A general method for biological inference: illustrated by the estimation of gene nucleotide transition probabilities

The method of maximum entropy inference developed by Jaynes can be a particularly useful method for obtaining unbiased estimates of biological parameters when the experimental knowledge about a system can be explicitly formulated. Base transition probabilities between genes, though central to evolutionary theory and understanding, present a difficult estimation problem because the ancestral genes are not experimentally accessible. The necessary estimates must therefore be made on the basis of experimental knowledge other than a direct frequency count of base replacements (A leads to C, for example) between contemporary genes. It is shown how maximum entropy inference together with the experimentally observed fact of compositional fidelity in a given gene family can be used to obtain meaningful gene base transition probabilities at each of the three nucleotide positions within codons. Both symmetric and asymmetric transition probabilities are considered. Tables of these probabilities are given for each codon position for the alpha-hemoglobin, beta-hemoglobin, myoglobin, cytochrome c, and the parvalbumin group genes. Tabular values of the average amino acid composition of these five protein families and the average nucleotide composition of their coding genes at varied codon loci are given. It is thus no longer necessary to assume in theories of evolutionary divergence equimolar base ratios A:C:G:U::1:1:1:1 or that each base has an equal chance of mutating to and being fixed as any one of the other three bases.     

A modified particle swarm optimization algorithm for parameter estimation of a biological system

Background

Mathematical modeling has achieved a broad interest in the field of biology. These models represent the associations among the metabolism of the biological phenomenon with some mathematical equations such that the observed time course profile of the biological data fits the model. However, the estimation of the unknown parameters of the model is a challenging task. Many algorithms have been developed for parameter estimation, but none of them is entirely capable of finding the best solution. The purpose of this paper is to develop a method for precise estimation of parameters of a biological model.

Methods

In this paper, a novel particle swarm optimization algorithm based on a decomposition technique is developed. Then, its root mean square error is compared with simple particle swarm optimization, Iterative Unscented Kalman Filter and Simulated Annealing algorithms for two different simulation scenarios and a real data set related to the metabolism of CAD system.

Results

Our proposed algorithm results in 54.39% and 26.72% average reduction in root mean square error when applied to the simulation and experimental data, respectively.

Conclusion

The results show that the metaheuristic approaches such as the proposed method are very wise choices for finding the solution of nonlinear problems with many unknown parameters.

     

Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems

Background  

We consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness.     

A simple method for estimation of phospholipids in biological objects

A simple method to estimate phospholipids is elaborated. This method is based on determination of optical density of phospholipid-molybdate complexes in chloroform. The method is used for the quantitative determination of phospholipids in biomembranes, liposomes and blood serum without their preliminary extraction, as well as in chloroform, methanol and chloroform-methanol solutions. It is also modified for the phospholipids determination in chromatographic fractions on silufol plates.     

Optimal experiment selection for parameter estimation in biological differential equation models

ABSTRACT: BACKGROUND: Parameter estimation in biological models is a common yet challenging problem. In this work we explore the problem for gene regulatory networks modeled by differential equations with unknown parameters, such as decay rates, reaction rates, Michaelis-Menten constants, and Hill coefficients. We explore the question to what extent parameters can be efficiently estimated by appropriate experimental selection. RESULTS: A minimization formulation is used to find the parameter values that best fit the experiment data. When the data is insufficient, the minimization problem often has many local minima that fit the data reasonably well. We show that selecting a new experiment based on the local Fisher Information of one local minimum generates additional data that allows one to successfully discriminate among the many local minima. The parameters can be estimated to high accuracy by iteratively performing minimization and experiment selection. We show that the experiment choices are roughly independent of which local minima is used to calculate the local Fisher Information. CONCLUSIONS: We show that by an appropriate choice of experiments, one can, in principle, efficiently and accurately estimate all the parameters of gene regulatory network. In addition, we demonstrate that appropriate experiment selection can also allow one to restrict model predictions without constraining the parameters using many fewer experiments. We suggest that predicting model behaviors and inferring parameters represent two different approaches to model calibration with different requirements on data and experimental cost.     

Body segment inertial parameter estimation for the general population of older adults

The practical determination of accurate body segment inertial parameters for the general older adult population remains a problem, especially in estimating these parameters for women and accounting for variations in body type. A method is presented for determining the mass and center of mass location of the body segments of individuals within the general population of older adults. Effects of sex and body type on older adult mass distribution are accounted for using 32 easily obtainable body measurements. The method is based on existing results from different data sources and employs a combination of validated estimation approaches, including: body mass and segment length proportions, linear and nonlinear regression equations, and a mathematical model of the trunk. The method was applied to a validation sample of healthy, community-dwelling older adults (29 men, 50 women). Predicted body mass was 96.7+/-4.8% and 95.7+/-3.7% of measured body mass in the men and women, respectively. The estimates of body segment mass and trunk center of mass location for the sample population approximate those reported in the literature, supporting the validity of the described method. By producing practical, subject-specific estimates of body segment inertial parameters, the method should allow more accurate biomechanical analyses of the older adult population.     

A method for the estimation of amino acid radioactivity in biological samples

A method for quantitative estimation of total radioactivity present in the free amino acid fraction of tissue samples has been described. Samples deproteinized with cold acetone were extracted, in acidic medium, with ethyl (peroxide free); after centrifugation, the aqueous phase was used for amino acid derivatization at 40°C for 15 h with 1-flouro-2,4-dinitrobenzene in bicarbonate-buffered medium. Aliquots of the derivatized samples were acidified and extracted twice again with ethyl ether. The combined organic phases were placed in glass scintilation vials, dried, and used for the determination of its radiactivity, corresponding to the radioactivity present in the free amino acid fraction of the sample. Deproteinized samples of rat blood plasma, as well as hen egg white and yolk were tested after addition of known quantities of ¹⁴C-labelled amino acids or glucose, for validation of the method. No glucose radioactivity was found in any of the extracted samples. All radioactivity added to the samples in the form of ¹⁴C-labelled alanine, glutamic acid, leucine and phenylalanine was quantitatively recovered in the derivatized fraction; only a fraction of arginine radioactivity was recovered.     

