonflagellar proteins suggest ancestral systems with functions other than motility. The model consists of six major stages: export apparatus, secretion system, adhesion system, pilus, undirected motility, and taxis-enabled motility. The selectability of each stage is documented using analogies with present-day systems. Conclusions include: (1) There is a strong possibility, previously unrecognized, of further homologies between the type III export apparatus and F₁F₀-ATP synthetase. (2) Much of the flagellum's complexity evolved after crude motility was in place, via internal gene duplications and subfunctionalization. (3) Only one major system-level change of function, and four minor shifts of function, need be invoked to explain the origin of the flagellum; this involves five subsystem-level cooption events. (4) The transition between each stage is bridgeable by the evolution of a single new binding site, coupling two pre-existing subsystems, followed by coevolutionary optimization of components. Therefore, like the eye contemplated by Darwin, careful analysis shows that there are no major obstacles to gradual evolution of the flagellum.

Keywords: dispersal, flagellum, evolution, complexity, motility

Contents:

1. Introduction
• 1.1. A complex contrivance
• 1.2. An evolutionary puzzle
• 1.4. Constructing and testing evolutionary models
2. Background
• 2.1. Modern flagella
• 2.2. Previous attempts to explain flagellar origins
• 2.2.1. Short discussions
• 2.2.2. Cavalier-Smith (1987)
• 2.2.3. Rizzotti (2000)
3. The Model
• 3.1. Phylogenetic context and assumed starting organism
• 3.2. Starting point: protein export system
• 3.2.1. Type III secretion systems
• 3.2.2. Are nonflagellar type III secretion systems derived from flagella?
• 3.2.3. An ancestral type III secretion system is plausible
• 3.2.4. The origin of a primitive type III export system
• 3.2.5. The relationship between type III export and the F₁F₀-ATP synthetase
• 3.3. Type III secretion system
• 3.4. Origin of a type III pilus
• 3.4.1. Filament-first hypothesis
• 3.4.2. Cap-first hypothesis
• 3.4.3. Modified filament-first hypothesis
• 3.4.4. Improvements on the type III pilus
• 3.5. The evolution of flagella
• 3.5.1. The selective advantage of undirected motility
• 3.5.2. Primitive flagella
• 3.5.3. Loss of outer membrane secretin
• 3.5.4. Refinements
• 3.5.5. Chemotaxis and switching
• 3.5.6. Hook and additional axial components
• 3.5.7. Modern variations
4. Conclusions
• 4.1. Evaluating the model
• 4.2. The evolution of other microbial motility systems
• 4.3. The construction of evolutionary models
5. Acknowledgements
6. References
7. Figure legends and tables

1. Introduction

1.1. A complex contrivance

The bacterial flagellum is one of the most striking devices found in biology. In Escherichia coli the flagellum is about 10 μm long, but the helical filament is only 20 nm wide and the basal body about 45 nm wide. The flagellum is made up of approximately 20 major protein parts with another 20-30 proteins with roles in construction and taxis (Berg, 2003; Macnab, 2003). Many but not all of these proteins are required for assembly and function, with modest variation between species. Over several decades, thousands of papers have gradually elucidated the structure, construction, and detailed workings of the flagellum. The conclusions have often been surprising. Berg and Anderson (1973) made the first convincing case that the flagellar filament was powered by a rotary motor. This hypothesis was dramatically confirmed when flagellar filaments were attached to coverslips and the rotation of cells was directly observed (Silverman and Simon, 1974). The energy source for the motor is proton motive force rather than ATP (Manson et al., 1977). The flagellar filament is assembled from the inside out, with flagellin monomers added at the distal tip after export through a hollow channel inside the flagellar filament (Emerson et al., 1970). The flagella of E. coli rotate bidirectionally at about 100 Hz, propelling the rod-shaped cell (dimensions 1x2 μm) approximately 30 μm/sec. The flagella of other species, powered by sodium ions rather than hydrogen ions, can rotate at over 1500 Hz and move cells at speeds of several hundred μm/sec. The efficiency of energy conversion from ion gradient to rotation may approach 100% (DeRosier, 1998). The bacterial flagellum is now one of the best understood molecular complexes, although numerous detailed questions remain concerning the function of various minor components and the exact mechanism of torque generation. However, the origins of this remarkable device have hardly been examined. This article will propose a detailed model for the evolutionary origin of the bacterial flagellum, along with an assessment of the available evidence and proposal of further tests. That the time is ripe for a serious consideration of this question is discussed below.

