Experimental and Theoretical Models to Probe Mechanisms of Biological Charge Flow

Nature is challenged to move charge efficiently over many length scales. From sub-nm to μm distances, electron-transfer proteins orchestrate energy conversion, storage, and release both inside and outside the cell. Uncovering the detailed mechanisms of biological electron-transfer reactions, which are often coupled to bond-breaking and bond-making events, is essential to designing durable, artificial energy conversion systems that mimic the specificity and efficiency of their natural counterparts. Here, we use theoretical modeling of long-distance charge hopping (Chapter 3), synthetic donor-bridge-acceptor molecules (Chapters 4, 5, and 6), and de novo protein design (Chapters 5 and 6) to investigate general principles that govern light-driven and electrochemically driven electron-transfer reactions in biology. We show that fast, μm-distance charge hopping along bacterial nanowires requires closely packed charge carriers with low reorganization energies (Chapter 3); singlet excited-state electronic polarization of supermolecular electron donors can attenuate intersystem crossing yields to lower-energy, oppositely polarized, donor triplet states (Chapter 4); the effective static dielectric constant of a small (~100 residue) de novo designed 4-helical protein bundle can change upon phototriggering an electron transfer event in the protein interior, providing a means to slow the charge-recombination reaction (Chapter 5); and a tightly-packed de novo designed 4-helix protein bundle can drastically alter charge-transfer driving forces of photo-induced amino acid radical formation in the bundle interior, effectively turning off a light-driven oxidation reaction that occurs in organic solvent (Chapter 6). This work leverages unique insights gleaned from proteins designed from scratch that bind synthetic donor-bridge-acceptor molecules that can also be studied in organic solvents, opening new avenues of exploration into the factors critical for protein control of charge flow in biology.

Predicting loss and fragmentation of habitat of the vulnerable subtropical rainforest tree Macadamia integrifolia with models developed from compiled ecological data

Habitat models are widely used in ecology, however there are relatively few studies of rare species, primarily because of a paucity of survey records and lack of robust means of assessing accuracy of modelled spatial predictions. We investigated the potential of compiled ecological data in developing habitat models for Macadamia integrifolia, a vulnerable mid-stratum tree endemic to lowland subtropical rainforests of southeast Queensland, Australia. We compared performance of two binomial models—Classification and Regression Trees (CART) and Generalised Additive Models (GAM)—with Maximum Entropy (MAXENT) models developed from (i) presence records and available absence data and (ii) developed using presence records and background data. The GAM model was the best performer across the range of evaluation measures employed, however all models were assessed as potentially useful for informing in situ conservation of M. integrifolia, A significant loss in the amount of M. integrifolia habitat has occurred (p < 0.05), with only 37% of former habitat (pre-clearing) remaining in 2003. Remnant patches are significantly smaller, have larger edge-to-area ratios and are more isolated from each other compared to pre-clearing configurations (p < 0.05). Whilst the network of suitable habitat patches is still largely intact, there are numerous smaller patches that are more isolated in the contemporary landscape compared with their connectedness before clearing. These results suggest that in situ conservation of M. integrifolia may be best achieved through a landscape approach that considers the relative contribution of small remnant habitat fragments to the species as a whole, as facilitating connectivity among the entire network of habitat patches.

Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

Models of collective cell spreading with variable cell aspect ratio : a motivation for degenerate diffusion models

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multi-scale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (pme). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the pme to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.

Hierarchical Bayesian models for estimating the extent of plant pest invasions

Plant biosecurity requires statistical tools to interpret field surveillance data in order to manage pest incursions that threaten crop production and trade. Ultimately, management decisions need to be based on the probability that an area is infested or free of a pest. Current informal approaches to delimiting pest extent rely upon expert ecological interpretation of presence / absence data over space and time. Hierarchical Bayesian models provide a cohesive statistical framework that can formally integrate the available information on both pest ecology and data. The overarching method involves constructing an observation model for the surveillance data, conditional on the hidden extent of the pest and uncertain detection sensitivity. The extent of the pest is then modelled as a dynamic invasion process that includes uncertainty in ecological parameters. Modelling approaches to assimilate this information are explored through case studies on spiralling whitefly, Aleurodicus dispersus and red banded mango caterpillar, Deanolis sublimbalis. Markov chain Monte Carlo simulation is used to estimate the probable extent of pests, given the observation and process model conditioned by surveillance data. Statistical methods, based on time-to-event models, are developed to apply hierarchical Bayesian models to early detection programs and to demonstrate area freedom from pests. The value of early detection surveillance programs is demonstrated through an application to interpret surveillance data for exotic plant pests with uncertain spread rates. The model suggests that typical early detection programs provide a moderate reduction in the probability of an area being infested but a dramatic reduction in the expected area of incursions at a given time. Estimates of spiralling whitefly extent are examined at local, district and state-wide scales. The local model estimates the rate of natural spread and the influence of host architecture, host suitability and inspector efficiency. These parameter estimates can support the development of robust surveillance programs. Hierarchical Bayesian models for the human-mediated spread of spiralling whitefly are developed for the colonisation of discrete cells connected by a modified gravity model. By estimating dispersal parameters, the model can be used to predict the extent of the pest over time. An extended model predicts the climate restricted distribution of the pest in Queensland. These novel human-mediated movement models are well suited to demonstrating area freedom at coarse spatio-temporal scales. At finer scales, and in the presence of ecological complexity, exploratory models are developed to investigate the capacity for surveillance information to estimate the extent of red banded mango caterpillar. It is apparent that excessive uncertainty about observation and ecological parameters can impose limits on inference at the scales required for effective management of response programs. The thesis contributes novel statistical approaches to estimating the extent of pests and develops applications to assist decision-making across a range of plant biosecurity surveillance activities. Hierarchical Bayesian modelling is demonstrated as both a useful analytical tool for estimating pest extent and a natural investigative paradigm for developing and focussing biosecurity programs.

