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Concentration oscillations are a ubiquitous characteristic of intracellular dynamics. The period of these oscillations can vary from few seconds to many hours, well known examples being calcium oscillations (seconds to minutes), glycolytic oscillations (minutes) and circadian rhythms (1 day). Considerable advances into understanding the mechanisms and functionality of concentration oscillations have been made since glycolytic oscillations were observed in the late 1950s, and mathematical methods have been an essential part of this process. With increasing ability to experimentally measure oscillations in single cells as well as in cell ensembles, the gold standard of modelling is to provide tools that can elucidate how the system-wide dynamics in complex organisms emerge from a system of single cells. Both abstract and detailed mechanistic models are complementary in the insight they can bring, and for networks of coupled cells considerations such as intrinsic intracellular noise, cellular heterogeneity and coupling strength are all expected to play a part. Here, we investigate separately the potential roles played by intrinsic noise arising from finite numbers of interacting molecules and by coupling among cellular oscillators. Regarding the former, it is well known that internal or molecular noise induces concentration oscillations in chemical systems whose deterministic models exhibit damped oscillations. We show, using the linear-noise approximation of the chemical master equation, that noise can also induce oscillations in biochemical systems whose deterministic descriptions admit no damped oscillations, i.e., systems with a stable node. This non-intuitive phenomenon is remarkable since, unlike noise-induced oscillations in systems with damped deterministic oscillations, it cannot be explained by noise excitation of the deterministic resonant frequency of the system. We here prove the following general properties of stable-node noise-induced oscillations for systems with two species: (i) the upper bound of their frequency is given by the geometric mean of the real eigenvalues of the Jacobian of the system, (ii) the upper bound of the Q-factor of the oscillations is inversely proportional to the distance between the real eigenvalues of the Jacobian, and (iii) these oscillations are not necessarily exhibited by all interacting chemical species in the system. The existence and properties of stable-node oscillations are verified by stochastic simulations of the Brusselator, a cascade Brusselator reaction system, and two other simple chemical systems involving autocatalysis and trimerization. We also show that external noise induces stable node oscillations with different properties than those stimulated by internal noise. Having demonstrated and explored this non-intuitive effect of noise, we extend the work to investigate the phenomenon of noise induced oscillations in cellular reaction systems characterised by the ‘bursty’ production of one or more species. Experiments have shown that proteins are typically translated in sharp bursts and similar bursty phenomena have been observed for protein import into subcellular compartments. We investigate the effect of such burstiness on the stochastic properties of downstream pathways by considering two identical systems with equal mean input rates, except in one system molecules (e.g., proteins) are input one at a time and in the other molecules are input in bursts according to some probability distribution. We find that the stochastic behaviour falls in three categories: (i) both systems display or do not display noise-induced oscillations; (ii) the non-bursty input system displays noiseinduced oscillations whereas the bursty input system does not; (iii) the reverse of (ii). We derive necessary conditions for these three cases to classify pathways involving autocatalysis, trimerization and genetic feedback loops. Our results suggest that single cell rhythms can be controlled by regulation of burstiness in protein production. We go on to investigate roles played by intercellular coupling in whole organ-level oscillations with an experimental analysis of circadian rhythms in Arabidopsis thaliana †. Circadian clocks in animals are known to be tightly coupled among the cells of some tissues, and this coupling profoundly affects cellular rhythmicity. However, research on the clock in plant cells has largely ignored intercellular coupling. Our research group used luciferase reporter gene imaging to monitor circadian rhythms in leaves of Arabidopsis thaliana plants, with both a lower resolution, high throughput method and a high-resolution (cellular level), lower throughput method. Leaves were grown and imaged in a variety of light conditions to test the relative importance of intercellular coupling and cellular coupling to the environmental signal. We analysed the high throughput data and described the circadian phase by the timing of peak expression. Leaves grown for three weeks without entrainment reproducibly showed spatio-temporal waves of gene expression, consistent with intercellular coupling. A range of patterns was observed among the leaves, rather than a unique spatio-temporal pattern, although some patterns were more often observed. All of the measured leaves exposed to lightdark entrainment cycles had fully synchronised rhythms, which could desynchronise rather quickly when placed in a non-entraining environment (i.e., constant light conditions). After four days in constant light some of these leaves were as desynchronised as leaves grown without any rhythmic input, as described by the phase coherence across the leaf. The same fast transition was observed in the reverse experimental scenario, i.e., applying light-dark cycles to leaves grown in constant light resulted in full synchronisation within two to four days. From these results we conclude that single-cell circadian oscillators were coupled far more strongly to external light-dark cycles than to the other cellular oscillators. Leaves did not spontaneously completely desynchronise, which is consistent with a presence of intercellular coupling among heterogeneous clocks. We also developed a methodology, based on the notion of two functional spatial scales of expression across the leaf, to analyse the high-resolution microscope data and determine whether there is a difference in the phase of circadian expression between vein cells and mesophyll cells in the leaf. The result from a single leaf suggests that the global phase wave dominates the phase behaviour but that there are small delays in the veins compared to their nearby mesophyll cells. This result can be validated by applying the methodology developed here to new microscope leaf data which is currently being collected in the research group. † This work was performed as a collaboration between David Toner (DT) and Benedicte Wenden (BW). BW designed and carried out the experiments, DT performed the data analysis and led on data visualisation.

