scholarly journals Estimating kinetic mechanisms with prior knowledge II: Behavioral constraints and numerical tests

2018 ◽  
Vol 150 (2) ◽  
pp. 339-354 ◽  
Author(s):  
Marco A. Navarro ◽  
Autoosa Salari ◽  
Mirela Milescu ◽  
Lorin S. Milescu
Keyword(s):  
Prior Knowledge ◽  
Estimation Procedure ◽  
Kinetic Mechanism ◽  
Arbitrary Parameter ◽  
Linear Parameter ◽  
Open Probability ◽  
Behavioral Constraints ◽  
Kinetic Mechanisms ◽  
Mathematical Relationships ◽  
Optimization Mechanism

Kinetic mechanisms predict how ion channels and other proteins function at the molecular and cellular levels. Ideally, a kinetic model should explain new data but also be consistent with existing knowledge. In this two-part study, we present a mathematical and computational formalism that can be used to enforce prior knowledge into kinetic models using constraints. Here, we focus on constraints that quantify the behavior of the model under certain conditions, and on constraints that enforce arbitrary parameter relationships. The penalty-based optimization mechanism described here can be used to enforce virtually any model property or behavior, including those that cannot be easily expressed through mathematical relationships. Examples include maximum open probability, use-dependent availability, and nonlinear parameter relationships. We use a simple kinetic mechanism to test multiple sets of constraints that implement linear parameter relationships and arbitrary model properties and behaviors, and we provide numerical examples. This work complements and extends the companion article, where we show how to enforce explicit linear parameter relationships. By incorporating more knowledge into the parameter estimation procedure, it is possible to obtain more realistic and robust models with greater predictive power.

scholarly journals Estimating kinetic mechanisms with prior knowledge I: Linear parameter constraints

2018 ◽  
Vol 150 (2) ◽  
pp. 323-338 ◽  
Author(s):  
Autoosa Salari ◽  
Marco A. Navarro ◽  
Mirela Milescu ◽  
Lorin S. Milescu
Keyword(s):  
Ion Channels ◽  
Prior Knowledge ◽  
Arbitrary Parameter ◽  
Model Parameters ◽  
Data Types ◽  
Complementary Method ◽  
Linear Relationships ◽  
Kinetic Mechanisms ◽  
Parameter Constraints ◽  
Independent Parameters

To understand how ion channels and other proteins function at the molecular and cellular levels, one must decrypt their kinetic mechanisms. Sophisticated algorithms have been developed that can be used to extract kinetic parameters from a variety of experimental data types. However, formulating models that not only explain new data, but are also consistent with existing knowledge, remains a challenge. Here, we present a two-part study describing a mathematical and computational formalism that can be used to enforce prior knowledge into the model using constraints. In this first part, we focus on constraints that enforce explicit linear relationships involving rate constants or other model parameters. We develop a simple, linear algebra–based transformation that can be applied to enforce many types of model properties and assumptions, such as microscopic reversibility, allosteric gating, and equality and inequality parameter relationships. This transformation converts the set of linearly interdependent model parameters into a reduced set of independent parameters, which can be passed to an automated search engine for model optimization. In the companion article, we introduce a complementary method that can be used to enforce arbitrary parameter relationships and any constraints that quantify the behavior of the model under certain conditions. The procedures described in this study can, in principle, be coupled to any of the existing methods for solving molecular kinetics for ion channels or other proteins. These concepts can be used not only to enforce existing knowledge but also to formulate and test new hypotheses.

scholarly journals Models to determine the kinetic mechanisms of ion-coupled transporters

2019 ◽  
Vol 151 (3) ◽  
pp. 369-380 ◽  
Author(s):  
Juke S. Lolkema ◽  
Dirk J. Slotboom
Keyword(s):  
Steady State ◽  
Kinetic Mechanism ◽  
Ion Concentration ◽  
Coupling Mechanism ◽  
Maximal Rate ◽  
Transport Reaction ◽  
Apparent Affinity ◽  
Kinetic Mechanisms ◽  
Experimental Approaches ◽  
Analyze Data

With high-resolution structures available for many ion-coupled (secondary active) transporters, a major challenge for the field is to determine how coupling is accomplished. Knowledge of the kinetic mechanism of the transport reaction, which defines the binding order of substrate and co-ions, together with the sequence with which all relevant states are visited by the transporter, will help to reveal this coupling mechanism. Here, we derived general mathematical models that can be used to analyze data from steady-state transport measurements and show how kinetic mechanisms can be derived. The models describe how the apparent maximal rate of substrate transport depends on the co-ion concentration, and vice versa, in different mechanisms. Similarly, they describe how the apparent affinity for the transported substrate is affected by the co-ion concentration and vice versa. Analyses of maximal rates and affinities permit deduction of the number of co-ions that bind before, together with, and after the substrate. Hill analysis is less informative, but in some mechanisms, it can reveal the total number of co-ions transported with the substrate. However, prior knowledge of the number of co-ions from other experimental approaches is preferred when deriving kinetic mechanisms, because the models are generally overparameterized. The models we present have wide applicability for the study of ion-coupled transporters.

