共查询到20条相似文献，搜索用时 46 毫秒
1.
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.2.
Edward Meeds Michael Chiang Mary Lee Olivier Cinquin John Lowengrub Max Welling 《BMC bioinformatics》2015,16(1):264
Background
In many domains, scientists build complex simulators of natural phenomena that encode their hypotheses about the underlying processes. These simulators can be deterministic or stochastic, fast or slow, constrained or unconstrained, and so on. Optimizing the simulators with respect to a set of parameter values is common practice, resulting in a single parameter setting that minimizes an objective subject to constraints.Results
We propose algorithms for post optimization posterior evaluation (POPE) of simulators. The algorithms compute and visualize all simulations that can generate results of the same or better quality than the optimum, subject to constraints. These optimization posteriors are desirable for a number of reasons among which are easy interpretability, automatic parameter sensitivity and correlation analysis, and posterior predictive analysis. Our algorithms are simple extensions to an existing simulation-based inference framework called approximate Bayesian computation. POPE is applied two biological simulators: a fast and stochastic simulator of stem-cell cycling and a slow and deterministic simulator of tumor growth patterns.Conclusions
POPE allows the scientist to explore and understand the role that constraints, both on the input and the output, have on the optimization posterior. As a Bayesian inference procedure, POPE provides a rigorous framework for the analysis of the uncertainty of an optimal simulation parameter setting.3.
Background
Mixtures of beta distributions are a flexible tool for modeling data with values on the unit interval, such as methylation levels. However, maximum likelihood parameter estimation with beta distributions suffers from problems because of singularities in the log-likelihood function if some observations take the values 0 or 1.Methods
While ad-hoc corrections have been proposed to mitigate this problem, we propose a different approach to parameter estimation for beta mixtures where such problems do not arise in the first place. Our algorithm combines latent variables with the method of moments instead of maximum likelihood, which has computational advantages over the popular EM algorithm.Results
As an application, we demonstrate that methylation state classification is more accurate when using adaptive thresholds from beta mixtures than non-adaptive thresholds on observed methylation levels. We also demonstrate that we can accurately infer the number of mixture components.Conclusions
The hybrid algorithm between likelihood-based component un-mixing and moment-based parameter estimation is a robust and efficient method for beta mixture estimation. We provide an implementation of the method (“betamix”) as open source software under the MIT license.4.
Background
Uncertainties exist in many biological systems, which can be classified as random uncertainties and fuzzy uncertainties. The former can usually be dealt with using stochastic methods, while the latter have to be handled with such approaches as fuzzy methods.Results
In this paper, we focus on a special type of biological systems that can be described using ordinary differential equations or continuous Petri nets (CPNs), but some kinetic parameters are missing or inaccurate. For this, we propose a class of fuzzy continuous Petri nets (FCPNs) by combining CPNs and fuzzy logics. We also present and implement a simulation algorithm for FCPNs, and illustrate our method with the heat shock response system.Conclusions
This approach can be used to model biological systems where some kinetic parameters are not available or their values vary due to some environmental factors.5.
Approximate parameter inference in systems biology using gradient matching: a comparative evaluation
Benn Macdonald Mu Niu Simon Rogers Maurizio Filippone Dirk Husmeier 《Biomedical engineering online》2016,15(1):80
Background
A challenging problem in current systems biology is that of parameter inference in biological pathways expressed as coupled ordinary differential equations (ODEs). Conventional methods that repeatedly numerically solve the ODEs have large associated computational costs. Aimed at reducing this cost, new concepts using gradient matching have been proposed, which bypass the need for numerical integration. This paper presents a recently established adaptive gradient matching approach, using Gaussian processes (GPs), combined with a parallel tempering scheme, and conducts a comparative evaluation with current state-of-the-art methods used for parameter inference in ODEs. Among these contemporary methods is a technique based on reproducing kernel Hilbert spaces (RKHS). This has previously shown promising results for parameter estimation, but under lax experimental settings. We look at a range of scenarios to test the robustness of this method. We also change the approach of inferring the penalty parameter from AIC to cross validation to improve the stability of the method.Methods
Methodology for the recently proposed adaptive gradient matching method using GPs, upon which we build our new method, is provided. Details of a competing method using RKHS are also described here.Results
We conduct a comparative analysis for the methods described in this paper, using two benchmark ODE systems. The analyses are repeated under different experimental settings, to observe the sensitivity of the techniques.Conclusions
Our study reveals that for known noise variance, our proposed method based on GPs and parallel tempering achieves overall the best performance. When the noise variance is unknown, the RKHS method proves to be more robust.6.