Probability distributed time delays: integrating spatial effects into temporal models

Background In order to provide insights into the complex biochemical processes inside a cell, modelling approaches must find a balance between achieving an adequate representation of the physical phenomena and keeping the associated computational cost within reasonable limits. This issue is particularly stressed when spatial inhomogeneities have a significant effect on system's behaviour. In such cases, a spatially-resolved stochastic method can better portray the biological reality, but the corresponding computer simulations can in turn be prohibitively expensive. Results We present a method that incorporates spatial information by means of tailored, probability distributed time-delays. These distributions can be directly obtained by single in silico or a suitable set of in vitro experiments and are subsequently fed into a delay stochastic simulation algorithm (DSSA), achieving a good compromise between computational costs and a much more accurate representation of spatial processes such as molecular diffusion and translocation between cell compartments. Additionally, we present a novel alternative approach based on delay differential equations (DDE) that can be used in scenarios of high molecular concentrations and low noise propagation. Conclusions Our proposed methodologies accurately capture and incorporate certain spatial processes into temporal stochastic and deterministic simulations, increasing their accuracy at low computational costs. This is of particular importance given that time spans of cellular processes are generally larger (possibly by several orders of magnitude) than those achievable by current spatially-resolved stochastic simulators. Hence, our methodology allows users to explore cellular scenarios under the effects of diffusion and stochasticity in time spans that were, until now, simply unfeasible. Our methodologies are supported by theoretical considerations on the different modelling regimes, i.e. spatial vs. delay-temporal, as indicated by the corresponding Master Equations and presented elsewhere.

Correlations between designability and various structural characteristics of protein lattice models

Using six kinds of lattice types (4×4 ,5×5 , and6×6 square lattices;3×3×3 cubic lattice; and2+3+4+3+2 and4+5+6+5+4 triangular lattices), three different size alphabets (HP ,HNUP , and 20 letters), and two energy functions, the designability of proteinstructures is calculated based on random samplings of structures and common biased sampling (CBS) of proteinsequence space. Then three quantities stability (average energy gap),foldability, and partnum of the structure, which are defined to elucidate the designability, are calculated. The authors find that whatever the type of lattice, alphabet size, and energy function used, there will be an emergence of highly designable (preferred) structure. For all cases considered, the local interactions reduce degeneracy and make the designability higher. The designability is sensitive to the lattice type, alphabet size, energy function, and sampling method of the sequence space. Compared with the random sampling method, both the CBS and the Metropolis Monte Carlo sampling methods make the designability higher. The correlation coefficients between the designability, stability, and foldability are mostly larger than 0.5, which demonstrate that they have strong correlation relationship. But the correlation relationship between the designability and the partnum is not so strong because the partnum is independent of the energy. The results are useful in practical use of the designability principle, such as to predict the proteintertiary structure.

Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the λ phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Velocity-jump models with crowding effects

Velocity jump processes are discrete random walk models that have many applications including the study of biological and ecological collective motion. In particular, velocity jump models are often used to represent a type of persistent motion, known as a “run and tumble”, which is exhibited by some isolated bacteria cells. All previous velocity jump processes are non-interacting, which means that crowding effects and agent-to-agent interactions are neglected. By neglecting these agent-to-agent interactions, traditional velocity jump models are only applicable to very dilute systems. Our work is motivated by the fact that many applications in cell biology, such as wound healing, cancer invasion and development, often involve tissues that are densely packed with cells where cell-to-cell contact and crowding effects can be important. To describe these kinds of high cell density problems using a velocity jump process we introduce three different classes of crowding interactions into a one-dimensional model. Simulation data and averaging arguments lead to a suite of continuum descriptions of the interacting velocity jump processes. We show that the resulting systems of hyperbolic partial differential equations predict the mean behavior of the stochastic simulations very well.

Bribie Island groundwater resources : challenges in development of conceptual and numerical models

Groundwater is a major resource on Bribie Island and its sustainable management is essential to maintain the natural and modified eco-systems, as well as the human population and the integrity of the island as a sand mass. An effective numerical model is essential to enable predictions, and to test various water use and rainfall/climate scenarios. Such a numerical model must, however, be based on a representative conceptual hydrogeological model to allow incorporation of realistic controls and processes. Here we discuss the various hydrogeological models and parameters, and hydrological properties of the materials forming the island. We discuss the hydrological processes and how they can be incorporated into these models, in an integrated manner. Processes include recharge, discharge to wetlands and along the coastline, abstraction, evapotranspiration and potential seawater intrusion. The types and distributions of groundwater bores and monitoring are considered, as are scenarios for groundwater supply abstraction. Different types of numerical models and their applicability are also considered

Models of collective cell behaviour with crowding effects : comparing lattice-based and lattice-free approaches

Individual-based models describing the migration and proliferation of a population of cells frequently restrict the cells to a predefined lattice. An implicit assumption of this type of lattice based model is that a proliferative population will always eventually fill the lattice. Here we develop a new lattice-free individual-based model that incorporates cell-to-cell crowding effects. We also derive approximate mean-field descriptions for the lattice-free model in two special cases motivated by commonly used experimental setups. Lattice-free simulation results are compared to these mean-field descriptions and to a corresponding lattice-based model. Data from a proliferation experiment is used to estimate the parameters for the new model, including the cell proliferation rate, showing that the model fits the data well. An important aspect of the lattice-free model is that the confluent cell density is not predefined, as with lattice-based models, but an emergent model property. As a consequence of the more realistic, irregular configuration of cells in the lattice-free model, the population growth rate is much slower at high cell densities and the population cannot reach the same confluent density as an equivalent lattice-based model.