Download II. E. Coli Chemotaxis as a System

BME 1450 Mid-term Paper
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E. Coli Chemotaxis as a Basic Systems Biology
Model
Daniel Cossever

Abstract—Chemotaxis of the peritrichous bacterium E. coli is
one of the most comprehensively studied and well understood
biological processes, whereby a single cell will propel itself to a
location of the most favorable environmental conditions. The
range of sensitivity to chemoeffectors makes it a one of the
simplest examples of the use of integral feedback control loops
and robust perfect adaptation. Using a two-state system to model
this adaptive behavior provides a means to computationally
determine system parameters, allows insight into the
understanding into the more complex underlying system
interactions, and provides links to finding a truly global cellular
model of chemotaxis. A complete systems view of the simple
chemotactic system aids in the understanding of yet more complex
systems employing the same principles and may also allow the
development of future technologies to be designed or optimized
using similar models.
Index Terms—adaptation, chemotaxis, integral control, systems
biology.
I. INTRODUCTION
B
chemotaxis, particularly that which occurs in
the bacterium Escherichia coli, is a well studied
phenomenon. The interest in E. coli lies in the fact that its
simplicity has allowed the identification of the behavioral
changes associated with chemotaxis, including the
identification of the major biochemical steps in the signal
transduction and processing pathways [1].
Every E. coli cell has several flagella spread over their
surface (known as peritrichous). These flagella are helical,
and thus produce different effects when rotated clockwise and
counterclockwise. In an environment that is neutral (contains
no chemoattractants or chemoreppellants that bind to E. coli
receptors), E. coli moves around in a random fashion produced
via two types of movements. The first is counterclockwise
flagella rotation that, due to the helical nature of the flagella,
causes them to bunch together and propel the cell in a fairly
straight, forward manner known as a ‘run’. The other type of
movement occurs when the flagella rotate clockwise, causing
them to split apart, and produce a random reorientation of the
cell, known as a ‘tumble’. In a neutral environment, the run
ACTERIAL
Manuscript received October 28, 2003. This work was supported in part
by the Bloorview Macmillan Children’s Center Research Foundation and the
National Science and Education Council.
Daniel Cossever is with the Department of Biomaterials and Biomedical
Engineering, University of Toronto, Toronto, ON, Canada (e-mail:
[email protected]).
time is on average 10 times longer than the tumble time [2].
Once the cell is in an environment with a chemoeffector
gradient, the ratio between run and tumble time changes. E.
coli will migrate to/from a chemoeffector by increasing the run
times that propel it in a favorable direction, or conversely,
increase tumbling frequency when headed in an unfavorable
direction. These flagella changes are due to changes in ligand
occupancy (bound receptors indirectly control the flagella
motors) and methylation states (sensory adaptation process to
unbias sensors after chemoeffector attachment in order to
maintain sensitivity) [2].
II.
E. COLI CHEMOTAXIS AS A SYSTEM
In order to use the information available on the process of
E. coli chemotaxis, it is important to understand the process as
a whole, rather than as a summation of individual events. This
is the basis of systems biology. The process of understanding
biological systems as ‘systems’ can be broken down into four
steps; system structure identification, system behavior analysis,
system control, and system design [4].
A. System Structure Identification
This step identifies the physical structure as well as the protein
interactions and regulatory relationships of the system [4].
Looking at tar, the E. coli chemoreceptor for the attractant
aspartate, can facilitate the system structure understanding of
E. coli chemotaxis. Tar is a trans-membrane methyl accepting
chemotaxis protein (MCP), which has periplasmic binding
sites and cytoplasmic signaling sites. The signals are sent to
the flagella motors through a complex sequence of protein
interactions [1].
MCPs form a stable complex with two cytoplasmic
signaling proteins, CheA and CheW. This complex generates
signals (in the form of phosphoryl group (P), caused by the
autophosphorylation of CheA when in this complex) used by
CheB and CheY effector proteins to control the direction of
flagella motor rotation. The phosphorylized CheY (CheYP)
interacts with the flagella motor to increase the probability of
clockwise rotation (tumbling). CheBP is part of the adaptive
circuit that terminates motor response [1].
