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One of the principle tasks of systems biology has been the reverse engineering of signaling networks. Because of the striking similarities to engineering systems, a number of analysis and design tools from engineering disciplines have been used in this process. This review looks at several examples including the analysis of homeostasis using control theory, the attenuation of noise using signal processing, statistical inference and the use of information theory to understand both binary decision systems and the response of eukaryotic chemotactic cells.

Though no two researchers are likely to agree on a definition of systems biology, there is no doubt that an important aspect is the way that it integrates research from an array of disciplines by combining novel experimental and computational tools. The various engineering disciplines have contributed many tools that facilitate experimentation, computation and data processing. Equally important is the role that our understanding of the engineering design process can have in deciphering biological systems. Issues such as modularity, robustness, optimality, tradeoffs, and physical constraints are dealt with every day in engineering design, and a large number of theoretical tools have been developed to facilitate this process. In studying biology, it is important to understand that these tradeoffs and constraints also arise and hence must be dealt with [

This review highlights how some of this understanding has played a role in the reverse engineering of biological systems. The emphasis is on a number of theoretical tools from research areas in engineering that in some sense deal with abstract representations of signals and systems and hence are readily amenable for use in system biology, particularly in the study of signal transduction pathways. An example is the set of design and analysis tools developed by control engineers. Though this field grew out of different application areas in chemical, electrical and aerospace engineering [

The rest of this review is divided into four parts. The first three look at different engineering disciplines, though it is important to stress that even within engineering, the divisions between these areas is not always so clear-cut. Finally, some concluding remarks are presented.

Since the work of Claude Bernard in the 19th century, the process by which an organism's internal state is kept constant—

If the state remains steady, there is an automatic arrangement whereby any tendency toward change is effectively met by increased action of the factor or factors which resist the change. (Cited in [

clearly expresses the need for negative feedback. The necessity of Cannon's principles, although a result of intuition based on his understanding of human physiology, can be stated in a mathematically formal way, as we will see below.

To illustrate how feedback arises in the context of a homeostatic response, we use a simple three-node network where an external stimulus (input; denoted _{ZY}

Based on these assumptions, the following set of differential equations describes the system, where

Suppose that we are interested in making the system insensitive to changes in the stimulus concentration. Because this is a dynamical system, we need to be more precise as to the class of inputs to which we would like to be insensitive, and we need a means for measuring sensitivity. For the former, it is customary to consider changes in the set point of the system—that is, we assume that the stimulus is at a steady-state value, _{i}_{f}_{i}_{i}_{f}_{f}_{i}_{i}_{f}_{i}_{i}_{i}_{i}_{i}_{f}_{f}

_{Y}_{−}_{Y}_{ZY}

To illustrate how integral feedback is providing infinite gain, it is useful to write the integrator in terms of a Fourier transform. In this case,
_{ZY}

The frequency domain analysis presented above forms one of the strongest tools of control engineering and signal processing. It does require that the particular system be linear, or at least linearized so that only small deviations from the steady-state are considered. In linearization, a signal (e.g.,

A second example is the network regulating the response to osmotic shock in

While the IMP states that integral control must be present in order to achieve perfect adaptation to step changes in stimuli, the nature of the integral control may not always be readily apparent. For example, though adaptation in the network of _{X}_{−}_{X}_{f}_{UX}_{−}_{X}_{f}_{f}_{XY}_{−}_{Y}_{f}

In the frequency domain, the transfer function

To express the sensitivity we consider the transfer function and write this as the product of two functions, _{0}(

Factors which may be antagonistic in one region, where they effect a balance, may be cooperative in another region. (Cited in [

Chandra and coworkers have shown how this constraint manifests itself during glycolysis, the process by which cells convert glucose into adenosine triphosphate [

The proper function of cells and organisms depends on their ability to sense their environment and to make correct decisions based on these observations. Both these steps are hampered by stochastic fluctuations inherent in biochemical systems, which have their origin in the random collisions that take place at the molecular level. These fluctuations are usually referred to as

