Technical Report CoSBi 15/2007
Chemotaxis mediated by non-adaptive
dynamics
Richard A. Goldstein
Mathematical Biology, National Institute for Medical Research Mill Hill, London, UK
richard.goldstein@nimr.mrc.ac.uk
Orkun S. Soyer
The Microsoft Research - University of Trento Centre for Computational and Systems Biology
soyer@cosbi.eu
This is the preliminary version of a paper that will appear in PLoS Computational Biology
Abstract
Chemotaxis is the ability of bacteria to locate high attractant sources in the environment. The extensive knowledge gained from the pathway in the model organism Escherichia coli shows that adaptation to stimuli is a hallmark underlying chemotaxis. Studies on certain mutant strains and other bacterial species, however, indicate that some form of chemotaxis could also be achieved without adaptation. It is not clear how efficient such chemotaxis is, how it could be mediated, and how widespread it is among different bacterial species.
In order to explore alternative pathway structures and dynamics that can underlie chemotaxis, we employ an evolutionary approach. This approach starts with a population of bacteria that move in a virtual environment based on the dynamics of simple pathways they harbour. As mutations lead to changes in pathway structure and dynamics, bacteria with better ability to localize with high attractant sources gain a selective advantage. We find that chemotaxis via non-adaptive dynamics evolves consistently under different model assumptions and environments. These dynamics directly couple tumbling probability of the cell to increasing attractant levels. Further analyses of evolved pathway structures show that this alternative behaviour can be mediated with as few as two components.
The non-adaptive mechanisms mediating chemotaxis provide an explanation for experimental observations made in mutant strains of E. coli and in wild type Rhodobacter sphaeroides and that could not be explained with existing knowledge. These mechanisms could allow a straightforward link between cell metabolism and chemotaxis. Furthermore, they could have acted as the origin of the conventional chemotaxis involving adaptation.
INTRODUCTION
Bacterial chemotaxis and the pathways mediating it are a model system for studying the molecular basis of behaviour. More than 30 years after the first studies of this behaviour in Escherichia coli [1,2], we now have extensive knowledge of the underlying pathway in this species [3,4]. Briefly, E. coli swims in a forward direction (undergoing some degree of rotational diffusion) when one or more of the reversible motor proteins on its outer membrane rotate counter-clockwise (CCW) and the attached flagella intertwine to form an effective propeller. When the motors reverse and rotate clockwise (CW), the flagella disassociate and cause the bacterium to tumble, resulting in a new swimming direction. The switching frequency of the motor is coupled to receptor activity by a series of proteins constituting a signalling pathway. With increasing attractant levels, the excitatory branch of the pathway causes direct suppression of CW rotation and tumbling, while the adaptation branch causes the cell to resume its original tumbling levels at constant attractant concentrations independently of this concentration level. The former branch involves the response regulator CheY, which in its phosphorylated form binds the motor and increases the probability of CW rotation. The adaptation is achieved via control of receptor methylation, and hence receptor sensitivity, through the proteins CheR and CheB. The combination of these two branches results in the tumbling frequency approximately following a time-derivative of the attractant concentration [5]. Adaptation is the hallmark of this response, allowing bacteria to perform temporal comparisons of attractant with high sensitivity and achieve proper chemotaxis [5-9]. In fact,
perfect adaptation is the most robust feature of the system in face of fluctuations in protein concentrations [10].
While the importance of adaptation in proper chemotaxis is well established, there are several indications that some form of chemotaxis could be possible without it. The earliest of these came from a mutant strain of E. coli that lacks CheR and CheB but is still capable of chemotaxis [11]. This ‘anomalous’ chemotaxis was suggested to result from random diffusion coupled with partial adaptation [12]. While there are possible mechanisms that could allow such receptor-independent adaptation [13,14], their relation to the chemotaxis seen in CheR-CheB mutant was not explored. Another observation involves the ‘gutted’ strain of E. coli, which lacks all proteins of the chemotaxis pathway except CheY [15]. While the dynamics mediating chemotaxis in this mutant is unknown, involvement of adaptation is highly unlikely. The most convincing case for non-adaptive chemotaxis comes from studies on Rhodobacter sphaeroides. In this species, adaptation to persisting stimuli seems to work much slower or not at all [16]. Interestingly, there are other observations from R. sphaeroides that cannot be explained by the knowledge gained from the E. coli system; cells grown under aerobic conditions give an ‘inverted’ response with limited adaptation [17] and chemotaxis to certain attractants requires transporters [18]. Currently, we lack detailed understanding of the molecular systems mediating chemotaxis in this species, however, it is known that it has a large number of proteins involved in this chemotaxic behaviour and that these are arranged into several distinct pathways [19].
