Michael Alastair Butler (0236742) MSc by Research in Neuroscience
    
    Molecular acoustics of cytoskeletal proteins:
    A novel method for investigating cellular biophysics
    
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    Musica… quasi ad omnia se extendit, ad Deum et ad creaturas, incorporeas et corporeas, coelestes et humanas, ad scientias theoricas et practices… (Music… reaches almost all things; God and creatures, incorporeal and corporeal, celestial and human, theoretical and practical aspects of knowledge…) Jacques de Liège (14th Century)
    
    …we have, as yet, scarcely touched the question of why music, for better or worse, has so much power. Oliver Sacks, Brain 2006
    
    The body cannot determine the mind to thinking, and the mind cannot determine the body to motion, to rest, or to anything else (if there is anything else). Benedict de Spinoza, Ethics, III P2
    
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    Contents
    Introduction Background: Acoustics, physical chemistry and biology
    • Mechanical vibration and acoustics o Mechanical vibration and acoustics o Mechanical vibration and chemistry o Normal modes of proteins o Functions of normal modes in polymerisation
    
    Mechanosensation, biology and neuroscience
    • • Introduction Molecular candidates of mechanosensation o Cell adhesion molecules – integrins and stress fibres o Cell adhesion molecules – Cadherins and other cell-adhesion molecules o Mechanosensory membrane proteins • Mechanotransduction, mechanosensation and acoustics
    
    Materials and Methods
    • • • Molecular Dynamics and Normal Mode Analysis Lattice Boltzmann Modelling Actin Polymerisation Assay and ultrasound experiment o Actin monomer preparation from acetone powder o Preparation of N-(1-pyrenyl)iodoacetamide-labelled actin o Actin polymerisation assay o Ultrasound equipment Set-up
    
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     
    
    Piezo-electric material choice Experimental set-up
    
    o Experimental procedure
    
    Results and Discussion
    • • • • • Introduction Protein normal mode frequency calculations Lattice-Boltzmann modelling of actin polymerisation in a standing wave. High frequency ultrasonic excitation of actin polymerisation Further work o Protein normal mode and Lattice-Boltzmann Modelling o High frequency excitation of proteins and other molecules
    
    Conclusion Acknowledgements Bibliography
    
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    Introduction
    This is project investigates the effects of acoustics on biochemistry. It concentrates upon the molecular vibrations of single proteins and assemblies of proteins, how these may be affected by the introduction of acoustic waves at a frequency corresponding to their normal modes and therefore how these may affect biological mechanisms. However, I do not wish to introduce this project immediately from a biochemical perspective, but instead give a better idea of the context in which it has grown. Research on the neuroscience of music often concentrates upon the biophysical mechanisms of hearing, the functional organisation of elements of musical perception or pathologies which affect either of these. These areas may be succinctly grouped as investigating the instrumental aspects of music, such as pitch, rhythm, tone and the perception thereof. However, in both science and the humanities the definition of music has historically been extended beyond merely instrumentalis. The 14th Century theologian Boethius described two other types of music, the music that imbues life into the body and the music of the heavenly spheres producing the motion of the universe; musica humana and musica mundana. In comparison, in the early 20th Century Schrödinger produced his statistical model of atomic structure, which is now the basis for understanding molecular structure and dynamics in biochemistry, by modelling particles as harmonic waves, whilst Einstein, using his general theory of relativity, applied this new formulation to the movement of large bodies of matter in space. Although these are very abstract notions, the most important and interesting idea is that music in this sense is viewed very differently to the common understanding of instrumental music; it is perhaps better described as complex dynamic patterns of reality, found in all things or simply a kind of universal energy. This project is interested in the musica humana, the complex dynamics of biochemistry and how this gives rise to life. It investigates how acoustic waves may affect the physical chemistry of bio-molecules and therefore how this may also affect the biological mechanisms in which they participate. As we shall see the description of musica humana is quite apt. The relationship between acoustics and physical chemistry is extremely complex, relying on harmonic modes of atoms and molecules, whilst interrelations between molecules may play on these modal aspects. Energy exchange between molecules can therefore be understood as a complex combination of modes over time, a type of molecular music. If we wish to excite these relations with acoustics, we may also need to compose complex harmonies of ultrasonic waves. By investigating the importance of acoustic phenomena in the development and maintenance of organisms, it may be possible to better understand the power of music over biological organisms whilst also exploring the deepest physical connections between life and the physical world.
    
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    Background
    Acoustics, physical chemistry and biology
    Mechanical vibration and acoustics
    Mechanical vibration is found in everything. Any mechanical movement, whether at the level of a planet, animal, peptide or atom, can be understood from the perspective of vibration. Indeed, one of the most influential theories of the 20th Century, without which many of the modern discoveries in biology would not have been possible, involved treating the world of tiny particles in terms of waves. In the 21st Century, increasing computational power has allowed quantum mechanics to predict the dynamics of larger molecules as well as providing the theory for NMR and Raman spectroscopy, both of which are only beginning to show their full potential in biochemistry. As biophysicists are gaining the tools to study larger and more complex systems, it is interesting and, I hope to show, important to ask how mechanical vibration is related to the underlying atomic dynamics. It is important to appreciate that mechanical vibration, pressure waves and acoustic waves all relate to different perspectives of the same continuous system, where vibration describes mechanical movement of a structure whilst waves describe the propagation of this movement between structures. Acoustics in this sense does not equate to the frequency range of human hearing, but to the entire range of mechanical frequencies found in nature. The ultrasonic vibrations that this project investigates include acoustic frequencies above conscious auditory perception and so have a range from about 20 KHz. Frequency range (approx.) High >10MHz >100KHz 20Hz–120KHz 20Hz-80KHz 20-100KHz 20Hz-20KHz Low <20Hz Biological response Sub-cellular/Molecular Cellular Aqueous animals Small land animals Human: Hypersonic Sonic Infrasonic Systems Sensory Protein? Membrane? Auditory Auditory Unknown Auditory Tactile Communicative Architectural? Mechanotransduction? Vocal/Vibratory Vocal/Vibratory None Known Vocal None known
    
    Figure 1. An overview of the relation between frequency and biological systems. Question marks denote possible associations.
    
