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.

An Architecture forRepresenting Biological Processes based on Networks of Bio-inspired Processors

n this paper we propose the use of Networks of Bio-inspired Processors (NBP) to model some biological phenomena within a computational framework. In particular, we propose the use of an extension of NBP named Network Evolutionary Processors Transducers to simulate chemical transformations of substances. Within a biological process, chemical transformations of substances are basic operations in the change of the state of the cell. Previously, it has been proved that NBP are computationally complete, that is, they are able to solve NP complete problems in linear time, using massively parallel computations. In addition, we propose a multilayer architecture that will allow us to design models of biological processes related to cellular communication as well as their implications in the metabolic pathways. Subsequently, these models can be applied not only to biological-cellular instances but, possibly, also to configure instances of interactive processes in many other fields like population interactions, ecological trophic networks, in dustrial ecosystems, etc.

Biological clocks

Circadian rhythms describe biological phenomena that oscillate with an ≈24-hour cycle. These rhythms include blood pressure, body temperature, hormone levels, the number of immune cells in blood, and the sleep-wake cycle. In this paper, we will focus on common genes between species that are responsible for determining the circadian behavior, especially some transcription factors (i.e., switch genes) that serve to regulate many circadian rhythm genes. The intent of this summary is to introduce the common molecular mechanism of biological clocks between flies and humans and then to describe the research from three laboratories that was presented in the session.

Mathematical modelling of chronic wound healing

Chronicwounds fail to proceed through an orderly process to produce anatomic and functional integrity and are a significant socioeconomic problem. There is much debate about the best way to treat these wounds. In this thesis we review earlier mathematical models of angiogenesis and wound healing. Many of these models assume a chemotactic response of endothelial cells, the primary cell type involved in angiogenesis. Modelling this chemotactic response leads to a system of advection-dominated partial differential equations and we review numerical methods to solve these equations and argue that the finite volume method with flux limiting is best-suited to these problems. One treatment of chronic wounds that is shrouded with controversy is hyperbaric oxygen therapy (HBOT). There is currently no conclusive data showing that HBOT can assist chronic wound healing, but there has been some clinical success. In this thesis we use several mathematical models of wound healing to investigate the use of hyperbaric oxygen therapy to assist the healing process - a novel threespecies model and a more complex six-species model. The second model accounts formore of the biological phenomena but does not lend itself tomathematical analysis. Bothmodels are then used tomake predictions about the efficacy of hyperbaric oxygen therapy and the optimal treatment protocol. Based on our modelling, we are able to make several predictions including that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds, treatment should continue until healing is complete and finding the right protocol for an individual patient is crucial if HBOT is to be effective. Analysis of the models allows us to derive constraints for the range of HBOT protocols that will stimulate healing, which enables us to predict which patients are more likely to have a positive response to HBOT and thus has the potential to assist in improving both the success rate and thus the cost-effectiveness of this therapy.

The role of the arachidonic acid pathway in NSCLC development and progression : novel approaches for therapeutic intervention