1.2. An evolutionary puzzle

Biologists find it almost inescapable to compare the bacterial flagellum to human designs: "More so than other structures, the bacterial flagellum resembles a human machine" (DeRosier, 1998). The impression is heightened by electron micrograph images (Figure 1) reminiscent of a engine turbine (e.g., Whitesides, 2001), and the scientific literature on the flagellum is filled with analogies to human-designed motors. There is no shortage of authorities willing to express mystification on the question of the evolutionary origin of flagella. In a 1978 review, Macnab concluded,

As a final comment, one can only marvel at the intricacy, in a simple bacterium, of the total motor and sensory system which has been the subject of this review and remark that our concept of evolution by selective advantage must surely be an oversimplification. What advantage could derive, for example, from a "preflagellum" (meaning a subset of its components), and yet what is the probability of "simultaneous" development of the organelle at a level where it becomes advantageous?" (Macnab, 1978).

The basic puzzle is that the flagellum is made up of dozens of protein components, and deletion experiments show that the flagellum will not assemble and/or function if any one of these components is removed (with some exceptions). How, then, could this system emerge in a gradual evolutionary fashion, if function is only achieved when all of the required parts are available?

1.3. Theory: the evolution of systems with multiple required components

The standard answer to this question was put forward by Darwin. Mivart (1871) argued that the "incipient stages of useful structures" could not have evolved gradually by variation and natural selection, because the intermediate stages of complex systems would have been nonfunctional. Darwin replied in the 6^th edition of Origin of Species (Darwin, 1872) by emphasizing the importance of change of function in evolution. Although Darwin's most famous discussion of the evolution of a complex system, the eye, was an example of massive improvement of function from a rudimentary ancestor (Salvini-Plawen and Mayr, 1977; Nilsson and Pelger, 1994), Darwin gave equal weight to examples of functional shift in evolution. These included the complex reproductive devices of orchids and barnacles, groups with which he was particularly familiar (Darwin, 1851, 1854, 1862). Intricate multi-component systems such as these could not have originated in a gradual, linear fashion, but if systems and components underwent functional shift, then intermediates could have been selected for a function different from the final one. The equal importance of improvement of function and change of function in understanding the evolutionary origin of novel complex systems has been similarly emphasized by later workers (Maynard Smith, 1975; Mayr, 1976). Recent studies give cooption of structures a key role in the origin of feathers (Prum and Brush, 2002), and novel organs (Pellmyr and Krenn, 2002); Mayr (1976) gives many other examples.

Do these common insights from classical, organismal evolutionary biology help us to understand the solution to the puzzle Macnab put forward regarding the origin of flagellum? Cooption at the molecular level is in fact as well-documented at it is at the macroscopic level (Ganfornina and Sanchez, 1999; Thornhill and Ussery, 2000; True and Carroll, 2002). It has been implicated in origin of ancient multi-component molecular systems such as the Krebs cycle (Melendez-Hevia et al., 1996) as well as the rapid origin of multi-component catabolic pathways for abiotic toxins that humans have recently introduced into the environment, such as pentachlorophenol (Anandarajah et al., 2000; Copley, 2000), atrazine (de Souza et al., 1998; Sadowsky et al., 1998; Seffernick and Wackett, 2001), and 2,4-dinitrotoluene (Johnson et al., 2002); many other cases of catabolic pathway evolution exist (Mortlock, 1992). All of these systems absolutely require multiple protein species for proper function. Even for some molecular systems equaling the flagellum in complexity, reasonably detailed reconstructions of evolutionary origins exist. Generally these are available for systems which originated relatively recently in geological history, which are well-studied due to medical importance, and where phylogeny is relatively well resolved; examples include the vertebrate blood-clotting cascade (Doolittle and Feng, 1987; Hanumanthaiah et al., 2002; Jiang and Doolittle, 2003) and the vertebrate immune system (Muller et al., 1999; Pasquier and Litman, 2000).

