Models Of Biochemical Systems Research Articles

Macroscopic limit for stochastic chemical reactions involving diffusion and spatial heterogeneity

To model bio-chemical reaction systems with diffusion one can either use stochastic, microscopic reaction–diffusion master equations or deterministic, macroscopic reaction–diffusion system. The connection between these two models is not only theoretically important but also plays an essential role in applications. This paper considers the macroscopic limits of the chemical reaction–diffusion master equation for first-order chemical reaction systems in highly heterogeneous environments. More precisely, the diffusion coefficients as well as the reaction rates are spatially inhomogeneous and the reaction rates may also be discontinuous. By carefully discretizing these heterogeneities within a reaction–diffusion master equation model, we show that in the limit we recover the macroscopic reaction–diffusion system with inhomogeneous diffusion and reaction rates.

Abstract 204: Quantitative evaluation of biomarkers for TGF-β-induced epithelial-mesenchymal transition in biochemical, cellular, and 3D spheroid model systems

Abstract Epithelial-mesenchymal transition (EMT) is a cellular differentiation process whereby epithelial cells lose epithelial features and acquire mesenchymal, fibroblast-like properties, leading to reduced cell-cell contacts and increased motility. EMT is a fundamental biological process required for normal embryonic development, but may be co-opted by malignant epithelial tumors to facilitate metastatic spread. A known driver of EMT is the TGF-β superfamily of growth factor ligands, which elicit receptor-mediated responses in cells, primarily via TGF-β/SMAD signaling pathways. In these pathways, receptor-mediated SMAD (R-SMAD) proteins serve as the primary downstream effector molecules, the activities of which are regulated through receptor-mediated phosphorylation. The magnitude and duration of ligand-induced receptor activation influences the level of SMAD phosphorylation, which in turn influences the magnitude of the downstream cellular response(s). In this study, we describe high-throughput methods to quantitatively evaluate the biochemical and cellular responses to TGF-β/SMAD pathway activation in a cellular model of TGF-β-induced EMT. Effects of pathway activation are examined at different levels of biological complexity (biochemical, cellular, and multicellular), using 2D and 3D (spheroid) models. Collectively, these approaches enable a comprehensive evaluation of TGF-β/SMAD pathway activation that is amenable to high-throughput analysis platforms. Citation Format: Antony W. Wood, Ernest Heimsath. Quantitative evaluation of biomarkers for TGF-β-induced epithelial-mesenchymal transition in biochemical, cellular, and 3D spheroid model systems [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 204.

Quantifying Parameter Interdependence in Stochastic Discrete Models of Biochemical Systems.

Stochastic modeling of biochemical processes at the cellular level has been the subject of intense research in recent years. The Chemical Master Equation is a broadly utilized stochastic discrete model of such processes. Numerous important biochemical systems consist of many species subject to many reactions. As a result, their mathematical models depend on many parameters. In applications, some of the model parameters may be unknown, so their values need to be estimated from the experimental data. However, the problem of parameter value inference can be quite challenging, especially in the stochastic setting. To estimate accurately the values of a subset of parameters, the system should be sensitive with respect to variations in each of these parameters and they should not be correlated. In this paper, we propose a technique for detecting collinearity among models' parameters and we apply this method for selecting subsets of parameters that can be estimated from the available data. The analysis relies on finite-difference sensitivity estimations and the singular value decomposition of the sensitivity matrix. We illustrated the advantages of the proposed method by successfully testing it on several models of biochemical systems of practical interest.

Sensitivity analysis of biochemical systems using bond graphs.

