Ctirad Matonoha

Phycobilisome Mobility and Its Role in the Regulation of Light Harvesting in Red Algae

Phycobilisomes are mobile in mesophilic and immobile in extremophilic red algae, affecting photoprotection and either state transitions or nonphotochemical quenching. Red algae represent an evolutionarily important group that gave rise to the whole red clade of photosynthetic organisms. They contain a unique combination of light-harvesting systems represented by a membrane-bound antenna and by phycobilisomes situated on thylakoid membrane surfaces. So far, very little has been revealed about the mobility of their phycobilisomes and the regulation of their light-harvesting system in general. Therefore, we carried out a detailed analysis of phycobilisome dynamics in several red alga strains and compared these results with the presence (or absence) of photoprotective mechanisms. Our data conclusively prove phycobilisome mobility in two model mesophilic red alga strains, Porphyridium cruentum and Rhodella violacea. In contrast, there was almost no phycobilisome mobility in the thermophilic red alga Cyanidium caldarium that was not caused by a decrease in lipid desaturation in this extremophile. Experimental data attributed this immobility to the strong phycobilisome-photosystem interaction that highly restricted phycobilisome movement. Variations in phycobilisome mobility reflect the different ways in which light-harvesting antennae can be regulated in mesophilic and thermophilic red algae. Fluorescence changes attributed in cyanobacteria to state transitions were observed only in mesophilic P. cruentum with mobile phycobilisomes, and they were absent in the extremophilic C. caldarium with immobile phycobilisomes. We suggest that state transitions have an important regulatory function in mesophilic red algae; however, in thermophilic red algae, this process is replaced by nonphotochemical quenching.

Estimation of diffusivity of phycobilisomes on thylakoid membrane based on spatio-temporal FRAP images ✩

Abstract The determination of phycobilisome diffusivity (diffusion coefficient D ) on thylakoid membrane from fluorescence recovery after photobleaching (FRAP) experiments is usually done by analytical models. However, analytical models need some unrealistic conditions to be supposed. This study describes the development of a method based on finite difference approximation of the process governed by the Fickian diffusion equation and on the minimization of an objective function representing the disparity between the experimental and simulated time-varying concentration profiles. Our method improves on other models by accounting for experimentally measured time-varying Dirichlet boundary conditions, and can include a reaction term as well. As a result we obtain both the overall (time averaged) diffusion coefficient D and the sequence of diffusivities D j based on two successive fluorescence profiles in j -th time interval. Due to the noisy data, we cope with an inverse ill-posed problem and a regularization technique is mandatory.

Interior point methods for large-scale nonlinear programming

In this paper we describe an algorithm for solving nonlinear nonconvex programming problems, which is based on the interior point approach. The main theoretical results concern direction determination and step-length selection. We split inequality constraints into active and inactive parts to overcome problems with instability. Inactive constraints are eliminated directly, whereas active constraints are used for defining a symmetric indefinite linear system. Inexact solution of this system is obtained iteratively using indefinitely preconditioned conjugate gradient method. Theorems confirming efficiency of the indefinite preconditioner are introduced. Furthermore, a new merit function is defined and a filter principle is used for step-length selection. The algorithm was implemented in the interactive system for universal functional optimization UFO. Results of numerical experiments are reported.

Algorithm 896: LSA: Algorithms for large-scale optimization

We present 14 basic Fortran subroutines for large-scale unconstrained and box constrained optimization and large-scale systems of nonlinear equations. Subroutines PLIS and PLIP, intended for dense general optimization problems, are based on limited-memory variable metric methods. Subroutine PNET, also intended for dense general optimization problems, is based on an inexact truncated Newton method. Subroutines PNED and PNEC, intended for sparse general optimization problems, are based on modifications of the discrete Newton method. Subroutines PSED and PSEC, intended for partially separable optimization problems, are based on partitioned variable metric updates. Subroutine PSEN, intended for nonsmooth partially separable optimization problems, is based on partitioned variable metric updates and on an aggregation of subgradients. Subroutines PGAD and PGAC, intended for sparse nonlinear least-squares problems, are based on modifications and corrections of the Gauss-Newton method. Subroutine PMAX, intended for minimization of a maximum value (minimax), is based on the primal line-search interior-point method. Subroutine PSUM, intended for minimization of a sum of absolute values, is based on the primal trust-region interior-point method. Subroutines PEQN and PEQL, intended for sparse systems of nonlinear equations, are based on the discrete Newton method and the inverse column-update quasi-Newton method, respectively. Besides the description of methods and codes, we propose computational experiments which demonstrate the efficiency of the proposed algorithms.