    Higher frequencies have smaller wavelengths and therefore will generally affect smaller systems; for instance mice squeak and hear higher frequencies than humans whilst large animals are correlated with a low frequency vocalisations and audition()1. In medical physics, higher resolution is gained by using higher frequencies of electromagnetic radiation and ultrasound2. The relationship between organism size
    1 2
    
    Hill, P., (2001) Silverman, R.H., et al, (2006)
    
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    and frequency can be quite complex, but the simple relationship between frequency and wavelength can be a useful reference for an overview of biological response to sound (see fig. 1). However, humans have been found to respond to both hypersonic (higher than conscious audition) and infrasonic (lower than conscious audition) frequencies3, so it may be possible that there is a wide bandwidth response throughout biology. Indeed, as I shall mention, there may be a deep evolutionary origin for mechanosensory response to high-frequencies; whether low frequency sound is important throughout biology however, remains to be studied. This project investigates frequencies above 1 MHz, specifically looking at wavelengths likely to affect cellular and sub-cellular mechanisms. For instance, there is experimental evidence that low intensity pulsed ultrasound (LIPUS) at 1 MHz can cause bone and skin cells to differentiate4. The molecular mechanisms of ultrasound mediated differentiation appear to be related to surface expression of integrins and phosphorylation of focal adhesion-related kinases5. Therefore, it is likely to be due to cell-extracellular matrix (ECM) integrin and focal adhesion interactions rather than a direct influence of ultrasound upon individual cellular mechanisms. Another group have used ultrasonic nodes to group cells together in vitro at 1MHz6, supporting the proposal that the effects of 1 MHz ultrasound may be too broad effects to directly affect the mechanisms of single cells. As we look at the smallest aspects of a system through which acoustic waves are channelled, for instance air or water, we find that the movement of waves can also be described as the inter-molecular structural changes of these small molecules. As an analogous illustration, recent work modelled the hydrophobic inter-relations between lipids and water using atomically derived molecular dynamics, an interaction that, although a truism in biological thought, had never been theoretically proven7. In contrast, in order to accurately describe the atomic structure of molecules, quantum mechanics determines that we must treat particles in terms of electromagnetic waves8. One could hypothesise that the particle-wave duality that is so integral to modern physics could also be used to describe the interaction between acoustics and molecular structure. It is far from the scope of this project to test this hypothesis, but it may eventually explore aspects that will confirm whether it is a plausible notion.
    
    Mechanical vibration and chemistry
    Mechanical vibration also does not exist as a single entity. Every mechanical movement from the level of molecules to the movement of a comet through the vacuum of space will influence and be influenced by its environment, whether that is through the mechanical propagation of pressure waves or through the gravitational effects of all objects with mass. Indeed much of particle and astronomical theory, including Einstein’s General Theory of Relativity, is based upon this idea of universal connectedness9.
    
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    Oohashi, T., et al, (2006) Sena, K., et al, (2005), Tang, C-H., et al, (2006), Zhou, S., (2004) 5 Tang, C-H., et al, (2006) 6 Coakley, W.T., (2004) 7 Giovambattista, N., (2007) 8 Hayward, D.O., (2002) 9 Heisenberg, W., (1958)
    
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    As a result, modelling molecular movement in terms of quantum particle-wave patterns is very difficult, since the patterns become extremely complicated even with a small number of atoms. With a simple homogenous physical system, it may eventually be possible to describe such molecular acoustics in terms of molecular structure, for instance in a pure gas10 (see fig. 2). However, this is complicated by the influence of the atmospheric pressure of earth, a high level description of the effects of gravity or more precisely the effects of the large planetary mass, and therefore the effects of pressure on space, literally position in threedimensions, in the molecular dynamics. These effects are generally described in classical terms of damping or signal attenuation in Figure 2. Plot of the acoustic resonance of gases against mass acoustics11. Whilst position is explicitly described in the physical chemical modelling of molecular dynamics, features of general relativity are rarely incorporated in practice. Work in space biology has confirmed the direct action of gravity even at the cellular level12, but there is little work exploring the general relativistic effect on the dynamics of molecules. Therefore, it is important to note that a complete description of mechanical vibration at a molecular level in biology must not only take into account interactions between the immediate environment, which can be adequately modelled by position at a constant pressure, but also the gravitational effects of the planetary environment. Once again, this goes well beyond the scope of this project, but is particularly relevant to the modelling work in this project, which only works with dynamics at a classically described constant pressure. Future work would hope to involve a more precise evaluation of molecular dynamics, but this would be dependent upon advances in physical chemistry or condensed matter physics. Normal modes of proteins The first section of this project utilises the molecular dynamics, Normal Modes Analysis (NMA) and lattice-boltzmann techniques which are available at present for modelling and analysing dynamics. These work respectively with semi-classical theory and a theory of gas dynamics that can be modified to produce an accurate description of liquid and active gel dynamics. The NMA program allows an analysis of molecules that have been entered and equilibrated in molecular dynamics program. The lattice-boltmann work builds upon models specific to actin polymerisation dynamics produced by Marenduzzo et al13. The ideas behind this work rely upon basic molecular dynamics, so I shall first describe the theory behind normal modes before describing the predicted effect upon polymerisation.
    10 11
    
    Matheson, A.J., (1971) Petculescu, A.G., Lueptow, R.M., (2005) 12 Yamashita, M., Baba, S.A., (2004) 13 Marenduzzo, D., Orlandini, E., Yeomans, J.M., (2007)
    
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    Figure 3. The figure on the left shows quantum vibrational states of a molecular mode. This is compared to the harmonics of tones with pitch C2 and C3 as well as an overview of the amplitude peaks found on the basilar membrane. (from Levine, R.D., 2005 and Campbell, M., 2001)
    
    Just like a violin string has many modes that make up its harmonics or every atom has quantal harmonics (see fig. 3), every molecule in our body has its own set of modes. These are based upon its chemical structure and the movement that this structure allows. As described earlier, these movements are intrinsically linked to the molecule’s interactions with its environment. Theoretically, these modes are very similar to acoustic modes, with resonant frequencies specific to the molecule that can influence and be influenced by the environment14. However, the molecular structures found in biology are generally more complex than those found in a one-dimensional string. For instance, a string would equate to the primary structure of a protein, whilst the secondary, tertiary and quaternary structures could all affect the modal features of a protein. In this project we only explore the modes found in ATP-bound monomeric g-actin, but modal properties, and therefore modal frequencies, would change with the alteration to tertiary and quaternary structure in dimeric, polymeric and ADP-bound actin. One of the central hypotheses of this project is that molecular vibration can be influenced by transduction through water of an acoustic signal at these modal frequencies. In acoustics this is described as a sympathetic resonance; if the environment is vibrating at a frequency that is also an inherent resonant frequency of the object, then that object will resonate in “sympathy” with the environmental stimulus. For instance, if you sing the musical note ‘A’ at the A-string of a violin, in other words sing a frequency of 440Hz at an object with a resonant frequency of 440Hz, then it will resonate. If you sing at 430Hz, so long as it is not tuned flat, it will not resonate. Similarly if you sing at 220Hz or 880Hz the string will resonate, although with much less intensity, since 440Hz will be present in the harmonic aspects of your sung note or as an inherent resonant harmonic of string. The right hand picture in figure 3 shows the harmonics of the lowest note written in musical notation; each note above the base note represents a multiple of the base frequency, ie. If the base note is 100Hz they will be 200Hz, 300Hz, 400Hz etc. The complexities of protein structure mean that calculating the modal frequencies of the molecule is much more complicated than describing the basic linear modal
    
