Event-related functional magnetic resonance imaging: modelling, inference and optimization.

Event-related functional magnetic resonance imaging is a recent and popular technique for detecting haemodynamic responses to brief stimuli or events. However, the design of event-related experiments requires careful consideration of numerous issues of measurement, modelling and inference. Here we review these issues, with particular emphasis on the use of basis functions within a general linear modelling framework to model and make inferences about the haemodynamic response. With these models in mind, we then consider how the properties of functional magnetic resonance imaging data determine the optimal experimental design for a specific hypothesis, in terms of stimulus ordering and interstimulus interval. Finally, we illustrate various event-related models with examples from recent studies.     

Soft tissue modelling for applications in virtual surgery and surgical robotics

Soft tissue modelling has gained a great deal of importance, for a large part due to its application in surgical training simulators for minimally invasive surgery (MIS). This article provides a structured overview of different continuum-mechanical models that have been developed over the years. It aims at facilitating model choice for specific soft tissue modelling applications. According to the complexity of the model, different features of soft biological tissue will be incorporated, i.e. nonlinearity, viscoelasticity, anisotropy, heterogeneity and finally, tissue damage during deformation. A brief summary of experimental methods for material characterisation and an introduction to methods for geometric modelling are also provided. The overview is non-exhaustive, focusing on the most important general models and models with specific biological applications. A trade-off in complexity must be made for enabling real-time simulation, but still maintaining realistic representation of the organ deformation. Depending on the organ and tissue types, different models with emphasis on certain features will prove to be more appropriate, meaning the optimal model choice is organ and tissue-dependent.     

Soft tissue modelling for applications in virtual surgery and surgical robotics

Soft tissue modelling has gained a great deal of importance, for a large part due to its application in surgical training simulators for minimally invasive surgery (MIS). This article provides a structured overview of different continuum-mechanical models that have been developed over the years. It aims at facilitating model choice for specific soft tissue modelling applications. According to the complexity of the model, different features of soft biological tissue will be incorporated, i.e. nonlinearity, viscoelasticity, anisotropy, heterogeneity and finally, tissue damage during deformation. A brief summary of experimental methods for material characterisation and an introduction to methods for geometric modelling are also provided.

The overview is non-exhaustive, focusing on the most important general models and models with specific biological applications. A trade-off in complexity must be made for enabling real-time simulation, but still maintaining realistic representation of the organ deformation. Depending on the organ and tissue types, different models with emphasis on certain features will prove to be more appropriate, meaning the optimal model choice is organ and tissue-dependent.     

Projecting Range Limits with Coupled Thermal Tolerance - Climate Change Models: An Example Based on Gray Snapper (Lutjanus griseus) along the U.S. East Coast

We couple a species range limit hypothesis with the output of an ensemble of general circulation models to project the poleward range limit of gray snapper. Using laboratory-derived thermal limits and statistical downscaling from IPCC AR4 general circulation models, we project that gray snapper will shift northwards; the magnitude of this shift is dependent on the magnitude of climate change. We also evaluate the uncertainty in our projection and find that statistical uncertainty associated with the experimentally-derived thermal limits is the largest contributor (∼ 65%) to overall quantified uncertainty. This finding argues for more experimental work aimed at understanding and parameterizing the effects of climate change and variability on marine species.     

ScrumPy: metabolic modelling with Python

ScrumPy is a software package used for the definition and analysis of metabolic models. It is written using the Python programming language that is also used as a user interface. ScrumPy has features for both kinetic and structural modelling, but the emphasis is on structural modelling and those features of most relevance to analysis of large (genome-scale) models. The aim is at describing ScrumPy's functionality to readers with some knowledge of metabolic modelling, but implementation, programming and other computational details are omitted. ScrumPy is released under the Gnu Public Licence, and available for download from http://mudshark.brookes.ac.uk/ ScrumPy.     

Combining Experiments and Simulations Using the Maximum Entropy Principle

A key component of computational biology is to compare the results of computer modelling with experimental measurements. Despite substantial progress in the models and algorithms used in many areas of computational biology, such comparisons sometimes reveal that the computations are not in quantitative agreement with experimental data. The principle of maximum entropy is a general procedure for constructing probability distributions in the light of new data, making it a natural tool in cases when an initial model provides results that are at odds with experiments. The number of maximum entropy applications in our field has grown steadily in recent years, in areas as diverse as sequence analysis, structural modelling, and neurobiology. In this Perspectives article, we give a broad introduction to the method, in an attempt to encourage its further adoption. The general procedure is explained in the context of a simple example, after which we proceed with a real-world application in the field of molecular simulations, where the maximum entropy procedure has recently provided new insight. Given the limited accuracy of force fields, macromolecular simulations sometimes produce results that are at not in complete and quantitative accordance with experiments. A common solution to this problem is to explicitly ensure agreement between the two by perturbing the potential energy function towards the experimental data. So far, a general consensus for how such perturbations should be implemented has been lacking. Three very recent papers have explored this problem using the maximum entropy approach, providing both new theoretical and practical insights to the problem. We highlight each of these contributions in turn and conclude with a discussion on remaining challenges.     