Trust-region interior-point method for large sparse l1 optimization

In this article, we propose an interior-point method for large sparse l 1 optimization. After a short introduction, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Thus, relatively difficult l 1 optimization problems can be solved successfully. The results of computational experiments given in this article confirm efficiency and robustness of the proposed method.

Growth impact of hydrodynamic dispersion in a Couette-Taylor bioreactor

The development of a distributed parameter model of microalgae growth is presented. Two modelling frameworks for photo-bioreactor modelling, Eulerian and Lagrangian, are discussed and the complications residing in the multi-scale nature of transport and reaction phenomena are clarified. It is shown why is the mechanistic two time-scale model of photosynthetic factory the adequate model for biotechnological purposes. For a special laboratory Couette-Taylor bioreactor with cylindrical geometry, we reached reliable simulation results using a steady-state Eulerian approach and the finite difference scheme. Moreover, we prove numerically that the resulting photosynthetic production rate in this reactor goes, for growing inner cylinder angular velocity, to a certain limit value, which depends on the average irradiance only.

FRAP & FLIP: Two Sides of the Same Coin?

The aim of this study is to point out the similarity and differences of data processing based on either FRAP (Fluorescence Recovery After Photobleaching) or FLIP (Fluorescence Loss In Photobleaching) experimental techniques. The core idea, closely related to the sensitivity analysis, is based on discerning between relevant and irrelevant data. Presented mathematical model allows to visualize the mutual relation between the FRAP and FLIP methods. The whole concept resides in the processing of full spatio-temporal data instead of the space averaged time series (FRAP recovery curves). The method theoretically confirms the empirical knowledge, that the mobility of fluorescent molecules can be determined with both FRAP and FLIP methods (using the full data approach). Our analysis, based on the idealized theoretical case study, supports the conclusions of our recent experiments and thus it validates the reliability of our new approach. The presented finding are expected to be reflected into experimental protocol setup as well as we will continue working on the further enhancing the method of parameter identification.

Modeling and Optimization of Microalgae Growth in Photobioreactors: A Multidisciplinary Problem

Microalgae have the potential to be a major biofuel source in the future. Computational biology plays a key role in understanding biological processes within microalgae and optimizing biofuel production. Here, we present a multidisciplinary, multi-timescale modeling approach of microalgae growth in photobioreactors. Our modeling framework bridges biology (cell growth), physics (hydrodynamics and light distribution), and optimization together. This framework consists of (i) the state system (mass balance equations in form of advection-diffusion-reaction PDEs), (ii) the fluid flow equations (the Navier-Stokes equations), and (iii) the optimization problem formulation. The modeling and optimization of microalgae growth in a Couette-Taylor reactor is presented to demonstrate this method. We show how the flashing light effect can be an intrinsic part of the model. Finally, we discuss further methodological integration with the metabolomic-transcriptomic kinetic model, which explains cellular concentrations of key metabolites in connection with cell growth.

On the connection and equivalence of two methods for solving an ill-posed inverse problem based on FRAP data

Two methods for solving an ill-posed inverse problem based on Fickian diffusion equation and spatio-temporal data from FRAP measurements are presented. The most usual method is the Tikhonov regularization. Nevertheless, in our specific problem we have detected difficulties residing in determination of the optimal regularization parameter α . Hence, an equivalent method based on least squares with a quadratic constraint regularization is proposed. This latter approach naturally takes into account the noise level in the data and corresponds to Morozovs discrepancy principle as well. The equivalence of both methods is rigorously proven and on a simple numerical example with synthetic input data practically documented.

Disc vs. Annulus: On the Bleaching Pattern Optimization for FRAP Experiments

This study deals with the problem of optimal setting of experimental design variables, which controls the accuracy of the numerical process of determining model parameters from data. Our approach, although case independent, is formulated as an inverse problem of a diffusion coefficient estimation using the FRAP (Fluorescence Recovery After Photobleaching) experimental technique. The key concept relies on the analysis of the sensitivity of the measured output with respect to the model parameters. Based on this idea, we optimize an experimental design factor being the initial concentration of some particles. Numerical experiments on a 2D finite domain show that the discretized optimal initial condition attains only two values representing the existence or non-existence of diffusive particles. The number of jumps between these values determines the connectivity (or the bleaching pattern) and is dependent on the value of a diffusion coefficient, e.g., the annulus shaped initial condition is better than a disc for some specific range of model parameters.