scholarly journals Estimating Kinetic Mechanisms with Prior Knowledge

2017 ◽  
Vol 112 (3) ◽  
pp. 243a
Author(s):  
Autoosa Salari ◽  
Zachary F. Elkins ◽  
Marco A. Navarro ◽  
Benton R. Berigan ◽  
Jenna L. Lin ◽  
...  
Keyword(s):  
Prior Knowledge ◽  
Kinetic Mechanisms

Comprehension of Mathematical Relationships Expressed in Graphs

1987 ◽  
Vol 18 (5) ◽  
pp. 382-393 ◽  
Author(s):  
Frances R. Curcio
Keyword(s):  
Reading Achievement ◽  
Mathematics Achievement ◽  
Prior Knowledge ◽  
Fourth Graders ◽  
Graphical Form ◽  
Seventh Graders ◽  
Mathematical Content ◽  
Graph Comprehension ◽  
And Mathematics ◽  
Mathematical Relationships

In this study, the schema-theoretic perspective of understanding general discourse was extended to include graph comprehension. Fourth graders (n=204) and seventh graders (n=185) were given a prior-knowledge inventory, a graph test, and the SRA Reading and Mathematics Achievement Tests during four testing sessions. The unique predictors of graph comprehension for Grade 4 included reading achievement, mathematics achievement, and prior knowledge of the topic, mathematical content, and form of the graph. The unique predictors for Grade 7 were the same except that prior knowledge of topic and graphical form were not included. The results suggest that children should be involved in graphing activities to build and expand relevant schemata needed for comprehension.

scholarly journals QUANTUM ESTIMATION OF RELATIVE INFORMATION

2006 ◽  
Vol 04 (01) ◽  
pp. 131-149 ◽  
Author(s):  
NETANEL H. LINDNER ◽  
PETRA F. SCUDO ◽  
DAGMAR BRUß
Keyword(s):  
Symmetry Group ◽  
Prior Knowledge ◽  
Reference Frame ◽  
Spatial Orientation ◽  
Degrees Of Freedom ◽  
Estimation Procedure ◽  
Quantum Systems ◽  
Relative Information ◽  
Rotation Parameters ◽  
Require Information

We derive optimal schemes for preparation and estimation of relational degrees of freedom between two quantum systems. We specifically analyze the case of rotation parameters representing relative angles between elements of the SU(2) symmetry group. Our estimation procedure does not assume prior knowledge of the absolute spatial orientation of the systems and as such does not require information on the underlying classical reference frame in which the states are prepared.

scholarly journals Comparison of the active sites of the purified carnitine acyltransferases from peroxisomes and mitochondria by using a reaction-intermediate analogue

1993 ◽  
Vol 294 (3) ◽  
pp. 645-651 ◽  
Author(s):  
N Nic a′ Bháird ◽  
G Kumaravel ◽  
R D Gandour ◽  
M J Krueger ◽  
R R Ramsay
Keyword(s):  
Active Sites ◽  
Random Order ◽  
Kinetic Mechanism ◽  
Product Inhibition ◽  
Binding Domains ◽  
Cell Compartments ◽  
Mitochondrial Inner Membrane ◽  
Kinetic Mechanisms ◽  
Carnitine Acyltransferases ◽  
Inhibition Studies

The carnitine acyltransferases contribute to the modulation of the acyl-CoA/CoA ratio in various cell compartments with consequent effects on many aspects of fatty acid metabolism. The properties of the enzymes are different in each location. The kinetic mechanisms and kinetic parameters for the carnitine acyltransferases purified from peroxisomes (COT) and from the mitochondrial inner membrane (CPT-II) were determined. Product-inhibition studies established that COT follows a rapid-equilibrium random-order mechanism, but CPT-II follows a strictly ordered mechanism in which acyl-CoA or CoA must bind before the carnitine substrate. Hemipalmitoylcarnitinium [(+)-HPC], a prototype tetrahedral intermediate analogue of the acyltransferase reaction, inhibits CPT-II 100-fold better than COT. (+)-HPC behaves as an analogue of palmitoyl-L-carnitine with COT. In contrast, with CPT-II(+)-HPC binds more tightly to the enzyme than do substrates or products, suggesting that it is a good model for the transition state and, unlike palmitoyl-L-carnitine, (+)-HPC can bind to the free enzyme. The data support the concept of three binding domains for the acyltransferases, a CoA site, an acyl site and a carnitine site. The CoA site is similar in COT and CPT-II, but there are distinct differences between the carnitine-binding site which may dictate the kinetic mechanism.