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    Tirion, M., et al (1996), Ben-Avraham, D. (1993) & (1995)
    
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    features of a musical note15. Modes will be unlikely to have a linear relationship between frequencies as seen in figure 3, but will be more likely to have closely related modes with a similar frequency. As one can see in the figure 4, research in this area has produced methods for simplifying modal analysis for conformational investigations16, but these simplified analyses cannot predict modal frequency. At present the most accurate method for calculating frequency is to perform a full normal mode analysis of an explicitly solvated protein, as described in this project. Future work may benefit from algorithms which improve and simplify frequency calculation, but this is unfortunately unavailable a present.
    Figure 4. a) The vector field of a low frequency mode of actin b) A graph showing the displacement of each of the amino acid residues in the dynamics of this mode. Both were calculated using simplified modal models (see Hinsen, K., 2000)
    
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    b)
    
    Functions of Normal Modes in polymerisation Normal Mode Analysis has become an increasingly important technique for biological study of not only single macromolecular molecules but also supramolecular complexes17. Its use includes work with crystallography refinement, enzyme specificity, conformational changes in proteins and viruses, NMR order parameters and electron transfer18. It is therefore very likely that many of the mechanisms associated with these functions would be affected by changing the dynamics of normal modes in a protein or a complex of proteins; if sympathetic resonance affects the rate or dynamics of protein conformational changes, this will affect that protein’s ability to perform its typical function. For example, changing conformational dynamics may affect the ability for g-actin monomers to bind and become a dimer or to exchange ADP for ATP. Whether this will cause a reduction, increase or no change in the rate of reaction, will depend upon which modes are excited and how they may change the conformation of the molecule. This project uses actin polymerisation as a model to experimentally investigate whether these mechanical modes may affect biochemical mechanisms. Actin monomers polymerise rapidly into filaments, with the phosphorylation of ATP to ADP usually occuring in each monomer shortly after assembly. Actin monomers continue to assemble at both ends until a steady state is reached during which monomers assemble on the ‘plus end’ of the filament whilst depolymerisation occurs
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    Of course acoustic properties of all instruments are affected by many factors including their construction, design and methods of sound production which make modelling their precise modal features and intonation extremely difficult; this is one of the areas covered by work on musical acoustics. 16 Hinsen, K., et al, (2000) 17 Tirion, M.M., (1996) 18 Wynsberghe, A., (2005)
    
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    at the ‘minus end’. This is a process known as treadmilling; in vitro this continues until all actin-ATP has been phosphorylated to ADP, whereas in vivo actin-ATP is replenished by nucleotide exchange reactions. Various actin-binding molecules can affect the assembly, stability and higher order structuring of filaments19. In the experimental section of this project, actin polymerisation is initiated in vitro and exposed to high frequency acoustic waves at the resonant frequencies of monomeric actin. Using the actin fluorescent marker N-(1-pyrenyl)iodoacetamide, which is strongly fluorescent upon polymerisation whilst only weakly fluorescent in the monomeric state20. The change in fluorescence in the emitted frequencies of 388 and 403nm upon actin polymerisation can therefore be measured using a fluorometer, enabling quantitative measurement of the effects of acoustic waves upon actin polymerisation. The Lattice-Boltzmann work aimed to see if the effects of conformational changes could be revealed in a high-level model of actin polymerisation. This was achieved by inserting a standing wave into a liquid crystal model solved by the Lattice-Boltzmann equation, which uses a modified gas model for studying liquid dynamics. This comes from work modelling the active properties of actin polymerisation produced by Marenduzzo et al21 that agreed with previous experimental work on the dynamics of actin polymerisation patterns. This work will therefore examine whether a high level model of actin dynamics, which does not take molecular dynamics into account, could predict the response of actin to acoustics. The work only covers a one-dimensional model, so further research would be necessary to extend the work to threedimensions. However, if the results from this model agree with experimental work it may show that the effects of molecular acoustics are directly related to the parameters necessary for an accurate model of polymerisation, and therefore have importance even in high-level understandings of dynamics.
    
    Mechanosensation, Biology and Neuroscience
    The previous section described the physical and chemical theory behind the simple system modelling and in vitro experimental work on actin polymerisation that will be studied in this project. In vivo, it will be much more difficult to understand the correlation between acoustics and the cytoskeletal. Therefore, in order to understand the significance of this work to biological systems, it will be necessary to study systems that are suitably related to mechanical vibration. In the complexity of a biological system, with its multiplicity of chemical structures, there is most likely to be a simple correlation between acoustics and molecular structure in systems specialising in mechanical signalling. I hope to describe the connection between these mechanosensory mechanisms, acoustics and the molecular structure upon which it may work.
    
    Molecular candidates of mechanosensation
    Much important neuroscientific work in the area of mechanical signals has concentrated upon the biophysics of inner ear cells, specifically elasticity of tip-gate
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    Alberts, B., (2002) Kouyama, T. and Mihashi, K., (1981) 21 Marenduzzo, D. et al, (2007)
    
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    mechanisms22, cilia dynamics23 and their connection to subsequent depolarisation of auditory pathways. More recent work in cellular biology has begun uncovering mechanosensory protein channels and mechanisms of inter and intracellular mechanotransduction signalling24. All of these processes involve a method for producing tension and sensing force through molecular structures; in comparison, inner ear cells are also thought to produce tension in the cilia and basilar membrane in order to sense force through mechanosensory channels. It is believed that myosin VII maintains cytoskeletal tension in the cilia of the inner ear cells, a process which has been recently shown with myosin VIIb25, whilst the candidate for mechanosensation is still controversial(). Mutation of myosin VIIa leads to deafness and balance anomalies in humans, mice and zebrafish. The mutation in humans, known as Usher Syndrome, disrupts both the auditory and visual system26. This visual pathology is understood to produce photoreceptor cell death27; disruption of these mechanisms therefore does not only affect cellular activities directly involved in mechanical sensation. The common evolutionary origins of the two systems may explain the use of this specific myosin in both systems, but many other cells have similar mechanisms.
    