Thornhill and Ussery (2000) summarized the general pathways by which systems with multiple required components may evolve. They delineate three gradual routes to such systems: parallel direct evolution (coevolution of components), elimination of functional redundancy ("scaffolding," the loss of once necessary but now unnecessary components) and adoption from a different function ("cooption," functional shift of components); a fourth route, serial direct evolution (change along a single axis), could not produce multiple-components-required systems. However, Thornhill and Ussery's analysis did not distinguish between the various levels of biological organization at which these pathways might operate. The above-cited literature on the evolution of complex molecular systems indicates that complex systems usually originate by a key shift in function of an ancestral system, followed by an intensive period of improvement of the originally crudely functioning design. At the level of the system, cooption is usually the key event in the origin of the modern system with the function of interest. However, a great deal of the complexity in terms of numbers of parts is added to the system after origination. These accessory parts get added by duplication and cooption of novel genes (for reviews of gene duplication in evolution, see Long, 2001; Chothia et al., 2003; Hooper and Berg, 2003) and/or duplication and subfunctionalization (Force et al., 1999) of genes already involved in the crudely-functioning system. Cooption of whole subsystems, linking them to the "core" system, may also occur.

Therefore, improvement of function at the system level might be implemented by cooption at the level of a protein or subsystem. Change of function at the system level might occur without any lower level cooption of new components. Thornhill and Ussery's four routes can be reduced to the two major pathways proposed by Darwin: improvement of current function (optimization) and shift of function (cooption). Cooption remains its own category, while the other three routes (serial direct evolution, parallel direct evolution, and elimination of functional redundancy) can be considered as three versions of functional improvement, with the lower-level components undergoing optimization, coevolutionary optimization, or loss, respectively. This conceptual framework is basically equivalent to the patchwork model for the evolution of metabolic pathways (Melendez-Hevia et al., 1996; Copley, 2000), where components are recruited from diverse sources and functional improvement or functional shift might occur at any organizational level, e.g. system, subsystem, protein, or protein domain.

1.4. Constructing and testing evolutionary models

In order to explain the origin of a specific system such as the flagellum, the general theory discussed above must be combined with the available evidence in order to produce a detailed, testable model. Detail in evolutionary scenarios makes them more testable, not less: "Specifying transitional stages in considerable detail is not unwarranted speculation, but a way of making the ideas sufficiently explicit to be more easily tested and rigorously evaluated" (Cavalier-Smith, 2001b). Obviously "detailed" cannot mean that every mutation and substitution event be recorded for events that occurred billions of years ago this is impossible. A detailed evolutionary model should reduce a puzzling event like the origin of the flagellum into a series of events that occur by well-understood processes.

In an ideal model, the origin of every protein component will fulfill three criteria. First, a putative ancestral protein with a different function (a homolog that can reasonably be suspected to precede the flagellum) should be identified. Second, the cooption of the protein should occur by a reasonably probable mutation event -- e.g., a mutation produces a single new binding site, which initially functions crudely but which can then undergo standard microevolutionary optimization. Third, the selective regime favoring retention of the coopted protein should be identified. Each of these three criteria encourages further testing against new data. Hypothesized homologies can be assessed by new data, e.g., structures. The plausibility of mutational steps can be investigated by examination of similar mutations observed today; and the selection forces invoked can be assessed by study of analogies and by mathematical modeling. Furthermore, an evolutionary model might have testable implications for other fields: for example, if a biological system is derived from a homologous system, similarities in mechanism between the two systems would be suspected. The fact that we do not have all of the data that we would like, and that uncertainty is high, are not problems unique to evolutionary models; rather, these problems are commonplace in any advancing science. For example, many contradictory models have been published for the mechanism of motor action in the flagellum, and most (or all) of them must be wrong, but this has not stopped anyone from proposing new models (Schmitt, 2003). Science is advanced by proposing and testing hypotheses, not by declaring questions unsolvable.

2. Background

2.1. Modern flagella

The canonical flagellum of E. coli is shown in Figure 2. Descriptions of the structural components are given in Table 1. Cytoplasmic components involved in regulation and assembly, as well as the chemotaxis components, are listed in Table 2. Excellent overviews of flagellar function and assembly are available elsewhere (Berg, 2003; Macnab, 2003) and so will not be discussed further here.