When attractants are bound to the MCP, the receptor
inhibits the autophosphorylation of CheA, and conversely,
when there are no bound attractants, the receptor stimulates
CheA activity. Therefore, the flux of P to CheB and CheY
depend on the ratio of complexes with and without bound
attractants, and changes in attractant concentrations alter this
BME 1450 Mid-term Paper
ratio, triggering flagella response [1]. It must be noted that
this is a linear interpretation of the system, where the total
output is considered as a simple sum of the individual receptor
outputs. There is no consideration for the interaction of
receptor complexes or the effect of multiple types of receptors
(for different chemoeffectors) on one and other. Regardless,
this illustrates the basic mechanism for converting attractants
to motor rotation, and thus is adequate in establishing the
system structure.
.
B. System Behavior Analysis
The system behavior must be understood in terms of factors
such as sensitivity of a behavior against external changes and
time to return to normal state after an external stimulus [4].
The sensitivity of the tar chemoreceptors occurs through the
change in MCP methylation state. Tar has residues that are
reversibly methylated by CheR, and demethylated by CheB.
CheR is unregulated, but CheB, as mentioned above, is
controlled by the phosphorylation of CheA. Therefore, the
receptor methylation is regulated through a feedback from the
MCP complex.
Both attractant binding and receptor
demethylation promote low CheA activity, while lack of
attractant and/or methylation cause high CheA activity. When
there is a combination, such as an attractant bound receptor
that is not highly methylated, CheA is only able to
autophosphorylate at a fairly low rate. This feature allows the
cell to remain sensitive to small changes in concentration
gradients, even in a high concentration environment [1].
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known as robustness, which is an important factor in many
biological systems. This perfect adaptation is an inherent
attribute of the system, and is independent of the system
parameters. Therefore, cells that are genetically identical may
exhibit different unstimulated behavior, likely due to factors
such as differences in signaling protein concentrations, but
each cell can return precisely to its unique initial behavior
following a stimulus [3].
E. coli is sensitive to a range of concentration levels over a
range of five orders of magnitude, yet can still sense changes
in the ratio of bound receptors as low as 0.1% per second [1]
The robustness of the circuit, or perfect adaptation over a wide
range of concentrations, comes from integral feedback control.
The chemotaxis circuit incorporates this integral feedback
control, where the difference between the current and base
output is integrated over time and fed back into the system. [3]
Fig. 2. Simple control model of integral feedback, where u is the input
(chemoeffector) for process k. The difference of the actual output, y1, versus
the steady state output, y0, represents the normalized output, y (receptor
activity). The time integral of y, x (methylation level of receptors), is fed
back into the system
Fig. 1. Schematic cycle of protein interactions causing flagella motor rotation
and methylation of receptor complexes in E. coli chemotaxis.
To affect the flagella motor, CheYp must reach the motor
before decaying. This is made more difficult by CheZ, which
breaks down CheYp, and by the fact that phosphorylation
enhances the affinity of CheY for CheZ. This likely is a
mechanism to reduce the effects of random fluctuations of
CheYp production, only letting a sustained synthesis of CheYp
overwhelm CheZ and reach the flagella motors [3].
Experimentally it has been found that perturbations to the
component parameters (reaction rates constants, protein
concentration, etc.) can dramatically affect the behavior of the
system. Regardless of these changes, E. coli still retains the
ability to precisely restore its prestimulus behaviors. This is
Receptor methylation is slow in comparison to CheY
phosphorylation. The reaction to an external stimulus is in the
range of milliseconds, while the time to reset the prestimulus
value so that the steady state behavior is independent of the
concentration of a homogeneous distribution of attractant is in
the order of minutes [6].
This scenario looks at the summation of individual receptors
as the input for the system behavior. There is the likelihood
that MCP’s interact with each other to form a receptor patch.