    Cell adhesion molecules - Integrins and stress fibres It is often necessary to use other cells or the extra-cellular matrix as an anchor point for migration or internal maintenance of tension. Proteins involved in ECM-cell and cell-cell interactions almost certainly had an important evolutionary and developmental role in the rise of complex cellular activity and multi-cellular organisms. A diverse range of integrins often facilitate adhesion of cytoskeletal structures to the ECM through intracellular focal complexes and mature focal adhesions whilst an equally diverse range of other membrane surface molecules such as cadherins and proteoglycans contribute to intercellular interactions; however, there is often an integration of function between many cell adhesion molecules28. Integrins and cadherins are extremely important in the development and plasticity of the nervous system; they are implicated in neuronal cell migration, neuronal differentiation as well as synapse formation and maintenance29. Given this importance in the nervous systems it also interesting to note that interactions between actin stress fibres, focal adhesions and cell adhesion molecules are also extremely important for understanding mechanosensory mechanisms. Stress fibres are bundles of actin fibres containing myosin and other actin-binding molecules that generate contractile forces in the cell. They are associated with focal adhesions which are accumulations of multiple proteins at the intracellular surface of the membrane that act as mediators between the stress fibres, integrins and the ECM. These are important for cell migration, intercellular interactions and structural
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    Sotomayor, M., (2005) Kozlov, A.S., (2007) 24 Ingber, D.E., (2006) 25 Henn, A., (2005) 26 Todi, S., (2005) 27 Reiners, J., (2005) 28 Hirayama, T., Yag, T., (2006) 29 Morishita, H., et al, (2006)
    
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    changes in most cells. For instance, recent work by Brophy, P. et al has shown laminin mediated development in myelin-forming Schwann Cells that works with integrins and focal adhesions30. An intracellular signalling pathway through integrins, Rho-type GTPases and myosin II is believed to modulate the action of actin stress fibres. It has recently been suggested that myosin II mediates actin bundle dynamics in the neuronal growth cone through this intercellular signalling pathway31. The pathway also appears to be conserved between human stress fibres and Drosophila wing hair cytoskeletal organisation (see fig. 5). As focal adhesions are large plaques attached to the ECM through integrins, they rarely move from where they have formed. In contrast, cell migration uses focal adhesions as a basis for producing cell motion through actin polymerisation and myosin-actin contraction; it has been found that the transmission of this force is regulated by focal adhesion molecules such as vinculin and talin32. However, focal adhesion complexes can respond, even without stress fibre formation, to increased force from the Figure 5. Similarities between signalling involved drosophila wing hair and stress ECM by increasing growth and dissociating fibre formation (Müller, U., (2001) when ECM force is reduced. Cell adhesion molecules – Cadherins and other cell-adhesion molecules The interactions of cadherins in cellular differentiation and intercellular interactions have become increasingly important in neuroscience. Cadherins are extremely important in neurodevelopment, for instance expression of N-cadherin and N-CAM distinguishes neural tube formation from adjacent ectoderm. Cadherins also have importance in the development of spines through neuronal stress fibres, allowing plasticity through new synaptic connections33. Catenins mediate between cadherins and the actin cytoskeleton, and allow regulation and organisation of actin assembly through similar GTPase signalling pathways as found in focal adhesions34. Cell adhesion molecules, including cadherins and integrins, therefore often modulate the interactions of cytoplasmic structures, but also often affect the interactions of other membrane bound molecules both through direct binding and intracellular pathways. Since cell adhesion molecules have such integrated pathways, it would seem likely that mechanotransduction would also occur in adherin junctions as well as focal adhesions. Very little is currently known about cadherin mediated traction forces, although preliminary results suggest they involve a similar system to focal
    30 31
    
    Grove, M. et al, (2007) Müller, U., Littlewood-Evans, A., (2001) 32 Hu, K., Ji, L., et al, (2007) 33 Bamji, S., (2005) 34 Drees, F., et al, (2005)
    
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    adhesions35. There are also many other cell-adhesion molecules that play a part in the dynamics of the nervous system; for instance adhesion molecules from Ig-family are thought to work with semaphorin for axonal guidance in neurodevelopment36 and other authors describe the interactions of nectin proteins37. Clearly, there is some way until a full characterisation of the ever increasing number of cell-adhesion molecules and their interactions can be achieved, but with an increasing number of molecules interacting with cytoskeletal and mechanotransduction mechanisms such as stress fibres and focal adhesions, it may be all the more important to characterise their mechanical dynamics. Mechanosensory membrane proteins In addition to cell adhesion molecules, there are some membrane bound protein channels and possibly ligand receptors that also respond to mechanical force. The MscL, MscS and MscK channels (Mechano-sensation channels Large conductance, Small conductance and Potassium, named after its primary cation) are found in E. coli and all react to changes in mechanical force through osmotic pressure. Channels of similar homology are found in all three branches of the phylogenetic tree, therefore they are predicted to have early evolutionary origins38. As shown in figure 6a, MscL is made up of five sub-units with two trans-membrane α-helices and is believed to open through an iris-like conformational change caused by an increase in membrane tension39. Mechanically-gated receptors were thought to be controlled by interactions with elements of the cytoskeleton but so far the evidence supports gating through membrane tension. Experiments on MscS (figure 6b) also show a reaction to increasing membrane tension, but only through sudden influx; slow application of increasing pressure does not open the channels. This slight difference is thought to be important in cell osmosregulation40. Also unlike MscL channels which are thought to be solely prokaryotic, MscS channels are widespread and are found in eukaryotes41. The mechanoreceptor channels involved in both audition and touch b) a) in drosophila are from the TRPsuperfamily of ion channels. These Figure 6. Structure of the closed (top) and open (bottom) have distant genetic homologies states of a) MscL and b) MscS (Blount, P., 2003)
    
    35 36
    
    Ganz, A., et al, (2006) Bechara, A., et al (2007) 37 Tsukasaki, Y., et al, (2007) 38 Martinac, B. (2001) 39 Kung, C. (2005) 40 Akitake, B. et al (2006) 41 Kung, C. (2005)
    