2.2. Previous attempts to explain flagellar origins

2.2.1. Short discussions

Occasional examples of very general suggestions about the evolutionary origin of flagella can be found in the literature, for example in discussions of how various aspects of the chemotaxis system are optimized (Berry, 2000); in the suggestion that prokaryote flagella may have been a relatively late invention, after biofilms and microbial mats had become well-developed and crowding on surface habitats became a problem (Stoodley et al., 2002); or in the alleged common ancestry of archaeal and bacterial flagella (Harshey and Toguchi, 1996). Archaeal and bacterial flagella were indeed once thought to be homologous (Jones et al., 1987), but they are actually totally distinct motility systems (Jarrell et al., 1996; Faguy and Jarrell, 1999; Thomas et al., 2001). Although both kinds of flagella rotate and are superficially similar, archaeal flagella are fundamentally different in many respects (Table 3). In archaeal flagella, the filaments are thinner, lack a central channel, and subunits are added from the base rather than the tip. Forward movement is typically attained by clockwise rather than counterclockwise motion. Additionally, archaeal flagella are probably powered by ATP rather than protonmotive force (suggested by homologies of FlaI to PilT/U (Jarrell et al., 1999; Thomas et al., 2001; Merz and Forest, 2002, although the literature is contradictory: Bardy et al. (2003) assert that archaeal flagella use protonmotive force, but cite no supporting evidence). Finally, the homologies of the two flagella to nonflagellar secretion systems are different. The bacterial and archaeal flagella are therefore a classic case of analogy, not homology (Faguy et al., 1994; Jarrell et al., 1996; Bayley and Jarrell, 1998; Faguy and Jarrell, 1999; Thomas et al., 2001; Thomas et al., 2002; Bardy et al., 2003). However, the misperception persists in the assumption that the flagella (Harshey and Toguchi, 1996; Campos-Garcia et al., 2000; Rizzotti, 2000) or their basal bodies (Cavalier-Smith, 2002a, 2002c) are homologous. On the other hand, the chemotaxis systems are indeed homologous, and are shared with nonflagellar motility systems as well (Faguy and Jarrell, 1999; Koretke et al., 2000).

A slightly more detailed attempt at explaining the origin of the bacterial flagellum was made by de Duve (1995), who apparently got the bacterial flagellum confused with the completely different eukaryotic cilium (also known as the eukaryotic flagellum or undulipodium in an interminable terminological dispute; see Corliss, 1980; Margulis, 1980; Cavalier-Smith, 1982). He suggested that the flagellum, which he acknowledges is rotary, was somehow descended from a simpler ATP-powered filament-bending motor. In a more reasonable vein, de Duve then gave a brief scenario for the gradual origin of chemotactic behavior from random swimming, but was again puzzling in postulating that essentially fully functional, bidirectional-switching flagella with specific positioning on the cell surface existed before the signal transduction system was coupled to the flagellum. What the purpose of switching would be without a chemotaxis system was not explained. De Duve furthermore stated that these well-developed but non-chemotactic flagella gave "little advantage" until they were chemotactically enabled, leaving unexplained the selective reason for the origin of the whole nearly-complete system in the first place.

Finally, Goodenough (1998; 2002) offers a short account deriving a flagellum from a proton-transducing membrane channel. She postulates that a coopted protein increased the efficiency of proton transport, and rotated the channel as a by-product. Later binding of a filament to the outside of this rotating channel produced primitive motility which increased food gathering ability. However, the original function of proton transport (which, uncoupled to another process, would simply de-energize the cytoplasmic membrane) is not specified. In her 2002 account Goodenough suggested that a fibrous protein binding to the F₁F₀-ATP synthetase produced the proto-flagellum. Presumably she meant that the proto-filament would bind to the distal side of a c-subunit of F₀. As recent work indicates that F₀-c and F₁-εγ rotate inside the F₀-ab and F₁-αβδ complex (Weber and Senior, 2003), Goodenough's suggestion is not immediately impossible, but suffers difficulties similar to those discussed for Rizzotti (2000), below.

