Estimating C4 photosynthesis parameters by fitting intensive A/Ci curves.

Measurements of photosynthetic assimilation rate as a function of intercellular CO2 (A/Ci curves) are widely used to estimate photosynthetic parameters for C3 species, yet few parameters have been reported for C4 plants, because of a lack of estimation methods. Here, we extend the framework of widely used estimation methods for C3 plants to build estimation tools by exclusively fitting intensive A/Ci curves (6-8 more sampling points) for C4 using three versions of photosynthesis models with different assumptions about carbonic anhydrase processes and ATP distribution. We use simulation analysis, out of sample tests, existing in vitro measurements and chlorophyll-fluorescence measurements to validate the new estimation methods. Of the five/six photosynthetic parameters obtained, sensitivity analyses show that maximal-Rubisco-carboxylation-rate, electron-transport-rate, maximal-PEP-carboxylation-rate, and carbonic-anhydrase were robust to variation in the input parameters, while day respiration and mesophyll conductance varied. Our method provides a way to estimate carbonic anhydrase activity, a new parameter, from A/Ci curves, yet also shows that models that do not explicitly consider carbonic anhydrase yield approximate results. The two photosynthesis models, differing in whether ATP could freely transport between RuBP and PEP regeneration processes yielded consistent results under high light, but they may diverge under low light intensities. Modeling results show selection for Rubisco of low specificity and high catalytic rate, low leakage of bundle sheath, and high PEPC affinity, which may further increase C4 efficiency.

Membership Function-Weighted Non-Linear Fitting Method for Optical-Sensing Modeling and Reconstruction.

Imprecise measurements present universally due to variability in the measurement error. We devised a very simple membership function to evaluate fuzzily the quality of optical sensing with a small dataset, where a normal distribution cannot be assumed. The proposed membership function was further used as a weighting function for non-linear curve fitting under expected mathematical model constraints, namely the membership function-weighted Levenberg⁻Marquardt (MFW-LM) algorithm. The robustness and effectiveness of the MFW-LM algorithm were demonstrated by an optical-sensing simulation and two practical applications. (1) In laser-absorption spectroscopy, molecular spectral line modeling was greatly improved by the method. The measurement uncertainty of temperature and pressure were reduced dramatically, by 53.3% and 43.5%, respectively, compared with the original method. (2) In imaging, a laser beam-profile reconstruction from heavy distorted observations was improved by the method. As the dynamic range of the infrared camera increased from 256 to 415, the detailed resolution of the laser-beam profiles increased by an amazing 360%, achieving high dynamic-range imaging to capture optical signal details. Therefore, the MFW-LM algorithm provides a robust and effective tool for fitting a proper physical model and precision parameters from low-quality data.

Structured Stochastic Curve Fitting without Gradient Calculation.

Optimization of parameters and hyperparameters is a general process for any data analysis. Because not all models are mathematically well-behaved, stochastic optimization can be useful in many analyses by randomly choosing parameters in each optimization iteration. Many such algorithms have been reported and applied in chemistry data analysis, but the one reported here is interesting to check out, where a naïve algorithm searches each parameter sequentially and randomly in its bounds. Then it picks the best for the next iteration. Thus, one can ignore irrational solution of the model itself or its gradient in parameter space.

TitrationAnalysis: a tool for high throughput binding kinetics data analysis for multiple label-free platforms.

Label-free techniques including Surface Plasmon Resonance (SPR) and Biolayer Interferometry (BLI) are biophysical tools widely used to collect binding kinetics data of bimolecular interactions. To efficiently analyze SPR and BLI binding kinetics data, we have built a new high throughput analysis tool named the TitrationAnalysis. It can be used as a package in the Mathematica scripting environment and ultilize the non-linear curve-fitting module of Mathematica for its core function. This tool can fit the binding time course data and estimate association and dissociation rate constants ( k a and k d respectively) for determining apparent dissociation constant ( K D) values. The high throughput fitting process is automatic, requires minimal knowledge on Mathematica scripting and can be applied to data from multiple label-free platforms. We demonstrate that the TitrationAnalysis is optimal to analyze antibody-antigen binding data acquired on Biacore T200 (SPR), Carterra LSA (SPR imaging) and ForteBio Octet Red384 (BLI) platforms. The k a, k d and K D values derived using TitrationAnalysis very closely matched the results from the commercial analysis software provided specifically for these instruments. Additionally, the TitrationAnalysis tool generates user-directed customizable results output that can be readily used in downstream Data Quality Control associated with Good Clinical Laboratory Practice operations. With the versatility in source of data input source and options of analysis result output, the TitrationAnalysis high throughput analysis tool offers investigators a powerful alternative in biomolecular interaction characterization.

Acute toxicity dataset for QSAR modeling and predicting missing data of six pesticides.

This data article presents 1) the acute toxicity (LC50 or EC50 (µg⋅L-1)) values of various chemicals for ten species, which were used to develop ten robust quantitative structure-activity relationship (QSAR) models, 2) the values of the various descriptors in the ten QSAR models, and 3) the acute toxicity values of six pesticides (acetochlor, chlorpyrifos, dimethoate, glyphosate, malathion, and paraquat) for various species, which were applied to establish species sensitivity distribution (SSD) models. The provided LC50 or EC50 (µg⋅L-1) data were collected from the PAN pesticide database and the United States Environmental Protection Agency ecotoxicology database and/or were predicted by the QSAR models. The values of the descriptors in the ten QSAR models were based on the optimal descriptors computed by the DRAGON software (version 7) and subsequently optimized by partial least squares modeling. All the data included in this manuscript are related to the research titled, "Conlecs: A novel procedure for deriving the concentration limits of chemicals outside the criteria of human drinking water using existing criteria and species sensitivity distribution based on quantitative structure-activity relationship prediction" [1].