Numerical Simulation of Biomass Derived Syngas Combustion in a Swirl Flame Combustor

2010 ◽  
Author(s):  
Andrea De Pascale ◽  
Marco Fussi ◽  
Antonio Peretto
Keyword(s):  
Kinetic Mechanism ◽  
Swirl Flow ◽  
General Purpose ◽  
Combustion Model ◽  
Test Case ◽  
Flamelet Model ◽  
Syngas Combustion ◽  
Kinetic Mechanisms ◽  
Swirl Flame ◽  
Swirled Flames

In this work a numerical investigation is carried out on a model combustor characterized by swirl flow conditions, fed with a biomass derived syngas fuel (which incorporates CH4, CO and H2) and operated in laboratory at atmospheric pressure. The combustor internal aerodynamics and heat release in case of syngas combustion have been simulated in the framework of CFD-RANS techniques, by means of different available models and by adopting different levels of kinetic mechanism complexity. In particular, the applicability of reduced mechanisms involving CO and H2 species and also of detailed kinetic mechanisms are assessed. The results obtained by means of the CFD simulations on the model combustor and a comparison with available experimental data on flow field and thermal field are presented in the paper. In the test-case of syngas-air swirled flames, the turbulent non premixed combustion “flamelet” model with detailed non-equilibrium chemistry, originally developed for methane-air combustion, provides encouraging results in terms of temperature distribution. Nevertheless, a simpler chemical path including the main fuel species integrated in a general purpose, widely used in industry, turbulent combustion model still provides acceptable results.

Modeling spray combustion using multi-component surrogate fuels

2021 ◽  
pp. 095765092110025
Author(s):  
Tao Yang ◽  
Ran Yi ◽  
Qiaoling Wang ◽  
Chien-Pin Chen
Keyword(s):  
Chemical Properties ◽  
Kinetic Mechanism ◽  
Chemical Kinetic ◽  
Spray Combustion ◽  
Surrogate Fuels ◽  
Diesel Fuels ◽  
Constant Volume Chamber ◽  
Kinetic Mechanisms ◽  
Lift Off ◽  
Evaporation Models

Kerosene and diesel fuels involved in spray combustion operations are complex fuels composed of a wide and diverse variety of hydrocarbon components. For practical numerical modeling of the evaporation and combustion phenomena in a combustor, well-designed surrogates fuels that can mimic the real fuel thermal and chemical properties can be utilized. In this study, predictions and validations of the influence of fuel on the liquid and vapor penetration characteristics within a constant-volume chamber were first performed utilizing a benchmark m-xylene/ n-dodecane, Jet-A, and diesel surrogate fuels. Then, simulations of reacting spray of a bi-component m-xylene/ n-dodecane fule, and a four-component Jet-A surrogate fuel ( n-dodecane (C12H26), iso-cetane (C16H34), trans-decalin (C10H18) and toluene (C7H8)) were studied aided by skeleton chemical kinetic mechanisms available from the literature. The results of ignition delay time, lift-off length, radicals, and the mass fraction histories of fuel species were comprehensively used to assess the performance of relevant thermophysical and chemical sub-models. Two different chemical mechanisms were compared in detail to investigate the effect of the chemical kinetics model on the flame structures and spray characteristics. It has been found that the spray ignition of multi-component fuels is remarkably influenced by the chosen chemical kinetic mechanism and less affected by the droplet evaporation models.

scholarly journals Deciding Between One-Step and Two-Step Irreversible Inhibition Mechanisms on the Basis of “Kobs” Data: A Statistical Approach

2020 ◽  
Author(s):  
Petr Kuzmic
Keyword(s):  
Drug Discovery ◽  
Statistical Approach ◽  
Enzyme Inhibitors ◽  
Chemical Reactivity ◽  
Kinetic Mechanism ◽  
Irreversible Inhibitor ◽  
Experimental Drugs ◽  
Covalent Inhibitors ◽  
Kinetic Mechanisms ◽  
One Step

Covalent (irreversible) enzyme inhibitors are an important group of actual or potential therapeutics. For example, Aspirin is an irreversible inhibitor of the cyclooxygenase enzyme. Evaluating covalent inhibitors in the drug discovery is exceptionally challenging, because their overall inhibitory potency consists of two separate but intertwined contributions: (1) initial binding affinity and (2) chemical reactivity. It is especially difficult to reliably asses the kinetic mechanism of inhibition. This paper describes an objective statistical approach that can be used to decide between two alternate kinetic mechanisms of covalent enzyme inhibition, from kinetic experiments based on the standard "kobs" method [Copeland (2013) "Evaluation of Enzyme Inhibitors in Drug Discovery", section 9.1]. The two alternatives are either a two-step kinetic mechanism, which involves a reversibly formed noncovalent intermediate, or a one-step kinetic mechanism, proceeding in a single bimolecular step. The proposed statistical toolkit uses four independent methods to arrive at a reliable mechanistic conclusion. The results are illustrated by using recently published experimental data on the inhibition of two different protein kinases by the experimental drugs ibrutinib (PCI-32765) and acalabrutinib [Hopper <i>et al.</i> (2020) <i>J. Pharm. Exp. Therap.</i> <b>372</b>, 331–338].

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