2.2.2. Cavalier-Smith (1987)

Cavalier-Smith is one of the few who has proposed detailed hypotheses for the origin of many fundamental features of eukaryotes and prokaryotes (Cavalier-Smith, 1987a, 1987b, 2001a, 2002b, 2002a, 2002c). He bases his work on a refreshingly clearly-stated philosophy for reconstructing the origin of complex systems, advocating a holistic approach considering environment, organism, mutation, and selection all together and emphasizing testability (Cavalier-Smith, 2001a). Although Cavalier-Smith has addressed the origin of the eukaryotic cilium on several occasions (Cavalier-Smith, 1978, 1982, 1987b, 2002b), Cavalier-Smith's only treatment of the origin of the bacterial flagellum is found in a 1987 article (Cavalier-Smith, 1987a). He makes two suggestions: first, that a mutant version of an outer membrane protein pore formed a tubular polymer extending through the outer membrane into the extracellular medium. Linking this to proton-conducting proteins in the cytoplasmic membrane provided the primitive motor. In this scheme, spirochete axial filaments were derived from regular flagella. His second suggestion was that flagella evolved from gliding motility systems, which are also widespread and powered by protonmotive force. Some early models of gliding motility postulated a spirochete-like mechanism, with rotating filaments in the periplasmic space, and on this basis spirochetes might represent a transitional stage. Motility would develop from rotating filaments first used just to stir the fluid in the periplasmic space and increase diffusion of nutrients. Either way, the rotary mechanism existed from the beginning of the evolutionary sequence. On either scenario, the first crude motility function would have been selected for because it increased random dispersal, useful in overcrowded regions depleted in nutrients. Much of the complexity could have post-dated the original crudely functioning motility.

Cavalier-Smith was hampered by the relatively primitive state of knowledge at the time, and he conceded that the actual evolutionary process must have been much more complicated than his suggestions. The linkage between the filament and motor is very complex, mediated by about ten proteins, and the filament subunits are secreted through the base of the flagellum via a type III export pathway, rather than via a type II pathway as might be expected for a protein derived from an outer membrane pore; type III virulence systems do utilize an outer membrane secretin secreted by the type II pathway, and the flagella P- and L-ring proteins FlgI and FlgH are similarly secreted via the type II pathway (Macnab, 2003). A secretin might therefore be more likely posited as the source for FlgH; this will be discussed in more detail below.

Regarding the postulated homology between gliding motility and the axial filaments of spirochetes, today it is apparent that gliding motility is not a matter of rotating periplasmic filaments. Two mechanisms for gliding motility have been clearly identified (Merz and Forest, 2002; Bardy et al., 2003). First, the social gliding of Myxococcus xanthus occurs via retraction of type IV pili, sometimes also called twitching motility (Merz and Forest, 2002). Second, the adventurous motility of M. xanthus is driven by the secretion of a polysaccharide gel (slime) via the junctional pore complex; a similar complex is found in gliding cyanobacteria. Gliding via the ratchet structure of Cytophaga and Flavobacterium is more mysterious, but may also involve slime secretion (Bardy et al., 2003). These latter forms of gliding motility inspired the comparison between flagella and gliding motility as they are powered by protonmotive force, and beads attached to the cell surface of Cytophaga will rotate (Eisenbach, 2000). Thus, it is occasionally suggested (Cavalier-Smith, 2002a), even in textbooks (e.g. Campbell, 1993), that flagella and gliding motility are homologous, and the gliding motility apparatus may be some version of the flagellum basal body without the flagellar filament. As our understanding of slime-related gliding motility is still limited (the relevant genes are still being identified, much less detailed mechanism or structure), the possibility of any connection between type III protein secretion and polysaccharide secretion is difficult to evaluate. However, the study of gliding motility bears close watching: the recent discovery of homology between M. xanthus gliding motility proteins AglS/AglV to TolR and of AglR/AglX to TolQ (Youderian et al., 2003) which are in turn homologs of the flagellar motor proteins MotA and MotB (Cascales et al., 2001) suggests that there may be a common mechanism for coupling proton flow to motility. If the general similarity between the junctional pore complex and type III secretion systems (Spormann, 1999; Merz and Forest, 2002) turns out to be more than skin deep, then the common descent of gliding motility and flagella from an ancestral motility organelle will have to be seriously considered. Cavalier-Smith's suggestion that stirring the periplasmic fluid may have been a precursor to primitive motility is similar to Rizzotti's main suggestion and will be discussed in the next section.

