Modelling Malaria Control by Introduction of Larvivorous Fish

Malaria creates serious health and economic problems which call for integrated management strategies to disrupt interactions among mosquitoes, the parasite and humans. In order to reduce the intensity of malaria transmission, malaria vector control may be implemented to protect individuals against infective mosquito bites. As a sustainable larval control method, the use of larvivorous fish is promoted in some circumstances. To evaluate the potential impacts of this biological control measure on malaria transmission, we propose and investigate a mathematical model describing the linked dynamics between the host–vector interaction and the predator–prey interaction. The model, which consists of five ordinary differential equations, is rigorously analysed via theories and methods of dynamical systems. We derive four biologically plausible and insightful quantities (reproduction numbers) that completely determine the community composition. Our results suggest that the introduction of larvivorous fish can, in principle, have important consequences for malaria dynamics, but also indicate that this would require strong predators on larval mosquitoes. Integrated strategies of malaria control are analysed to demonstrate the biological application of our developed theory.     

Non-parametric Decoding on Discrete Time Series and Its Applications in Bioinformatics

We address the question: How do we non-parametrically decode the unknown state-space vector underlying a lengthy discrete time series? The time series of concern is governed by one non-autonomous dynamics with only two internal states. This question pertinently reflects the dilemma of computing infeasibility against inferential bias found in many scientific areas. This dilemma becomes an issue when considering whether to have, or not to have likely very unrealistic structural assumptions on the state-space dynamics in most of real-world applications. To resolve this dilemma, the decoding problem is transformed into an event-intensity change-point problem without prior knowledge of the number of change-points involved. A new decoding algorithm, called Hierarchical Factor Segmentation (HFS), is proposed to achieve computability and robustness. Performance of the HFS algorithm in terms of total decoding error is compared to the decoding benchmark Viterbi algorithm through computer experiments. Under Hidden Markov Model (HMM) settings with true parameter values, our HFS algorithm is competitive against the Viterbi algorithm. Interestingly, when the Viterbi algorithm operates with maximum likelihood estimated (MLE) parameter values, our HFS algorithm performs significantly better. Similar favorable results are found when the Markov assumption is violated. We further demonstrate one very important application of our HFS algorithm in bioinformatics as a promising computational solution for finding CpG islands—DNA segments with aggregated CpG dinucleotides—on a genome sequence. A real illustration on a subsequence of human chromosome ^#22 is carried out and compared with one popular search algorithm.     

Studies on the Decomposition of Raffinose by α-Galactosidase of Actinomycetes

α-Galactosidase was isolated from the culture broth of Streptomyces olivaceus and was partially purified by chromatography on a DEAE-sephadex column. The optimum pH of the preparation was found to be 5.2 for raffinose and the preparation was inactivated completely by maintaining it at 60°C for 15 minutes. p-Chloromercuribenzoate, HgCl₂ and AgNO₃ caused complete inhibition of the enzyme activity at 2 × 10^?5 M concentration. The preparation showed transglycosylase activity. A sugar spot, chromatographically identical with that of stachyose, appeared in the digest of raffinose. However, the preparation hydrolyzed raffinose completely into galactose and sucrose after a prolonged incubation.

A simple raffinose estimation method was developed using the enzyme preparation, and it was found that the method allowed to estimate 125~500 μg of raffinose with an accuracy of ±5%. The method was applied to the estimation of raffinose in beet molasses.     

Studies on the Decomposition of Raffinose by α-Galactosidase of Mold

A mold which produced α-galactosidase and little invertase was isolated and identified as Mortierella vinacea. α-Galactosidase formation of the mold was induced by galactose, melibiose, raffinose and lactose. Among these inducers lactose showed the most stimulative effect. α-Galactosidase was produced by either Koji method or submerged culture method, but in the latter most α-galactosidase was found in the mycelium fraction.

Hydrolysis of raffinose in beet molasses was studied with the α-galactosidase in the mycelium fraction and about 80% of raffinose was found to be hydrolyzed by the enzyme preparation.     

Hierarchical Dynamics of Ecological Communities: Do Scales of Space and Time Match?

