Pearu Peterson

F2PY: a tool for connecting Fortran and Python programs

In this paper we tackle the problem of connecting low-level Fortran programs to high-level Python programs. The difficulties of mixed language programming between Fortran and C are resolved in an almost compiler and platform independent way. We provide a polished software tool F2PY that can (semi-)automatically build interfaces between the Python and Fortran languages and hence almost completely hide the difficulties from the target user: a research scientist who develops a computer model using a high-performance scripting approach.

Application of regularized Richardson–Lucy algorithm for deconvolution of confocal microscopy images

Although confocal microscopes have considerably smaller contribution of out‐of‐focus light than widefield microscopes, the confocal images can still be enhanced mathematically if the optical and data acquisition effects are accounted for. For that, several deconvolution algorithms have been proposed. As a practical solution, maximum‐likelihood algorithms with regularization have been used. However, the choice of regularization parameters is often unknown although it has considerable effect on the result of deconvolution process. The aims of this work were: to find good estimates of deconvolution parameters; and to develop an open source software package that would allow testing different deconvolution algorithms and that would be easy to use in practice. Here, Richardson–Lucy algorithm has been implemented together with the total variation regularization in an open source software package IOCBio Microscope. The influence of total variation regularization on deconvolution process is determined by one parameter. We derived a formula to estimate this regularization parameter automatically from the images as the algorithm progresses. To assess the effectiveness of this algorithm, synthetic images were composed on the basis of confocal images of rat cardiomyocytes. From the analysis of deconvolved results, we have determined under which conditions our estimation of total variation regularization parameter gives good results. The estimated total variation regularization parameter can be monitored during deconvolution process and used as a stopping criterion. An inverse relation between the optimal regularization parameter and the peak signal‐to‐noise ratio of an image is shown. Finally, we demonstrate the use of the developed software by deconvolving images of rat cardiomyocytes with stained mitochondria and sarcolemma obtained by confocal and widefield microscopes.

On the long-time behaviour of soliton ensembles

The paper is focused on the details of the emergence of Korteweg-de Vries (KdV) solitons from an initial harmonic excitation. Although the problem is a classical one, numerical simulations over a large range of dispersion parameters in the long run have demonstrated new features: the existence of soliton ensembles including also virtual (hidden) solitons and the periodic patterns of the wave-profile maxima.

Analysis of Molecular Movement Reveals Latticelike Obstructions to Diffusion in Heart Muscle Cells

Intracellular diffusion in muscle cells is known to be restricted. Although characteristics and localization of these restrictions is yet to be elucidated, it has been established that ischemia-reperfusion injury reduces the overall diffusion restriction. Here we apply an extended version of raster image correlation spectroscopy to determine directional anisotropy and coefficients of diffusion in rat cardiomyocytes. Our experimental results indicate that diffusion of a smaller molecule (1127 MW fluorescently labeled ATTO633-ATP) is restricted more than that of a larger one (10,000 MW Alexa647-dextran), when comparing diffusion in cardiomyocytes to that in solution. We attempt to provide a resolution to this counterintuitive result by applying a quantitative stochastic model of diffusion. Modeling results suggest the presence of periodic intracellular barriers situated ∼1 μm apart having very low permeabilities and a small effect of molecular crowding in volumes between the barriers. Such intracellular structuring could restrict diffusion of molecules of energy metabolism, reactive oxygen species, and apoptotic signals, enacting a significant role in normally functioning cardiomyocytes as well as in pathological conditions of the heart.

Long-time behaviour of soliton ensembles. Part I––Emergence of ensembles

Abstract This paper is focused on the emergence of the KdV solitons from an initial harmonic excitation. In the long run this process is characterized not so much by regular soliton trains but rather by soliton ensembles. It has been shown explicitly that under indicated initial conditions the width of emerging solitons are mostly larger than the distance between maxima of wave profiles. Consequently, visible are the ensembles formed by several simultaneously interacting solitons including also hidden (virtual) solitons. The conditions for emerging such ensembles are studied over the wide range of amplitude ratios for typical dispersion parameters. Based on that analysis, it is possible to cast more light to the recurrence and periodicity in the long run (see Part II).

Long-time behaviour of soliton ensembles. Part II––Periodical patterns of trajectories

Abstract The emergence and interaction of KdV solitons generated by harmonic initial conditions are studied in the long run (hundreds of recurrence time tR). After the initial train of solitons has emerged, the further process is characterised by propagation of soliton ensembles and in numerical calculations the local maxima of wave profiles can be traced (see Part I for the description of ensembles and the corresponding trajectories of single solitons vs those within an ensemble). The geometrical patterns of trajectories of those maxima are analysed. In the short run arc-like patterns are formed but in the long run regular rhombus-like patterns are detected. The backbones of those rhombi are balanced trajectories which correspond to interacting solitons whose phase-shifts to the right are balanced by phase-shifts to the left. Consequently, over long time and space intervals these trajectories can be approximated by straight lines. A rhombus in the x–t plane has the space periodicity 2π dictated by the initial excitation and time periodicity 2tP or tP, dictated by balanced trajectories and related to the recurrence time tR. Such a pattern is a steady feature of regularity in the soliton emergence process that usually is taken to be shadowed by the loss of the recurrence in the strict sense.

