An approach to modelling in immunology

Like most other fields in biology, immunology has been revolutionised by the techniques of molecular biology and the resulting explosion in available experimental data. It is argued that efforts to integrate the data to gain insight into how various subsystems in the immune system interact and function require mathematical modelling and computer simulation in close collaboration with experimentalists. This paper illustrates some of the techniques available for modelling immune systems, and highlights the issues that should be borne in mind by anyone starting down the modelling path.     

Gene regulatory network inference: Data integration in dynamic models—A review

Systems biology aims to develop mathematical models of biological systems by integrating experimental and theoretical techniques. During the last decade, many systems biological approaches that base on genome-wide data have been developed to unravel the complexity of gene regulation. This review deals with the reconstruction of gene regulatory networks (GRNs) from experimental data through computational methods. Standard GRN inference methods primarily use gene expression data derived from microarrays. However, the incorporation of additional information from heterogeneous data sources, e.g. genome sequence and protein–DNA interaction data, clearly supports the network inference process. This review focuses on promising modelling approaches that use such diverse types of molecular biological information. In particular, approaches are discussed that enable the modelling of the dynamics of gene regulatory systems. The review provides an overview of common modelling schemes and learning algorithms and outlines current challenges in GRN modelling.     

Multi-Formalism Modelling and Simulation: Application to Cardiac Modelling

Cardiovascular modelling has been a major research subject for the last decade. Different cardiac models have been developed at a cellular level as well as at the whole organ level. Most of these models are defined by a comprehensive cellular modelling using continuous formalisms or by a tissue-level modelling often based on discrete formalisms. Nevertheless, both views still suffer from difficulties that reduce their clinical applications: the first approach requires heavy computational resources while the second one is not able to reproduce certain pathologies. This paper presents an original methodology trying to gather advantages from both approaches, by means of a hybrid model mixing discrete and continuous formalisms. This method has been applied to define a hybrid model of cardiac action potential propagation on a 2D grid of endocardial cells, combining cellular automata and a set of cells defined by the Beeler-Reuter model. For simulations under physiological and ischemic conditions, results show that the action potential propagation as well as electrogram reconstructions are consistent with clinical diagnosis. Finally, the advantage of the proposed approach is discussed within the frame of cardiac modelling and simulation.     

Modular assembly of dynamic models in systems biology

It is widely acknowledged that the construction of large-scale dynamic models in systems biology requires complex modelling problems to be broken up into more manageable pieces. To this end, both modelling and software frameworks are required to enable modular modelling. While there has been consistent progress in the development of software tools to enhance model reusability, there has been a relative lack of consideration for how underlying biophysical principles can be applied to this space. Bond graphs combine the aspects of both modularity and physics-based modelling. In this paper, we argue that bond graphs are compatible with recent developments in modularity and abstraction in systems biology, and are thus a desirable framework for constructing large-scale models. We use two examples to illustrate the utility of bond graphs in this context: a model of a mitogen-activated protein kinase (MAPK) cascade to illustrate the reusability of modules and a model of glycolysis to illustrate the ability to modify the model granularity.     

Extended statistical approaches to modelling spatial pattern in biodiversity in northeast New South Wales. II. Community-level modelling

Regional conservation planning can often make more effective use of sparse biological data by linking these data to remotely mapped environmental variables through statistical modelling. While modelling distributions of individual species is the best known and most widely used approach to such modelling, there are many situations in which more information can be extracted from available data by supplementing, or replacing, species-level modelling with modelling of communities or assemblages. This paper provides an overview of approaches to community-level modelling employed in a series of major land-use planning processes in the northeast New South Wales region of Australia, and evaluates how well communities and assemblages derived using these techniques function as surrogates in regional conservation planning. We also outline three new directions that may enhance the effectiveness of community-level modelling by: (1) more closely integrating modelling with traditional ecological mapping (e.g. vegetation mapping); (2) more tightly linking numerical classification and spatial modelling through application of canonical classification techniques; and (3) enhancing the applicability of modelling to data-poor regions through employment of a new technique for modelling spatial pattern in compositional dissimilarity.     