2.2.3. Rizzotti (2000)

The only major recent attempt at explaining the origin of the flagellum is that of Rizzotti (2000), which, like Goodenough, proposes that the flagellum was derived from the F₁F₀ ATP synthetase. The initial appeal of this hypothesis derives from the spate of recent comparisons between the flagellum and ATP synthetase as proton-driven, rotary motors (Block, 1997; Boyer, 1997; Khan, 1997; Sabbert and Junge, 1997; Berg, 1998; Oplatka, 1998a, 1998b; Berry, 2000; Walz and Caplan, 2002), sometimes leading to the suggestion of homology (Oster and Wang, 2003). These comparisons go back at least to Cox et al.'s (1984) proposal that the ATP synthetase had a rotary mechanism, and continued through the testing and refinement of this hypothesis (Mitchell, 1985; Sabbert and Junge, 1997; Weber and Senior, 2003), followed by the conclusive demonstration of rotation by direct observation of an actin filament tethered to the gamma subunit of F₁-ATPase (Noji et al., 1997). A relationship between the F₁F₀ ATP synthetase and the flagellum is further suggested by homology between the flagellar ATPase FliI and the β subunit of F₁-ATPase, indicated by ~30% sequence similarity (Albertini et al., 1991; Vogler et al., 1991). The α and β subunit ATP synthetase subunits are themselves paralogous, with only the β subunit retaining catalytic activity (Gogarten et al., 1989; Gogarten and Kibak, 1992).

In a creative scenario (Figure 3), Rizzotti imagined that an accidental insertion in the middle of the F₁-γ subunit created a short filament outside the cytoplasmic membrane, between the membrane and the cell wall. As the synthetase subunits rotated, this protofilament served to mix the nearby fluid, increasing the diffusion of molecules in and out of the cell. This provided sufficient selective benefit to retain the mutation. Production of a more sophisticated mixing instrument occurred via duplication and modification of the mutant γ subunit, so that branches of the filament extended above the cell wall. In the process, the ε and δ subunits were lost, along with ATPase activity, resulting in a proton-powered stirring mechanism with incipient motility function. From here, a process of optimization ensued. Selection first favored random motion of the cell that further improved nearby fluid mixing and diffusion. More powerful motility followed by extension of the filament and by duplications of the proton-transmitting proteins of the stator (in this scenario, derived from the c subunit of the F₀ structure). The F₁-αβ complex apparently became the rotor inside the stator ring. Rizzotti concluded by discussing a number of other steps that must have happened along the way, although the order is not specified. However, it seems that he considered the origin of the export apparatus a relatively late event. Rizzotti hypothesized that once the central cavity became large enough, a secretion complex (presumably a type III export apparatus already functioning elsewhere) was patched in at the base of the rotor, allowing the secretion of a more complex filament.

Rizzotti argued that bacteria with a single membrane were simpler and therefore probably ancestral to gram-negative bacteria with both an inner and outer membrane. He hypothesized that the outer membrane arose as an alimentary adaptation from extensions of the inner membrane. The L- and P-rings arose as the developing outer membrane encroached on the flagellum (gram positive bacteria, lacking outer membranes, have no requirement for the L- and P-rings altogether). Rizzotti discounted the alternative scenario, whereby the flagellum arose in a bacterium already possessing a double membrane, because he deemed the simultaneous origin of the rings and filament too difficult.

This scenario is considerably more detailed than any other available, but remains vague on the specific origin of almost all of the proteins that make up the flagellum. Although Rizzotti does make use of some interesting similarities between the flagellum and ATP synthetase, and he is able to come up with a proposal that includes rotary motion from the beginning, there are major flaws which shall be discussed shortly. Before the critique, however, it is worth noting that Rizzotti's scenario has been cited by Cavalier-Smith (2001a) as well as others (Rosenhouse, 2002), apparently for lack of anything better.