Uncovering directional sensing: where are we headed?

We survey aspects of directional sensing, i.e. how a cell interprets differences in the external concentration of a chemoattractant to guide its motion, from the perspective of systems biology. We focus on questions that need to be addressed using a combination of modelling and experimental approaches. After briefly summarising the ideas underlying recent modelling efforts, we discuss a variety of experimental questions which are motivated by these models. Some of these questions focus on basic features of the chemotactic response, without involving much biochemistry, while others focus on filling some of the gaps in the biochemistry, which have been brought to light by the models. The emphasis is on systematic quantitative experiments that will unambiguously resolve many of these issues. Finally, we describe some current challenges for theoretical modelling and survey some of the theoretical tools and approaches employed to model the chemotaxis pathways.     

Muscle force estimation in clinical gait analysis using AnyBody and OpenSim

A variety of musculoskeletal models are applied in different modelling environments for estimating muscle forces during gait. Influence of different modelling assumptions and approaches on model outputs are still not fully understood, while direct comparisons of standard approaches have been rarely undertaken. This study seeks to compare joint kinematics, joint kinetics and estimated muscle forces of two standard approaches offered in two different modelling environments (AnyBody, OpenSim). It is hypothesised that distinctive differences exist for individual muscles, while summing up synergists show general agreement. Experimental data of 10 healthy participants (28 ± 5 years, 1.72 ± 0.08 m, 69 ± 12 kg) was used for a standard static optimisation muscle force estimation routine in AnyBody and OpenSim while using two gait-specific musculoskeletal models. Statistical parameter mapping paired t-test was used to compare joint angle, moment and muscle force waveforms in Matlab. Results showed differences especially in sagittal ankle and hip angles as well as sagittal knee moments. Differences were also found for some of the muscles, especially of the triceps surae group and the biceps femoris short head, which occur as a result of different anthropometric and anatomical definitions (mass and inertia of segments, muscle properties) and scaling procedures (static vs. dynamic). Understanding these differences and their cause is crucial to operate such modelling environments in a clinical setting. Future research should focus on alternatives to classical generic musculoskeletal models (e.g. implementation of functional calibration tasks), while using experimental data reflecting normal and pathological gait to gain a better understanding of variations and divergent behaviour between approaches.     

Mathematical modeling of the dynamics of frequency of the mutation process. I. Age features of SA frequency dynamics tendency]

A mathematical method for modelling SA frequency dynamics tendencies, depending on age, for different fixation moments and in general for the whole interval of observation is suggested. The criteria of remainder dispersion attitude is used for choosing an optimal model. The initial hypothesis about discrepancies distribution law is used for checking adequateness of the optimal model to the research process. In addition, aposteriory trust intervals are built for the initial and forecast SA frequency values and the hit into them corresponding the experimental values of SA frequencies is controlled. An example of practical realization of the model proposed is considered and the results obtained analysed.     

Development of a new version of the Liverpool Malaria Model. II. Calibration and validation for West Africa

Mathematical models have been used to provide an explicit framework for understanding malaria transmission dynamics in human population for over 100 years. With the disease still thriving and threatening to be a major source of death and disability due to changed environmental and socio-economic conditions, it is necessary to make a critical assessment of the existing models, and study their evolution and efficacy in describing the host-parasite biology. In this article, starting from the basic Ross model, the key mathematical models and their underlying features, based on their specific contributions in the understanding of spread and transmission of malaria have been discussed. The first aim of this article is to develop, starting from the basic models, a hierarchical structure of a range of deterministic models of different levels of complexity. The second objective is to elaborate, using some of the representative mathematical models, the evolution of modelling strategies to describe malaria incidence by including the critical features of host-vector-parasite interactions. Emphasis is more on the evolution of the deterministic differential equation based epidemiological compartment models with a brief discussion on data based statistical models. In this comprehensive survey, the approach has been to summarize the modelling activity in this area so that it helps reach a wider range of researchers working on epidemiology, transmission, and other aspects of malaria. This may facilitate the mathematicians to further develop suitable models in this direction relevant to the present scenario, and help the biologists and public health personnel to adopt better understanding of the modelling strategies to control the disease     