Many people around the world still lack access to a reliable electricity grid. Supplying electricity to remote off grid areas like villages around Leticia, Colombia is often interrelated with high costs and geographical limitations. Today most of the electricity demand is met through the usage of diesel generators. The generators are easy to use and have a relatively reliable functionality. However, fuel is expensive and there are other negative aspects as fumes and sound pollution. In order to provide a cleaner, more reliable and cost efficient alternative the company Jabe Energy AB has in cooperation with the volunteer organization Ankarstiftelsen developed a new type of hydrokinetic turbine (slow moving none damming turbine). Previous studies have shown that there is potential for hydrokinetic turbines to increase their power output simply by their relative placement (coupling potential). That is, it might be possible to extrude more power from a system where two hydrokinetic turbines are placed in a close relation rather than being completely separated. Since the turbine investigated is newly developed there have been no previous studies regarding its specific coupling potential. To investigate this potential given the conditions in the Amazon basin, a field study is conducted where measurements on water velocity at different heights in the water column is collected. The data is later used as input conditions for a turbine model developed in the program COMSOL. The aim is to use simulations in order to determine whether a turbine is sensitive for its relative placement to a former (coupling potential) and furthermore to investigate a possible optimal turbine coupling position. The results will show that the turbine is coupling sensitive and that there exists more advantageous placements. Comparing the best and worst case of the coupling study displays an 11.87% difference in possible energy output. The conclusion is that further empirical studies are necessary in order to validate the results. Finally a suggestion on how these studies should be conducted is presented and discussed.

This thesis explores both the optical and catalytic properties of cubic shaped nanoparticles. The investigation begins with the sensing capabilities of cubic metal dimers. Of all the plasmonic solid nanoparticles, single Ag or Au nanocubes exhibit the strongest electromagnetic fields. When two nanoparticles are in close proximity to each other the formation of hot spots between plasmonic nanoparticles is known to greatly enhance these electromagnetic fields even further. The sensitivity of these electromagnetic fields as well as the sensitivity of the plasmonic extinction properties is important to the development of plasmonic sensing. However, an investigation of the electromagnetic fields and the corresponding sensing capabilities of cubic shaped dimers are currently lacking. In Chapters 2-5 the optical properties of cubic dimers made of either silver or gold are examined as a function of separation distance, surrounding environment, and dimer orientation. A detailed DDA simulation of Au–Au and Ag-Ag dimers oriented in a face-to-face configuration is conducted in Chapter 2. In this Chapter a distance dependent competition between two locations for hot spot formation is observed. The effect of this competition on the sensing capabilities of these dimers is further explored in Chapters 3 and 4. This competition originates from the generation of two different plasmonic modes. Each mode is defined by a unique electromagnetic field distribution between the adjacent nanocubes. In Chapter 4 the maximum value of the electromagnetic field intensity is investigated for each mode. Notably the magnitude of the electromagnetic field is not directly proportional to its extinction intensity. Furthermore, the sensitivity of a plasmonic mode does not depend on its extinction intensity. The sensitivity is rather a function of the magnitude of the electromagnetic field intensity distribution. Also, the presence of a high refractive index substrate drastically affects the optical properties and subsequent sentivity of the dimer. In Chapter 5 the sensing properties of a cubic dimer is investigated as a function of orientation. As the separation distance of the nanocube dimer is decreased the orientation of the dimer drastically affects its coupling behavior. The expected dipole-dipole exponential coupling behavior of the dimer is found to fail at a separation distance of 14 nm for the edge-to-edge arrangement. The failure of the dipole-dipole coupling mechanism results from an increased contribution from the higher order multipoles (eg. quadrupole-dipole). This behavior begins at a separation distance of 6 nm for the face-to-face dimer. As a result, the relative ratio of the multipole to the dipole moment generated by the edge-to-edge dimer must be larger than the ratio for the face-to-face orientation. In the last section of this thesis the catalytic properties of cubic nanoparticles composed of a platinum-silver alloy are investigated. The catalytic activity and selectivity towards a given reaction is intimately related to the physical and electronic structure of the catalyst. These cubic platinum-silver alloys are utilized as catalysts for the oxygen reduction reaction (ORR). A maximum enhancement in the specific activity (3.5 times greater than pure platinum) towards the ORR is observed for the cubic platinum-silver alloy with the lowest platinum content. This activity is investigated as a function of the physical structure of a cubic shaped catalyst as well as the electronic modifications induced by the formation of a platinum-silver alloy.

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