To make well-informed decisions, cells must be able to sense their environments accurately. This process is usually done with cell-surface receptors in a reversible binding process we describe by
_{i}_{i}

As an example of this optimal statistical inference, Libby

The inference problem considered above relies on a probabilistic description of the environment and the observations that can be expected. An alternate view of how the non-deterministic nature of the signaling system gives rise to fluctuations is possible. Here we assume that the observed signal, now denoted by _{D}_{off}/_{on} is the dissociation constant for the receptor. Over time,

As we see that the bandwidth has an important effect on the sensed signal, it is worth asking whether there is an optimal bandwidth. A number of reports have considered this question with respect to the signaling pathway controlling chemotaxis in

To a great extent, cell survival requires the ability to make informed decisions based on imprecise measurements of the external environment. Though filtering can help reduce the effect of random perturbations, even the best filtering may not sufficiently remove noise to allow adequate information about the environment to be transmitted to the cell. Prompted by the problem of transmitting signals reliably, Claude Shannon developed a framework that is now known as

Before seeing how the theory can be used to gain insight into biological systems, it is useful first to understand how information is quantified. The framework is probabilistic. A random signal _{i}_{i}_{2} _{i}

A related notion is that of

One of Shannon's remarkable results was to provide an upper bound on the information transmission capability of a communication channel. The set-up is as in ^{2}. Shannon proved that the

Cheong

This study also showed that negative feedback has a limited role in improving the information capability of the network. Lestas

The measurements of the NF-

Not all the relevant information in cell signaling is binary. For example, chemotactic cells must interpret spatial differences (as small as 1%) in the concentration of diffusible chemical in order to guide their locomotion. The information-processing capabilities of these cells has led to a number of interesting studies in both amoebae [

To estimate mutual information between the chemoattractant gradient and the spatial response, the cell membrane can be divided into _{s}_{D}_{r}

Rate distortion theory has also been used to compute the optimal stimulus response maps for chemotaxis [

This review has highlighted some successes in understanding how biological systems can be studied using analysis and design tools from engineering. Our coverage is by no means exhaustive. Among the areas that we have not touched upon include tools developed to study biological reactions when the number of molecules is sufficiently small that continuum descriptions are not possible (see, for example, [

The analogy between biological and engineering systems can sometimes be carried too far, as the general setting between the two is quite different. As an example, we turn to the standard paradigm of control systems that delineates between two subsystems: the

Where they are most suitable is when they highlight fundamental limitations and can thus be used to consider the performance of biological systems in relation to some optimal level of performance, or in light of tradeoffs that need to be made. Interestingly, this

This work was supported in part by the National Institute of General Medical Sciences of the National Institutes of Health under award number R01GM86704. It was written while the author was a visiting scientist at the Max Planck Institute for the Physics of Complex Systems, in Dresden, Germany, whose support is greatly acknowledged. The author also thanks Geoff Goodhill who pointed him to some references on normative biology in neural systems.

This appendix provides some more details about the mathematical derivations as well as simulations.

If the input and set-point are denoted by _{0} and (_{0},_{0},_{0}), respectively, we compute the partial derivatives in the Jacobian [

If 1 − _{0} ≫ _{Y}

The simulations were computed using MATLAB (Mathworks, Natick, MA). The deterministic simulations of _{UX}_{XZ}^{−1}, _{−}_{X}_{−}_{Y}_{−}_{Z}^{−1},

Stochastic simulations were carried out using Gillespie's stochastic simulation algorithm [

_{i}_{f}_{i}_{max}) before settling to a final steady-state (_{f}_{i}_{f}

_{off} = _{on}^{−1}). The green line shows the expected number of occupied receptors over time, which is given by the solution to the deterministic ordinary differential _{on}^{−1} for the first 60 seconds, and _{on}^{−1} thereafter. Note how the lower bandwidth (smaller

_{Y}_{∣}_{X}_{s}_{r}_{3} in response to the gradient [