A systems model for the pupil size effect

The human pupillary control system is a paradigm for linearized biological control systems. It also exhibits a series of interesting nonlinear behaviors, particularly asymmetry, “pupillary escape”, and “pupillary capture.” We present a nonlinear model in which a signal dependent upon pupil size is fed back internally to cause a change in system parameters related to gains and rates of light adaptation. The model was simulated on a digital computer, a variety of experimental data was well matched, and improvements over previous pupil models demonstrated. A candidate physiological mechanism for adaptive components of the model might have the form of an inverse “Henneman coded” neuronal pool.     

A fully predictive model for one-dimensional light attenuation by Chlamydomonas reinhardtii in a torus photobioreactor

The light attenuation in a photobioreactor is determined using a fully predictive model. The optical properties were first calculated, using a data bank of the literature, from only the knowledge of pigments content, shape, and size distributions of cultivated cells which are a function of the physiology of the current species. The radiative properties of the biological turbid medium were then deduced using the exact Lorenz-Mie theory. This method is experimentally validated using a large-size integrating sphere photometer. The radiative properties are then used in a rectangular, one-dimensional two-flux model to predict radiant light attenuation in a photobioreactor, considering a quasi-collimated field of irradiance. Combination of this radiative model with the predictive determination of optical properties is finally validated by in situ measurement of attenuation profiles in a torus photobioreactor cultivating the microalgae Chlamydomonas reinhardtii, after a complete and proper characterization of the incident light flux provided by the experimental set-up.     

生物组织光散射等效颗粒模型及Mie相函数计算

为研究生物组织的散射特性,将其从散射效果上等效为离散的球形散射体的集合,结合经典的Mie散射理论对生物组织散射相函数进行数值计算。计算结果表明:Mie散射相函数能够描述生物组织后向(大角度)散射光强振荡特性与等效粒径的对应关系,可为基于后向散射光的无创伤或微创伤诊疗提供理论依据;Mie散射相函数能够解释生物组织散射光空间分布与波长的相关性,为医学诊疗上入射光波长选择提供参考;合理选择集群散射体粒度分布参数,可实现对复杂生物组织散射相函数的精确描述。     

传递函数在生物组织光传输问题中的应用

本文将传递函数的概念引入生物组织光传输问题,并将传递函数理论用于面光源照射下生物组织内特定深度层面上光场强度分布的理论计算。结合Monte Carlo模拟获取脉冲相应函数,我们分析了不同面光源照射下层状组织样品透射面上的光场强度分布。理论计算结果与实验测试结果的一致性较好,这充分说明了本文建立的基于Monte Carlo模拟的传递函数方法是一种处理面光源照射下生物组织内光场空间的直接而有效的手段。     

Size distribution of submicron particles by dynamic light scattering measurements: analyses considering normalization errors

Errors in the experimental baseline used to normalize dynamic light scattering data can seriously affect the size distribution resulting from the data analysis. A revised method, which incorporates the characteristics of this error into the size distribution algorithm CONTIN (Ruf 1989), is tested with experimental data of high statistical accuracy obtained from a sample of phospholipid vesicles. It is shown that the various commonly used ways of accumulating and normalizing dynamic light scattering data are associated with rather different normalization errors. As a consequence a variety of solutions differing in modality, as well as in width, are obtained on carrying out data analysis in the common way. It is demonstrated that a single monomodal solution is retrieved from all these data sets when the new method is applied, which in addition provides the corresponding baseline errors quantitatively. Furthermore, stable solutions are obtainable with data of lower statistical accuracy which results from measurements of shorter duration. The use of an additional parameter in data inversion reduces the occurrence of spurious peaks. This stabilizing effect is accompanied by larger uncertainties in the width of the size distribution. It is demonstrated that these uncertainties are reduced by nearly a factor of two on using the normalization error function instead of the ‘dust term’ option for the analysis of noisy data sets.     

