Polaron Dynamics in the Alpha Helix: Models of Electron Transport in Hydrogen-Bonded Polypeptides

In this thesis, I present two mathematical models which are capable of explaining the phenomenon of directed electron transport in α-helical regions of protein macromolecules. The models are built upon the framework of polaron theory, which originated in condensed matter physics, and which I argue is applicable to biophysical systems such as an extra electron interacting electromagnetically with peptide units in an α-helix. The two models concern the electron’s coupling to, respectively, picosecond-scale intrapeptide oscillators and nanosecond-scale hydrogen bond phonons in the α-helix. I show that the models permit the auto-localisation of the electron in stationary polaron states, and that certain electromagnetic fields cause the polaron to propagate along the polypeptide, transporting the electron in a solitonic manner. Taking effects of the cell environment into account, I demonstrate that stochastic forces arising from thermal fluctuations can enhance the electron transport, and that the stability of the polaron dynamics exhibit contrasting degrees of tolerance to temperature in the two models. When interpreting my results, I describe their biological implications, as well as the physical realisability of the models’ forcing parameters. In particular, I establish that some electromagnetic fields which can facilitate directed electron transport are intrinsic physical features of the cell

A generalised Davydov-Scott model for polarons in linear peptide chains

We present a one-parameter family of mathematical models describing the dynamics of polarons in periodic structures, such as linear polypeptides, which, by tuning the model parameter, can be reduced to the Davydov or the Scott model. We describe the physical significance of this parameter and, in the continuum limit, we derive analytical solutions which represent stationary polarons. On a discrete lattice, we compute stationary polaron solutions numerically. We investigate polaron propagation induced by several external forcing mechanisms. We show that an electric field consisting of a constant and a periodic component can induce polaron motion with minimal energy loss. We also show that thermal fluctuations can facilitate the onset of polaron motion. Finally, we discuss the bio-physical implications of our results

A continuum mechanics model of the plant cell wall reveals interplay between enzyme action and cell wall structure

Plant cell growth is regulated through manipulation of the cell wall network, which consists of oriented cellulose microfibrils embedded within a ground matrix incorporating pectin and hemicellulose components. There remain many unknowns as to how this manipulation occurs. Experiments have shown that cellulose reorients in cell walls as the cell expands, while recent data suggest that growth is controlled by distinct collections of hemicellulose called biomechanical hotspots, which join the cellulose molecule together. The enzymes expansin and Cel12A have both been shown to induce growth of the cell wall; however, while Cel12A’s wall-loosening action leads to a reduction in the cell wall strength, expansin’s has been shown to increase the strength of the cell wall. In contrast, members of the XTH enzyme family hydrolyse hemicellulose but do not appear to cause wall creep. This experimentally observed behaviour still awaits a full explanation. We derive and analyse a mathematical model for the effective mechanical properties of the evolving cell wall network, incorporating cellulose microfibrils, which reorient with cell growth and are linked via biomechanical hotspots made up of regions of crosslinking hemicellulose. Assuming a visco-elastic response for the cell wall and using a continuum approach, we calculate the total stress resultant of the cell wall for a given overall growth rate. By changing appropriate parameters affecting breakage rate and viscous properties, we provide evidence for the biomechanical hotspot hypothesis and develop mechanistic understanding of the growth-inducing enzymes. </p

Terahertz Pulse Shaping Using Diffractive Surfaces

Recent advances in deep learning have been providing non-intuitive solutions to various inverse problems in optics. At the intersection of machine learning and optics, diffractive networks merge wave-optics with deep learning to design task-specific elements to all-optically perform various tasks such as object classification and machine vision. Here, we present a diffractive network, which is used to shape an arbitrary broadband pulse into a desired optical waveform, forming a compact pulse engineering system. We experimentally demonstrate the synthesis of square pulses with different temporal-widths by manufacturing passive diffractive layers that collectively control both the spectral amplitude and the phase of an input terahertz pulse. Our results constitute the first demonstration of direct pulse shaping in terahertz spectrum, where a complex-valued spectral modulation function directly acts on terahertz frequencies. Furthermore, a Lego-like physical transfer learning approach is presented to illustrate pulse-width tunability by replacing part of an existing network with newly trained diffractive layers, demonstrating its modularity. This learning-based diffractive pulse engineering framework can find broad applications in e.g., communications, ultra-fast imaging and spectroscopy.Comment: 27 pages, 6 figure