In this case, sensitivity of the system could be augmented if
binding of a single ligand produced a disproportionately large
response by triggering kinase regulation in other MCPs. By
the same idea, if coupling between MCP were adjustable
according to methylation, the range of stimulus on a cellular
level would be dramatically increased. This is the next step in
a true systems level understanding, where the single
interactions that comprise the basic control system are
integrated to provide an overall cellular control system [3].
Even further in determining a true cellular level control system
is to integrate any cross talk between signaling pathways for
different chemoreceptors.
A single E. coli cell has
approximately 30 similar two-component regulatory systems
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operating simultaneously. The insulation between signals is
likely not perfect, or designed as to provide redundancy of
sorts. The interaction of such crosstalk might also be a factor
in the process optimization [3].
C. System Control
Generally, this step is to use the previous two steps in order
to establish a method to control the state of the biological
system as needed [4]. This is because system biology is more
than just the understanding on a systems level, it is the science
by which this information can be used in order to augment
understanding and usability of the system. In this case, control
of the runs and tumbles is desired in order to keep the cell in
its optimal environment. Therefore, the question of control is
related to the optimization of the system, rather than the ability
to have control over the state it is in. In order to understand
this optimization of the system, it is necessary to model it in
order to be able to control the system parameters that are
critical to such optimization. This also allows the process to
undergo computer simulation, and run simulations using
different system parameters.
Bacterial chemotaxis has served as a prototype for twocomponent regulatory systems, a signaling transduction
strategy widely used in prokaryotes, plants, and fungi for
response to a broad range of extracellular stimuli. A relatively
simple two-state model of the chemotaxis network seems to
adequately match experimental data, and a quantitative
description of the model comes from a set of coupled
differential equations.
The main component of the model is the MCP/CheA/CheR
receptor complex, modeled as E. It has two functional states,
active and inactive (active being the kinase activity of CheA
that ultimately sends a signal to the flagella motors). The
output is the system activity, A, which is the average number
of receptor in the active state (simplified version, assuming no
receptor patch).
The receptor activity is probabilistic, and depends on the
methylation on m sites (Em, m=1,…,M) (again, simplified
assuming no interactive effects), ligand occupancy (Eo, Eu),
and activity probabilities (αm for Eum, αmo for Eom). The
network input is the ligand concentration, l, while the network
output is the average complex activity.
Fig. 3. Simplified E. coli chemotaxis network (a) converted into a general
two-component regulatory system (b).
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A quantitative description of the model can then be given by
a set of coupled differential equations.
B(R) is the
concentration of CheB (CheR),
Similar equations can be written to describe kinetics of
{EmuB}, {EmuR}, Em0, {Em0B} and {Em0R}. For fixed αm and
αm0 the biochemical parameters of this system include nine
different rate constants (kl, k-l, ar, a'r, dr, kr, ab, db, kb) and three
enzyme concentrations (total concentrations of CheR, CheB
and receptor complexes).
This is not the only model possible, but the simplest one that
is consistent with experimental data.
The three main
assumptions of this model are as follows; ligand binding is
rapid and independent of receptor activity and degree of
methylation, methylation and demethylation are slower events,
and CheB demethylates only active receptors (important
property for robust adaptation).
Although these are
assumptions, they have generally been verified as correct
through experimentation [8].
Robust adaptation is shown to be maintained even with a
wide range of variation in network protein concentrations. E.
coli exhibits adaptation precision as a robust property, while
other properties, such as adaptation time and steady state
behavior may be dependent on biochemical parameters.
Therefore, the parameters that are part of the robust adaptation
do not need to be robust themselves. This is due to the fact
that only properties that are critical to network functionality
are actually required to be robust, as to deal with natural
variations. This means that exact adaptation is required for
chemotaxis, whereas chemotaxis ability is not dependent on
precise adaptation time or tumbling frequency. This has been
shown by experiment, where mutant bacteria show an inability
to taxi when selected Che proteins are deleted, even though
steady state tumbling frequency matches that of normal E. coli.
Conversely, cells with regular protein makeup will have
comparable taxiing ability, regardless of variations in tumbling
frequencies [7].