The sensitivity of systems biology models to parameter variation can give insights into which parameters are most important for physiological function, and also direct efforts to estimate parameters. However, in general, kinetic models of biochemical systems do not remain thermodynamically consistent after perturbing parameters. To address this issue, we analyse the sensitivity of biological reaction networks in the context of a bond graph representation. We find that the parameter sensitivities can themselves be represented as bond graph components, mirroring potential mechanisms for controlling biochemistry. In particular, a sensitivity system is derived which re-expresses parameter variation as additional system inputs. The sensitivity system is then linearized with respect to these new inputs to derive a linear system which can be used to give local sensitivity to parameters in terms of linear system properties such as gain and time constant. This linear system can also be used to find so-called sloppy parameters in biological models. We verify our approach using a model of the Pentose Phosphate Pathway, confirming the reactions and metabolites most essential to maintaining the function of the pathway.

BioSANS: A software package for symbolic and numeric biological simulation.

Modeling biochemical systems can provide insights into behaviors that are difficult to observe or understand. It requires software, programming, and understanding of the system to build a model and study it. Softwares exist for systems biology modeling, but most support only certain types of modeling tasks. Desirable features including ease in preparing input, symbolic or analytical computation, parameter estimation, graphical user interface, and systems biology markup language (SBML) support are not seen concurrently in one software package. In this study, we developed a python-based software that supports these features, with both deterministic and stochastic propagations. The software can be used by graphical user interface, command line, or as a python import. We also developed a semi-programmable and intuitively easy topology input method for the biochemical reactions. We tested the software with semantic and stochastic SBML test cases. Tests on symbolic solution and parameter estimation were also included. The software we developed is reliable, well performing, convenient to use, and compliant with most of the SBML tests. So far it is the only systems biology software that supports symbolic, deterministic, and stochastic modeling in one package that also features parameter estimation and SBML support. This work offers a comprehensive set of tools and allows for better availability and accessibility for studying kinetics and dynamics in biochemical systems.

Effective Finite-Difference Techniques for Estimating Sensitivities for Stochastic Biochemical Systems

Cellular environments are in essence stochastic, owing to the random character of the biochemical reaction events in a single cell. Stochastic fluctuations may substantially contribute to the dynamics of systems with small copy numbers of some biochemical species. Then, stochastic models are indispensable for properly portraying the behaviour of the system. Sensitivity analysis is one of the central tools for studying stochastic models of cellular dynamics. Here, we propose some finite-difference strategies for estimating parametric sensitivities of higher-order moments of the system state for stochastic discrete biochemical kinetic models. To reduce the variance of the sensitivity estimator, we employ various coupling techniques. The advantages of the proposed methods are illustrated in several models of biochemical systems of practical relevance.

A Probabilistic Approach to Explore Signal Execution Mechanisms With Limited Experimental Data.

Mathematical models of biochemical reaction networks are central to the study of dynamic cellular processes and hypothesis generation that informs experimentation and validation. Unfortunately, model parameters are often not available and sparse experimental data leads to challenges in model calibration and parameter estimation. This can in turn lead to unreliable mechanistic interpretations of experimental data and the generation of poorly conceived hypotheses for experimental validation. To address this challenge, we evaluate whether a Bayesian-inspired probability-based approach, that relies on expected values for quantities of interest calculated from available information regarding the reaction network topology and parameters can be used to qualitatively explore hypothetical biochemical network execution mechanisms in the context of limited available data. We test our approach on a model of extrinsic apoptosis execution to identify preferred signal execution modes across varying conditions. Apoptosis signal processing can take place either through a mitochondria independent (Type I) mode or a mitochondria dependent (Type II) mode. We first show that in silico knockouts, represented by model subnetworks, successfully identify the most likely execution mode for specific concentrations of key molecular regulators. We then show that changes in molecular regulator concentrations alter the overall reaction flux through the network by shifting the primary route of signal flow between the direct caspase and mitochondrial pathways. Our work thus demonstrates that probabilistic approaches can be used to explore the qualitative dynamic behavior of model biochemical systems even with missing or sparse data.

Symmetry structures in dynamic models of biochemical systems.

