Tuesday, April 14, 2009

Molecular computers -- A historical perspective. Part 1

I've been having discussions lately with Andy regarding biological/molecular computers and these discussions have frequently turned to the history of analog and digital computers as a reference -- a history not well-known by biologists and chemists. I find writing blog entries to be a convenient way to develop bite-sized pieces of big ideas and therefore what follows is the first (of many?) entries on this topic.

In order to understand molecular computers -- be they biological or engineered -- it is valuable to understand the history of human-built computers. We begin with analog computers -- devices that are in many ways directly analogous to most biological processes.

Analog computers are ancient. The first surviving example is the astonishing Antikythera Mechanism (watch this excellent Nature video about it). Probably built by the descendants of Archimedes' school, this device is a marvel of engineering that computed astronomical values such as the phase of the moon. The device predated equivilent devices by at least a thousand years -- thus furthering Archimedies' already incredible reputation. Mechanical analog computers all work by the now familiar idea of inter-meshed gear-work -- input dials are turned and the whiring gears compute the output function by mechanical transformation.

(The Antikythera Mechanism via WikiCommons.)

Mechanical analog computers are particularly fiddly to "program", especially to "re-program". Each program -- as we would call it now -- is hard-coded into the mechanism, indeed it is the mechanism. Attempting to rearrange the gear-work to represent a new function requires retooling each gear not only to change their relative sizes but also because the wheels will tend to collide with one another if not arranged just so.

Despite these problems, mechanical analog computers advanced significantly over the centuries and by the 1930s sophisticated devices were in use. For example, shown below is the Cambridge Differential Analyzer that had eight integrators and appears to be easily programmable by nerds with appropriately bad hair and inappropriately clean desks. (See this page for more diff. analyzers including modern reconstructions).

(The Cambridge differential analyzer. Image from University of Cambridge via WikiCommons).

There's nothing special about using mechanical devices as a means of analog computation; other sorts of energy transfer are equally well suited to building such computers. For example, in 1949 MONIAC was a hydraulic analog computer that simulated an economy by moving water from container to container via carefully calibrated valves.

(MONIAC. Image by Paul Downey via WikiCommons)

By the 1930's electrical amplifiers were being used for such analog computations. An example is the 1933 Mallock machine that solved simultaneous linear equations.

(Image by University of Cambridge via WikiCommons)

Electronics have several advantages over mechanical implementation: speed, precision, and ease of arrangement. For example, unlike gear-work electrical computers can have easily re-configurable functional components. Because the interconnecting wires have small capacitance and resistance compared to the functional parts, the operational components can be conveniently rewired without having to redesign the physical aspects of mechanism, i.e. unlike gear-work wires can easily avoid collision.

Analog computers are defined by the fact that the variables are encoded by the position or energy level of something -- be it the rotation of a gear, the amount of water in a reservoir, or the charge across a capacitor. Such simple analog encoding is very intuitive: more of the "stuff" (rotation, water, charge, etc) encodes more of represented variable. For all its simplicity however, such analog encoding has serious limitations: range, precision, and serial amplification.

All real analog devices have limited range. For example, a water-encoded variable will overflow when the volume of its container is exceeded.

(An overflowing water-encoded analog variable. Image from Flickr user jordandouglas.)

In order to expand the range of variables encoded by such means all of the containers -- be they cups, gears, or electrical capacitors -- must be enlarged. Building every variable for the worst-case scenario has obvious cost and size implications. Furthermore, such simple-minded containers only encode positive numbers. To encode negative values requires a sign flag or a second complementary container; either way, encoding negative numbers significantly reduces the elegance of the such methods.

Analog variables also suffer from hard-to-control precision problems. It might seem that an analog encoding is nearly perfect -- for example, the water level in a container varies with exquisite precision, right? While it is true that the molecular resolution of the water in the cup is incredibly precise, an encoding is only as good as the decoding. For example, a water-encoded variable might use a small pipe to feed the next computational stage and as the last drop leaves the source resivoir, a meniscus will form due to water's surface tension and therefore the quantity of water passed to the next stage will differ from what was stored in the prior stage. This is but one example of many such real-world complications. For instance, electrical devices, suffer from thermal effects that limit precision due to added noise. Indeed, the faster one runs an electrical analog computer the more heat is generated and the more noise pollutes the variables.

(The meniscus of water in a container -- one example of the complications that limit the precision of real-world analog devices. Image via WikiCommons).

Owing to such effects, the precision of all analog devices is usually much less than one might intuit. The theoretical limit of the precision is given by Shannon's formula. Precision (the amount of information encoded by the variable, measured in bits) is log2( 1+S/N ). It is worth understanding this formula in detail as it applies to any sort of information storage and is therefore just as relevant to a molecular biologist studying a kinase as it is to an electrical engineering studying a telephone.

.... to be continued.

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