Meghan E. Hall Nima Khadem Mohtaram Stephanie M. Willerth 《Journal of biological engineering》2017,11(1):38
Background
Human induced pluripotent stem cells (hiPSCs) can form any tissue found in the body, making them attractive for regenerative medicine applications. Seeding hiPSC aggregates into biomaterial scaffolds can control their differentiation into specific tissue types. Here we develop and analyze a mathematical model of hiPSC aggregate behavior when seeded on melt electrospun scaffolds with defined topography.Results
We used ordinary differential equations to model the different cellular populations (stem, progenitor, differentiated) present in our scaffolds based on experimental results and published literature. Our model successfully captures qualitative features of the cellular dynamics observed experimentally. We determined the optimal parameter sets to maximize specific cellular populations experimentally, showing that a physiologic oxygen level (～?5%) increases the number of neural progenitors and differentiated neurons compared to atmospheric oxygen levels (～?21%) and a scaffold porosity of ～?63% maximizes aggregate size.Conclusions
Our mathematical model determined the key factors controlling hiPSC behavior on melt electrospun scaffolds, enabling optimization of experimental parameters.7.
Background
Mathematical modeling is a powerful tool to analyze, and ultimately design biochemical networks. However, the estimation of the parameters that appear in biochemical models is a significant challenge. Parameter estimation typically involves expensive function evaluations and noisy data, making it difficult to quickly obtain optimal solutions. Further, biochemical models often have many local extrema which further complicates parameter estimation. Toward these challenges, we developed Dynamic Optimization with Particle Swarms (DOPS), a novel hybrid meta-heuristic that combined multi-swarm particle swarm optimization with dynamically dimensioned search (DDS). DOPS uses a multi-swarm particle swarm optimization technique to generate candidate solution vectors, the best of which is then greedily updated using dynamically dimensioned search.Results
We tested DOPS using classic optimization test functions, biochemical benchmark problems and real-world biochemical models. We performed \(\mathcal {T}\) = 25 trials with \(\mathcal {N}\) = 4000 function evaluations per trial, and compared the performance of DOPS with other commonly used meta-heuristics such as differential evolution (DE), simulated annealing (SA) and dynamically dimensioned search (DDS). On average, DOPS outperformed other common meta-heuristics on the optimization test functions, benchmark problems and a real-world model of the human coagulation cascade.Conclusions
DOPS is a promising meta-heuristic approach for the estimation of biochemical model parameters in relatively few function evaluations. DOPS source code is available for download under a MIT license at http://www.varnerlab.org.8.
Objectives
Biomass subpopulations in mammalian cell culture processes cause impurities and influence productivity, which requires this critical process parameter to be monitored in real-time.Results
For this reason, a novel soft sensor concept for estimating viable, dead and lysed cell concentration was developed, based on the robust and cheap in situ measurements of permittivity and turbidity in combination with a simple model. It could be shown that the turbidity measurements contain information about all investigated biomass subpopulations. The novelty of the developed soft sensor is the real-time estimation of lysed cell concentration, which is directly correlated to process-related impurities such as DNA and host cell protein in the supernatant. Based on data generated by two fed-batch processes the developed soft sensor is described and discussed.Conclusions
The presented soft sensor concept provides a tool for viable, dead and lysed cell concentration estimation in real-time with adequate accuracy and enables further applications with respect to process optimization and control.9.
Background
Ordinary differential equations (ODEs) are often used to understand biological processes. Since ODE-based models usually contain many unknown parameters, parameter estimation is an important step toward deeper understanding of the process. Parameter estimation is often formulated as a least squares optimization problem, where all experimental data points are considered as equally important. However, this equal-weight formulation ignores the possibility of existence of relative importance among different data points, and may lead to misleading parameter estimation results. Therefore, we propose to introduce weights to account for the relative importance of different data points when formulating the least squares optimization problem. Each weight is defined by the uncertainty of one data point given the other data points. If one data point can be accurately inferred given the other data, the uncertainty of this data point is low and the importance of this data point is low. Whereas, if inferring one data point from the other data is almost impossible, it contains a huge uncertainty and carries more information for estimating parameters.Results
G1/S transition model with 6 parameters and 12 parameters, and MAPK module with 14 parameters were used to test the weighted formulation. In each case, evenly spaced experimental data points were used. Weights calculated in these models showed similar patterns: high weights for data points in dynamic regions and low weights for data points in flat regions. We developed a sampling algorithm to evaluate the weighted formulation, and demonstrated that the weighted formulation reduced the redundancy in the data. For G1/S transition model with 12 parameters, we examined unevenly spaced experimental data points, strategically sampled to have more measurement points where the weights were relatively high, and fewer measurement points where the weights were relatively low. This analysis showed that the proposed weights can be used for designing measurement time points.Conclusions
Giving a different weight to each data point according to its relative importance compared to other data points is an effective method for improving robustness of parameter estimation by reducing the redundancy in the experimental data.10.
