Sunday, June 26, 2011

MAPK: Feedback Amplifier, Part I

 A recent paper by Sturm et al., report results that support the hypothesis that the MAPK cascade acts as a negative feedback amplifier.

The systems biology literature is full of reviews and articles about oscillators and bistable systems and very little else other than Uri Alon et al's refreshingly unique work on feedforward systems. An alien race, upon reading the literature, would most likely believe that the only thing biochemical networks can do is oscillate, show bistability and perhaps a little ultrasensitivity. This is probably because many of the modelers and theoreticians in systems biology are unaware of the possible signal processing capabilities offered by the engineering field. For example, an engineer looking at the MAPK cascade would probably immediately think of a negative feedback amplifier. Mention the word negative feedback amplifier to a systems biologist however and you're likely to get a blank stare. So what is a negative feedback amplifier? Let's start with some recent history.

ndustrial Revolution

Probably the most famous modern device that employed negative feedback was the governor. Thomas Mead in 1787 took out a patent on a device that could regulate the speed of windmill sails. His idea was to measure the speed of the mill by the centrifugal motion of a revolving pendulum and use this to regulate the position of the sail. Very shortly afterwards in early 1788, James Watt is told of this device in a letter from his partner, Matthew Boulton. Watt recognizes the utility of the governor as a device to regulate the new steam engines that were rapidly becoming an important source of new power for the industrial revolution. The image below illustrates an engraving of a governor from an early book entitled ”An Elementary Treatise on Stream and the Steam-engine by Clark and Sewell published in 1892.

The operation of the governor is simple (See Figure below), its purpose is to maintain the speed of a rotating engine at a constant predetermined value in spite of changes in load and steam pressure. The vertical axle of the governor is connected to the rotation of the steam engine. As the steam engine, for one reason or another, speeds up, the rotation increases, thereby causing the centrifugal pendulums to swing out. A linkage transmits this motion to the stream valve in such a manner that the flow of steam is reduced thus slowing down the engine. If the engine slows down too much, as a result of a sudden load, the flyweights will swing back and the steam value is opened so that the steam engine can accelerate. The governor was a highly successful device and it is estimated that by 1868, 75,000 governors were in operation (A History of Control Engineering, 1800-1930 By Stuart Bennett, 1979).

Figure: Illustration of a Governor from ”An Elementary Treatise on Stream and the Steam-engine by Clark and Sewell published in 1892.

This description of the governor illustrates one of the basic operational characteristics of negative feedback. The output of the device, in this case the steam engine speed, is ”fed back” to control the rate of steam entering the steam engine and thus influence the engine speed.

The Greeks

Although the governor is an example of one of the earliest negative feedback systems in modern times, the concept actually goes back much further in history. There is documentary evidence to show that the ancient Greeks were aware of the concept and used it in a wide variety of ways to control different mechanisms. Probably the most famous of these was the use of floats in water clocks to maintain a steady flow of water which could be used to measure time. The earliest recorded water clock that used negative feedback was described by Ktesibios who probably lived between 285 and 247 BC in Alexandria. Further work was done by Philon and particularly Heron (13 AD) who left us with an extensive book (Pneumatica) detailing many amusing water devices that employed negative feedback.

Figure: Ktesibios (270 BC) negative feeback value to regulate water flow. Modified from Stefano Penzier (

Modern Times

In more recent times negative feedback has been used extensively in the electronics industry to confer, among other things, electrical stability to electronic devices and amplifiers. In fact, without negative feedback considerable swathes of modern technology would not be able to function. The application of negative feedback to modern devices is probably one of the most important innovations of the 20th century. Before continuing, let's make sure we understand what an amplifier is. The purpose of an amplifier is to faithfully scale up the power of a small time-varying electrical signal without adding distortion. This is an important task in both man-made and biological systems as we are often confronted with weak signals that need a boost to make them useful.

The story of how negative feedback came to be used in amplifiers begins in 1921 when Harold Black, who recently graduated from Worcester Polytechnic Institute in electrical engineering, took a job at Western Electric, the forerunner of Bell Labs. One of the challenges facing engineers in the 1920s in the US was how to design amplifiers that didn't distort the signal over long distances. In the early days, engineers would install what were called repeaters. Such repeaters would boost the signal but would also add their own distortions. By the time the signal had traveled 4000 miles across the country with repeaters less than 1000 miles apart, the signal at the end was barely intelligible.  These difficulties were ultimately overcome by the introduction of the feedback amplifier, designed in 1927 by Harold S. Black (Mindell, 2000). The basic idea was to introduce a negative feedback loop from the output of the amplifier to its input. At first sight, the addition of negative feedback to an amplifier might seem counterproductive. Indeed, Black had to contend with just such opinions when introducing the concept—his director at Western Electric dissuaded him from following up on the idea, and his patent applications were at first dismissed. In his own words ‘our patent application was treated in the same manner as one for a perpetual motion machine’ (Black, 1977). While Black’s detractors were correct in insisting that the negative feedback would reduce the gain of the amplifier, they failed to appreciate his key insight—that the reduction in gain is accompanied by increased robustness of the amplifier and improved fidelity of signal transfer. Since then, negative feedback has been widely used in the electrical industry (See opamps).


The reader may be wondering what on earth has this story got to do with MAPK cascades? Simple, we have a small hormonal signal coming in via receptors but need a larger signal inside the cell but without adding distortion and unwanted noise. You may be asking, where does the distortion and noise come from? The most obvious source of noise is the natural variability in protein levels due to stochastic events at the transcription and translation layers and source of the distortion is the nonlinear behavior of protein cascades. This combination is a recipe for disaster and to me at least, it isn't a surprise that evolution hit on the idea of wrapping the MAPK cascade in a negative feedback loop.

To understand the role of negative feedback is a system such as MAPK we need to examine more closely the advantages (and sometimes disadvantages) of negative feedback.

Go to Part II - under construction!

Black, H.S., 1977. Inventing the negative feedback amplifier. IEEE Spectrum 14, 55–60.

Mindell, D. (2000). Opening black’s box. Technology and Culture, 14, 405–434.

Sturm OE , Orton R , Grindlay J , Birtwistle M , Vyshemirsky V , Gilbert D , Calder M , Pitt A , Kholodenko B , Kolch W (2010) The mammalian MAPK/ERK pathway exhibits properties of a negative feedback amplifier. Sci Signal 3: ra90


No comments: