Design Principles for Two-Dimensional Molecular Aggregates Using Kasha's Model: Tunable Photophysics in Near and Short-Wave Infrared

Technologies which utilize near-infrared (700 – 1000 nm) and short-wave infrared (1000 – 2000 nm) electromagnetic radiation have applications in deep-tissue imaging, telecommunications and satellite telemetry due to low scattering and decreased background signal in this spectral region. It is therefore necessary to develop materials that absorb light efficiently beyond 1000 nm. Transition dipole moment coupling (e.g. J-aggregation) allows for redshifted excitonic states and provides a pathway to highly absorptive electronic states in the infrared. We present aggregates of two cyanine dyes whose absorption peaks redshift dramatically upon aggregation in water from ~800 nm to 1000 nm and 1050 nm respectively with sheet-like morphologies and high molar absorptivities (e ~ 105 M-1cm-1). We use Frenkel exciton theory to extend Kasha’s model for J and H aggregation and describe the excitonic states of 2-dimensional aggregates whose slip is controlled by steric hindrance in the assembled structure. A consequence of the increased dimensionality is the phenomenon of an intermediate “I-aggregate”, one which redshifts yet displays spectral signatures of band-edge dark states akin to an H-aggregate. We distinguish between H-, I- and J-aggregates by showing the relative position of the bright (absorptive) state within the density of states using temperature dependent spectroscopy. I-aggregates hold potential for applications as charge injection moieties for semiconductors and donors for energy transfer in NIR and SWIR. Our results can be used to better design chromophores with predictable and tunable aggregation with new photophysical properties

Systems control theory applied to natural and synthetic musical sounds

Systems control theory is a far developped field which helps to study stability, estimation and control of dynamical systems. The physical behaviour of musical instruments, once described by dynamical systems, can then be controlled and numerically simulated for many purposes. The aim of this paper is twofold: first, to provide the theoretical background on linear system theory, both in continuous and discrete time, mainly in the case of a finite number of degrees of freedom ; second, to give illustrative examples on wind instruments, such as the vocal tract represented as a waveguide, and a sliding flute

A physics-based model of swarming jellyfish

We propose a model for the structure formation of jellyfish swimming based on active Brownian particles. We address the phenomena of counter-current swimming, avoidance of turbulent flow regions and foraging. We motivate corresponding mechanisms from observations of jellyfish swarming reported in the literature and incorporate them into the generic modelling framework. The model characteristics is tested in three paradigmatic flow environments.Comment: 35 pages, 14 figure

Waves and patterning in developmental biology: vertebrate segmentation and feather bud formation as case studies

In this article we will discuss the integration of developmental patterning mechanisms with waves of competency that control the ability of a homogeneous field of cells to react to pattern forming cues and generate spatially heterogeneous patterns. We base our discussion around two well known patterning events that take place in the early embryo: somitogenesis and feather bud formation. We outline mathematical models to describe each patterning mechanism, present the results of numerical simulations and discuss the validity of each model in relation to our example patterning processes

Competition through selective inhibitory synchrony

Models of cortical neuronal circuits commonly depend on inhibitory feedback to control gain, provide signal normalization, and to selectively amplify signals using winner-take-all (WTA) dynamics. Such models generally assume that excitatory and inhibitory neurons are able to interact easily, because their axons and dendrites are co-localized in the same small volume. However, quantitative neuroanatomical studies of the dimensions of axonal and dendritic trees of neurons in the neocortex show that this co-localization assumption is not valid. In this paper we describe a simple modification to the WTA circuit design that permits the effects of distributed inhibitory neurons to be coupled through synchronization, and so allows a single WTA to be distributed widely in cortical space, well beyond the arborization of any single inhibitory neuron, and even across different cortical areas. We prove by non-linear contraction analysis, and demonstrate by simulation that distributed WTA sub-systems combined by such inhibitory synchrony are inherently stable. We show analytically that synchronization is substantially faster than winner selection. This circuit mechanism allows networks of independent WTAs to fully or partially compete with each other.Comment: in press at Neural computation; 4 figure

Adding Adhesion to a Chemical Signaling Model for Somite Formation

Somites are condensations of mesodermal cells that form along the two sides of the neural tube during early vertebrate development. They are one of the first instances of a periodic pattern, and give rise to repeated structures such as the vertebrae. A number of theories for the mechanisms underpinning somite formation have been proposed. For example, in the “clock and wavefront” model (Cooke and Zeeman in J. Theor. Biol. 58:455– 476, 1976), a cellular oscillator coupled to a determination wave progressing along the anterior-posterior axis serves to group cells into a presumptive somite. More recently, a chemical signaling model has been developed and analyzed by Maini and coworkers (Collier et al. in J. Theor. Biol. 207:305–316, 2000; Schnell et al. in C. R. Biol. 325:179– 189, 2002; McInerney et al. in Math. Med. Biol. 21:85–113, 2004), with equations for two chemical regulators with entrained dynamics. One of the chemicals is identified as a somitic factor, which is assumed to translate into a pattern of cellular aggregations via its effect on cell–cell adhesion. Here, the authors propose an extension to this model that includes an explicit equation for an adhesive cell population. They represent cell adhesion via an integral over the sensing region of the cell, based on a model developed previousl

Modeling the Interplay of Oscillatory Synchronization and Aggregation via Cell-Cell Adhesion

We present a model of systems of cells with intracellular oscillators ('clocks'). This is motivated by examples from developmental biology and from the behavior of organisms on the threshold to multicellularity. Cells undergo random motion and adhere to each other. The adhesion strength between neighbors depends on their clock phases in addition to a constant baseline strength. The oscillators are linked via Kuramoto-type local interactions. The model is an advection-diffusion partial differential equation with nonlocal advection terms. We demonstrate that synchronized states correspond to Dirac-delta measure solutions of a weak version of the equation. To analyze the complex interplay of aggregation and synchronization, we then perform a linear stability analysis of the incoherent, spatially uniform state. This lets us classify possibly emerging patterns depending on model parameters. Combining these results with numerical simulations, we determine a range of possible far-from equilibrium patterns when baseline adhesion strength is zero: There is aggregation into separate synchronized clusters with or without global synchrony; global synchronization without aggregation; or unexpectedly a ``phase wave" pattern characterized by spatial gradients of clock phases. A 2D Lattice-Gas Cellular Automaton model confirms and illustrates these results