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    with the Msc channels found in E. Coli, suggesting an evolutionary connection between the two families42. Hearing in Drosophila occurs through mechanical wave transduction in the fly’s antennae and the subsequent deformation of scolopidia. Scolopidia are cells attached to two cuticles, responding to changes of cuticle orientation by opening TRP mechanoreceptor ion channels. This in turn evokes an action potential in neurons associated with the scolopidia. Touch in Drosophila is also thought to occur through the interaction of cilia between an extra-cellular bristle and the associated neuron via mechanosensory ion channels. Mutations in genes producing proteins involved in the transduction of sound, for instance myosin VIIa or the actin fibre cross-linking protein harmonin, have been found to affect both auditory and tactile responses43. Additionally, the TRP-family receptors are found in the human cochlear, giving a strong and perhaps ancient evolutionary connection between the various forms of mechanoreceptor44. They have also recently been investigated for their poly-modal response to cold and molecules that mimic the effects of cold45. Determining the strength of this connection will require further research; however, it seems likely that the auditory and tactile systems of all life have a common ancestral mechanoreceptor.
    
    Mechanotransduction, mechanosensation and acoustics
    Having described the molecular candidates of mechanosensory mechanisms, this last section will explain how the various systems may be related to acoustic wave transduction. As described earlier, the structure and function of many molecules or complexes of molecules may be understood in terms of normal mode dynamics. If sympathetic resonance can occur in the dynamic relations between water and a protein then we will know for certain that acoustics signals imposed upon smaller molecular substrate can transduce resonant frequencies into larger molecules. However, sympathetic resonance should also be transduced between similarly sized or structured molecules that have similar acoustic resonance spectra. For instance, we may find that the resonant spectrum of an actin-binding protein allows preferential binding to actin if it has a similar spectrum to that of actin. With phosphorylation its resonant spectrum may change and causes its resonance features to be incompatible with those of actin. Of course, this is pure speculation, but it would be extremely Figure 7. Biophysics work on MscS channel inefficient for a molecular system to opening with respect to membrane geometry continually work against the resonant (Meyer, G.R., et al 2006)
    42 43
    
    Kung, C. (2005) Eberl, D. (2000) 44 Boekhoff-Falk, G. (2005) 45 Proudfoot, C.J. et al, (2006)
    
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    features of the molecules involved. Indeed, it would seem likely that evolution would work towards the least energetically involved mechanisms for transducing signals in cellular dynamics. For instance, biological organisms often prefer specific isomers of molecules; using a single isomer may have been an adaptation to overcome threedimensional spectral resonance differences between the structures of the isomers. If transduction is transferred through similarly resonant molecules, allowing a reduction in attenuation or damping, then it would be extremely useful to compare resonant features of molecules in cell adhesion, focal adhesion and cytoskeletal processes. Large macromolecular system dynamics could then be predicted through comparative resonance studies based upon crystallographic data. Finally, protein channel mechanoreceptors such as Msc or TRP receptors may be directly linked to liquid-transduction of high frequency acoustic waves. As seen in mechanisms of cell motility, lipid bilayers are extremely dynamic areas of the cell. Recent work on the dynamics of the MscL mechanoreceptor suggests that the geometry and the composition of the lipid bilayer (see fig. 7) can affect channel gating even at very short time periods46. Whether this means that external or internal pressure waves may gate channels as well as osmotic pressure remains unclear, but it may be possible to elucidate such a mechanism with further work.
    
    46
    
    Meyer, G.R., et al, (2006)
    
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    Materials and methods
    Molecular Dynamics modelling and Normal Mode Analysis
    A Protein Data Bank file (.pdb) for the crystal structure of monomeric ATP-bound actin from Drosophila (2HF4) was taken from the Research Collaboratory for Structural Bioinformatics (RCSB) data bank. Atomic descriptions from this file were modified to align with the coding practice of the AMBER 8.0 molecular dynamics program. Preparation files (.prep) and force field modification files (frcmod or .dat) for ATP and metal ions were taken from work by Meagher, K.L., et al (2003) and Bradbrook, G.M. et al (1998) respectively. The leaprc.ff99 force field was modified to include additional oxygen bond types not found in the original force field file. These files were then loaded into the LEAP program using both the modified leaprc.ff99 and leaprc.gaff files to account for non-typical amino acid groups. Sodium ions were added in order to neutralise the molecule’s charge and a solvate box of water was added around the finished actin molecule. Finally, input coordinates (.inpcrd) and topology parameter (.prmtop) files were saved for use in the molecular dynamics program. This process was repeated for the implicitly solvated actin (without adding the solvate box) and for producing new molecular dynamics files for the limited explicit model and modified protein data bank files. Minimisation of the explicitly system, involved four stages: 1. Minimisation of the water and ions (holding protein fixed) using SHAKE 2. Minimisation of the entire system 3. Heating the entire system up to 300K 4. Equilibrating the pressure of the entire system to 1 Atmosphere. The system was then set to run as a dynamics for a short period (1µs) for a final relaxation. Normal mode analysis was then carried out on the final co-ordinates of the system using the ‘nmode’ program from the AMBER 8.0 suite.
    
    Lattice Boltzmann modelling
    Using a pre-made model of actin polymerisation dynamics in one-dimension solved using the Lattice-Boltzmann equation, a cosine change in density was added to the code to simulate a standing wave. The frequency of the standing wave (λ) and activity (ζ) of the actin were then progressively changed. For the unit ζ, negative is contractile active whilst positive is extensile active. The effect of the standing wave was then visualised by comparing the flow of the active gel (corresponding to the density change) to the direction of actin polymerisation.
    
