Manifestation of dynamic Jahn-Teller distortions and surface interactions in scanning tunnelling microscopy images of fullerene anion C−60

Using scanning tunnelling microscopy (STM), it is possible to observe detailed structure of the molecular orbitals (MOs) of fullerene anions C−60. However, understanding the experimental observations is not straightforward because of the inherent presence of Jahn–Teller (JT) interactions, which (in general) split the MOs in one of a number of equivalent ways. Tunnelling between equivalent distortions means that any observed STM image will be a superposition of images arising from the individual configurations. Interactions with the surface substrate must also be taken into account. We will show how simple ideas involving a symmetry analysis and Hückel molecular orbital theory can be used to understand observed STM images without need for the more usual but more complicated density functional calculations. In particular, we will show that when the fullerene ion is adsorbed with a pentagon, hexagon or double-bond facing the surface, STM images involving the lowest unoccupied molecular orbital (LUMO) can be reproduced by adding together just two images of squares of components of the LUMO, in ratios that depend on the strength of the JT effect and the surface interaction. It should always be possible to find qualitative matches to observed images involving any of these orientations by simply looking at images of the components, without doing any detailed calculations. A comparison with published images indicates that the JT effect in the C−60 ion favours D3d distortions

Whole-body mathematical model for simulating intracranial pressure dynamics

A whole-body mathematical model (10) for simulating intracranial pressure dynamics. In one embodiment, model (10) includes 17 interacting compartments, of which nine lie entirely outside of intracranial vault (14). Compartments (F) and (T) are defined to distinguish ventricular from extraventricular CSF. The vasculature of the intracranial system within cranial vault (14) is also subdivided into five compartments (A, C, P, V, and S, respectively) representing the intracranial arteries, capillaries, choroid plexus, veins, and venous sinus. The body's extracranial systemic vasculature is divided into six compartments (I, J, O, Z, D, and X, respectively) representing the arteries, capillaries, and veins of the central body and the lower body. Compartments (G) and (B) include tissue and the associated interstitial fluid in the intracranial and lower regions. Compartment (Y) is a composite involving the tissues, organs, and pulmonary circulation of the central body and compartment (M) represents the external environment

Experimental Biological Protocols with Formal Semantics

Both experimental and computational biology is becoming increasingly automated. Laboratory experiments are now performed automatically on high-throughput machinery, while computational models are synthesized or inferred automatically from data. However, integration between automated tasks in the process of biological discovery is still lacking, largely due to incompatible or missing formal representations. While theories are expressed formally as computational models, existing languages for encoding and automating experimental protocols often lack formal semantics. This makes it challenging to extract novel understanding by identifying when theory and experimental evidence disagree due to errors in the models or the protocols used to validate them. To address this, we formalize the syntax of a core protocol language, which provides a unified description for the models of biochemical systems being experimented on, together with the discrete events representing the liquid-handling steps of biological protocols. We present both a deterministic and a stochastic semantics to this language, both defined in terms of hybrid processes. In particular, the stochastic semantics captures uncertainties in equipment tolerances, making it a suitable tool for both experimental and computational biologists. We illustrate how the proposed protocol language can be used for automated verification and synthesis of laboratory experiments on case studies from the fields of chemistry and molecular programming

Design and analysis of DNA strand displacement devices using probabilistic model checking

Designing correct, robust DNA devices is difficult because of the many possibilities for unwanted interference between molecules in the system. DNA strand displacement has been proposed as a design paradigm for DNA devices, and the DNA strand displacement (DSD) programming language has been developed as a means of formally programming and analysing these devices to check for unwanted interference. We demonstrate, for the first time, the use of probabilistic verification techniques to analyse the correctness, reliability and performance of DNA devices during the design phase. We use the probabilistic model checker prism, in combination with the DSD language, to design and debug DNA strand displacement components and to investigate their kinetics. We show how our techniques can be used to identify design flaws and to evaluate the merits of contrasting design decisions, even on devices comprising relatively few inputs. We then demonstrate the use of these components to construct a DNA strand displacement device for approximate majority voting. Finally, we discuss some of the challenges and possible directions for applying these methods to more complex designs

Jahn-Teller effects and surface interactions in multiply-charged fullerene anions and the effect on scanning tunneling microscopy images

We investigate the combined effects of Jahn-Teller (JT) coupling and interactions with a surface substrate on fullerene anions C$_{60}^{2-}$ to C$_{60}^{4-}$. JT coupling alone causes the C$_{60}$ ions to instantaneously distort from the icosahedral symmetry of the neutral molecule to a lower symmetry, with the molecule moving dynamically between a set of equivalent distortions. When adsorbed on a surface, the number of equivalent minimum-energy distortions is reduced. The implications of this on observed scanning tunneling microscopy (STM) images will be discussed, and comparisons made with existing experimental data. We show that a consistent interpretation of the images from all of the charge states of C$_{60}$ can only be obtained using a JT model in which the symmetry is further reduced by surface interactions. The comparison with experimental data also allows us to determine relationships between the quadratic Jahn-Teller coupling and surface interaction parameters