Background
Drug development considering individual varieties among patients becomes crucial to improve clinical development success rates and save healthcare costs. As a useful tool to predict individual phenomena and correlations among drug characteristics and individual varieties, recently, whole-body physiologically based pharmacokinetic (WB- PBPK) models are getting more attention. WB-PBPK models generally have a lot of drug-related parameters that need to be estimated, and the estimations are difficult because the observed data are limited. Furthermore, parameter estimation in WB-PBPK models may cause overfitting when applying to individual clinical data such as urine/feces drug excretion for each patient in which Cluster Newton Method (CNM) is applicable for parameter estimation. In order to solve this issue, we came up with the idea of constraint-based perturbation analysis of the CNM. The effectiveness of our approach is demonstrated in the case of irinotecan WB-PBPK model using common organ-specific tissue-plasma partition coefficients (Kp) among the patients as constraints in WB-PBPK parameter estimation.Results
We find strong correlations between age, renal clearance and liver functions in irinotecan WB-PBPK model with personalized physiological parameters by observing the distributions of optimized values of strong convergence drug-related parameters using constraint-based perturbation analysis on CNM. The constraint-based perturbation analysis consists of the following three steps: (1) Estimation of all drug-related parameters for each patient; the parameters include organ-specific Kp. (2) Fixing suitable values of Kp for each organ among all patients identically. (3) Re-estimation of all drug-related parameters other than Kp by using the fixed values of Kp as constraints of CNM.Conclusions
Constraint-based perturbation analysis could yield new findings when using CNM with appropriate constraints. This method is a new technique to find suitable values and important insights that are masked by CNM without constraints.11.
12.
Hualiang Zhong Stephen Brown Suneetha Devpura X. Allen Li Indrin J. Chetty 《Theoretical biology & medical modelling》2018,15(1):23
Background
Personalized medicine for patients receiving radiation therapy remains an elusive goal due, in part, to the limits in our understanding of the underlying mechanisms governing tumor response to radiation. The purpose of this study was to develop a kinetic model, in the context of locally advanced lung cancer, connecting cancer cell subpopulations with tumor volumes measured during the course of radiation treatment for understanding treatment outcome for individual patients.Methods
The kinetic model consists of three cell compartments: cancer stem-like cells (CSCs), non-stem tumor cells (TCs) and dead cells (DCs). A set of ordinary differential equations were developed to describe the time evolution of each compartment, and the analytic solution of these equations was iterated to be aligned with the day-to-day tumor volume changes during the course of radiation treatment. A least squares fitting method was used to estimate the parameters of the model that include the proportion of CSCs and their radio-sensitivities. This model was applied to five patients with stage III lung cancer, and tumor volumes were measured from 33 cone-beam computed tomography (CBCT) images for each of these patients. The analytical solution of these differential equations was compared with numerically simulated results.Results
For the five patients with late stage lung cancer, the derived proportions of CSCs are 0.3 on average, the average probability of the symmetry division is 0.057 and the average surviving fractions of CSCs is 0.967, respectively. The derived parameters are comparable to the results from literature and our experiments. The preliminary results suggest that the CSC self-renewal rate is relatively small, compared to the proportion of CSCs for locally advanced lung cancers.Conclusions
A novel mathematical model has been developed to connect the population of cancer stem-like cells with tumor volumes measured from a sequence of CBCT images. This model may help improve our understanding of tumor response to radiation therapy, and is valuable for development of new treatment regimens for patients with locally advanced lung cancer.13.
Background
A deterministic model is developed for the spatial spread of an epidemic disease in a geographical setting. The disease is borne by vectors tosusceptible hosts through criss-cross dynamics. The model is focused on an outbreak that arises from a small number of infected hosts imported into a subregion of the geographical setting. The goal is to understand how spatial heterogeneity of the vector and host populations influences the dynamics of the outbreak, in both the geographical spread and the final size of the epidemic.Methods
Partial differential equations are formulated to describe the spatial interaction of the hosts and vectors. The partial differential equations have reaction-diffusion terms to describe the criss-cross interactions of hosts and vectors. The partial differential equations of the model are analyzed and proven to be well-posed. A local basic reproduction number for the epidemic is analyzed.Results
The epidemic outcomes of the model are correlated to the spatially dependent parameters and initial conditions of the model. The partial differential equations of the model are adapted to seasonality of the vector population, and applied to the 2015–2016 Zika seasonal outbreak in Rio de Janeiro Municipality in Brazil.Conclusions
The results for the model simulations of the 2015–2016 Zika seasonal outbreak in Rio de Janeiro Municipality indicate that the spatial distribution and final size of the epidemic at the end of the season are strongly dependent on the location and magnitude of local outbreaks at the beginning of the season. The application of the model to the Rio de Janeiro Municipality Zika 2015–2016 outbreak is limited by incompleteness of the epidemic data and by uncertainties in the parametric assumptions of the model.14.
Background
The dynamics of biochemical networks can be modelled by systems of ordinary differential equations. However, these networks are typically large and contain many parameters. Therefore model reduction procedures, such as lumping, sensitivity analysis and time-scale separation, are used to simplify models. Although there are many different model reduction procedures, the evaluation of reduced models is difficult and depends on the parameter values of the full model. There is a lack of a criteria for evaluating reduced models when the model parameters are uncertain.Results
We developed a method to compare reduced models and select the model that results in similar dynamics and uncertainty as the original model. We simulated different parameter sets from the assumed parameter distributions. Then, we compared all reduced models for all parameter sets using cluster analysis. The clusters revealed which of the reduced models that were similar to the original model in dynamics and variability. This allowed us to select the smallest reduced model that best approximated the full model. Through examples we showed that when parameter uncertainty was large, the model should be reduced further and when parameter uncertainty was small, models should not be reduced much.Conclusions
A method to compare different models under parameter uncertainty is developed. It can be applied to any model reduction method. We also showed that the amount of parameter uncertainty influences the choice of reduced models.15.
Background
This study uses dimensional analysis to derive the general second-order differential equation that underlies numerous physical and natural phenomena described by common mathematical functions. It eschews assumptions about empirical constants and mechanisms. It relies only on the data plot’s mathematical properties to provide the conditions and constraints needed to specify a second-order differential equation that is free of empirical constants for each phenomenon.Results
A practical example of each function is analyzed using the general form of the underlying differential equation and the observable unique mathematical properties of each data plot, including boundary conditions. This yields a differential equation that describes the relationship among the physical variables governing the phenomenon’s behavior. Complex phenomena such as the Standard Normal Distribution, the Logistic Growth Function, and Hill Ligand binding, which are characterized by data plots of distinctly different sigmoidal character, are readily analyzed by this approach.Conclusions
It provides an alternative, simple, unifying basis for analyzing each of these varied phenomena from a common perspective that ties them together and offers new insights into the appropriate empirical constants for describing each phenomenon.16.
Run Du Rui Yan Zhang Lin Lu Ying Shen Li Jin Pu Zheng Bin Zhu Qi Zhang Jian Hu Zhen Kun Yang Feng Hua Ding Jian Sheng Zhang Wei Feng Shen 《Cardiovascular diabetology》2018,17(1):149
Background
Negative coronary artery remodeling is frequent in patients with diabetes, but its mechanism remains unclear. We here evaluated the association of serum levels of glycated albumin (GA) and endogenous secretory receptor for advanced glycation end products (esRAGE) with coronary artery remodeling in type 2 diabetic patients.Methods
Serum levels of GA and esRAGE were measured and intravascular ultrasound was performed in 136 consecutive diabetic patients with 143 coronary intermediate lesions. The remodeling index (RI) was calculated as the ratio between external elastic membrane (EEM) area at the lesion site and EEM area at the reference segment. Negative remodeling (NR) was defined as an RI?<?0.95 and intermediate or positive remodeling as an RI?≥?0.95.Results
Mean plaque burden at the lesion site was 70.96?±?9.98%, and RI was 0.96?±?0.18. Negative coronary arterial remodeling existed in 81 (56.6%) lesions. RI correlated closely with serum esRAGE level (r?=?0.236, P?=?0.005) and was inversely related to serum GA level (r?=???0.240, P?=?0.004) and plasma low-density lipoprotein cholesterol (LDL-C) (r?=???0.206, P?=?0.014) and total cholesterol levels (r?=???0.183, P?=?0.028). Generalized estimating equations logistic regression analysis identified esRAGE (OR 0.037; 95% CI 0.012–0.564, P?=?0.021), GA (OR 1.093; 95% CI 1.013–1.179, P?=?0.018) and LDL-C (OR 1.479; 95% CI 1.072–2.835, P?=?0.023) as independent predictors for negative remodeling.Conclusions
In diabetic patients, negative coronary artery remodeling is associated with increased GA and decreased esRAGE levels in serum.17.