蒙特卡罗模拟多束光辐照下生物组织中的光吸收分布

用蒙特卡罗方法模拟了均匀分布光和高斯分布光在生物组织内的传播。通过比较单束以及多束均匀分布光和高斯分布光照射下组织内的光子能量分布规律,分析了不同光源和光斑大小对光吸收分布的影响。结果表明:与均匀光束比较,高斯光束辐照时,激光能量较为集中,但侧向传播范围较窄。在总功率相同的情况下,使用单束大功率宽光源与多束功率较小的小光斑光源均能明显地增大光的侧向传播距离,但使用多束功率较小的小光斑光辐照时生物组织中的最大光吸收率增大。多束组合光源光束间距对光吸收分布影响很大。     

生物组织中有限束宽光吸收的蒙特卡罗模拟

用蒙特卡罗法模拟了有限束宽均匀分布和高斯分布光在生物组织中的传播,分析了生物组织的光学参数及光源特性对光吸收分子的影响,结果表明：只要有效光吸收系数增加,最大光吸收率就会增加,光的侧向传输能力主要依赖于光的有效散射,光束宽度增加,辐照范围加宽,高斯光束的吸收分布的梯度更大。     

Bayesian hierarchical error model for analysis of gene expression data

MOTIVATION: Analysis of genome-wide microarray data requires the estimation of a large number of genetic parameters for individual genes and their interaction expression patterns under multiple biological conditions. The sources of microarray error variability comprises various biological and experimental factors, such as biological and individual replication, sample preparation, hybridization and image processing. Moreover, the same gene often shows quite heterogeneous error variability under different biological and experimental conditions, which must be estimated separately for evaluating the statistical significance of differential expression patterns. Widely used linear modeling approaches are limited because they do not allow simultaneous modeling and inference on the large number of these genetic parameters and heterogeneous error components on different genes, different biological and experimental conditions, and varying intensity ranges in microarray data. RESULTS: We propose a Bayesian hierarchical error model (HEM) to overcome the above restrictions. HEM accounts for heterogeneous error variability in an oligonucleotide microarray experiment. The error variability is decomposed into two components (experimental and biological errors) when both biological and experimental replicates are available. Our HEM inference is based on Markov chain Monte Carlo to estimate a large number of parameters from a single-likelihood function for all genes. An F-like summary statistic is proposed to identify differentially expressed genes under multiple conditions based on the HEM estimation. The performance of HEM and its F-like statistic was examined with simulated data and two published microarray datasets-primate brain data and mouse B-cell development data. HEM was also compared with ANOVA using simulated data. AVAILABILITY: The software for the HEM is available from the authors upon request.     

Evaluation of biological nutrient removal from wastewater by Twin Circulating Fluidized Bed Bioreactor (TCFBBR) using a predictive fluidization model and AQUIFAS APP

A two-phase and three-phase predictive fluidization model based on the characteristics of a system such as media type and size, flow rates, and reactor cross sectional area was proposed to calculate bed expansion, solid, liquid and gas hold up and specific surface area (SSA) of the biofilm particles. The model was subsequently linked to 1d AQUIFAS APP software (Aquaregen) to model biological nutrient removal in two phase (anoxic) and three phase (aerobic) fluidized bed bioreactors. The credibility of the proposed model for biological nutrient removal was investigated using the experimental data from a Twin Circulating Fluidized Bed Bioreactors (TCFBBR) treating synthetic and municipal wastewater.The SSA of bio-particles and volume of the expanded bed were simulated as a function of operational parameters. Two-sided t-tests demonstrated that simulated SCOD, NH₄-N, NO₃-N, TN, VSS and biomass yields agreed with the experimental values at the 95% confidence level.     

Population Dynamics of a Salmonella Lytic Phage and Its Host: Implications of the Host Bacterial Growth Rate in Modelling

The prevalence and impact of bacteriophages in the ecology of bacterial communities coupled with their ability to control pathogens turn essential to understand and predict the dynamics between phage and bacteria populations. To achieve this knowledge it is essential to develop mathematical models able to explain and simulate the population dynamics of phage and bacteria. We have developed an unstructured mathematical model using delay-differential equations to predict the interactions between a broad-host-range Salmonella phage and its pathogenic host. The model takes into consideration the main biological parameters that rule phage-bacteria interactions likewise the adsorption rate, latent period, burst size, bacterial growth rate, and substrate uptake rate, among others. The experimental validation of the model was performed with data from phage-interaction studies in a 5 L bioreactor. The key and innovative aspect of the model was the introduction of variations in the latent period and adsorption rate values that are considered as constants in previous developed models. By modelling the latent period as a normal distribution of values and the adsorption rate as a function of the bacterial growth rate it was possible to accurately predict the behaviour of the phage-bacteria population. The model was shown to predict simulated data with a good agreement with the experimental observations and explains how a lytic phage and its host bacteria are able to coexist.     

