Interplay between local protein interactions and water bridging of a proton antenna carboxylate cluster.

Proteins that bind protons at cell membrane interfaces often expose to the bulk clusters of carboxylate and histidine sidechains that capture protons transiently and, in proton transporters, deliver protons to an internal site. The protonation-coupled dynamics of bulk-exposed carboxylate clusters, also known as proton antennas, is poorly described. An essential open question is how water-mediated bridges between sidechains of the cluster respond to protonation change and facilitate transient proton storage. To address this question, here I studied the protonation-coupled dynamics at the proton-binding antenna of PsbO, a small extrinsinc subunit of the photosystem II complex, with atomistic molecular dynamics simulations and systematic graph-based analyses of dynamic protein and protein-water hydrogen-bond networks. The protonation of specific carboxylate groups is found to impact the dynamics of their local protein-water hydrogen-bond clusters. Regardless of the protonation state considered for PsbO, carboxylate pairs that can sample direct hydrogen bonding, or bridge via short hydrogen-bonded water chains, anchor to nearby basic or polar protein sidechains. As a result, carboxylic sidechains of the hypothesized antenna cluster are part of dynamic hydrogen bond networks that may rearrange rapidly when the protonation changes.

SBML to bond graphs: From conversion to composition.

The Systems Biology Markup Language (SBML) is a popular software-independent XML-based format for describing models of biological phenomena. The BioModels Database is the largest online repository of SBML models. Several tools and platforms are available to support the reuse and composition of SBML models. However, these tools do not explicitly assess whether models are physically plausible or thermodynamically consistent. This often leads to ill-posed models that are physically impossible, impeding the development of realistic complex models in biology. Here, we present a framework that can automatically convert SBML models into bond graphs, which imposes energy conservation laws on these models. The new bond graph models are easily mergeable, resulting in physically plausible coupled models. We illustrate this by automatically converting and coupling a model of pyruvate distribution to a model of the pentose phosphate pathway.

Formalization of bond graph using higher-order-logic theorem proving.

Bond graph is a unified graphical approach for describing the dynamics of complex engineering and physical systems and is widely adopted in a variety of domains, such as, electrical, mechanical, medical, thermal and fluid mechanics. Traditionally, these dynamics are analyzed using paper-and-pencil proof methods and computer-based techniques. However, both of these techniques suffer from their inherent limitations, such as human-error proneness, approximations of results and enormous computational requirements. Thus, these techniques cannot be trusted for performing the bond graph based dynamical analysis of systems from the safety-critical domains like robotics and medicine. Formal methods, in particular, higher-order-logic theorem proving, can overcome the shortcomings of these traditional methods and provide an accurate analysis of these systems. It has been widely used for analyzing the dynamics of engineering and physical systems. In this paper, we propose to use higher-order-logic theorem proving for performing the bond graph based analysis of the physical systems. In particular, we provide formalization of bond graph, which mainly includes functions that allow conversion of a bond graph to its corresponding mathematical model (state-space model) and the verification of its various properties, such as, stability. To illustrate the practical effectiveness of our proposed approach, we present the formal stability analysis of a prosthetic mechatronic hand using HOL Light theorem prover. Moreover, to help non-experts in HOL, we encode our formally verified stability theorems in MATLAB to perform the stability analysis of an anthropomorphic prosthetic mechatronic hand.

Modular dynamic biomolecular modelling with bond graphs: the unification of stoichiometry, thermodynamics, kinetics and data.

Renewed interest in dynamic simulation models of biomolecular systems has arisen from advances in genome-wide measurement and applications of such models in biotechnology and synthetic biology. In particular, genome-scale models of cellular metabolism beyond the steady state are required in order to represent transient and dynamic regulatory properties of the system. Development of such whole-cell models requires new modelling approaches. Here, we propose the energy-based bond graph methodology, which integrates stoichiometric models with thermodynamic principles and kinetic modelling. We demonstrate how the bond graph approach intrinsically enforces thermodynamic constraints, provides a modular approach to modelling, and gives a basis for estimation of model parameters leading to dynamic models of biomolecular systems. The approach is illustrated using a well-established stoichiometric model of Escherichia coli and published experimental data.

Meeting the multiscale challenge: representing physiology processes over ApiNATOMY circuits using bond graphs.

We introduce, and provide examples of, the application of the bond graph formalism to explicitly represent biophysical processes between and within modular biological compartments in ApiNATOMY. In particular, we focus on modelling scenarios from acid-base physiology to link distinct process modalities as bond graphs over an ApiNATOMY circuit of multiscale compartments. The embedding of bond graphs onto ApiNATOMY compartments provides a semantically and mathematically explicit basis for the coherent representation, integration and visualisation of multiscale physiology processes together with the compartmental topology of those biological structures that convey these processes.

Modelling the heart with the atrioventricular plane as a piston unit.

Medical imaging and clinical studies have proven that the heart pumps by means of minor outer volume changes and back-and-forth longitudinal movements in the atrioventricular (AV) region. The magnitude of AV-plane displacement has also shown to be a reliable index for diagnosis of heart failure. Despite this, AV-plane displacement is usually omitted from cardiovascular modelling. We present a lumped-parameter cardiac model in which the heart is described as a displacement pump with the AV plane functioning as a piston unit (AV piston). This unit is constructed of different upper and lower areas analogous with the difference in the atrial and ventricular cross-sections. The model output reproduces normal physiology, with a left ventricular pressure in the range of 8-130 mmHg, an atrial pressure of approximatly 9 mmHg, and an arterial pressure change between 75 mmHg and 130 mmHg. In addition, the model reproduces the direction of the main systolic and diastolic movements of the AV piston with realistic velocity magnitude (∼10 cm/s). Moreover, changes in the simulated systolic ventricular-contraction force influence diastolic filling, emphasizing the coupling between cardiac systolic and diastolic functions. The agreement between the simulation and normal physiology highlights the importance of myocardial longitudinal movements and of atrioventricular interactions in cardiac pumping.

Metodología de los gráficos de unión (bond graphs) en aplicaciones biomédicas / Bond graph methodology in biomedical applications

Se presentan las aplicaciones realizadas en el campo de la medicina y la biología usando la técnica gráfica de modelado conocida como gráficos de unión (bond graphs), con el objetivo de mostrar las diferentes formas en las que se han usado los gráficos de unión como herramienta para la obtención de modelos y simulaciones de sistemas biológicos. Para el análisis de los trabajos realizados por los investigadores se hace una clasificación de los campos de aplicación con el fin de tener una visión más clara de lo diversa que ha sido la adaptación de esta metodología. Asimismo se discuten las posibilidades aún no exploradas, es decir, se habla de la aplicabilidad de los gráficos de unión en campos adicionales a los tratados en las referencias...

The paper presents applications carried out in the field of medicine and biology using the graphical modeling technique known as bond graphs, with the purpose of showing the different ways in which bond graphs have been used to obtain models and simulations of biological systems. To approach the work done by researchers, a classification is made of the fields of application, so as to obtain a clearer view of the variety of adaptations undergone by the methodology. Possibilities not yet explored are also discussed, i.e. comments are included on the applicability of bond graphs to fields other than those mentioned in the references...