Online Book 2a

Online Book 2a

ONLINE BOOK AVAILABLE ON AMAZON: The sites online book 'Consciousness, Biology and Fundamental Physics' is now available on Amazon both as a paperback and as a kindle book. New paperbacks currently priced from £9.05 and kindle books from £2.63. Text remains free on this site.

3.2: In its ground state, the carbon atom has two electrons in the first shell, and this is not normally involved in bonding. In its second and outer shell it has two ‘s’ electrons filling an orbital, and two ‘p’ electrons, one p_x and one p_y, each in a half-filled orbital. If the carbon atom is excited, say by the positive charge attraction of the nucleus of a nearby hydrogen atom, an ‘s’ electron in the outer shell can be excited into a ‘p’ orbital, so that the outer shell now has one ‘s’ electron and three ‘p’ electrons, one each in an x, y and z orientation. The four outer shell electrons are now deemed to be not distinct ‘s’ and ‘p’ electrons but four ‘sp’ electrons, here described as sp³, because the configuration is one quarter ‘s’ electron and three-quarters ‘p’ electrons. The arrangement allows the formation of four σ covalent bonds. Carbon atoms can use sp² hybridisation where one ‘s’ electron and two ‘p’ electrons in the outer shell are hybridised. There is also ‘sp’ hybridisation where the ‘s’ orbital mixes with just one of the ‘p’ orbitals. P. With the C=O double bond, the two atoms in the double bond are sp² hybridised. The carbon atom uses all three orbitals in the sp²arrangement to form σ bonds with other orbitals, but the oxygen atoms use only one of these. In addition a ‘p’ electron from each atom forms a π bond.

3.3: Delocalisation and conjugation
The joining together or conjugation of double bonds is important for organic structures. π bonds can form into a framework over a large number of atoms, and are seen to account for the stability of some compounds. The structure of benzene is relevant in this respect. Benzene is based on a ring of six carbon atoms. The carbon atoms are sp² hybridised, leaving one ‘p’ electron per carbon atom free, or six electrons altogether. These six electrons are spread equally over the six carbon atoms of the ring. These are π bonds delocalised over all six atoms in the carbon ring, rather than being localised in particular double bonds.

Delocalisation emphasises the spatial spread of the electron waves, and occurs over the whole of the conjugated system. This is sometimes referred to as resonance. Sequences of double and single bonds also occur as chains rather than rings. Conjugation refers to the sequence of single and double bonds that form either a ring or a chain. Double bonds between carbon and oxygen can be conjugated in the same way as double bonds between carbon atoms. Conjugation involves there being only one single bond between each double bond. Two double bonds together also do not permit conjugation. These ‘rules’ relate to the need to have ‘p’ orbitals available to delocalise over the system.

In both rings and chains every carbon atom is sp² hybridised leaving a third ‘p’ electron to overlap with its neighbours, and form an uninterrupted chain. The double bonds that are conjugated with single bonds are seen to have different properties from double bonds not arranged in this way. Here again conjugation leads to a significantly different chemical behaviour. P. Chlorophyll, the pigment molecule in plants, is a good example of a conjugated ring of single and double bonds, and the colour of all pigments and dyes depends on conjugation. The colour involved depends on the length of the conjugated chain. Each bond increases the wavelength of the light absorbed. With less than eight bonds light is absorbed in the ultra-violet.

The colours of objects and materials around us are a function of the interaction of light with pigments. Pigments are characterised by having a large number of double bonds between atoms. The pigment, lycopene, responsible for the red in tomatoes and some berries, comprises a long chain of alternating double and single bonds, allowing the molecule to form π bonds. An extensive network of π bonds across a large number of atoms is involved in the chemistry of many compounds. It is responsible for the high degree of stability in aromatic compounds such as benzene.

The compound ethylene (CH₂=CH₂) has all its atoms in the same plane, and is therefore described as planar. In this molecule, the two carbon atoms are joined by a double bond. Hybridisation involves mixing the 2s orbital on each carbon atom with two out of the three ‘p’ orbital on each carbon atom to give three sp₂ orbitals. The third ‘p’ orbital on each atom overlaps with the ‘p’ orbital of the other atom to form a π bond. The ‘p’ orbitals of the two atoms also have to be parallel to one another in order to form a π bond. This bond prevents the rotation of the double bond between the carbon atoms. However, sufficient energy, such as that of ultra violet light, can break the π bond, and thus allow the double bond to rotate.