Although this simple model aids in the understanding of the
system, the goal of systems biology is to have a true systems
model, where not only the interaction between signaling
complexes is taken into account, but the interaction with other
cellular processes are as well. There are several other
considerations for a true systems model.
The spatial
organization of the circuit elements in the cell, for example, is
not taken into account in this model. Since the phosphates will
tend to dissociate from CheYP, the distance traveled (and thus
travel time) will determine the total amount of motor input that
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will be received. Related to this is the fact that CheZ is absent
from the model, and the inhibitory effects of CheZ on CheY P
are therefore neglected [2]. Once a true systems model of
chemotaxis has been created, it must then be integrated with
other E. coli biological networks to have a true cellular model.
D. System Design
Ultimately, all the previous steps are used in order to
establish technologies that allow the design of useful
biological systems.
The conversion of information from an extracellular
messenger to a usable intracellular form is an important
process in multicellular and unicellular organisms, and the
process of signal transduction is used in both prokaryotes and
eukaryotes alike. Every type of cell that uses this process of
communication does so in a different manner, but all exhibit a
number of common operating principles. As such, details into
the nature of operation of the signaling and feedback systems
of simple E. coli chemotaxis may offer insights as to the
functioning of other more complex systems [3].
A good example of using the simple E. coli example of
robust perfect adaptation to understand a more complex
system is when compared with the human homeostatic system.
The maintenance of physiological conditions is the backbone
of homeostasis, where concentrations, enzyme activity, etc. are
held in a very narrow range. Robust tracking is necessary for
maintenance of a steady state value, and as seen with E. coli,
can be implemented with a simple biochemical network. As
such, it seems logical that integral control is an important
strategy for maintaining a homeostatic environment. The
levels of second messengers, such as calcium, fluctuate
drastically in response to internal and external factors. Integral
control, with calcium as the input, and the enzyme that
create/remove these molecules are the output, can provide a
robust mechanism for restoring initial concentrations to the
optimal steady state levels [6].
Associated with the human homeostatic system is the
secretion of powerful hormones that are required to counter or
create effects over a wide range, and return exactly to a set
point. There is evidence that counter-regulatory pairs of
hormones operate as integral controllers, where a steady state
disturbance will always be brought back to a set point by
responding to the time integral of a disturbance induced error
(time multiplied by error). For example, the insulin output
from a glucose-deprived pancreas will not increase
proportionally to the lack of glucose, but a progressively
increasing insulin output with time [5]. Integral control is not
only an important strategy for homeostasis on a cellular and
organism level, but may well be applicable even for an
ecosystem level.
Outside of biological systems, we find integral feedback in
all types of man-made machines. Many aspects of aircraft,
from circuits to instruments to actuators, and even the whole
aircraft (autopilot) use integral control loops. Electric grids
use these types of loops to regulate voltage and frequency
throughout their networks. Integral control is also found in oil
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refineries, and even in network computers to regulate internet
traffic [6].
When trying to reverse engineer a biological system,
mechanisms such as integral feedback control become very
important. When a system is observed to have robust
adaptation, then integral feedback control must be a property
of the system. Therefore, based on external behavior, possible
internal mechanism could be greatly constrained. It would
therefore be helpful to catalogue the types of biological
networks that may exhibit this, and more sophisticated types of
integral feedback control to understand the underlying need for
such a type of system [6].
III. CONCLUSION
The thorough characterization of the biological processing
network of E. coli chemotaxis makes it an excellent model for
computer simulations in the field of systems biology, as well
as a prototype for two-component regulatory systems.
Although the model is rudimentary in certain aspects, the
results of the model fit very closely to experimental data,
suggesting that the more important parameters have been
considered. A possible next step would be to move away from
simplified models that have wide applicability, towards a more
detailed model that includes all interaction, such as receptor
patches and all proteins. Although such a model would be
only applicable to E. coli, explanations of more complex
features of the system would aid in the understanding of
similar traits in more complex networks. It would also be
great help when designing artificial biological systems
requiring an even greater range of sensitivity than currently
seen with bacterial chemotaxis.
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