# Switching elements (gates)

### From Biomatics.org

The fundamental building blocks of artificial computation (computers) as we know it today are gates and flip-flops.

Gates are the basic elements of combinatorial circuits while flip-flops are essential for sequential circuits (where output values depend not only on the inputs, but also on previous input and output values).

In biological systems at the atomic and molecular level there are several potential mechanisms for carrying out these same functions. These include but are not limited to:

- Shift of electronic charge within a molecule: Molecular wires.
- Rotation about covalent bonds resulting in stereochemical steppings.

- Catalysis of protein reactions by enzymes

## Atomic orbital

An **atomic orbital** is a mathematical function that describes the wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. The term may also refer to the physical region defined by the function where the electron is likely to be.^{[1]} Specifically, atomic orbitals are the possible quantum states of an individual electron in the electron cloud around a single atom, as described by the function.

The term "orbital" was coined by Robert Mulliken in 1932.^{[2]} However, the idea that electrons might revolve around a compact nucleus in an orbit-like path was convincingly argued at least 19 years earlier by Niels Bohr,^{[3]} and perhaps the most iconic image of the atom, with electrons orbiting a nucleus along three symmetric directions, was drawn in 1904 by Japanese physicist Hantaro Nagaoka.^{[4]} Explaining the behavior of these electron "orbits" was one of the driving forces behind the development of quantum mechanics.^{[5]}

Atomic orbitals are typically described as hydrogen-like wave functions over space, indexed by the *n*, *l*, and *m* quantum numbers or by the names used in electron configurations. Despite the obvious analogy to planets revolving around the Sun, electrons cannot be described as solid particles and so atomic orbitals rarely, if ever, resemble a planet's elliptical path. A more accurate analogy might be that of a large and often oddly-shaped atmosphere (the electron), distributed around a relatively tiny planet (the atomic nucleus). Because of the difference from classical mechanical orbits, the term "orbit" for electrons in atoms, has been replaced with the term *orbital*. The orbital names (s, p, d, f) are derived from the characteristics of their spectroscopic lines: **s**harp, **p**rincipal, **d**iffuse, and **f**undamental, the rest being named in alphabetical order.^{[6][7]}

**Formal quantum mechanical definition
**

^{In }^{quantum mechanics}^{, the state of an atom, i.e. the }^{eigenstates}^{ of the atomic }^{Hamiltonian}^{, is expanded (see }^{configuration interaction}^{ expansion and }^{basis (linear algebra)}^{) into }^{linear combinations}^{ of anti-symmetrized products (}^{Slater determinants}^{) of one-electron functions. The spatial components of these one-electron functions are called atomic orbitals. (When one considers also their }^{spin}^{ component, one speaks of atomic spin orbitals.)}

^{In }^{atomic physics}^{, the }^{atomic spectral lines}^{ correspond to transitions (}^{quantum leaps}^{) between }^{quantum states}^{ of an atom. These states are labelled by a set of }^{quantum numbers}^{ summarized in the }^{term symbol}^{ and usually associated to particular electron configurations, i.e. by occupations schemes of atomic orbitals (e.g. 1s2 2s2 2p6 for the ground state of }^{neon}^{ -- term symbol: 1S0).}

^{This notation means that the corresponding Slater determinants have a clear higher weight in the }^{configuration interaction}^{ expansion. The atomic orbital concept is therefore a key concept for visualizing the excitation process associated to a given }^{transition}^{. For example, one can say for a given transition that it corresponds to the excitation of an electron from an occupied orbital to a given unoccupied orbital. Nevertheless one has to keep in mind that electrons are }^{fermions}^{ ruled by }^{Pauli exclusion principle}^{ and cannot be distinguished from the other electrons in the atom. Moreover, it sometimes happens that the configuration interaction expansion converges very slowly and that one cannot speak about simple one-determinantal wave function at all. This is the case when }^{electron correlation}^{ is large.}

^{Fundamentally, an atomic orbital is a one-electron wavefunction, even though most electrons do not exist in one-electron atoms, and so the one-electron view is an approximation. When thinking about orbitals, we are often given an orbital vision which (even if it is not spelled out) is heavily influenced by this }^{Hartree–Fock}^{ approximation, which is one way to reduce the complexities of molecular orbital theory.}

[Tour 1998] synthesized a number of organic molecules based on benzene and investigated their computational possibilities. Since these molecules can be controllably synthesized in vast numbers, they have great potential as building blocks for nanoelectronic circuits. Noting that transporting electrons through networks of such molecules would generate unacceptable amounts of heat, [Tour 1998] proposed using small changes in electron density to pass information and perform logic functions. While [Tour 1998] discussed quantum calculations to support the notion of using electron density changes for logic, it's unclear how the small signals proposed could be distinguished from thermal noise [Bauschlicher 1999], an issue not addressed in [Tour 1998]. Nonetheless, if these molecules can be connected appropriately, noise problems overcome, and a variety of other problems conquered, these molecules could lead to molecular computers operating at femtosecond time scales.

http://alglobus.net/NASAwork/papers/NanoSpace1999/paper.html

Logic analysis^{ }of phylogenetic profiles identifies triplets of proteins whose^{ }presence or absence obey certain logic relationships… For example,^{ }protein C may be present in a genome only if proteins A and^{ }B are both present. (http://www.sciencemag.org/cgi/content/abstract/306/5705/2246)

Molecular computation

Logic analysis

^{ }of phylogenetic profiles identifies triplets of proteins whose

^{ }presence or absence obey certain logic relationships… For example,

^{ }protein C may be present in a genome only if proteins A and

^{ }B are both present. (http://www.sciencemag.org/cgi/content/abstract/306/5705/2246)

Tubulin tail conformational solitons could propagate along the outer microtubular surface

providing a dissipationless mechanism for transmission of information. The soliton collisions could act as elementary logical gates and implement a subneuronal form of computation.

http://cogprints.org/3894/1/Tubulin_tail_solitons.htm

### BioSwitching and Finite BioAutomata

Preliminaries

Combinational logic

- Switching Algebras
- Isomorphic Systems
- Electronic Gate Networks
- Boolean Algebras
- Logic Design
- Functional Decomposition and Symmetric Functions

Finite State Machines

- Synchronous Sequential Circuits and Iterative Networks
- Synchronous and Asynchronous Operation
- http://en.wikipedia.org/wiki/Sequential_logic
- http://www.ee.surrey.ac.uk/Projects/Labview/Sequential/Course/03-Seq_Intro/Intro.html

- Capabilities, Minimization, and Transformation of Sequential Machines
- Asynchronous Sequential Circuits
- Finite State Recognizers

## Computational functions in biochemical reaction networks. Arkin A, Ross J. Department of Chemistry, School of Medicine, Stanford University, CA 94305

In prior work we demonstrated the implementation of logic gates, sequential computers (universal Turing machines), and parallel computers by means of the kinetics of chemical reaction mechanisms. In the present article we develop this subject further by first investigating the computational properties of several enzymatic (single and multiple) reaction mechanisms: we show their steady states are analogous to either Boolean or fuzzy logic gates…With these enzymatic gates, we construct combinational chemical networks that execute a given truth-table…The mechanism, in this case, switches the pathway's mode from glycolysis to gluconeogenesis in response to chemical signals of low blood glucose (cAMP) and abundant fuel for the TCA cycle (acetyl coenzyme A). http://www.ncbi.nlm.nih.gov/pubmed/7948674