Spectrally-Encoded Single-Pixel Machine Vision Using Diffractive Networks

3D engineering of matter has opened up new avenues for designing systems that can perform various computational tasks through light-matter interaction. Here, we demonstrate the design of optical networks in the form of multiple diffractive layers that are trained using deep learning to transform and encode the spatial information of objects into the power spectrum of the diffracted light, which are used to perform optical classification of objects with a single-pixel spectroscopic detector. Using a time-domain spectroscopy setup with a plasmonic nanoantenna-based detector, we experimentally validated this machine vision framework at terahertz spectrum to optically classify the images of handwritten digits by detecting the spectral power of the diffracted light at ten distinct wavelengths, each representing one class/digit. We also report the coupling of this spectral encoding achieved through a diffractive optical network with a shallow electronic neural network, separately trained to reconstruct the images of handwritten digits based on solely the spectral information encoded in these ten distinct wavelengths within the diffracted light. These reconstructed images demonstrate task-specific image decompression and can also be cycled back as new inputs to the same diffractive network to improve its optical object classification. This unique machine vision framework merges the power of deep learning with the spatial and spectral processing capabilities of diffractive networks, and can also be extended to other spectral-domain measurement systems to enable new 3D imaging and sensing modalities integrated with spectrally encoded classification tasks performed through diffractive optical networks.Comment: 21 pages, 5 figures, 1 tabl

Acute Ethanol Inhibition of γ Oscillations Is Mediated by Akt and GSK3β

Hippocampal network oscillations at gamma band frequency (γ, 30–80 Hz) are closely associated with higher brain functions such as learning and memory. Acute ethanol exposure at intoxicating concentrations (≥50 mM) impairs cognitive function. This study aimed to determine the effects and the mechanisms of acute ethanol exposure on γ oscillations in an in vitro model. Ethanol (25–100 mM) suppressed kainate-induced γ oscillations in CA3 area of the rat hippocampal slices, in a concentration-dependent, reversible manner. The ethanol-induced suppression was reduced by the D1R antagonist SCH23390 or the PKA inhibitor H89, was prevented by the Akt inhibitor triciribine or the GSk3β inhibitor SB415286, was enhanced by the NMDA receptor antagonist D-AP5, but was not affected by the MAPK inhibitor U0126 or PI3K inhibitor wortmanin. Our results indicate that the intracellular kinases Akt and GSk3β play a critical role in the ethanol-induced suppression of γ oscillations and reveal new cellular pathways involved in the ethanol-induced cognitive impairment

A continuum mechanics model of the plant cell wall reveals interplay between enzyme action and cell wall structure

Plant cell growth is regulated through manipulation of the cell wall net- work, which consists of oriented cellulose microfibrils embedded within a ground matrix incorporating pectin and hemicellulose components. There remain many unknowns as to how this manipulation occurs. Experiments have shown that cellulose reorients in cell walls as the cell expands, while recent data suggest that growth is controlled by dis- tinct collections of hemicellulose called biomechanical hotspots which join the cellulose molecule together. The enzymes expansin and Cel12A have both been shown to induce growth of the cell wall, however whilst Cel12A’s wall-loosening action leads to a reduction in the cell wall strength, expansin’s has been shown to increase the strength of the cell wall. In contrast, members of the XTH enzyme family hydrolyse hemicellulose but do not appear to cause wall creep. This experimen- tally observed behaviour still awaits a full explanation. We derive and analyse a mathematical model for the effective mechanical properties of the evolving cell wall network, incorporating cellulose microfibrils, which reorient with cell growth and are linked via biomechanical hotspots made up of regions of crosslinking hemicellulose. Assuming a visco-elastic response for the cell wall and using a continuum approach we calculate the total stress resultant of the cell wall for a given overall growth rate. By changing appropriate parameters affecting breakage rate and viscous properties we provide evidence for the biomechanical hotspot hypothesis and develop mechanistic understanding of the growth-inducing enzymes