In this example of a molecular machine we are able to switch between two molecular states (shapes) in a controlled manner as part of a repetitious mechanical cycle. An azobenzene molecule can exist in two forms (left: *trans* with the bulky groups on opposite sides of the double bond, and right: *cis* with the bulky groups on the same side). The bulky groups can be moved closer together or further apart by switching between the *cis* and *trans* forms (see also, Fig. 8b). This switching can be performed by using light of two different colours, one to go from *cis* to *trans*, the other to reverse the process.

# Biomatic Strings

### From Biomatics.org

## Contents |

### Strings

In physics, a **string** is a physical object that appears in string theory and related subjects. Unlike elementary particles, which are zero-dimensional or point-like by definition, strings are one-dimensional extended objects. Theories in which the fundamental objects are strings rather than point particles automatically have many properties that are expected to hold in a fundamental theory of physics. Most notably, a theory of strings that evolve and interact according to the rules of quantum mechanics will automatically describe quantum gravity.

In string theory, the strings may be open (forming a segment with two endpoints) or closed (forming a loop like a circle) and may have other special properties. Prior to 1995, there were five known versions of string theory incorporating the idea of supersymmetry, which differed in the type of strings and in other aspects. Today these different string theories are thought to arise as different limiting cases of a single theory called M-theory.

In theories of particle physics based on string theory, the characteristic length scale of strings is typically on the order of the Planck length, the scale at which the effects of quantum gravity are believed to become significant. On much larger length scales, such as the scales visible in physics laboratories, such objects would be indistinguishable from zero-dimensional point particles, and the vibrational state of the string would determine the type of particle. Strings are also sometimes studied in nuclear physics where they are used to model flux tubes.

As it propagates through spacetime, a string sweeps out a two-dimensional surface called its worldsheet. This is analogous to the one-dimensional worldline traced out by a point particle. The physics of a string is described by means of a two-dimensional conformal field theory associated with the worldsheet. The formalism of two dimensional conformal field theory also has many applications outside of string theory, for example in condensed matter physics and parts of pure mathematics.

Strings can be either open or closed. A **closed string** is a string that has no end-points, and therefore is topologically equivalent to a circle. An **open string**, on the other hand, has two end-points and is topologically equivalent to a line interval. Not all string theories contain open strings, but every theory must contain closed strings, as interactions between open strings can always result in closed strings.

The oldest superstring theory containing open strings was type I string theory. However, the developments in string theory in the 1990s have shown that the open strings should always be thought of as ending on a new type of objects called D-branes, and the spectrum of possibilities for open strings has increased greatly.

Open and closed strings are generally associated with characteristic vibrational modes. One of the vibration modes of a closed string can be identified as the graviton. In certain string theories the lowest-energy vibration of an open string is a tachyon and can undergo tachyon condensation. Other vibrational modes of open strings exhibit the properties of photons and gluons.

### Branes

In string theory, **D-branes** are a class of extended objects upon which open strings can end with Dirichlet boundary conditions, after which they are named. D-branes were discovered by Dai, Leigh and Polchinski, and independently by Hořava in 1989. In 1995, Polchinski identified D-branes with black p-brane solutions of supergravity, a discovery that triggered the Second Superstring Revolution and led to both holographic and M-theory dualities.

D-branes are typically classified by their spatial dimension, which is indicated by a number written after the *D.* A D0-brane is a single point, a D1-brane is a line (sometimes called a "D-string"), a D2-brane is a plane, and a D25-brane fills the highest-dimensional space considered in bosonic string theory. There are also instantonic D(-1)-branes, which are localized in both space and time.

The equations of motion of string theory require that the endpoints of an open string (a string with endpoints) satisfy one of two types of boundary conditions: The Neumann boundary condition, corresponding to free endpoints moving through spacetime at the speed of light, or the Dirichlet boundary conditions, which pin the string endpoint. Each coordinate of the string must satisfy one or the other of these conditions. There can also exist strings with mixed boundary conditions, where the two endpoints satisfy NN, DD, ND and DN boundary conditions. If p spatial dimensions satisfy the Neumann boundary condition, then the string endpoint is confined to move within a p-dimensional hyperplane. This hyperplane provides one description of a Dp-brane.

## Biomatic String Theory

Proteins are chains of amino acids. The so called backbone of the protein is simply a chain of carbon atoms with the same topology as the above mentioned open ended "strings". The universe is infinitely small as assuredly as it is infinitely big. Thus subatomic strings will probably have some properties similar to protein chains or more accurately carbon chains. At any rate, as a purely mathematical exercise we need to look at and classify all possible strings and their vibrations. Strings with different lengths and geometries, for example. Carbon chains have a tetrahedral based geometry which gives proteins certain "vibrational" properties. Likewise, subatomic vibrating strings must have some set of geometries, based on the properties of the pivot points of vibration perhaps, including tetrahedral as one possibility.

One classification scheme would be to consider the "vibrations" where the covalent bonds, in the case of carbon chain strings, all rotate at some constant rate. They could of course also rotate at dynamically changing rates as well as in a constrained discrete way e.g. between trans conformations. One way of studying and classifying the vibration of strings is to focus on the free end of the string as it moves in space. It is as if a paintbrush is attached to the free end. It is a Biomatic string theory because we will look at the computational and mathematical implications of the possible vibrational modes. Smart strings if you will.

### The kinesins

Kinesins were discovered as MT-based anterograde intracellular transport motors.^{[1]} The founding member of this superfamily, kinesin-1, was isolated as a heterotetrameric fast axonal organelle transport motor consisting of 2 identical motor subunits (KHC) and 2 "light chains" (KLC) via microtubule affinity purification from neuronal cell extracts.^{[2]} Subsequently a different, heterotrimeric plus-end-directed MT-based motor named kinesin-2, consisting of 2 distinct KHC-related motor subunits and an accessory "KAP" subunit, was purified from echinoderm egg/embryo extracts^{[3]} and is best known for its role in transporting protein complexes (IFT particles) along axonemes during cilium biogenesis.^{[4]} Molecular genetic and genomic approaches have led to the recognition that the kinesins form a diverse superfamily of motors that are responsible for multiple intracellular motility events in eukaryotic cells.^{[5]}^{[6]}^{[7]}^{[8]} For example, the genomes of mammals encode more than 40 kinesin proteins,^{[9]} organized into at least 14 families named kinesin-1 through kinesin-14.^{[10]}

Here are two more animations of the the Kinesin protein "string":

A Day in the Life of a Motor Protein

__Figure 1: What makes a molecule a machine?__

### Molecular String Programs

Given a molecular chain of carbon atoms fixed at one end, one can define a set of functions which describe the motion about each covalent bond in the chain. The position of the free tip of the molecule is thus a function of the form: (x,y,z) = f1(b1) + f2(b2)...+ fn(bn). In other words if one specifies the various fn then one has specified a molecular program. One simple example would be if all the bonds are spinning at the same angular velocity. Other interesting possibilities include various combinations of Fibonacci numbers e.g. one bond spins at 3 units/t while another spins at 2 or 5 units/t.

In general a string must be some collection of segments vibrating according to some function of time. In a protein, for example, the segments are a sequence of covalent bonds each at about an angle of about 109.5 degrees. This being a property of carbon atom chains. In vivo these proteins have the property that every third bond tends to almost always be relatively stable due to an oxygen bond.