A different approach to generating the data for parameter estimation with the heterotrophic activity method

This paper outlines a different approach to generating the data for V_max and T_t estimation with the Wright-Hobbie [1] method of measuring heterotrophic activities in aquatic environments. To be certain that the incubation times chosen are appropriate for all concentrations of substrate tested, and to increase the precision of the kinetic parameter estimates, we have adopted the approach of using kinetic plots derived from independent time-course studies performed at each concentration of substrate and analyzed by non-linear regression analysis. In keeping with our interest in the impact of acidification on aquatic microbial activities, we have applied this approach to the sediments and water column of the acid-stressed Silver Lake.     

A Bayesian framework for parameter estimation in dynamical models

Mathematical models in biology are powerful tools for the study and exploration of complex dynamics. Nevertheless, bringing theoretical results to an agreement with experimental observations involves acknowledging a great deal of uncertainty intrinsic to our theoretical representation of a real system. Proper handling of such uncertainties is key to the successful usage of models to predict experimental or field observations. This problem has been addressed over the years by many tools for model calibration and parameter estimation. In this article we present a general framework for uncertainty analysis and parameter estimation that is designed to handle uncertainties associated with the modeling of dynamic biological systems while remaining agnostic as to the type of model used. We apply the framework to fit an SIR-like influenza transmission model to 7 years of incidence data in three European countries: Belgium, the Netherlands and Portugal.     

A methodology for parameter estimation in seaweed productivity modelling

This paper presents a combined approach for parameter estimation in models of primary production. The focus is on gross primary production and nutrient assimilation by seaweeds.A database of productivity determinations, biomass and mortality measurements and nutrient uptake rates obtained over one year for Gelidium sesquipedale in the Atlantic Ocean off Portugal has been used. Annual productivity was estimated by harvesting methods, and empirical relationships using mortality/wave energy and respiration rates have been derived to correct for losses and to convert the estimates to gross production. In situ determinations of productivity have been combined with data on the light climate (radiation periods, intensity, mean turbidity) to give daily and annual productivity estimates. The theoretical nutrient uptake calculated using a Redfield ratio approach and determinations of in situ N and P consumption by the algae during incubation periods have also been compared.The results of the biomass difference and incubation approaches are discussed in order to assess the utility of coefficients determined in situ for parameter estimation in seaweed production models.     

A robust methodology for kinetic model parameter estimation for biocatalytic reactions

Effective estimation of parameters in biocatalytic reaction kinetic expressions are very important when building process models to enable evaluation of process technology options and alternative biocatalysts. The kinetic models used to describe enzyme‐catalyzed reactions generally include several parameters, which are strongly correlated with each other. State‐of‐the‐art methodologies such as nonlinear regression (using progress curves) or graphical analysis (using initial rate data, for example, the Lineweaver‐Burke plot, Hanes plot or Dixon plot) often incorporate errors in the estimates and rarely lead to globally optimized parameter values. In this article, a robust methodology to estimate parameters for biocatalytic reaction kinetic expressions is proposed. The methodology determines the parameters in a systematic manner by exploiting the best features of several of the current approaches. The parameter estimation problem is decomposed into five hierarchical steps, where the solution of each of the steps becomes the input for the subsequent step to achieve the final model with the corresponding regressed parameters. The model is further used for validating its performance and determining the correlation of the parameters. The final model with the fitted parameters is able to describe both initial rate and dynamic experiments. Application of the methodology is illustrated with a case study using the ω‐transaminase catalyzed synthesis of 1‐phenylethylamine from acetophenone and 2‐propylamine. © 2012 American Institute of Chemical Engineers Biotechnol. Prog., 2012     

Spectrophotometric method for estimation of aliphatic primary amines in biological samples

A method based on Rimini test for aliphatic amines was studied and developed for quantitative estimation of aliphatic primary amines. The method involves action of the amine with acetone to form schiff base which complexes with sodium nitroprusside to give violet colour. The absorption maximum in the visible range of the spectrum, for the reaction mixture was found to be 550 nm. The pH (8–11) and reaction time scan for the assay were optimized. A linear relation of concentration (0.2–3 mg/mL) of amine against absorbance at 550 nm was established. Interference due to other reaction components was negligible (±0.02 mg/mL) as compared to the sample in buffer. 1, 3-dimethyl butylamine was used as the model amine and the method was applied to other amines; it was observed that when electron-withdrawing substituents are present in the molecule the reaction is retarded, as the incubation time was longer. This method is useful for estimation of aliphatic primary amine in biological samples.     

A computationally efficient optimization kernel for material parameter estimation procedures

Estimating material parameters is an important part in the study of soft tissue mechanics. Computational time can easily run to days, especially when all available experimental data are taken into account. The material parameter estimation procedure is examplified on a set of homogeneous simple shear experiments to estimate the orthotropic constitutive parameters of myocardium. The modification consists of changing the traditional least-squares approach to a weighted least-squares. This objective function resembles a L(2)-norm type integral which is approximated using Gaussian quadrature. This reduces the computational time of the material parameter estimation by two orders of magnitude.