Polycyclic aromatic hydrocarbons as plausible prebiotic membrane components

Aromatic molecules delivered to the young Earth during the heavy bombardment phase in the early history of our solar system were likely to be among the most abundant and stable organic compounds available. The Aromatic World hypothesis suggests that aromatic molecules might function as container elements, energy transduction elements and templating genetic components for early life forms. To investigate the possible role of aromatic molecules as container elements, we incorporated different polycyclic aromatic hydrocarbons (PAH) in the membranes of fatty acid vesicles. The goal was to determine whether PAH could function as a stabilizing agent, similar to the role that cholesterol plays in membranes today. We studied vesicle size distribution, critical vesicle concentration and permeability of the bilayers using C(6)-C(10) fatty acids mixed with amphiphilic PAH derivatives such as 1-hydroxypyrene, 9-anthracene carboxylic acid and 1,4 chrysene quinone. Dynamic Light Scattering (DLS) spectroscopy was used to measure the size distribution of vesicles and incorporation of PAH species was established by phase-contrast and epifluorescence microscopy. We employed conductimetric titration to determine the minimal concentration at which fatty acids could form stable vesicles in the presence of PAHs. We found that oxidized PAH derivatives can be incorporated into decanoic acid (DA) vesicle bilayers in mole ratios up to 1:10 (PAH:DA). Vesicle size distribution and critical vesicle concentration were largely unaffected by PAH incorporation, but 1-hydroxypyrene and 9-anthracene carboxylic acid lowered the permeability of fatty acid bilayers to small solutes up to 4-fold. These data represent the first indication of a cholesterol-like stabilizing effect of oxidized PAH derivatives in a simulated prebiotic membrane.     

Photolytic Generation of Nitric Oxide through a Porous Glass Partitioning Membrane

We report a new method of generating nitric oxide that possesses several potential advantages for experimental use. This method consists of a microphotolysis chamber where NO is released by illuminating photolabile NO donors with light from a xenon lamp. NO then diffuses through a porous glass membrane to the experimental preparation. We observed that the rate of NO generation is a linear function of light intensity. Due to a dynamic equilibrium between the mechanisms of NO generation and dissipation (by diffusion or oxidation) the NO concentration in the experimental cuvette can be reversibly and reproducibly controlled. The major potential advantages of this device include its use as a NO point source, and the ability to partition the NO donor compound from the experimental preparation by a porous glass membrane. The diffusion of the caging moiety through the membrane is insignificant as seen by absorption spectroscopy due to its large relative size to NO. In this way, the porous glass membrane protects the preparation from the potential bioactive effects of the caging moiety, which is an important consideration for biological experiments.     

A wiring of the human nucleolus

Recent proteomic efforts have created an extensive inventory of the human nucleolar proteome. However, approximately 30% of the identified proteins lack functional annotation. We present an approach of assigning function to uncharacterized nucleolar proteins by data integration coupled to a machine-learning method. By assembling protein complexes, we present a first draft of the human ribosome biogenesis pathway encompassing 74 proteins and hereby assign function to 49 previously uncharacterized proteins. Moreover, the functional diversity of the nucleolus is underlined by the identification of a number of protein complexes with functions beyond ribosome biogenesis. Finally, we were able to obtain experimental evidence of nucleolar localization of 11 proteins, which were predicted by our platform to be associates of nucleolar complexes. We believe other biological organelles or systems could be "wired" in a similar fashion, integrating different types of data with high-throughput proteomics, followed by a detailed biological analysis and experimental validation.     

Experimental analysis and modelling of in vitro HUVECs proliferation in the presence of various types of drugs

Objectives: This study focuses on experimental analysis and corresponding mathematical simulation of in vitro HUVECs (human umbilical vein endothelial cells) proliferation in the presence of various types of drugs. Materials and methods: HUVECs, once seeded in Petri dishes, were expanded to confluence. Temporal profiles of total count obtained by classic haemocytometry and cell size distribution measured using an electronic Coulter counter, are quantitatively simulated by a suitable model based on the population balance approach. Influence of drugs on cell proliferation is also properly simulated by accounting for suitable kinetic equations. Results and discussion: The models’ parameters have been determined by comparison with experimental data related to cell population expansion and cell size distribution in the absence of drugs. Inhibition constant for each type of drug has been estimated by comparing the experimental data with model results concerning temporal profiles of total cell count. The reliability of the model and its predictive capability have been tested by simulating cell size distribution for experiments performed in the presence of drugs. The proposed model will be useful in interpreting effects of selected drugs on expansion of readily available human cells.     