Sensitivity of the inverse wave crest problem

In a previous paper [Physica D 141 (3-4) (2000) 316], the inverse problem for wave crests was introduced and a solution strategy for two-wave interactions was given. Here these solutions are actually constructed, in particular for the cases with small interaction angle, moderate phase shifts, and/or symmetric interactions. Two detailed examples are presented and analyzed. The sensitivity of the method is investigated, and conclusions about the practical applicability are given.

Molecular Dynamics Simulations of Creatine Kinase and Adenine Nucleotide Translocase in Mitochondrial Membrane Patch

Background: Functional coupling between mitochondrial creatine kinase (MtCK) and adenine nucleotide translocase (ANT) can determine energy transfer pathways in the cell. Results: We composed a molecular dynamics model of a mitochondrial inner membrane patch, ANT, and MtCK. Conclusion: Cardiolipin plays an important role in stabilizing MtCK-membrane binding. Significance: This is a first step in the development of an MtCK, ANT, and membrane interaction model. Interaction between mitochondrial creatine kinase (MtCK) and adenine nucleotide translocase (ANT) can play an important role in determining energy transfer pathways in the cell. Although the functional coupling between MtCK and ANT has been demonstrated, the precise mechanism of the coupling is not clear. To study the details of the coupling, we turned to molecular dynamics simulations. We introduce a new coarse-grained molecular dynamics model of a patch of the mitochondrial inner membrane containing a transmembrane ANT and an MtCK above the membrane. The membrane model consists of three major types of lipids (phosphatidylcholine, phosphatidylethanolamine, and cardiolipin) in a roughly 2:1:1 molar ratio. A thermodynamics-based coarse-grained force field, termed MARTINI, has been used together with the GROMACS molecular dynamics package for all simulated systems in this work. Several physical properties of the system are reproduced by the model and are in agreement with known data. This includes membrane thickness, dimension of the proteins, and diffusion constants. We have studied the binding of MtCK to the membrane and demonstrated the effect of cardiolipin on the stabilization of the binding. In addition, our simulations predict which part of the MtCK protein sequence interacts with the membrane. Taken together, the model has been verified by dynamical and structural data and can be used as the basis for further studies.

Bidirectionality and Compartmentation of Metabolic Fluxes Are Revealed in the Dynamics of Isotopomer Networks

Isotope labeling is one of the few methods of revealing the in vivo bidirectionality and compartmentalization of metabolic fluxes within metabolic networks. We argue that a shift from steady state to dynamic isotopomer analysis is required to deal with these cellular complexities and provide a review of dynamic studies of compartmentalized energy fluxes in eukaryotic cells including cardiac muscle, plants, and astrocytes. Knowledge of complex metabolic behaviour on a molecular level is prerequisite for the intelligent design of genetically modified organisms able to realize their potential of revolutionizing food, energy, and pharmaceutical production. We describe techniques to explore the bidirectionality and compartmentalization of metabolic fluxes using information contained in the isotopic transient, and discuss the integration of kinetic models with MFA. The flux parameters of an example metabolic network were optimized to examine the compartmentalization of metabolites and and the bidirectionality of fluxes in the TCA cycle of Saccharomyces uvarum for steady-state respiratory growth.

Tight coupling of Na+/K+-ATPase with glycolysis demonstrated in permeabilized rat cardiomyocytes.

The effective integrated organization of processes in cardiac cells is achieved, in part, by the functional compartmentation of energy transfer processes. Earlier, using permeabilized cardiomyocytes, we demonstrated the existence of tight coupling between some of cardiomyocyte ATPases and glycolysis in rat. In this work, we studied contribution of two membrane ATPases and whether they are coupled to glycolysis - sarcoplasmic reticulum Ca2+ ATPase (SERCA) and plasmalemma Na+/K+-ATPase (NKA). While SERCA activity was minor in this preparation in the absence of calcium, major role of NKA was revealed accounting to ∼30% of the total ATPase activity which demonstrates that permeabilized cell preparation can be used to study this pump. To elucidate the contribution of NKA in the pool of ATPases, a series of kinetic measurements was performed in cells where NKA had been inhibited by 2 mM ouabain. In these cells, we recorded: ADP- and ATP-kinetics of respiration, competition for ADP between mitochondria and pyruvate kinase (PK), ADP-kinetics of endogenous PK, and ATP-kinetics of total ATPases. The experimental data was analyzed using a series of mathematical models with varying compartmentation levels. The results show that NKA is tightly coupled to glycolysis with undetectable flux of ATP between mitochondria and NKA. Such tight coupling of NKA to PK is in line with its increased importance in the pathological states of the heart when the substrate preference shifts to glucose.