Some Mathematical Properties of Cumulative Damage Models Regarding Their Application in Cancer Epidemiology

In an earlier paper, cumulative damage models (CD models) were proposed for modelling the epidemiological aspects of carcinogenesis. In the present paper, further, mainly mathematical support is given for the adequacy of this approach. In the first place, this concerns the aspect that the cumulative damage process is a compound Poisson process. Secondly, it will be demonstrated that the CD models can be considered as a formal generalization of certain well-known special carcinogenesis models. A more intensive investigation of these models themselves makes it evident that, on account of their mathematical qualities, they will possibly place very efficient new measures at the disposal of epidemiology. A diffusion approximation, however, does, after first experiments, not appear to make the handling of the models any easier but, on the contrary, to lead to a loss of certain pleasant qualities.     

Validation protocol of models for centre of mass estimation.

The estimation of the body centre-of-mass (COM) position requires the modelling of the human body as a system of rigid segments and the measurement of the position of related external anatomical landmarks. Many models for COM position estimation have been proposed with different levels of complexity and, in some cases, specific protocols have been used for model accuracy evaluation. In this paper, we propose a general method for the quantitative assessment of any COM model in relation to a determined set of movements. It consists of an experimental protocol and of a set of comparative indices, which quantify the congruence among the estimated kinematic variables and their expected values. The general applicability of the method is specifically addressed to models' comparison, aiming to support the user in the process of choice and validation of the most suitable model for her/his purposes. In this frame, the results of the analytical comparison among two kinematic models with different levels of complexity are reported.     

Statistical inference on spontaneous neuronal discharge patterns

A statistical analysis was performed on extracellularly recorded spike trains of spontaneously active mesencephalic reticular neurons of rats. Only stationary records were used for detailed examination. The moments of interspike intervals were computed, hypothesis of renewal process and its specific forms was tested. Implications for statistical methodology are considered on the basis of the results. The main emphasis is laid on the connection between experimental results and stochastic neuronal models.     

Modelling of simple and complex calcium oscillations. From single-cell responses to intercellular signalling.

This review provides a comparative overview of recent developments in the modelling of cellular calcium oscillations. A large variety of mathematical models have been developed for this wide-spread phenomenon in intra- and intercellular signalling. From these, a general model is extracted that involves six types of concentration variables: inositol 1,4,5-trisphosphate (IP3), cytoplasmic, endoplasmic reticulum and mitochondrial calcium, the occupied binding sites of calcium buffers, and the fraction of active IP3 receptor calcium release channels. Using this framework, the models of calcium oscillations can be classified into 'minimal' models containing two variables and 'extended' models of three and more variables. Three types of minimal models are identified that are all based on calcium-induced calcium release (CICR), but differ with respect to the mechanisms limiting CICR. Extended models include IP3--calcium cross-coupling, calcium sequestration by mitochondria, the detailed gating kinetics of the IP3 receptor, and the dynamics of G-protein activation. In addition to generating regular oscillations, such models can describe bursting and chaotic calcium dynamics. The earlier hypothesis that information in calcium oscillations is encoded mainly by their frequency is nowadays modified in that some effect is attributed to amplitude encoding or temporal encoding. This point is discussed with reference to the analysis of the local and global bifurcations by which calcium oscillations can arise. Moreover, the question of how calcium binding proteins can sense and transform oscillatory signals is addressed. Recently, potential mechanisms leading to the coordination of oscillations in coupled cells have been investigated by mathematical modelling. For this, the general modelling framework is extended to include cytoplasmic and gap-junctional diffusion of IP3 and calcium, and specific models are compared. Various suggestions concerning the physiological significance of oscillatory behaviour in intra- and intercellular signalling are discussed. The article is concluded with a discussion of obstacles and prospects.     

Contrasting alternative hypotheses about rodent cycles by translating them into parameterized models

Ecologists working on population cycles of arvicoline (microtine) rodents consider three ecological mechanisms as the most likely explanations of this long-standing puzzle in population ecology: maternal effects, interaction with specialist predators, and interaction with the food supply. Each of these hypotheses has now been translated into parameterized models, and has been shown to be capable of generating second-order oscillations (that is, population cycles driven by delayed density dependence). This development places us in a unique situation for population ecology. We can now practice "strong inference" by explicitly and quantitatively comparing the predictions of the three rival hypotheses with data. In this review, we contrast the ability of each hypothesis to explain various empirically observed features of rodent cycles, with a particular emphasis on the well-studied case of Microtus agrestis and other small rodents in Fennoscandia (Finland, Sweden and Norway). Our conclusion is that the current evidence best supports the predation hypothesis.     