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    Actin polymerisation assay and ultrasound experiment
    Actin monomer preparation from acetone powder
    This method was originally taken from Spudich, J. and Watt, S. (1971) and reproduced from protocols by Sutherland MacIver. All chemical were purchased from Sigma-Aldritch. Except where stated all procedures were carried out and stored in a cold room: 1. Produce 1M MgCl2 solution using 4.6g per 100ml. 2. Produce 0.1M EGTA pH 8.0 using 3.8g per 100ml. 3. Produce buffer G solution: 2mM Tris-HCl pH 8.0 0.2mM ATP 0.5mM DTT 0.2mM CaCl2 0.002% NaN3 Stock Dry Dry Dry Dry Dry Per litre 0.242g 55.1g 0.077g 0.022g 0.20g
    
    4. Add 2.5g acetone powder (from rabbit muscle) to 100ml of Buffer G. 5. Extract by stirring on ice for 30 minutes. 6. Remove insoluble material by filtration using filter paper on a scintered funnel. 7. Re-filter until clear, finally using a 0.2 µm filter. 8. Add 6g of KCl for every 100ml of solution 9. Add 0.2ml of 1M MgCl2 per 100ml 10. Finally add 1ml of 0.1M EGTA pH8.0 11. Stir slowly at room temperature for 15 minutes, then on ice for 30 minutes. 12. Centrifuge for 2 hours in a Ti45 Beckman at 37krpm at 4°C 13. Suspend pellet in 500ml Buffer G and homogenise with a hand homogeniser. 14. Dialyse using Visking tubing in a measuring cylinder against 1L of Buffer G with 2 changes for at least 2 days 15. Centrifuge for 2 hours in a Ti45 Beckman at 37krpm at 4°C. 16. Set up a large S-300 Column for removal of oligomers. 17. Equilibrate the column with at least 1L of Buffer G. 18. Run supernatant over column. 19. Read the OD290 against buffer G 20. Calculate concentration of actin monomer solution using the following values: 0.63 OD290 = 1 mg/ml = 23.8microM
    
    Preparation of N-(1-pyrenyl)iodoacetamide-labelled Actin
    This method was taken from Kouyama, T. and Mihashi, K. (1981) also reproduced from a MacIver protocol. 1. Produce 10mM Dimethylformamide solution: 3.85g per litre
    
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    2. Produce dialysis buffer: 25mM Tris-HCl pH 8.0 0.3mM ATP 0.1mM KCl 2mM MgCl2 3mM NaN3 Stock Dry Dry Dry 1M solution Dry Per litre 3.025g 55.1g 7.46g 2ml of stock 0.195g
    
    3. Dialysed 30-80mg of actin against dialysis buffer 4. Clarify a 1ml sample by centrifuging at a low speed and read OD290. 5. Dilute the remainder to 1mg/ml and calculate the number of moles 6. Transfer to a 100ml flask with a magnetic flee 7. Produce 0.01M of pyrenyl marker in Dimethylformamide solvent. 8. Add 4-7 mol pyrenyl per mol of actin, while gently stirring. 9. Cover with foil and leave overnight at 4°C. 10. Centrifuge at low speed to pellet the precipitated dye. 11. Centrifuge the cleared supernatant for 2 hours in a Ti45 Beckman at 38krpm at 4°C. 12. Homogenise the pellet in Buffer G and make-up to a concentration of about 6mg/ml by reading the OD290. 13. Dialyse against Buffer G for 2 days, with 2 changes of buffer. 14. Centrifuge in a Ti45 Beckman at 38krpm at 4°C. 15. Gel filter with the S-300 column having equilibriated with Buffer G. 16. Read the OD344 and OD290 for each fraction. 17. Calculate the concentrations using the following values: [pyrene, µM] = OD344 / 2.2 x 104 (M-1) [Actin, µM] = (OD290 - (OD344 * 0.127)) / 2.66 x 104 (M-1)
    
    Actin polymerisation assay
    A Perkin-Elmer LS50 fluormeter is used for excitation and measuring emission of pyrenyllabelled actin in quartz cuvettes with 10mm and 4mm inner widths. Polymerisation of the actin is induced by the making-up a 10mM actin solution to 5mM with the following solution: 1 mM MgCl2, 0.1 M KCl, 10Mm Tris-HCl pH 8.0 and 1mM EGTA. Fluorometry measurements are output as 3-d intensity plots showing excitation and emission properties or spectrographic plots (see fig 8).
    Figure 8. Output from spectrofluorometer
    
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    Ultrasound equipment set-up
    Piezo-electric material choice The choice of piezo-electric for transduction and sensing is dependent both upon the materials available and the needs of the experiment. As seen in the figure 9, a number of possible candidates for both the transducer and sensor are available. However, it was chosen that Lithium Niobate would be used for the transducer, for its highfrequency response and large bandwidth, whilst the much cheaper and more versatile PVdF film would be used for sensing at the base of the cuvette. Both transducer and sensor need calibration in a buffer filled cuvette with a pre-calibrated 0.01mm, 40 MHz PVdF needle hydrophone from Precision Acoustics. Additionally, the VSWR (voltage standing wave ratio) needs to be measured, if possible during the experiment, using a frequency analyzer in order to ascertain the level of signal reflectance between the amplifier and transducer. A low reflectance means a good coupling between the transducer and the experimental medium; a high reflectance should be avoided as it will cause temperature increase in the transducer and poor signal transduction, which may need to be rectified through changing the transducer impedance with coupling materials.
    Material Quartz Lithium Niobate Immersion Use Poor Good Contact Use Poor Excellent Disadvantages Week Trans & Rec. not much used Expensive Advantages Inexpensive and rugged
    
    Good to excellent bandwidth, rugged and can operate to very high temp Lithium Sulfate Excellent Dissolves in Water None PZT-4 Excellent Good Narrow Band Good penetration & inexpensive PZT-5A Excellent Excellent Narrow Band Good penetration & inexpensive Zinc Oxide Excellent Above 20 MHz Only Good bandwidth & & expensive operable to GHz frequencies Barium Titanate Excellent Excellent Very Narrow Excellent penetration & Bandwidth inexpensive Lead metaniobate Excellent Excellent Expensive Good bandwidth & sensitivity PVDF Excellent Good Poor Trans. Excellent bandwidth & inexpensive Figure 9. Table of general transducer material properties (from www.ultrasonic.de)
    
    Experimental set-up The method is repeated with both the 10mm and 4mm cuvettes. This allows some control over possible artefacts from resonance created by the architecture of the cuvettes; each cuvette will have different resonant features and therefore it may be possible to minimise the impact of these features by comparing the results from each size of cuvette. The basic set-up of the experiment is shown in figure 10. The acoustic signal is generated, amplified and transduced into the experimental medium in the cuvette.
    
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    The acoustic signal is recorder throughout using the calibrated PVdF sensor and an oscilloscope or spectrum analyser attached to a measurement-recording program. Similarly the fluorometer excites the medium whilst measuring and recording the emission spectrum on LabView.
    
    Signal generator
    
    Amplifier
    
    Piezo-elec. transducer
    
    Actin poly/ buffer
    
    Fluorometer
    
    PC Piezo-elec. sonsor
    Oscilloscope
    
    Figure 10. Basic flow diagram of experimental set-up
    
    As seen in the detailed view of figure 11, the cuvette will be placed in the fluorometer with the acoustic transducer and sensor in place (in blue) whilst the signal generation equipment (in orange) and measurement equipment will be outwith the fluorometer.
    