Rizzotti's suggestion that stirring might be a primitive function of a proto-flagellum is intuitively appealing, but intuition is a poor guide to life at a low Reynolds number (Purcell, 1977; Vogel, 1994; Purcell, 1997). Bacteria live in a world dominated by Brownian motion, where viscous forces overwhelm inertia and small molecules spread much faster by diffusion than by bulk movement of fluid. The scale at which moving fluid (stirring) or moving through fluid (swimming) will increase diffusion into the cell is determined by comparing the time for transport by diffusion (t_d) versus the time for transport by bulk flow such as stirring (t_s) (Purcell, 1977). For diffusion, the average time t_d for transport of a particle a distance l, with diffusion coefficient D is (Berg, 1993):

(1)

while the corresponding time for bulk flow transport via stirring (t_s) is approximately (Purcell, 1977):

(2)

that is, the distance l divided by the fluid velocity v induced by stirring. Stirring "works" only if the transport time using stirring is less than the transport time from simple diffusion:

(3)

(4)

(5)

The ratio in equation gives the Péclet number, Pé, which must be greater than unity for bulk flow to have substantial impact on diffusion (Vogel, 1994). For a typical small molecule (e.g. sucrose) in water, D=10^-10 m²s^‑1. For a typical-length bacterium (1 μm) moving fluid past with the swimming velocity of a typical fully functional flagellum (30 μm/s), P = 0.06 << 1 (Vogel, 1994). For Rizzotti's primitive stirrer, P would be even lower. As Purcell (1977) noted, in the world of low Reynolds number, "stirring isn't any good". Bacteria that do induce currents for their benefit (e.g., Thar and Kuhl, 2002) succeed because of the large number of bacteria cooperating in the effort, in effect increasing body size. Another postulated function of primitive motility, swimming for the sake of running into more molecules, also does not work: Purcell calculated that a bacterium would have to swim 700 μm/sec in order to gather only 10% more food molecules. Thus, if diffusion of molecules into the cell is the only matter of concern, a bacterium will do just as well by sitting still as it will by stirring or swimming. The reason bacteria swim is not to increase diffusion but to find locations with a higher concentration of nutrient molecules (Purcell, 1977; Berg, 1993; Vogel, 1994). Purcell's argument breaks down in situations where the uptake rate parameter, a, representing the fraction of available molecules being consumed each second, is greater than 1 s^-1. However, a typical value for a is 0.01, where uptake is considered negligible (Dillon et al., 1995; Mitchell, 2002). Thus, fundamental physical considerations make the hypothesized stirring filament an unlikely intermediate.

Additional difficulties with Rizzotti's model exist. While it is unrealistic to expect sequence similarity to give evidence for the ancestry of every component of the 3+ billion year old flagellum, considering the time lapse and large nature of some of the changes that must be postulated on any scenario, a scenario certainly should not contradict those homologies that have been identified. The Rizzotti scenario (Figure 3) implies homology between the synthetase F₁-αβ subunits and FliF/FliG (the flagellar rotor), but the homology that inspired the scenario is between F₁-αβ and FliI (the ATPase that energizes export of rod, hook, and filament). Similarly, Rizzotti (2000) implies that the F₀-c subunit is homologous with the flagellar motor proteins MotAB, but sequence homology has instead been discovered between MotAB and a phylogenetically widespread family of proteins that couple protonmotive force to diverse membrane transport processes. These homologs, namely ExbBD (Kojima and Blair, 2001) and TolQR (Cascales et al., 2001), provide a simpler and much more direct ancestor for MotAB. The homologies could be explained by invoking additional independent cooption events, but this would require a rather more complex scenario than that presented by Rizzotti.

As Rizzotti's scenario fails on the twin tests of homology and a simple model of stirring at a low Reynolds number, it is now time to see if Rizzotti can be improved upon. It should be noted that although published proposals about flagellar evolution are very limited, the topic is a popular one as the flagellum is the icon of the antievolutionary "Intelligent Design" movement. Therefore several of the ideas proposed here have been previously raised in informal debates about flagellar evolution. Musgrave (2004) reviews this aspect of the debate in detail, and proposes a model that is similar in outline to that presented here, although his account is more general.

3. The Model

3.1. Phylogenetic context and assumed starting organism

The paradigm for prokaryote phylogeny, if there is one, is the universal rRNA tree. This shows a number of widely separated bacterial lineages, with archaea and eukaryotes separated from them all by a very long branch. This tree is unrooted, and practically every possible rooting has been proposed in the literature somewhere. As these are the most remote and difficult phylogenetic events it is possible to study, and as there is by definition no outgroup to life in general, the debate can be expected to continue for some time. For current purposes the most important point is that flagella are widespread across the bacterial phylogenetic tree, with losses in various taxa and no clearly primit