Michael A. Rowland Hannah Wear Karen H. Watanabe Kurt A. Gust Michael L. Mayo 《BMC systems biology》2018,12(1):81
Background
A challenge of in vitro to in vivo extrapolation (IVIVE) is to predict the physical state of organisms exposed to chemicals in the environment from in vitro exposure assay data. Although toxicokinetic modeling approaches promise to bridge in vitro screening data with in vivo effects, they are often encumbered by a need for redesign or re-parameterization when applied to different tissues or chemicals.Results
We demonstrate a parameterization of reverse toxicokinetic (rTK) models developed for the adult zebrafish (Danio rerio) based upon particle swarm optimizations (PSO) of the chemical uptake and degradation rates that predict bioconcentration factors (BCF) for a broad range of chemicals. PSO reveals a relationship between chemical uptake and decomposition parameter values that predicts chemical-specific BCF values with moderate statistical agreement to a limited yet diverse chemical dataset, and all without a need to retrain the model to new data.Conclusions
The presented model requires only the octanol-water partitioning ratio to predict BCFs to a fidelity consistent with existing QSAR models. This success begs re-evaluation of the modeling assumptions; specifically, it suggests that chemical uptake into arterial blood may be limited by transport across gill membranes (diffusion) rather than by counter-current flow between gill lamellae (convection). Therefore, more detailed molecular modeling of aquatic respiration may further improve predictive accuracy of the rTK approach.18.
Background
Glatiramer acetate is worldwide used as first line treatment in relapsing remitting multiple sclerosis. Local skin reactions associated with glatiramer acetate are common, however, only isolated cases of severe local injection site reactions known as Nicolau Syndrome have been reported so far.Case presentation
We describe the case of a recurrent Nicolau Syndrome occurred during longstanding glatiramer acetate treatment in a woman with multiple sclerosis. The haemorrhagic patch necrotized and was treated locally as a deep second degree burn with excision of dead skin tissue and was healed. Treatment with glatiramer acetate was definitely suspended.Conclusions
GA injections can be complicated by isolated or recurrent Nicolau Syndrome, a potentially life-threatening condition of which neurologists should be aware.19.
Background
In mathematical epidemiology, age-structured epidemic models have usually been formulated as the boundary-value problems of the partial differential equations. On the other hand, in engineering, the backstepping method has recently been developed and widely studied by many authors.Methods
Using the backstepping method, we obtained a boundary feedback control which plays the role of the threshold criteria for the prediction of increase or decrease of newly infected population. Under an assumption that the period of infectiousness is same for all infected individuals (that is, the recovery rate is given by the Dirac delta function multiplied by a sufficiently large positive constant), the prediction method is simplified to the comparison of the numbers of reported cases at the current and previous time steps.Results
Our prediction method was applied to the reported cases per sentinel of influenza in Japan from 2006 to 2015 and its accuracy was 0.81 (404 correct predictions to the total 500 predictions). It was higher than that of the ARIMA models with different orders of the autoregressive part, differencing and moving-average process. In addition, a proposed method for the estimation of the number of reported cases, which is consistent with our prediction method, was better than that of the best-fitted ARIMA model ARIMA(1,1,0) in the sense of mean square error.Conclusions
Our prediction method based on the backstepping method can be simplified to the comparison of the numbers of reported cases of the current and previous time steps. In spite of its simplicity, it can provide a good prediction for the spread of influenza in Japan.20.
Jeffrey L. Gum Leah Y. Carreon Jacob M. Buchowski Lawrence G. Lenke Steven D. Glassman 《Scoliosis》2016,11(1):25