Arachidonic acid metabolism through cyclooxygenase (COX), lipoxygenase (LOX) and cytochrome P-450 epoxygenase (EPOX) pathways is responsible for the formation of biologically active eicosanoids, including prostanoids, leukotrienes, hydroxyeicosatetraenoic acid, epoxyeicosatrienoic acid and hydroperoxyeicosatetraenoic acids. Altered eicosanoid expression levels are commonly observed during tumour development and progression of a range of malignancies, including non-small cell lung cancer (NSCLC). Arachidonic acid-derived eicosanoids affect a range of biological phenomena to modulate tumour processes such as cell growth, survival, angiogenesis, cell adhesion, invasion and migration and metastatic potential. Numerous studies have demonstrated that eicosanoids modulate NSCLC development and progression, while targeting these pathways has generally been shown to inhibit tumour growth/progression. Modulation of these arachidonic acid-derived pathways for the prevention and/or treatment of NSCLC has been the subject of significant interest over the past number of years, with a number of clinical trials examining the potential of COX and LOX inhibitors in combination with traditional and novel molecular approaches. However, results from these trials have been largely disappointing. Furthermore, enthusiasm for the use of selective COX-2 inhibitors for cancer prevention/treatment waned, due to their association with adverse cardiovascular events in chemoprevention trials. While COX and LOX targeting may both retain promise for NSCLC prevention and/or treatment, there is an urgent need to understand the downstream signalling mechanisms through which these and other arachidonic acid-derived signalling pathways mediate their effects on tumourigenesis. This will allow for development of safer and potentially more effective strategies for NSCLC prevention and/or treatment. Chemoprevention studies with PGI2 analogues have demonstrated considerable promise, while binding to/signalling through PGE2 receptors have also been the subject of interest for NSCLC treatment. In this chapter, the role of the eicosanoid signalling pathways in non-small cell lung cancer will be discussed. In particular, the effect of the eicosanoids on tumour cell proliferation, their roles in induction of cell death, effects on angiogenesis, migration, invasion and their regulation of the immune response will be assessed, with signal transduction pathways involved in these processes also discussed. Finally, novel approaches targeting these arachidonic acid-derived eicosanoids (using pharmacological or natural agents) for chemoprevention and/or treatment of NSCLC will be outlined. Elucidating the molecular mechanisms underlying the effects of specific or general arachidonic acid pathway modulators may lead to the design of biologically and pharmacologically targeted therapeutic strategies for NSCLC prevention/treatment, which may be used alone or in combination with conventional therapies.

From bio-inspired computing to e-Biology

Several algorithms and techniques widely used in Computer Science have been adapted from, or inspired by, known biological phenomena. This is a consequence of the multidisciplinary background of most early computer scientists. The field has now matured, and permits development of tools and collaborative frameworks which play a vital role in advancing current biomedical research. In this paper, we briefly present examples of the former, and elaborate upon two of the latter, applied to immunological modelling and as a new paradigm in gene expression.

Paranormal, superstitious, magical, and religious beliefs

A lack of conceptual clarity and multivariate studies has impeded research on paranormal, superstitious, and magical beliefs. In this series of studies a new conceptual framework of these beliefs was presented. A general belief in the paranormal was shown to lead to specific paranormal, superstitious, and magical beliefs. The beliefs were defined equally as category mistakes where the core attributes of psychological, physical, and biological phenomena are confused with each other. This definition was supported by an empirical examination: Paranormal believers confused more core knowledge than skeptics. A multivariate study revealed that the best predictors of paranormal beliefs were intuitive thinking and a humanistic world view, while low analytical thinking was a less important predictor. Another study showed that women s greater belief in the paranormal compared to men was partially explained by women s higher intuitive and lower analytical thinking. Additionally, it was shown that university students were originally more skeptical than vocational school students, but university studies did not increase skepticism. The finding that paranormal beliefs mainly arise from an intuitive system, instead of a malfunctioning analytical system, explains why the beliefs do not vanish with the increase of education, scientific knowledge, and rational thinking. Religious and paranormal beliefs share important qualities and generally, they were positively related. The most religious people, however, abandoned paranormal beliefs. Religious people and paranormal believers differed from the skeptics similarly by being more intuitive, having experienced more mystical phenomena, and having peers and parents with more positive attitudes toward the supernatural. Religious people had, however, higher conservation and benevolence values than paranormal believers. The new conceptual framework presented in this series of studies integrates research on paranormal, superstitious, magical, and religious beliefs. Hopefully it will enable researchers to develop more elaborated hypotheses and theoretical statements about paranormal beliefs in the future.

The Gerbera cDNA Microarray: A Tool for Large-Scale Identification of Genes Involved in Flower Development

During the past ten years, large-scale transcript analysis using microarrays has become a powerful tool to identify and predict functions for new genes. It allows simultaneous monitoring of the expression of thousands of genes and has become a routinely used tool in laboratories worldwide. Microarray analysis will, together with other functional genomics tools, take us closer to understanding the functions of all genes in genomes of living organisms. Flower development is a genetically regulated process which has mostly been studied in the traditional model species Arabidopsis thaliana, Antirrhinum majus and Petunia hybrida. The molecular mechanisms behind flower development in them are partly applicable in other plant systems. However, not all biological phenomena can be approached with just a few model systems. In order to understand and apply the knowledge to ecologically and economically important plants, other species also need to be studied. Sequencing of 17 000 ESTs from nine different cDNA libraries of the ornamental plant Gerbera hybrida made it possible to construct a cDNA microarray with 9000 probes. The probes of the microarray represent all different ESTs in the database. From the gerbera ESTs 20% were unique to gerbera while 373 were specific to the Asteraceae family of flowering plants. Gerbera has composite inflorescences with three different types of flowers that vary from each other morphologically. The marginal ray flowers are large, often pigmented and female, while the central disc flowers are smaller and more radially symmetrical perfect flowers. Intermediate trans flowers are similar to ray flowers but smaller in size. This feature together with the molecular tools applied to gerbera, make gerbera a unique system in comparison to the common model plants with only a single kind of flowers in their inflorescence. In the first part of this thesis, conditions for gerbera microarray analysis were optimised including experimental design, sample preparation and hybridization, as well as data analysis and verification. Moreover, in the first study, the flower and flower organ-specific genes were identified. After the reliability and reproducibility of the method were confirmed, the microarrays were utilized to investigate transcriptional differences between ray and disc flowers. This study revealed novel information about the morphological development as well as the transcriptional regulation of early stages of development in various flower types of gerbera. The most interesting finding was differential expression of MADS-box genes, suggesting the existence of flower type-specific regulatory complexes in the specification of different types of flowers. The gerbera microarray was further used to profile changes in expression during petal development. Gerbera ray flower petals are large, which makes them an ideal model to study organogenesis. Six different stages were compared and specifically analysed. Expression profiles of genes related to cell structure and growth implied that during stage two, cells divide, a process which is marked by expression of histones, cyclins and tubulins. Stage 4 was found to be a transition stage between cell division and expansion and by stage 6 cells had stopped division and instead underwent expansion. Interestingly, at the last analysed stage, stage 9, when cells did not grow any more, the highest number of upregulated genes was detected. The gerbera microarray is a fully-functioning tool for large-scale studies of flower development and correlation with real-time RT-PCR results show that it is also highly sensitive and reliable. Gene expression data presented here will be a source for gene expression mining or marker gene discovery in the future studies that will be performed in the Gerbera Laboratory. The publicly available data will also serve the plant research community world-wide.

Synthesis of neoglycoconjugates and oligosaccharides with potential anti-Helicobacter pylori activity

The significance of carbohydrate-protein interactions in many biological phenomena is now widely acknowledged and carbohydrate based pharmaceuticals are under intensive development. The interactions between monomeric carbohydrate ligands and their receptors are usually of low affinity. To overcome this limitation natural carbohydrate ligands are often organized as multivalent structures. Therefore, artificial carbohydrate pharmaceuticals should be constructed on the same concept, as multivalent carbohydrates or glycoclusters. Infections of specific host tissues by bacteria, viruses, and fungi are among the unfavorable disease processes for which suitably designed carbohydrate inhibitors represent worthy targets. The bacterium Helicobacter pylori colonizes more than half of all people worldwide, causing gastritis, gastric ulcer, and conferring a greater risk of stomach cancer. The present medication therapy for H. pylori includes the use of antibiotics, which is associated with increasing incidence of bacterial resistance to traditional antibiotics. Therefore, the need for an alternative treatment method is urgent. In this study, four novel synthesis procedures of multivalent glycoconjugates were created. Three different scaffolds representing linear (chondroitin oligomer), cyclic (γ-cyclodextrin), and globular (dendrimer) molecules were used. Multivalent conjugates were produced using the human milk type oligosaccharides LNDFH I (Lewis-b hexasaccharide), LNnT (Galβ1-4GlcNAcβ1-3Galβ1-4Glc), and GlcNAcβ1-3Galβ1-4GlcNAcβ1-3Galβ1-4Glc all representing analogues of the tissue binding epitopes for H. pylori. The first synthetic method included the reductive amination of scaffold molecules modified to express primary amine groups, and in the case of dendrimer direct amination to scaffold molecule presenting 64 primary amine groups. The second method described a direct procedure for amidation of glycosylamine modified oligosaccharides to scaffold molecules presenting carboxyl groups. The final two methods that were created both included an oxime-linkage on linkers of different length. All the new synthetic procedures synthesized had the advantage of using unmodified reducing sugars as starting material making it easy to synthesize glycoconjugates of different specificity. In addition, the binding activity of an array of neoglycolipids to H. pylori was studied. Consequently, two new neolacto-based structures, Glcβ1-3Galβ1-4GlcNAcβ1-3Galβ1-4Glcβ1-Cer and GlcAβ1-3Galβ1-4GlcNAcβ1-3Galβ1-4Glcβ1-Cer, with binding activity toward H. pylori were discovered. Interestingly, N-methyl and N-ethyl amide modification of the GlcAβ1-3Galβ1-4GlcNAcβ1-3Galβ1-4Glcβ1-Cer glucuronic acid residue resulted in more effective H. pylori binding epitopes than the parent molecule.

Models of Dispersal and Diversification

Ecology and evolutionary biology is the study of life on this planet. One of the many methods applied to answering the great diversity of questions regarding the lives and characteristics of individual organisms, is the utilization of mathematical models. Such models are used in a wide variety of ways. Some help us to reason, functioning as aids to, or substitutes for, our own fallible logic, thus making argumentation and thinking clearer. Models which help our reasoning can lead to conceptual clarification; by expressing ideas in algebraic terms, the relationship between different concepts become clearer. Other mathematical models are used to better understand yet more complicated models, or to develop mathematical tools for their analysis. Though helping us to reason and being used as tools in the craftmanship of science, many models do not tell us much about the real biological phenomena we are, at least initially, interested in. The main reason for this is that any mathematical model is a simplification of the real world, reducing the complexity and variety of interactions and idiosynchracies of individual organisms. What such models can tell us, however, both is and has been very valuable throughout the history of ecology and evolution. Minimally, a model simplifying the complex world can tell us that in principle, the patterns produced in a model could also be produced in the real world. We can never know how different a simplified mathematical representation is from the real world, but the similarity models do strive for, gives us confidence that their results could apply. This thesis deals with a variety of different models, used for different purposes. One model deals with how one can measure and analyse invasions; the expanding phase of invasive species. Earlier analyses claims to have shown that such invasions can be a regulated phenomena, that higher invasion speeds at a given point in time will lead to a reduction in speed. Two simple mathematical models show that analysis on this particular measure of invasion speed need not be evidence of regulation. In the context of dispersal evolution, two models acting as proof-of-principle are presented. Parent-offspring conflict emerges when there are different evolutionary optima for adaptive behavior for parents and offspring. We show that the evolution of dispersal distances can entail such a conflict, and that under parental control of dispersal (as, for example, in higher plants) wider dispersal kernels are optimal. We also show that dispersal homeostasis can be optimal; in a setting where dispersal decisions (to leave or stay in a natal patch) are made, strategies that divide their seeds or eggs into fractions that disperse or not, as opposed to randomized for each seed, can prevail. We also present a model of the evolution of bet-hedging strategies; evolutionary adaptations that occur despite their fitness, on average, being lower than a competing strategy. Such strategies can win in the long run because they have a reduced variance in fitness coupled with a reduction in mean fitness, and fitness is of a multiplicative nature across generations, and therefore sensitive to variability. This model is used for conceptual clarification; by developing a population genetical model with uncertain fitness and expressing genotypic variance in fitness as a product between individual level variance and correlations between individuals of a genotype. We arrive at expressions that intuitively reflect two of the main categorizations of bet-hedging strategies; conservative vs diversifying and within- vs between-generation bet hedging. In addition, this model shows that these divisions in fact are false dichotomies.

Quantum clustering and network analysis of MD simulation trajectories to probe the conformational ensembles of protein-ligand interactions

In this article, we present a novel application of a quantum clustering (QC) technique to objectively cluster the conformations, sampled by molecular dynamics simulations performed on different ligand bound structures of the protein. We further portray each conformational population in terms of dynamically stable network parameters which beautifully capture the ligand induced variations in the ensemble in atomistic detail. The conformational populations thus identified by the QC method and verified by network parameters are evaluated for different ligand bound states of the protein pyrrolysyl-tRNA synthetase (DhPylRS) from D. hafniense. The ligand/environment induced re-distribution of protein conformational ensembles forms the basis for understanding several important biological phenomena such as allostery and enzyme catalysis. The atomistic level characterization of each population in the conformational ensemble in terms of the re-orchestrated networks of amino acids is a challenging problem, especially when the changes are minimal at the backbone level. Here we demonstrate that the QC method is sensitive to such subtle changes and is able to cluster MD snapshots which are similar at the side-chain interaction level. Although we have applied these methods on simulation trajectories of a modest time scale (20 ns each), we emphasize that our methodology provides a general approach towards an objective clustering of large-scale MD simulation data and may be applied to probe multistate equilibria at higher time scales, and to problems related to protein folding for any protein or protein-protein/RNA/DNA complex of interest with a known structure.

Contact instabilities of anisotropic and inhomogeneous soft elastic films

Anisotropy plays important roles in various biological phenomena such as adhesion of geckos and grasshoppers enabled by the attachment pods having hierarchical structures like thin longitudinal setae connected with threads mimicked by anisotropic films. We study the contact instability of a transversely isotropic thin elastic film when it comes in contact proximity of another surface. In the present study we investigate the contact stability of a thin incompressible transversely isotropic film by performing linear stability analysis. Based on the linear stability analysis, we show that an approaching contactor renders the film unstable. The critical wavelength of the instability is a function of the total film thickness and the ratio of the Young's modulus in the longitudinal direction and the shear modulus in the plane containing the longitudinal axis. We also analyze the stability of a thin gradient film that is elastically inhomogeneous across its thickness. Compared to a homogeneous elastic film, it becomes unstable with a longer wavelength when the film becomes softer in going from the surface to the substrate.

Spatial Filter Based Bessel-Like Beam for Improved Penetration Depth Imaging in Fluorescence Microscopy

Monitoring and visualizing specimens at a large penetration depth is a challenge. At depths of hundreds of microns, several physical effects (such as, scattering, PSF distortion and noise) deteriorate the image quality and prohibit a detailed study of key biological phenomena. In this study, we use a Bessel-like beam in-conjugation with an orthogonal detection system to achieve depth imaging. A Bessel-like penetrating diffractionless beam is generated by engineering the back-aperture of the excitation objective. The proposed excitation scheme allows continuous scanning by simply translating the detection PSF. This type of imaging system is beneficial for obtaining depth information from any desired specimen layer, including nano-particle tracking in thick tissue. As demonstrated by imaging the fluorescent polymer-tagged-CaCO3 particles and yeast cells in a tissue-like gel-matrix, the system offers a penetration depth that extends up to 650 mu m. This achievement will advance the field of fluorescence imaging and deep nano-particle tracking.

How should biologists engage with controversial mathematical theory?

Mathematics is beautiful and precise and often necessary to understand complex biological phenomena. And yet biologists cannot always hope to fully understand the mathematical foundations of the theory they are using or testing. How then should biologists behave when mathematicians themselves are in dispute? Using the on-going controversy over Hamilton's rule as an example, I argue that biologists should be free to treat mathematical theory with a healthy dose of agnosticism. In doing so biologists should equip themselves with a disclaimer that publicly admits that they cannot entirely attest to the veracity of the mathematics underlying the theory they are using or testing. The disclaimer will only help if it is accompanied by three responsibilities - stay bipartisan in a dispute among mathematicians, stay vigilant and help expose dissent among mathematicians, and make the biology larger than the mathematics. I must emphasize that my goal here is not to take sides in the on-going dispute over the mathematical validity of Hamilton's rule, indeed my goal is to argue that we should refrain from taking sides.

BIOCARDS AND LEVEL OF ABSTRACTION

Biocards are formal descriptions of biological phenomena and their underlying functional principles. They are used in bioinspired design to document search results and to communicate the findings for use in the further design process. The present study explored the effect of abstraction level used in biocards. This was done in two workshops conducted with design students in Denmark and India. Students were given a design assignment and instructions for how to perform the BID ideation work. Half of the students were given biocards with abstract descriptions while the other half got biocards with concrete descriptions. The novelty of found solutions was evaluated by the students by rating novelty of each solution on a scale from 1 to 5. Mean values for abstract descriptions were 0,3 higher than for concrete descriptions indicating that more innovative solutions were found when students used biocards with abstract descriptions compared to concrete descriptions. The difference in mean value is significant with a confidence level better than 1%. It seems likely that more abstract descriptions in biocards helps avoiding design fixation in biomimetic design work.