Unravelling the regulatory structure of biochemical networks using stimulus response experiments and large-scale model selection

To unravel the complex in vivo regulatory interdependences of biochemical networks, experiments with the living organism are absolutely necessary. Stimulus response experiments (SREs) have become increasingly popular in recent years. The response of metabolite concentrations from all major parts of the central metabolism is monitored over time by modem analytical methods, producing several thousand data points. SREs are applied to determine enzyme kinetic parameters and to find unknown enzyme regulatory mechanisms. Owing to the complex regulatory structure of metabolic networks and the amount of measured data, the evaluation of an SRE has to be extensively supported by modelling. If the enzyme regulatory mechanisms are part of the investigation, a large number of models with different enzyme kinetics have to be tested for their ability to reproduce the observed behaviour. In this contribution, a systematic model-building process for data-driven exploratory modelling is introduced with the aim of discovering essential features of the biological system. The process is based on data pre-processing, correlation-based hypothesis generation, automatic model family generation, large-scale model selection and statistical analysis of the best-fitting models followed by an extraction of common features. It is illustrated by the example of the aromatic amino acid synthesis pathway in Escherichia coli.     

Learning related interactions among neuronal systems involved in memory processes

Functional neuroimaging techniques using positron emission tomography (PET) and functional magnetic resonance imaging (fMRI) have provided new insights in our understanding of brain function from the molecular to the systems level. While subtraction strategy based data analyses have revealed the involvement of distributed brain regions in memory processes, covariance analysis based data analysis strategies allow functional interactions between brain regions of a neuronal network to be assessed. The focus of this chapter is to (1) establish the functional topography of episodic and working memory processes in young and old normal volunteers, (2) to assess functional interactions between modules of networks of brain regions by means of covariance based analyses and systems level modelling and (3) to relate neuroimaging data to the underpinning neural networks. Male normal young and old volunteers without neurological or psychiatric illness participated in neuroimaging studies (PET, fMRI) on working and episodic memory. Distributed brain areas are involved in memory processes (episodic and working memory) in young volunteers and show much of an overlap with respect to the network components. Systems level modelling analyses support the hypothesis of bihemispheric, asymmetric networks subserving memory processes and revealed both similarities in general and differences in the interactions between brain regions during episodic encoding and retrieval as well as working memory. Changes in memory function with ageing are evident from studies in old volunteers activating more brain regions compared to young volunteers and revealing more and stronger influences of prefrontal regions. We finally discuss the way in which the systems level models based on PET and fMRI results have implications for the understanding of the underlying neural network functioning of the brain.     

Structural Model of the CaV1.2 Pore

Understanding the structure and functional mechanisms of voltage-gated calcium channels remains a major task in membrane biophysics. In the absence of three dimensional structures, homology modelling techniques are the method of choice, to address questions concerning the structure of these channels. We have developed models of the open Cav1.2 pore, based on the crystal structure of the mammalian voltage-gated potassium channel Kv1.2 and a model of the bacterial sodium channel NaChBac. Our models are developed to be consistent with experimental data and modelling criteria. The models highlight major differences between voltage-gated potassium and calcium channels, in the P segments, as well as the inner pore helices. Molecular dynamics simulations support the hypothesis of a clockwise domain arrangement and experimental observations of asymmetric calcium channel behaviour. In the accompanying paper these models were used to study structural effects of a channelopathy mutation.     

Issues in high-throughput comparative modelling: a case study using the ubiquitin E2 conjugating enzymes

Sequences of the ubiquitin-conjugating enzyme (UBC or E2) family were used as a test set to investigate issues associated with the high-throughput comparative modelling of protein structures. A semi-automatic method was initially developed with particular emphasis on producing models of a quality suitable for structural comparison. Structural and sequence features of the E2 family were used to improve the sequence alignment and the quality of the structural templates. Initially, failure to correct for subtle structural inconsistencies between templates lead to problems in the comparative analysis of the UBC electrostatic potentials. Modelling of known UBC structures using Modeller 4.0 showed that multiple templates produced, on average, no better models than the use of just one template, as judged by the root-mean-squared deviation between the comparative model and crystal structure backbones. Using four different quality-checking methods, for a given target sequence, it was not possible to distinguish the model most similar to the experimental structure. The UBC models were thus finally modelled using only the crystal structure template with the highest sequence identity to the target to be modelled, and producing only one model solution. Quality checking was used to reject models with obvious structural anomalies (e.g., bad side-chain packing). The resulting models have been used for a comparison of UBC structural features and of their electrostatic potentials. The work was extended through the development of a fully automated pipeline that identifies E2 sequences in the sequence databases, aligns and models them, and calculates the associated electrostatic potential.