An important feature of benzene is the ability to preserve its ring structure through a variety of chemical reactions. Benzene and other compounds that have this property are termed aromatic. In looking at these structures, the important feature is not the number of conjugated atoms, but the number of electrons involved in the π system The six π electrons of benzene leave all its molecular orbitals fully occupied in a closed shell, and account for its stability. A closed shell of electrons in bonding orbitals is a definition of aromacity.

In benzene, the lowest energy ‘p’ orbitals comprise electron density above and below the plane of the molecule. These electron orbitals are spread over, delocalised over or conjugated over all six carbon molecules in the benzene ring. The delocalised ‘p’ orbitals can themselves be thought of as a ring. Expressed another way, this type of delocalisation is an uninterrupted sequence of double and single bonds, and it is this which is described as conjugation. The properties of this type of system are seen to be different from its component parts.

Benzene has six π electrons, and in consequence all its bonding orbitals are full, giving the molecule a closed structure, which is often not the case for quite similar molecules with a lot of double bonds. This is referred to as a molecule being aromatic. The general rule is that there has to be a low energy bonding orbital with the ‘p’ orbitals in-phase. There is a closed shell giving greater stability in aromatic systems, where there are two ‘p’ orbitals forming a π bond and four other electrons.

Carbon and oxygen bonds
It is not essential in these systems to have carbon-to-carbon bonds. Carbon and oxygen also often form double bonds, separated by just one single bond. Here to the behaviour of the double-bonded system is quite different from the behaviour of the component parts. These structures are special in the sense of only arising where there are ‘p’ orbitals on different atoms available to overlap with one another. In many other molecules, there is a similarity in terms of a large number of double bonds, but they are insulated from one another by the lack of ‘p’ orbitals available to overlap with one another.

Amide groups, amino acids and protein P. The amide group is crucial to protein, and therefore to living systems as a whole, in that it forms the links between amino acid molecules that in turn make up protein, the basic building blocks of life. The amino group on one amino acid molecule combines with the carboxylic group on another amino acid molecule to give an amide group. When a chain of this kind forms it is a peptide or polypeptide, and longer chains are classed as proteins. Conjugation arises from the bonding of a lone pair of ‘p’ orbitals, and this is vital in stabilising the link between the amino acids, and making it relatively difficult to disrupt the amino acid chains that make up protein.

3.4: Structure of molecules
The structure of the individual atom is also the basis for the structure of molecules. Atomic orbitals are wave functions, and the orbital wave functions of different atoms are like waves, in that if they are in phase, their amplitudes are added together. When this happens, the increased amplitude of the wave function works against the mutual repulsion of the positively charged atomic nuclei of different atoms, and works to bond the atoms together. This is referred to as a bonding molecular orbital.

When the orbitals are out-of-phase, they are on the far sides of the atomic nuclei, which continue to repel one another due to like positive electric charges, and this arrangement is known as the anti-bonding molecular orbital. Collectively the two types of molecular orbital are referred to as MOs. The antibonding MOs usually have higher energy than the bonding MOs. Energy applied to an atom can promote a low-energy bonding orbital to a higher-energy anti-bonding orbital, and this process can break the bond between two atoms. When ‘s’ orbitals combine, the MOs are symmetrical, and this type of orbital overlap has sigma (σ) symmetry, and is described as a sigma (σ) bond.

When there is a combination of 'p' orbitals, there is a possibility of three different 'p' orbitals on axes that are perpendicular to one another. One of these can overlap end-on with an orbital in another atom, and these two orbitals are described as 2pσ and 2pσ*. Two other orbitals can overlap with those on other atoms side-on, and will not be symmetrical about the nuclear axis. These are described as π orbitals and form π bonds. P. In discussing bonding, only the electrons in the outermost shell of the atoms are usually relevant. For example, in a nitrogen molecule formed by the bonding of two nitrogen atoms, only the electrons in the second, ‘n’ = 2, shell are involved in bonding. The nitrogen atom has seven electrons, so there are fourteen on the two atoms that bond to form a nitrogen molecule. Two electrons in the inner shell of each atom are not involved, leaving five on each atom and ten altogether in the second shells. The 2s electrons on each atom cancel out, and are described as lone pairs. The bonding work thus devolves on three electrons in each atom, or six in the whole molecule. These form one σ bond and two π bonds. This is described as a triple-bonded structure. Orbitals overlap better when they are in the same shell of their respective atoms. So electrons in the second shell will overlap more readily with other second shell electrons than with third or fourth shell electrons. Further to that 'p' electrons must have the right orientation and p_x electrons can only interact with other p_x electrons and so on, because the x, y and z electrons are perpendicular or orthogonal to one another.