Theory posits that community dynamics organize at distinct hierarchical scales of space and time, and that the spatial and temporal patterns at each scale are commensurate. Here we use time series modeling to investigate fluctuation frequencies of species groups within invertebrate metacommunities in 26 boreal lakes over a 20-year period, and variance partitioning analysis to study whether species groups with different fluctuation patterns show spatial signals that are commensurate with the scale-specific fluctuation patterns identified. We identified two groups of invertebrates representing hierarchically organized temporal dynamics: one species group showed temporal variability at decadal scales (slow patterns of change), whilst another group showed fluctuations at 3 to 5-year intervals (faster change). This pattern was consistently found across all lakes studied. A spatial signal was evident in the slow but not faster-changing species groups. As expected, the spatial signal for the slow-changing group coincided with broad-scale spatial patterns that could be explained with historical biogeography (ecoregion delineation, and dispersal limitation assessed through a dispersal trait analysis). In addition to spatial factors, the slow-changing groups correlated with environmental variables, supporting the conjecture that boreal lakes are undergoing environmental change. Taken together our results suggest that regionally distinct sets of taxa, separated by biogeographical boundaries, responded similarly to broad-scale environmental change. Not only does our approach allow testing theory about hierarchically structured space-time patterns; more generally, it allows assessing the relative role of the ability of communities to track environmental change and dispersal constraints limiting community structure and biodiversity at macroecological scales.     

Multiscale Modelling of Fluid and Drug Transport in Vascular Tumours

A model for fluid and drug transport through the leaky neovasculature and porous interstitium of a solid tumour is developed. The transport problems are posed on a micro-scale characterized by the inter-capillary distance, and the method of multiple scales is used to derive the continuum equations describing fluid and drug transport on the length scale of the tumour (under the assumption of a spatially periodic microstructure). The fluid equations comprise a double porous medium, with coupled Darcy flow through the interstitium and vasculature, whereas the drug equations comprise advection–reaction equations; in each case the dependence of the transport coefficients on the vascular geometry is determined by solving micro-scale cell problems.     

Aberrant Behaviours of Reaction Diffusion Self-organisation Models on Growing Domains in the Presence of Gene Expression Time Delays

Turing’s pattern formation mechanism exhibits sensitivity to the details of the initial conditions suggesting that, in isolation, it cannot robustly generate pattern within noisy biological environments. Nonetheless, secondary aspects of developmental self-organisation, such as a growing domain, have been shown to ameliorate this aberrant model behaviour. Furthermore, while in-situ hybridisation reveals the presence of gene expression in developmental processes, the influence of such dynamics on Turing’s model has received limited attention. Here, we novelly focus on the Gierer–Meinhardt reaction diffusion system considering delays due the time taken for gene expression, while incorporating a number of different domain growth profiles to further explore the influence and interplay of domain growth and gene expression on Turing’s mechanism. We find extensive pathological model behaviour, exhibiting one or more of the following: temporal oscillations with no spatial structure, a failure of the Turing instability and an extreme sensitivity to the initial conditions, the growth profile and the duration of gene expression. This deviant behaviour is even more severe than observed in previous studies of Schnakenberg kinetics on exponentially growing domains in the presence of gene expression (Gaffney and Monk in Bull. Math. Biol. 68:99–130, 2006). Our results emphasise that gene expression dynamics induce unrealistic behaviour in Turing’s model for multiple choices of kinetics and thus such aberrant modelling predictions are likely to be generic. They also highlight that domain growth can no longer ameliorate the excessive sensitivity of Turing’s mechanism in the presence of gene expression time delays. The above, extensive, pathologies suggest that, in the presence of gene expression, Turing’s mechanism would generally require a novel and extensive secondary mechanism to control reaction diffusion patterning.     

The Influence of Hydrologic Residence Time on Lake Carbon Cycling Dynamics Following Extreme Precipitation Events

The frequency and magnitude of extreme events are expected to increase in the future, yet little is known about effects of such events on ecosystem structure and function. We examined how extreme precipitation events affect exports of terrestrial dissolved organic carbon (t-DOC) from watersheds to lakes as well as in-lake heterotrophy in three north-temperate lakes. Extreme precipitation events induced large influxes of t-DOC to our lakes, accounting for 45–58% of the seasonal t-DOC load. These large influxes of t-DOC influenced lake metabolism, resulting in lake net heterotrophy following 67% of the extreme precipitation events across all lakes. Hydrologic residence time (HRT) was negatively related to t-DOC load and heterotrophy; lakes with short HRT had higher t-DOC loads and greater net heterotrophy. The fraction of t-DOC mineralized within each lake following extreme precipitation events generally exhibited a positive relationship with lake HRT, similar to the previous studies of fractions mineralized at annual and supra-annual time scales. Event-associated turnover rate of t-DOC was higher than what is typically reported from laboratory studies and modeling exercises and was also negatively related to lake HRT. This study demonstrates that extreme precipitation events are ‘hot moments’ of carbon load, export, and turnover in lakes and that lake-specific characteristics (for example, HRT) interact with climatic patterns to set rates of important lake carbon fluxes.     