Novel non-linear curve fitting to resolve protein unfolding transitions in intrinsic fluorescence differential scanning fluorimetry.

In biotherapeutic protein research, an estimation of the studied protein's thermal stability is one of the important steps that determine developability as a function of solvent conditions. Differential Scanning Fluorimetry (DSF) can be applied to measure thermal stability. Label-free DSF measures amino acid fluorescence as a function of temperature, where conformational changes induce observable peak deformation, yielding apparent melting temperatures. The estimation of the stability parameters can be hindered in the case of multidomain, multimeric or aggregating proteins when multiple transitions partially coincide. These overlapping protein unfolding transitions are hard to evaluate by the conventional methodology, as peak maxima are shifted by convolution. We show how non-linear curve fitting of intrinsic fluorescence DSF can deconvolute highly overlapping transitions in formulation screening in a semi-automated process. The proposed methodology relies on synchronous, constrained fits of the fluorescence intensity, ratio and their derivatives, by combining linear baselines with generalized logistic transition functions. The proposed algorithm is applied to data from three proteins; a single transition, a double separated transition and a double overlapping transition. Extracted thermal stability parameters; apparent melting temperatures Tm,1, Tm,2 and melting onset temperature Tonset are obtained and compared with reference software analysis. The fits show R2 = 0.94 for single and R2 = 0.88 for separated transitions. Obtaining values and trends for Tonset in a well-described and automated way, will aid protein scientist to better evaluate the thermal stability of proteins.

Fourier transform assisted deconvolution of skewed peaks in complex multi-dimensional chromatograms.

Lower order peak moments of individual peaks in heavily fused peak clusters can be determined by fitting peak models to the experimental data. The success of such an approach depends on two main aspects: the generation of meaningful initial estimates on the number and position of the peaks, and the choice of a suitable peak model. For the detection of meaningful peaks in multi-dimensional chromatograms, a fast data scanning algorithm was combined with prior resolution enhancement through the reduction of column and system broadening effects with the help of two-dimensional fast Fourier transforms. To capture the shape of skewed peaks in multi-dimensional chromatograms a formalism for the accurate calculation of exponentially modified Gaussian peaks, one of the most popular models for skewed peaks, was extended for direct fitting of two-dimensional data. The method is demonstrated to successfully identify and deconvolute peaks hidden in strongly fused peak clusters. Incorporation of automatic analysis and reporting of the statistics of the fitted peak parameters and calculated properties allows to easily identify in which regions of the chromatograms additional resolution is required for robust quantification.

Assessment of Non-permeability of Gd-DTPA for Dynamic Susceptibility Contrast in Human Brain: A Preliminary Study Using Non-linear Curve Fitting

To develop an advanced non-linear curve fitting (NLCF) algorithm for performing dynamic susceptibility contrast study of the brain. The first pass effects give rise to spuriously high estimates of Ktrans for the voxels that represent the large vascular components. An explicit threshold value was used to reject voxels. The blood perfusion and volume estimation were accurately evaluated in the T2*-weighted dynamic contrast enhanced (DCE)-MR images. From each of the recalculated parameters, a perfusion weighted image was outlined by using the modified non-linear curve fitting algorithm. The present study demonstrated an improvement of an estimation of the kinetic parameters from the DCE T2*-weighted magnetic resonance imaging data with using contrast agents.

Reducing the Scan Time in Gastric Emptying Scintigraphy by Using Mathematical Models / 대한핵의학회잡지

PURPOSE: Gastric emptying scan (GES) is usually acquired up to 2 hours. Our study investigated whether a fraction of meal-retention in the stomach at 120 minutes (FR120) was predicted from the data measured for 90 minutes by using non-linear curve fitting. We aimed at saving the delayed imaging by utilizing mathematical models. MATERIALS AND METHODS: Ninety-six patients underwent GES immediately after taking a boiled egg with 74 MBq (2 mCi) Tc-99m DTPA. The patients were divided into Group I (T1/2 < or=90 min) and Group II (90 min< T1/2< or=120 min). Group I (n=51) had 21 men and 30 women, and Group II (n=45) 15 men and 30 women. There was no significant difference in age and sex between the two groups. Simple exponential, power exponential, and modified power exponential curves were acquired from the measured fraction of meal-retention at each time (0, 15, 30, 45, 60, 75, and 90 min) by non-linear curve fitting (MATLAB (R) 5.3) and another simple exponential fitting was performed on the fractions at late times (60, 75, and 90 min). A predicted FR120 was calculated from the acquired functional formulas. A correlation coefficient between the measured FR120 and the predicted FR120 was computed (MedCalc (R) 6.0). RESULTS: Correlation coefficients (r) between the measured FR120 and the predicted FR120 of each mathematical functions were as follows: simple exponential function (Group I: 0.8858, Group II: 0.5982, p< 0.0001), power exponential function (Group I: 0.8755, Group II: 0.6008, p< 0.0001), modified power exponential function (Group I: 0.8892, Group II: 0.5882, p< 0.0001), and simple exponential function at the late times (Group I: 0.9085, Group II: 0.6832, p< 0.0001). In all the fitting models, the predicted FR120 were significantly correlated with the measured FR120 in Group I but not in Group II. There was no statistically significant difference in correlation among the 4 mathematical models. CONCLUSION: In the cases with T1/2 < or=90 min, the predicted FR120 is significantly correlated with the measured FR120. Therefore, FR120 can be predicted from the data measured for 90 minutes by using non-linear curve fitting, saving the delayed imaging after 90 minutes when T1/2 < or=90 min is ascertained.