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have a role sphaeroides at mechanism -day bacteria olution and different o study th e use virtua two-dimens pre-determin ese bacteria hway consis other’s ac o kinases an These protein e local attrac when activa g its direction onary simula h of which c e initially no xplore the en g of a certai dicate existen taxis, some mics. The exa
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cate more tim the entire po tant source is to swim random activated updated, time step activated selected tant they re is a lters the hway. To couple vel (i.e. evel (i.e. f fitness lutionary of four improves early, the teria are emotaxis. me spent ironment bacterial attractant lize with re. Such structure co. The bacteria. sitions of a fitness contour me spent opulation s fixed at
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as long as rial tumblin ria to spend swim stra her words, th hemotaxis st oit an attracta not put too m
olutionary sim f 2 to 5 prot ominant one ive vs. non-a hosphorylated model present concentration y simulation d he cartoon rep an attractant 00 and remove amics (kineti Material). At e concentrat d the bacteriu ure 2). Whe fector is rapi this is pres ng. Such pa more time in aight when he pathway trategy, wher ant source w much effort mulations re teins, this m e. adaptive path d CheY conce ted in [22] and
for the most described in F presentation o t of arbitrary ed at time 300 ic parameter steady stat tion of activ um mostly sw en the bacte idly activated sent, resultin athway dyna n regions of n the attra dynamics le reby bacteria when it encou in searchin epeated five t mechanism al hway dynam entration (top) d the time cou frequent path Figure 1 (botto of this pathway concentratio 0. rs are te, in vated wims erium d and ng in amics f high actant ad to a can unters g for times lways o M t a o c t r i t t b t u d e c p r e a T m c i e m w b l g s r i s p s p i s r ‘ i p w a a s g mics. ), as urse way om). y. In n is Using a s of bacteria a Methods). Th the present accumulating of the attrac chemotaxis c that does no results in increasing att to E. coli, tumbling pro by rapid adap There are the chemotax underlined b dynamics. F environmenta chemotaxis particular, th reduce the evolutionary adaptive pa Thirdly, ther metabolism communicati included in th evolution of To expl mechanisms we ran sim background location of generation ( suggested as response to internal para simulations pathways w simulations, pathways w inverted resp showed lim response. Th ‘normal’ res increasing a probability. T were depend attractants re and dynamic simulations a given in Supp simple mode as mediated his model sh ted dynami g proportiona ctant. In oth can be achiev ot display a increases i tractant. Bot where the obability wit ptation [5] (s e a number o xis pathways by an ‘inver Firstly, it al situations mediated v he consistenc need for processes as athways m re could be of attra ion, and mu he model an chemotaxis m lore the e in more rea mulations attractant d bacteria we (see Metho s a method fluctuations ameters [23] lead only with adaptiv we observ with strictly ponse. One s mited adapta e fifth simul sponse at lo attractant ca The dynami dent on the esulted in in cs of repre are shown in plementary M el, we can ca by such path hows that in ics should ally with the her words, a ved with the any adaptatio in tumbling th features ar e pathway th increasing see Figure 2) of different e s evolved in t rted’ respons might be s are particu via non-adap cy of the attr r adaptatio s modelled h more evoluti e several oth actant sou ulti-state rec nd that could mediated by effectiveness alistic fluctu where the distribution, ere chosen a ds). As ad to preserve in the exte , it could b to evoluti ve dynamics ve three si y non-adapt simulation ev ation, also lation resulte ower levels aused a de ics of these level of at nverted respo esentative pa n Figure 3 (k Material). apture the m hway dynam simple envir lead to e local conce an efficient e presented d on to attrac g probabilit re in striking ensures de g attractant f ). explanations these simula se and non-that the m larly well su ptive dynam ractant sourc on. Second here might m ionarily ac her factors, urce, intra ceptors that be importan other dynam s of non-uating enviro attractant and initial at random f daptation ha e robustness rnal environ e possible th ion of che s. In five imulations tive dynam volved pathw with an ed in pathway of attractant crease in t pathways, h ttractant, and onses. The athways fro inetic param movement mics (see ronments bacteria entration form of dynamics tant and ty with g contrast ecreasing followed for why ations are -adaptive modelled uited for mics. In ce might dly, the make non-ccessible. such as a-cellular are not nt for the mics. -adaptive onments, source, starting for each as been s of the nment or hat such emotaxis separate evolving mics and ways that inverted ys with a t, where tumbling however, d higher structure m these meters are
T adap fluct the e to perf initi path [24] evol inve thes non-effic This lack dyna how dyna all e featu B are Inve E. c obse mole high to th from sign non-coup self-inter The the s be a Figu cours and simu Each show adde The while These results ptive dynami tuating envir efficiency of that media formed addit al bacteria hways with . In five se lved pathwa erted respons e simulation -adaptive dy cient chemot s indicates th k of an ev amics obser wever, that amics is sup environmenta ures as ment Both non-ad observed i erted respons coli [15]. In erved, althou ecular mech hly likely tha he pathways m simulation nalling system -adaptive dy pling of the -regulation ractions or p striking sim speculation t achieved wi ure 3: Diverse se of active unique pathw ulations with fl h row display wn in the inse ed at time 100 first pathway e others were s indicate tha ics result in ronments. To f chemotaxis ated by co tional simula al populatio dynamics si eparate simu ays with n se. In other w ns, there alw ynamics and taxis than th hat the resu volutionary rved in E. chemotaxis perior as it w al conditions ioned above aptive dynam in wild typ ses are also n both case ugh the exa hanisms cou at these mech s presented s with two p ms to achie ynamics (se signal to an of both p processes su mplicity of th that non-ada ithout any e mechanism effector conce ways obtained uctuating attra s dynamics fo et. An attracta 00 (3000) and y structure w found in one e at inverted re efficient ch o further exp s mediated b onventional ations. These on containi imilar to th ulations, the non-adaptive words, under ways existed d that coul he original a ults we obtai route to t coli. It do mediated was not poss
s and other p . mics and in pe R. spha observed in es, efficient act nature o uld not be d hanisms form here. An an proteins reve eve chemota ee Figure 4 n effector via proteins (th uch as auto-p hese minima aptive chemo signalling p s mediating entration for from five diff actant dynam for a specific nt of low (high d removed at was found in each. esponses and emotaxis ev plore and con by such dyna dynamics, e started wit ing biochem at found E. bacteria al e dynamics the conditio d a pathway d mediate adaptive path in are not du the convent oes not indi by non-ada ible to repro ossibly impo nverted respo aeroides [16 gutted strai chemotaxis f the under determined. m systems sim nalysis of re eals the mini axis mediate 4). They inv a a receptor, hrough allos phosphorylat al systems le otaxis could proteins; a s chemotaxis.