The state of plant population modelling in light of environmental change

Plant population modelling has been around since the 1970s, providing a valuable approach to understanding plant ecology from a mechanistic standpoint. It is surprising then that this area of research has not grown in prominence with respect to other approaches employed in modelling plant systems. In this review, we provide an analysis of the development and role of modelling in the field of plant population biology through an exploration of where it has been, where it is now and, in our opinion, where it should be headed. We focus, in particular, on the role plant population modelling could play in ecological forecasting, an urgent need given current rates of regional and global environmental change. We suggest that a critical element limiting the current application of plant population modelling in environmental research is the trade-off between the necessary resolution and detail required to accurately characterize ecological dynamics pitted against the goal of generality, particularly at broad spatial scales. In addition to suggestions how to overcome the current shortcoming of data on the process-level we discuss two emerging strategies that may offer a way to overcome the described limitation: (1) application of a modern approach to spatial scaling from local processes to broader levels of interaction and (2) plant functional-type modelling. Finally we outline what we believe to be needed in developing these approaches towards a ‘science of forecasting’.     

The beginning of a beautiful friendship: cross-linking/mass spectrometry and modelling of proteins and multi-protein complexes

After more than a decade of method development, cross-linking in combination with mass spectrometry and bioinformatics is finally coming of age. This technology now provides improved opportunities for modelling by mapping structural details of functional complexes in solution. The structure of proteins or protein complexes is ascertained by identifying amino acid pairs that are positioned in close proximity to each other. The validity of this technique has recently been benchmarked for large multi-protein complexes, by comparing cross-link data with that from a crystal structure of RNA polymerase II. Here, the specific nature of this cross-linking data will be discussed to assess the technical challenges and opportunities for model building. We believe that once remaining technological challenges of cross-linking/mass spectrometry have been addressed and cross-linking/mass spectrometry data has been incorporated into modelling algorithms it will quickly become an indispensable companion of protein and protein complex modelling and a corner-stone of integrated structural biology.     

Biology by numbers: mathematical modelling in developmental biology

In recent years, mathematical modelling of developmental processes has earned new respect. Not only have mathematical models been used to validate hypotheses made from experimental data, but designing and testing these models has led to testable experimental predictions. There are now impressive cases in which mathematical models have provided fresh insight into biological systems, by suggesting, for example, how connections between local interactions among system components relate to their wider biological effects. By examining three developmental processes and corresponding mathematical models, this Review addresses the potential of mathematical modelling to help understand development.     

Prediction of protein conformation in water and on surfaces by Monte Carlo simulations using united-atom method

The united-atom method has been used to model an avian pancreatic polypeptide (APP) in water and the adsorption process of an albumin subdomain (AS) onto graphite surface to observe the capability of this lumped modelling approach to generate structures observed in protein data bank (PDB) and from atomistic modelling. The subdomain structure of a protein is simplified by the united-atom approximation where the side chains and peptide groups are represented by lumped spheres. The total potential energy of the adsorption process involves the interaction between these lumped spheres by means of virtual bond chain interaction and the interaction of the spheres with the graphite surface by means of Lennard-Jones potential. The protein/polypeptide structure has been perturbed by Monte Carlo with energy minimisation to obtain the global minimum. Results on the APP in water showed a near-to-experimental PDB conformation revealing the two α-helix structures of this small protein molecule with the root mean square deviation among carbon backbone atoms of 5.9 Å. Protein adsorption on biosurfaces has been made by modelling AS, which has 60 amino acids. The surface is graphite, which is characterised by its hydrophobicity. Graphite was chosen because of its widely used applications in certain implants that interact with blood. Our simulation results showed final conformation close to that obtained by atomistic modelling. It also proved that the whole pattern of intramolecular hydrogen bonds was distorted. The model also demonstrated the random conformation of the original α-helix secondary structures of AS consistent with experimental and atomistic results. While atomistic simulation works well for simulating individual small proteins, the united-atom model is more efficient when simulating macromolecular and multiple protein adsorption where time and limiting computer capacity are key factors.     