Combining counts and incidence data: an efficient approach for estimating the log-normal species abundance distribution and diversity indices

Obtaining accurate estimates of diversity indices is difficult because the number of species encountered in a sample increases with sampling intensity. We introduce a novel method that requires that the presence of species in a sample to be assessed while the counts of the number of individuals per species are only required for just a small part of the sample. To account for species included as incidence data in the species abundance distribution, we modify the likelihood function of the classical Poisson log-normal distribution. Using simulated community assemblages, we contrast diversity estimates based on a community sample, a subsample randomly extracted from the community sample, and a mixture sample where incidence data are added to a subsample. We show that the mixture sampling approach provides more accurate estimates than the subsample and at little extra cost. Diversity indices estimated from a freshwater zooplankton community sampled using the mixture approach show the same pattern of results as the simulation study. Our method efficiently increases the accuracy of diversity estimates and comprehension of the left tail of the species abundance distribution. We show how to choose the scale of sample size needed for a compromise between information gained, accuracy of the estimates and cost expended when assessing biological diversity. The sample size estimates are obtained from key community characteristics, such as the expected number of species in the community, the expected number of individuals in a sample and the evenness of the community.     

Simulation of a nonphotochemical quenching in plant leaf under different light intensities

An analysis of photosynthetic response on action of stressors is an important problem, which can be solved by experimental and theoretical methods, including mathematical modeling of photosynthetic processes. The aim of our work was elaboration of a mathematical model, which simulated development of a nonphotochemical quenching under different light conditions. We analyzed two variants of the model: the first variant included a light-induced activation of the electron transport chain; in contrast, the second variant did not describe this activation. Both variants of the model described interactions between transitions from open reaction centers to closed ones (and vice versa) and development of the nonphotochemical quenching. Investigation of both variants of the model showed well qualitative and quantitative accordance between simulated and experimental changes in coefficient of the nophotochemical quenching which were analyzed under different light regimes: (i) the stepped increase of the light intensity without dark intervals between steps, (ii) periodical illuminations by different light intensities with constant durations which were separated by constant dark intervals, and (iii) periodical illuminations by the constant light intensity with different durations which were separated by different dark intervals. Thus, the model can be used for theoretical prediction of stress changes in photosynthesis under fluctuations in light intensity and search of optimal regimes of plant illumination.     

Hub-centered gene network reconstruction using automatic relevance determination

Network inference deals with the reconstruction of biological networks from experimental data. A variety of different reverse engineering techniques are available; they differ in the underlying assumptions and mathematical models used. One common problem for all approaches stems from the complexity of the task, due to the combinatorial explosion of different network topologies for increasing network size. To handle this problem, constraints are frequently used, for example on the node degree, number of edges, or constraints on regulation functions between network components. We propose to exploit topological considerations in the inference of gene regulatory networks. Such systems are often controlled by a small number of hub genes, while most other genes have only limited influence on the network's dynamic. We model gene regulation using a Bayesian network with discrete, Boolean nodes. A hierarchical prior is employed to identify hub genes. The first layer of the prior is used to regularize weights on edges emanating from one specific node. A second prior on hyperparameters controls the magnitude of the former regularization for different nodes. The net effect is that central nodes tend to form in reconstructed networks. Network reconstruction is then performed by maximization of or sampling from the posterior distribution. We evaluate our approach on simulated and real experimental data, indicating that we can reconstruct main regulatory interactions from the data. We furthermore compare our approach to other state-of-the art methods, showing superior performance in identifying hubs. Using a large publicly available dataset of over 800 cell cycle regulated genes, we are able to identify several main hub genes. Our method may thus provide a valuable tool to identify interesting candidate genes for further study. Furthermore, the approach presented may stimulate further developments in regularization methods for network reconstruction from data.     

A fluorescence-based technique to construct size distributions from single-object measurements: application to the extrusion of lipid vesicles

We report a novel approach to quantitatively determine complete size distributions of surface-bound objects using fluorescence microscopy. We measure the integrated intensity of single particles and relate it to their size by taking into account the object geometry and the illumination profile of the microscope, here a confocal laser scanning microscope. Polydisperse (as well as monodisperse) size distributions containing objects both below and above the optical resolution of the microscope are recorded and analyzed. The data is collected online within minutes, which allows the user to correlate the size of an object with the response from any given fluorescence-based biochemical assay. We measured the mean diameter of extruded fluorescently labeled lipid vesicles using the proposed method, dynamic light scattering, and cryogenic transmission electron microscopy. The three techniques were in excellent agreement, measuring the same values within 7-9%. Furthermore we demonstrated here, for the first time that we know of, the ability to determine the full size distribution of polydisperse samples of nonextruded lipid vesicles. Knowledge of the vesicle size distribution before and after extrusion allowed us to propose an empirical model to account for the effect of extrusion on the complete size distribution of vesicle samples.