Technical Report CoSBi 15/2007

Chemotaxis mediated by non-adaptivedynamics

Richard A. Goldstein

Mathematical Biology, National Institute for Medical ResearchMill Hill, London, UK

richard.goldstein@nimr.mrc.ac.uk

Orkun S. Soyer

The Microsoft Research - University of TrentoCentre for Computational and Systems Biology

soyer@cosbi.eu

This is the preliminary version of a paper that will appear inPLoS Computational Biology

available at http://www.ploscompbiol.org/home.action

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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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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