On the Modelling of Biological Patterns with Mechanochemical Models: Insights from Analysis and Computation

The diversity of biological form is generated by a relatively small number of underlying mechanisms. Consequently, mathematical and computational modelling can, and does, provide insight into how cellular level interactions ultimately give rise to higher level structure. Given cells respond to mechanical stimuli, it is therefore important to consider the effects of these responses within biological self-organisation models. Here, we consider the self-organisation properties of a mechanochemical model previously developed by three of the authors in Acta Biomater. 4, 613–621 (2008), which is capable of reproducing the behaviour of a population of cells cultured on an elastic substrate in response to a variety of stimuli. In particular, we examine the conditions under which stable spatial patterns can emerge with this model, focusing on the influence of mechanical stimuli and the interplay of non-local phenomena. To this end, we have performed a linear stability analysis and numerical simulations based on a mixed finite element formulation, which have allowed us to study the dynamical behaviour of the system in terms of the qualitative shape of the dispersion relation. We show that the consideration of mechanotaxis, namely changes in migration speeds and directions in response to mechanical stimuli alters the conditions for pattern formation in a singular manner. Furthermore without non-local effects, responses to mechanical stimuli are observed to result in dispersion relations with positive growth rates at arbitrarily large wavenumbers, in turn yielding heterogeneity at the cellular level in model predictions. This highlights the sensitivity and necessity of non-local effects in mechanically influenced biological pattern formation models and the ultimate failure of the continuum approximation in their absence.     

Modelling Foot-and-Mouth Disease Virus Dynamics in Oral Epithelium to Help Identify the Determinants of Lysis

Foot-and-mouth disease virus (FMDV) causes an economically important disease of cloven-hoofed livestock; of interest here is the difference in lytic behaviour that is observed in bovine epithelium. On the skin around the feet and tongue, the virus rapidly replicates, killing cells, and resulting in growing lesions, before eventually being cleared by the immune response. In contrast, there is usually minimal lysis in the soft palate, but virus may persist in tissue long after the animal has recovered from the disease. Persistence of virus has important implications for disease control, while identifying the determinant of lysis in epithelium is potentially important for the development of prophylactics. To help identify which of the differences between oral and pharyngeal epithelium are responsible for such dramatically divergent FMDV dynamics, a simple model has been developed, in which virus concentration is made explicit to allow the lytic behaviour of cells to be fully considered. Results suggest that localised structuring of what are fundamentally similar cells can induce a bifurcation in the behaviour of the system, explicitly whether infection can be sustained or results in mutual extinction, although parameter estimates indicate that more complex factors may be involved in maintaining viral persistence, or that there are as yet unquantified differences between the intrinsic properties of cells in these regions.     

Modelling Nutrient Uptake by Individual Hyphae of Arbuscular Mycorrhizal Fungi: Temporal and Spatial Scales for an Experimental Design

Arbuscular mycorrhizas, associations between plant roots and soil fungi, are ubiquitous among land plants. Arbuscular mycorrhizas can be beneficial for plants by overcoming limitations in nutrient supply. Hyphae, which are long and thin fungal filaments extending from the root surface into the soil, increase the volume of soil accessible for plant nutrient uptake. However, no models so far specifically consider individual hyphae. We developed a mathematical model for nutrient uptake by individual fungal hyphae in order to assess suitable temporal and spatial scales for a new experimental design where fungal uptake parameters are measured on the single hyphal scale. The model was developed based on the conservation of nutrients in an artificial cylindrical soil pore (capillary tube) with adsorbing wall, and analysed based on parameter estimation and non-dimensionalisation. An approximate analytical solution was derived using matched asymptotic expansion. Results show that nutrient influx into a hypha from a small capillary tube is characterized by three phases: Firstly, uptake rapidly decreases as the hypha takes up nutrients, secondly, the depletion zone reaches the capillary wall and thus uptake is sustained by desorption of nutrients from the capillary wall, and finally, uptake goes to zero after nutrients held on the capillary wall have been completely depleted. Simulating different parameter regimes resulted in recommending the use of capillaries filled with hydrogel instead of water in order to design an experiment operating over measurable time scales.     