RADBIOMOD: A simple program for utilising biological modelling in radiotherapy plan evaluation

PurposeRadiotherapy plan evaluation is currently performed by assessing physical parameters, which has many limitations. Biological modelling can potentially allow plan evaluation that is more reflective of clinical outcomes, however further research is required into this field before it can be used clinically.MethodsA simple program, RADBIOMOD, has been developed using Visual Basic for Applications (VBA) for Microsoft Excel that incorporates multiple different biological models for radiotherapy plan evaluation, including modified Poisson tumour control probability (TCP), modified Zaider–Minerbo TCP, Lyman–Kutcher–Burman normal tissue complication probability (NTCP), equivalent uniform dose (EUD), EUD-based TCP, EUD-based NTCP, and uncomplicated tumour control probability (UTCP). RADBIOMOD was compared to existing biological modelling calculators for 15 sample cases.ResultsComparing RADBIOMOD to the existing biological modelling calculators, all models tested had mean absolute errors and root mean square errors less than 1%.ConclusionsRADBIOMOD produces results that are non-significantly different from existing biological modelling calculators for the models tested. It is hoped that this freely available, user-friendly program will aid future research into biological modelling.     

Evaluation of the bioavailability of radionuclides from soil in cattle by an in vitro method

Factors have been examined which influence the radionuclides sorption from soil particles by fluid imitating rumen liquid of the cattle. It is noted that the extent of extractability of 137Cs from soil is influenced mainly by presence of potassium ions in modelling liquid. Major factor influencing the release of 90Sr from soil is pH value of the medium. The presence of heavy metals salts affected the release of radionuclides from soil particles. The data observed make it possible to use the modelling solutions to predict bioavailability of radionuclides from soil as well as to predict possible contamination of animal products (milk and meat).     

On the effects of different strategies in modelling balloon-expandable stenting by means of finite element method

In recent years, computational structural analyses have emerged as important tools to investigate the mechanical response of stent placement into arterial walls. Although most coronary stents are expanded by inflating a polymeric balloon, realistic computational balloon models have been introduced only recently. In the present study, the finite element method is applied to simulate three different approaches to evaluate stent-free expansion and stent expansion inside an artery. Three different stent expansion modelling techniques were analysed by: (i) imposing a uniform pressure on the stent internal surface, (ii) a rigid cylindrical surface expanded with displacement control and (iii) modelling a polymeric deformable balloon. The computational results showed differences in the free and confined-stent expansions due to different expansion techniques. The modelling technique of the balloon seems essential to estimate the level of injury caused on arterial walls during stent expansion.     

BI-BII transitions in B-DNA.

Molecular modelling is used to study the conformational and energetic aspects of BI-BII transitions within the backbone of a B-DNA dodecamer d(CATGACGTCATG) whose fine structure has previously been determined by molecular modelling combined with NMR spectroscopy. It is shown that while the dodecamer under investigation does not contain any BII junctions, the central CpG step can most easily undergo the transition. More generally, it is also found that the base sequence and hence the backbone geometry of a DNA segment, strongly influences both the conformational impact of the transition, the associated energy barrier and the stability of the resulting BII state.     

Molecular recognition of tyrosinyl adenylate analogues by prokaryotic tyrosyl tRNA synthetases

Molecular modelling and synthetic studies have been carried out on tyrosinyl adenylate and analogues to probe the interactions seen in the active site of the X-ray crystal structure of tyrosyl tRNA synthetase from Bacillus stearothermophilus, and to search for new inhibitors of this enzyme. Micromolar and sub-micromolar inhibitors of tyrosyl tRNA synthetases from both B. stearothermophilus and Staphylococcus aureus have been synthesised. The importance of the adenine ring to the binding of tyrosinyl adenylate to the enzyme, and the importance of water-mediated hydrogen bonding interactions, have been highlighted. The inhibition data has been further supported by homology modelling with the S. aureus enzyme, and by ligand docking studies.     