the most freq ferent evolutio ics (see Meth
pathway stru h) concentrati time 2000 (4 three simulat non-en in ntrast amics we th an mical . coli lways and ons of with more hway. ue to tional icate, aptive oduce ortant onses 6,17]. ns of was rlying It is milar esults imum ed by volve with steric tion). ad to even small m i t e o c b f m e l t [ s D c o h d w l d t a a a Time quent onary hods). ucture ion is 000). tions, F c a p e w p a p molecule, tha into the cell tumbling pro exactly such observed in g causes increa binds the mo fumarate can motor swit experimental lead to chem that transpor [18] suggest straightforwa DISCUSSIO Adaptatio chemotaxis. other bacteri however, in dynamics co we provide leads to effic dynamics is tumbling fre an absence o Using co and biochem adaptive dy Figure 4: M chemotaxis. active effector pathways wit evolutionary s were found in panels show f and the time-population. at is a by-pr l via a tran obability of h a scenario gutted E. co ases in fuma otor and incr n involve in tching [26 lly but the e motaxis was rters involve
that non-ada ard way to lin
ON
on to stimu Several ex ial species ndicate that
uld also lead direct eviden cient chemo an inverted quency with f adaptation. omputational mical pathw ynamics rea Minimal non Cartoon rep r concentration h two prote simulations. T n one and fou fitness curves -averaged dis roduct of me nsporter, cou f the cell. W o is respons oli. Attractan arate levels in reases tumbl chemotaxis 6] have b exact dynam unknown. in chemotax aptive dynam nk metabolis uli is the h xperimental and mutant other, pos d to a form nce for one otaxis. The m response, l h increasing . models of ways, we sh adily evolv -adaptive pa presentation a n for the most ins obtained The pathway ur simulations s for the corre
stribution of p
etabolism or uld directly We hypothes sible for che nt related me
nside the cel ing probabil [25] and can been demo mics of how Further, the xis in R. sph mics could p sm and chem hallmark of observation t strains of ssibly non-a of chemotax such dynam main feature eading to in attractant le bacteria m how that su ve under athways me and time co t frequent and from five d on the left a respectively. esponding sim positions of t is taken regulate size that emotaxis etabolism ll, which lity. That n control onstrated it could e finding haeroides provide a motaxis. f proper ns from E. coli, adaptive, xis. Here mics that s of this ncreasing evels and movement uch non-different ediating urse of d unique different nd right Bottom mulations he final
environmental conditions and model assumptions and allow bacteria to achieve chemotaxis. Further, we find the efficiency of such chemotaxis to be equal to a case where bacteria would accumulate in space proportional to local attractant concentration. This type of chemotaxis favours exploitation of attractant sources over searching and could be especially efficient in conditions of abundant attractant. The minimal system for achieving non-adaptive dynamics mediating chemotaxis requires only two signalling components.
These findings provide a possible explanation for the chemotaxic ability of gutted E. coli cells and the complex chemotaxis behaviour of wild-type R. sphaeroides. In both cases and possibly in other current-day bacteria, chemotaxis pathways with non-adaptive and inverted responses could work in conjunction with the conventional chemotaxis pathway. These pathways could be remnants of evolution or functional pathways. They could involve in the fine-tuning of chemotaxis under certain environmental conditions or in providing a link between cell metabolism and chemotaxis.
ACKNOWLEDGEMENTS
R.A.G. acknowledges the support of the National Institute for Medical Research (Medical Research Council, UK). O. S. S acknowledges the support of Italian Ministry of University and Research (MUR – FIRB project RBPR0523C3).
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