    Signal generation set-up
    
    SMA/BNC connector Sig. Gen. (i.e NI/agilent) 0.1-3300 MHz 50 Ω out Amp. (MC/Avantek) 0.1-1000 MHz 50 Ω in/out
    
    SMA/BNC to electrode
    
    Lithium Niobate Piezo To 100MHz Ω Dependent
    
    USB/serial
    
    Buffer/actin Modified plastic cuvette Cuvette set-up in fluorometer
    
    PVdF sensor PC NI Labview/ FL WinLab USB/ serial Oscilloscope/ amplifier 1 µΩ Electrode BNC/SMA To 100 MHz Ω Dependent
    
    Figure 11. Detailed flow diagram
    
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    Signal Generator
    
    Amplifier
    
    Oscilloscope/ Amplifier
    
    Transducer
    
    PC
    
    Fluorometer Input - UV
    
    Fluorometer Output - UV
    
    Temperature Probe
    
    a)
    
    b)
    
    Figure 12. a) side and top view of the cuvette design b) flow diagram including the cuvette
    
    Figure 12a shows the cuvette set-up for the 4mm cuvetter. The transducer, cut to a 4x4mm square, is inset into the cuvette lid with its surface towards the experimental medium and attached by an electrode to the amplifier outside the fluorometer. The sensor is integrated into the base of the cuvette, so that problems from averaged response to multiple waves, as may be found in sensors set into the side of the cuvette, should be avoided. This is also attached to an electrode which runs out of the fluorometer to the oscilliscope, with optional amplification. A non-contact infrared needle temperature probe will be placed to the side of the transducer, as shown at the bottom of figure 12a, to measure temperature change throughout the experiment. The lid and transducer construct can be moved and used in both the 4mm and 10mm sized cuvettes, whereas the sensors on each cuvette are calibrated separately.
    
    Experimental procedure
    1. For each batch of actin monomer: a. The fluorometry output is calibrated (without acoustic excitation) to producing an averaged output. b. The experimental procedure is repeated with both pyrenyl-labelled actin and pyrenyl marker in Buffer G to control for any acoustic effects upon pyrenyl fluorescence. c. The experimental procedure is also repeated in the 4mm and 10mm cuvettes.
    
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    2. The experiment tests the following inputs by the signal generator: o Sweep signal: 100 steps for 3 sec each (5 min) from 10 MHz to 1 GHz continuous signals. o Sweep signal: 10 steps for 30 seconds each (5 min) based upon any responsive frequencies in the sweep results o Continuous signal: single and combination of any responsive frequencies found 3. The experimental procedure is as follows: a. Start actin polymerisation assay in the cuvette with attached sensor and start stopwatch b. Attach transducer c. Place in spectrofluorometer and begin readings - stop stopwatch when the first data point arrives and note dead time d. Compare with typical actin polymerisation and note any deviations e. Begin specified ultrasonic signal generation after specified time for comparison - note spectroflurometer time f. Finish ultrasonic signal generation after specified time - note time g. Continue and complete actin polymerisation assay - save results h. Clean apparatus i. Repeat
    
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    Results and Discussion
    Introduction
    This dissertation relates to the three connected yet independent sections of this project; as two of the sections depended upon the implementation of relatively new technology, high computational power for the explicit calculation of protein mode frequencies and very high frequency ultrasonic wave generation, initial difficulties were to be expected. The Lattice Boltzmann model was completed and tested, whilst the normal mode frequency calculations and the ultrasound-polymerisation experiments have both met with complications; increased computational power was found to be necessary for the modelling whilst more time was necessary for the technical set-up and calibration of the ultrasonic equipment. Although this is still a work in progress, it is possible to discuss the strengths of the experimental methodology conducted so far, improvements that could be made and further work that may follow. In the discussion that follows I shall examine the method and results of the first modelling project before considering the current experimental work and how this may be extended.
    
    Protein normal mode frequency calculations
    The normal mode frequency calculations could not be completed due to the current parallel-computational cluster memory size not being great enough to compute the dynamics of all the atoms in the fully solvated model. When the minimised model was limited to a smaller number of water molecules, thus decreasing the number of atoms to be calculated, the reduction in accuracy was too great to produce useful results, with frequencies ranging into negative numbers (see Fig. 13). As one would expect, this was also true of the much Figure 13. Snapshot of the first 20 frequencies in less accurate implicitly minimised an nmode output file from a limited model models. As computational power continues to grow, it may soon be possible to calculate the full explicit model. However, the normal mode analysis of molecular frequencies is known to lose accuracy with increasing molecular size (Case, D.A, Darden, T.A., et al, 2004), so further work would ideally involve both greater computational power and improvements upon the current analysis algorithms. This may be achieved both through corresponding experimental work as well by adhering more closely to quantum theory, although this would also require enhanced computational capability.
    
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    Lattice Boltzmann modelling of actin polymerisation in a standing wave
    The Lattice Boltzmann work produced viable results, but as a one-dimensional simulation requires further work to translate the results to three-dimensions. The following graphs show the stable state results of the model describing actin in extensile (ζ = 0.001), passive (ζ = 0) and contractile (ζ = -0.001) states. These correspond to the environmental conditions that would promote polymerisation, treadmilling or depolymerisation respectively. Each of these states is then subjected to standing waves at three different frequencies. In all graphs the x-axis corresponds to the length of the container (10 Microns) whilst the flow, direction and order of the actin filaments are plotted on the y-axis.
    
    Figure 14. Filament flow (y) against position along the container (x)
    
    Figure 15. Filament direction (y) against position along the container (x)
    
    Figure 16. Filament order (y) against position along the container (x) Figures 14., 15. And 16. Passive model at 574MHz (Left), Extensile model at 1.1GHz (Central) and Contractile model at 2.2GHz (right)
    
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    The Lattice-Boltzmann model found that actin de-polymerisation (ζ = -0.001) was most affected by the presence of a standing wave, whilst a standing wave made no difference to extensile activity (ζ = 0.001).   Without the presence of a standing wave only extensile activity deviated from the passive model (ζ = 0) When a standing wave was included: o Filament flow, which is directly related to the pressure gradient, showed signs of additional low frequency artefacts at higher frequencies. o The extensile activity model showed no change in reaction rate at all three frequencies. o The passive model showed a very slight slowing of equilibrium in both the order and direction of the fibres. o The contractile activity model showed large changes in filament direction at the lowest frequency but this effect was cancelled out at higher frequencies of standing wave.
    