Molecular bonding also applies to molecules that are formed out of different types of atoms, as distinct from molecules formed from atoms of the same element such as the nitrogen molecule discussed above. If the atomic orbitals of different atoms are very different, they cannot combine, and the atom cannot form covalent bonds (sharing the electron between two atoms). Instead an electron can transfer from one atom to another, transforming the first atom into a negative ion, and the second atom into a positive ion, with the molecule now held together by the attraction between the oppositely charged ions. This is known as ionic bonding. Covalent bonds with overlapping orbitals can only be formed when the difference in energy is not too great. P. Hybridisation

Hybridisation is an important factor in the formation of molecular bonds. The ‘s’ and ‘p’ orbitals are those most important for organic chemistry, and for the bonding of atoms such carbon, oxygen, nitrogen, sulphur and phosphorous. Hybridised orbitals are viewed as ‘s’ and ‘p’ orbitals superimposed on one another.

3.5: QUANTUM COHERENCE AND ENTANGLEMENT IN BIOLOGICAL SYSTEMS
The key argument against quantum states having a practical role in neural processing is that in the conditions of the brain quantum decoherence would happen too rapidly for the states to be relevant. This view was crystallised by the (9. Tegmark, 2000) paper published in the prestigious journal, Physical Review E. The paper itself was not remarkable. For reasons that have never been properly explained, it used a model of quantum processing that has never been proposed elsewhere, and it failed to discuss or even mention arguments for the shielding of quantum processing in the brain. Nevertheless, it succeeded in confirming in a prestigious way the views of the numerous opponents of quantum consciousness.

The situation remained like that between 2000 and 2007, after which the debate over quantum states in biological systems was moved to a new stage by the discovery that quantum coherence has a functional role in the transfer of energy within photosynthetic organisms (10. Engel et al, 2007). This moved the discussion of what sort of coherent biological features could support consciousness on from a phase of pure theorising, to a phase, in which ideas can be related to features that have been shown to exist in biological matter.

3.6: The Engel study
The Engel et al paper studied photosynthesis in green sulphur bacteria. The photosynthetic complexes (chromophores) in the bacteria are tuned to capturing light and transmitting its energy to long-term storage areas. It should be stressed that in this system, photons (the light quanta) only provide the initial excitation, and the coherence and entanglement discussed here involves electrons in biological systems. The Engel study documented the dependence of energy transport on the spatially extended properties of the wave function of the photosynthetic complexes. In particular, the timescale of the quantum coherence observed was much longer than would normally be predicted for a biological environment, with a duration of at least 660 femtoseconds (femtosecond=10^-15seconds), nearly three times as long as the classically predicted times of 250 femtoseconds. In the latter case, rapid destruction of coherence would prevent it from influencing the system. The wavelike process noted by Engel was suggested to account for the efficiency of the system, at 98% compared to the 60-70% predicted for a classical system.

3.7: Limited dephasing
Another researcher in this area, Martin Plenio, argues that where temperatures are relatively high, there is likely to be some dephasing of the quanta, but contrary to the popular view that this would be the end of quantum processing, the efficiency of energy transportation could actually be enhanced by this limited dephasing. Referring to a quantum experiment with beam splitters and detectors, he suggests that partial dephasing might actually allow the wider and therefore more efficient exploration of the system.

3.8: Cheng & Fleming: - the protein environment
In a paper by Cheng & Fleming published in ‘Science’ (11.) a study of long-lived quantum coherence in photosynthetic bacteria, demonstrates strong correlations between chromophore molecules. One experiment looked at two chromophore molecules. The system provided near unity efficiency of energy transfer, and also demonstrates energy transfer between the chromophores.

The experiment also shows that the time for dephasing of these molecules is substantially longer than would have been traditionally estimated. The traditional approach in particular ignored the coherence between donor and acceptor states. The adaptive advantages of this lie in the efficiency of the search for the electron donor. The longer time to dephasing of one as compared to the other of the experimental chromophores was taken to indicate a strong correlation of the energy fluctuations of the two molecules. This meant that the two molecules were embedded in the same protein environment.

Another study by Fleming et al that also observed long-lasting coherence in a photosynthetic indicated that this could be explained by correlations between protein motions that modulate the transition energies of neighbouring chromophores. This suggests that protein environments works to preserve electronic coherence in photosynthetic complexes, and thus optimise excitatory energy transfer.

Chains of polymers
Elizabetta Collini and Gregory Scholes conducted an experiment also reported in ‘Science’ (12.) that observed quantum coherence dynamics in relation to electronic energy transfer. The experiment examined polymer samples with different chain conformations at room temperature, and recorded intrachain, but not interchain, coherent electronic energy transfer.