Homology modelling of the human eukaryotic initiation factor 5A (eIF-5A).

Homology modelling of the human eIF-5A protein has been performed by using a multiple predictions strategy. As the sequence identity between the target and the template proteins is nearly 30%, which is lower than the commonly used threshold to apply with confidence the homology modelling method, we developed a specific predictive scheme by combining different sequence analyses and predictions, as well as model validation by comparison to structural experimental information. The target sequence has been used to find homologues within sequence databases and a multiple alignment has been created. Secondary structure for each single protein has been predicted and compared on the basis of the multiple sequence alignment, in order to evaluate and adjust carefully any gap. Therefore, comparative modelling has been applied to create the model of the protein on the basis of the optimized sequence alignment. The quality of the model has been checked by computational methods and the structural features have been compared to experimental information, giving us a good validation of the reliability of the model and its correspondence to the protein structure in solution. Last, the model was deposited in the Protein Data Bank to be accessible for studies on the structure-function relationships of the human eIF-5A.     

Making the use of scenarios in LCA easier: the superstructure approach

The International Journal of Life Cycle Assessment - Much progress has recently been made in modelling future background systems for LCA by including future scenario data,...     

Combined NMR-crystallographic and modelling investigation of the inclusion of molsidomine into alpha-, beta- and gamma-cyclodextrins

A NMR spectroscopic and crystallographic investigation supported by molecular modelling methods has been employed to describe the inclusion properties of molsidomine into the three underivatized alpha-, beta- and gamma-cyclodextrins, aimed to point out the factors affecting the complexation selectivity and stabilization. The NMR results were compared and validated by the analysis of crystallographic data as retrieved from the Cambridge Structural Database and molecular modelling studies.     

Model of cytosine-, thymine-containing olygodeoxyribonucleotide protonation in solution

In the present study, the experimental data on the pH-induced formation of the i-motif structure in the nucleotide sequence 5'-CCTTTCCTTTTCCTTTCC-3' (25oC, pH 3.3-8.9) obtained by spectroscopic techniques, such as UV molecular absorption and circular dichroism, has been analysed using the chemometric soft modelling-based MCR-ALS approach and the hard modelling-based matrix method. Soft modelling using 2 or 3 spectral species correctly reproduced spectral variations observed experimentally. The use of hard chemical modelling enabled us to propose the equilibrium model, which describes spectral changes as functions of solution acidity. Additionally, the intrinsic protonation constant Kin, and the cooperativity parameter w have been calculated from the fitting procedure of the circular dichroism as well as molecular absorption spectra. The results indicated that folding was accompanied by a cooperative process, i.e. the enhancement of protonated structure stability upon protonation.     

Cooperative binding of 2,2′‐bipyridine into polynucleotide poly(A)–poly(U‐) in an alkaline aqueous solution

UV absorption data analysis has been used to evaluate equilibrium constants of the pH‐induced interaction of 2,2′‐Bipy with polyadenylnic‐polyuridylic acid in aqueous solution. The conditional probabilities hard model has been adopted in treatment of concentration diagrams calculated by the soft modelling‐based Multivariate Curve Resolution‐Alternating Least Squares approach. Intrinsic binding constant (lgK_g = 1.93), and the cooperativity parameter (ω = 340), were calculated as the best fit. The plot of the experimental binding constant versus 2,2′‐Bipy equilibrium concentration shows two modes of ligand with polymer interactions. The equilibrium hard model correctly reproduced the binding constant variations observed in the experiment. The results indicated that ligand binding in two steps is governed by a cooperative process, that is, the enhancement of deprotonated structure stability. It would appear that proposed calculation approach can be used in future combined hard modelling theoretical and soft modelling experimental works. © 2013 Wiley Periodicals, Inc. Biopolymers 99:621–627, 2013.