    The acoustic properties of the active gel container must first be understood in a discussion of these results; the frequencies of the standing waves, and therefore many of the changes of activity, are produced by the length of the container. Therefore, most of the larger effects of frequency change are merely changes in the resonance of the container; this can be most easily seen in the filament flow and order at high frequency (Central and Right) as large waveforms with two or three amplitude peaks. The activity reduction found at high frequencies may have been due to these low resonant frequencies (large wavefoms) that were produced by the container. On the other hand, the frequencies used in this model (574MHz, 1.1GHz, 2.2GHz) were much higher than those predicted to affect both actin monomer and polymer activity (about 100MHz); so the lower frequencies may have been more likely to cause the predicted effects. The use of frequencies was constrained by the size of the container used in the model, so further experiments may produce more variation in activity by modelling a larger container and therefore using lower frequencies. The accuracy of this model rests upon an assumption that the complex attributes of acoustic pressure waves could be predicted by the model’s response to pressure gradients. Due to the nature of this model, which can be rudimentarily described as using a condensed gas model for studying liquids, there is a direct relation between pressure and filament flow. The Navier-Stokes equation that is used to model flow in this work (solved through Lattice-Boltzmann) has been widely used in studies of fluid dynamics and acoustics (Haydock, D., et al 2003, 2005, Ali, I., Marenduzzo, D., 2004). The active flow of the gel used in the model has also been shown to be a good model for cytoskeletal activity (Surrey, T. et al, 2001). However, it remains to be seen from experimental work whether the model is a good approximation for both cytoskeletal activity and acoustic fluid dynamics. Finally, the model used in this work only represents a one-dimensional system. However, this should not affect the validity of the results, since the same model has been used for good approximation of three-dimensional actin polymerisation activity (Marenduzzo, D., 2007).
    
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    High-frequency ultrasonic excitation of actin polymerisation
    As mentioned in the introduction, complications in the acoustics set-up have delayed the experimental investigation. Actin fibre pellets were produced and stored in order to retain better quantitative accuracy of the polymerisation assay than would be possible with the storage of actin monomer solutions. However, one batch of actinpyrene is being processed for deep freeze storage, since marker doping allows fresh actin to be marked with small amounts of actin-pyrene from storage. Currently, the acoustic set-up described in the materials and method is unavailable, so it is difficult to discuss improvements to this system. It was predicted that the excitation of actin monomers with high-frequency ultrasound at the resonant frequency of monomeric actin would cause a change in polymerisation rate of reaction. Due to the computational difficulties in the Normal Mode Analysis it was not possible to predict the resonant modal frequencies of an actin monomer. Experimental work with shear acoustic wave transduction of surfaces on which IgG protein has been adhered suggests frequencies of about 400MHz for the resonance of small proteins (Stevenson, A.C., et al, 2004), whilst Raman spectroscopy studies have suggested that the mode important for conformational changes of actin has a frequency of about 100MHz (Zeng, H.H., 1997). It may be useful for future experiments to limit the frequency range used so that important frequencies can be quickly characterised and the acoustic set-up is simplified to a smaller and therefore more manageable and cost-effective bandwidth. However, this will not be possible until the range of frequencies can be accurately predicted either through experimental work or modelling.
    
    Further work
    Protein Normal Mode and Lattice-Boltzmann Modelling
    Until computational power will allow the calculation of the normal mode frequencies of large proteins, it may be more useful to calculate the frequencies of smaller proteins that are also implicated in mechanotransduction mechanisms. With the modal frequencies of many smaller proteins one could then determine modal relationships between intra-cellular mechanisms and compare this to functional relationships. This may also influence which proteins one may wish to investigate experimentally. As described, the Lattice Boltzmann modelling in this paper could be extended to three-dimensions for further exploration. With a greater flexibility to modify pressure parameters than molecular dynamics programs, positive results in this model may suggest that it would be a more convenient modelling paradigm than the more processor consuming semi-classical models.
    
    High-frequency excitation of proteins and other molecules
    With positive results, limitless further experiments could follow this experimental investigation. Any molecule, whether or not implicated in mechanosensory mechanisms, may be investigated using this technique. For instance, proteins implicated in neurological diseases may be excited in order to break up protein plaques, alter membrane protein reaction rates to aid neuronal differentiation or down-regulate autonomous signalling in cancerous growths. However, this technique
    
    27
    
    must be treated with caution until well researched; the same frequency range may affect similarly sized molecules and selective resonance of a protein may involve a more complex ultrasonic treatment. As discussed in the background, mechanical vibration does not act as a single entity, so applications may need to involve systems controlling various molecules by combining and altering ultrasonic signals over time. Even if there is not a positive result, one could investigate the effect of acoustic waves upon Gwell-understood mechanisms of mechanosensation, such as the MscS Channels in E. Coli or TRP channels in neural or other somatic cells. Investigations could include looking at the effects of acoustic excitation of mechanosensory systems on cellular behaviour, development and differentiation. Further work could examine the theoretical importance of acoustic phenomena upon the evolution and development of both single cell and multi-cellular life.
    
    Conclusion
    It is perhaps safe to say that this work was extremely ambitious. As a project that spans theoretical and experimental disciplines as well as the large expanse between biology and physics, complexities in organising such inter-disciplinary experiments were to be expected. Additionally, a solid theoretical basis must bring together research from the three basic sciences whilst also endeavouring to maintain a critical judgement of sources in all three; I hope that I have achieved an adequate level of cogency and accuracy in writing on such a protracted subject. As areas of research become progressively more inter-disciplinary, with work in neuroscience as an obvious paradigm, experience of the intricacies of cross-disciplinary work may ultimately become a necessity. This project has allowed me an opportunity to directly experience inter-disciplinary theoretical and experimental research. Although this is still very much a work in progress, there have been some very promising results from work on Lattice-Boltzmann modelling and many of the other experiments are close to completion. As one can see from both the background and the section on further work, there is still much to be done in order to gain a complete understanding of this area. However, it is an area that directly relates to some of the most exciting work in cell biology and neuroscience, and may eventually be applied to numerous specialised fields in medicine and biology.
    
    Acknowledgements
    I would like to thank Dr. John Cosgrove and Dr. Nick Kilyeni for supporting the project work. Also thanks to Dr. Sutherland MacIver and Dr. Paul Mclaughlin for help with the actin purification and polymerisation protocols, Andy Turner for help with and use of the EastChem computational cluster.
    
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