It is pointed out that natural photosynthetic proteins and artificial polymers organise light absorbing molecules (chromophores) to channel photon energy. The excitation energy from the absorbed light can be shared quantum mechanically among the chromophores. Where this happens, electronic coupling predominates over the tendency towards quantum decoherence, (loss of coherence due to interaction with the environment), and is viewed as comprising a standing wave connecting donor and acceptor paths, with the evolution of the system entangled in a single quantum state. Within chains of polymers there can be conformational subunits 2 to 12 repeat units long, which are the primary absorbing units or chromophores. Neighbouring chromophores along the backbone of a polymer have quite a strong electronic coupling, and electronic transfer between these is coherent at room temperature.

3.9: Quantum entanglement considered - Sarovar et al (2009)
In a 2009 paper, Sarovar et al (13.) examined the subject of possible quantum entanglement in photosynthetic complexes. The paper starts by discussing quantum coherence between the spatially separated chromophore molecules found in these systems. Modelling of the system showed that entanglement would rapidly decrease to zero, but then resurge after about 600 femtoseconds. Entanglement could in fact survive for considerably longer than coherence, with a duration of five picoseconds at 77K, falling to two picoseconds at room temperature. The entanglement examined here is the non-local correlation between the electronic states of spatially separated chromophores. Coherence is a necessary and sufficient state for entanglement to exist.

Ishizaki and Fleming (2009)
This paper (14.) developed an equation that allows modelling of the photosynthetic systems discussed above. Where this deals with the sites to be excited by the light energy, the initial entanglement rapidly decreases to zero, but then increases again after about 600 femtoseconds. This is thought to be a function of the entanglement of the initial sites being transported and localised at other sites, but remaining coherent at these other sites, from which further entanglement can subsequently resurge. Other studies appear to confirm the existence of picosecond timescales for entanglement in chromophores. It is not clear to the authors that entanglement is actually functional in chromophores. Coherence appears to be sufficient for very efficient transport of energy, and entanglement may be only a by-product of coherence. This looks to remain an area of scientific debate.

Earlier studies such as Engel’s were performed at low temperatures, whereas quantum coherence becomes more fragile at higher temperatures, because of the higher amplitude of environmental fluctuations. In the Ishizaki and Fleming paper, the equation supplied by the authors suggest that coherence could persist for several hundred femtoseconds even at physiological temperatures of 300 Kelvin.

This study deals with the Fenna-Matthews-Olson (FMO) pigment-protein complex found in low light-adapted green sulphur bacteria. The FMO is situated between the chlorosome antenna and the reaction centre, and its function is to transport energy harvested from sunlight by the antenna to the reaction centre. The FMO complex is a trimer of identical sub-units, each comprised of seven bacteriochlorphyl (BChl) molecules. This structure has been extensively studied.

Each unit of the FMO comprises 7 BChl molecules. BChl 1 and 6 are orientated towards the chlorosome antenna, and are the initially excited pigment, and BChl 3 and 4 are orientated towards the reaction centre. Even at the physiological temperatures, quantum coherence can be observed for up to 350 femtoseconds in this structure. This suggests that long-lived electronic coherence is sustained among the BChls, even at physiological temperatures, and may play a role in the high efficiency of EET in photosynthetic proteins. P. BChl 1 and 6 are seen as capturing and conveying onward the initial electronic energy excitation. Quantum coherence is suggested to allow rapid sampling of pathways to BChl 3 that connects to the reaction centre. If the process was entirely classical, trapping of energy in subsidiary minima would be inevitable, whereas quantum delocalisation can avoid such traps, and aid the capture of excitation by pigments BChl 3 and 4. BChl 6 is strongly coupled to BChl 5 and 7, which are in turn stongly coupled to BChl 4, ensuring transfer of excitation energy.

Delocalisation of energy over several of the molecules allows exploration of the lowest energy site in BChl 3. The study predicts that quantum coherence could be sustained for 350 femtoseconds, but if the calculation is adjusted for a possible longer phonon relaxation time, this could extend to 550 femtoseconds, still at physiological temperatures.

Cia et al (2008): - resetting entanglement
A 2008 paper from Cia et al (15.) also looked at the possibility of quantum entanglement in the type of system studied in the Engel paper. Cia takes the view that entanglement can exist in hot biological environments. Cia says traditional thinking on biological systems is based on the assumption of thermal equilibrium, whereas biological systems are far from thermal equilibrium. He points out that the conformation of protein involves interactions at the quantum level. These are usually treated classically, but Cia wonders whether a proper understanding of protein dynamics does not require quantum mechanics. It is said not to be clear, whether or not entanglement is generated during the motions of protein, but that it is possible that entanglement could have important implications for the functioning of protein.

Continued Online Book 3