Expression and Secretion of Bifidobacterium adolescentis Amylase by Bifidobacterium Longum

Bifidobacterium adolescentis Int-57 (INT57), isolated from human feces, secretes an amylase. We have shot-gun cloned, sequence analyzed and expressed the gene encoding this amylase in B. longum. The sequenced 2477 bp fragment was homologous to other extracellular amylases. The encoded protein was predicted to be composed of 595 amino acids with a molecular weight of 64 kDa, and was designated AmyB. Highly conserved amylase domains were found in AmyB. The signal sequence and cleavage site was predicted by sequence analysis. AmyB was subcloned into pBES2, a novel E. coli–Bifidobacterium shuttle vector, to construct pYBamy59. Subsequently, B. longum, with no apparent amylase activity, was transformed with pYBamy59. More than 90% of the amylase activity was detected in the culture broth. This approach may open the way for the development of more efficient expression and secretion systems for Bifidobacterium. Both authors contributed equally Received 17 June 2005; Revisions requested 13 July 2005 and 26 September 2005; Revisions received 12 September 2005 and 8 November 2005; Accepted 11 November 2005     

The Nature of Progression in Parkinson’s Disease: An Application of Non-Linear,Multivariate, Longitudinal Random Effects Modelling

Background

To date, statistical methods that take into account fully the non-linear, longitudinal and multivariate aspects of clinical data have not been applied to the study of progression in Parkinson’s disease (PD). In this paper, we demonstrate the usefulness of such methodology for studying the temporal and spatial aspects of the progression of PD. Extending this methodology further, we also explore the presymptomatic course of this disease.

Methods

Longitudinal Positron Emission Tomography (PET) measurements were collected on 78 PD patients, from 4 subregions on each side of the brain, using 3 different radiotracers. Non-linear, multivariate, longitudinal random effects modelling was applied to analyze and interpret these data.

Results

The data showed a non-linear decline in PET measurements, which we modelled successfully by an exponential function depending on two patient-related covariates duration since symptom onset and age at symptom onset. We found that the degree of damage was significantly greater in the posterior putamen than in the anterior putamen throughout the disease. We also found that over the course of the illness, the difference between the less affected and more affected sides of the brain decreased in the anterior putamen. Younger patients had significantly poorer measurements than older patients at the time of symptom onset suggesting more effective compensatory mechanisms delaying the onset of symptoms. Cautious extrapolation showed that disease onset had occurred some 8 to 17 years prior to symptom onset.

Conclusions

Our model provides important biological insights into the pathogenesis of PD, as well as its preclinical aspects. Our methodology can be applied widely to study many other chronic progressive diseases.     

Engineered Bi-Histidine Metal Chelation Sites Map the Structure of the Mechanical Unfolding Transition State of an Elastomeric Protein Domain GB1

Determining the structure of the transition state is critical for elucidating the mechanism behind how proteins fold and unfold. Due to its high free energy, however, the transition state generally cannot be trapped and studied directly using traditional structural biology methods. Thus, characterizing the structure of the transition state that occurs as proteins fold and unfold remains a major challenge. Here, we report a novel (to our knowledge) method that uses engineered bi-histidine (bi-His) metal-binding sites to directly map the structure of the mechanical unfolding transition state of proteins. This method is adapted from the traditional ψ-value analysis, which uses engineered bi-His metal chelation sites to probe chemical (un)folding transition-state structure. The ϕ^M2+_U-value is defined as ΔΔG_‡-N/ΔΔG_U-N, which is the energetic effects of metal chelation by the bi-His site on the unfolding energy barrier (ΔG_‡-N) relative to its thermodynamic stability (ΔG_U-N) and can be used to obtain information about the transition state in the mutational site. As a proof of principle, we used the small protein GB1 as a model system and set out to map its mechanical unfolding transition-state structure. Using single-molecule atomic force microscopy and spectrofluorimetry, we directly quantified the effect of divalent metal ion binding on the mechanical unfolding free energy and thermodynamic stability of GB1, which allowed us to quantify ϕ^M2+_U-values for different sites in GB1. Our results enabled us to map the structure of the mechanical unfolding transition state of GB1. Within GB1’s mechanical unfolding transition state, the interface between force-bearing β-strands 1 and 4 is largely disrupted, and the first β-hairpin is partially disordered while the second β-hairpin and the α-helix remain structured. Our results demonstrate the unique application of ψ-value analysis in elucidating the structure of the transition state that occurs during the mechanical unfolding process, offering a potentially powerful new method for investigating the design of novel elastomeric proteins.