Understanding the complex interactions of biochemical processes underlying human disease represents the holy grail of systems biology. When processes are modelled in ordinary differential equation (ODE) fashion, the most common tool for their analysis is linear stability analysis where the long-term behaviour of the model is determined by linearizing the system around its steady states. However, this asymptotic behaviour is often insufficient for completely determining the structure of the underlying system. A complementary technique for analysing a system of ODEs is to consider the set of symmetries of its solutions. Symmetries provide a powerful concept for the development of mechanistic models by describing structures corresponding to the underlying dynamics of biological systems. To demonstrate their capability, we consider symmetries of the nonlinear Hill model describing enzymatic reaction kinetics and derive a class of symmetry transformations for each order of the model. We consider a minimal example consisting of the application of symmetry-based methods to a model selection problem, where we are able to demonstrate superior performance compared to ordinary residual-based model selection. Moreover, we demonstrate that symmetries reveal the intrinsic properties of a system of interest based on a single time series. Finally, we show and propose that symmetry-based methodology should be considered as the first step in a systematic model building and in the case when multiple time series are available it should complement the commonly used statistical methodologies.

Mechanistic Modeling of Biochemical Systems without A Priori Parameter Values Using the Design Space Toolbox v.3.0.

SummaryMechanistic models of biochemical systems provide a rigorous description of biological phenomena. They are indispensable for making predictions and elucidating biological design principles. To date, mathematical analysis and characterization of these models encounter a bottleneck consisting of large numbers of unknown parameter values. Here, we introduce the Design Space Toolbox v.3.0 (DST3), a software implementation of the Design Space formalism enabling mechanistic modeling without requiring previous knowledge of parameter values. This is achieved by using a phenotype-centric modeling approach, in which the system is first decomposed into a series of biochemical phenotypes. Parameter values realizing phenotypes of interest are subsequently predicted. DST3 represents the most generally applicable implementation of the Design Space formalism and offers unique advantages over earlier versions. By expanding the Design Space formalism and streamlining its distribution, DST3 represents a valuable tool for elucidating biological design principles and designing novel synthetic circuits.

Over-Approximation of Fluid Models

Fluid models are a popular formalism in the quantitative modeling of biochemical systems and analytical performance models. The main idea is to approximate a large-scale Markov chain by a compact set of ordinary differential equations (ODEs). Even though it is often crucial for a fluid model under study to satisfy some given properties, a formal verification is usually challenging. This is because parameters are often not known precisely due to finite-precision measurements and stochastic noise. In this paper, we present a novel technique that allows one to efficiently compute formal bounds on the reachable set of time-varying nonlinear ODE systems that are subject to uncertainty. To this end, we a) relate the reachable set of a nonlinear fluid model to a family of inhomogeneous continuous time Markov decision processes and b) provide optimal and suboptimal solutions for the family by relying on optimal control theory. The proposed technique is efficient and can be expected to provide tight bounds. We demonstrate its potential by comparing it with a state-of-the-art over-approximation approach.

Comparison of Two Nature-inspired Algorithms for Parameter Estimation of S-system Models

Parameter estimation for models of biochemical systems is computationally expensive due to the nonlinearity and high dimensionality of the coupled systems of ordinary differential equations underlying the models. Hence, it is important to apply novel methods to the problem and evaluate their performance. We consider the Bat algorithm (BA) and the Firefly algorithm (FA) with respect to parameter estimation of S-system models. Using three S-systems of increasing complexity from the MADMan benchmarking framework, we assess and compare the relative performance of the two algorithms relative to various data sets, initial conditions, and noise levels. Simulation results show that both algorithms can be effectively used in estimating parameters of the S-system models. In particular, in all three S-systems used, the FA performed better than the BA based on the final cost function values and relative estimate errors. The introduction of noise to data significantly affected the convergence of both algorithms.

Synthesis and Crystal Structure of Bis(N’-(Pyridine-3-Carboxaldehyde) Isonicotinoylhydrazone) Zinc(II)

Zinc complexes of Schiff base ligands exhibit interesting properties which could be exploited for potential applications as catalysts and models for biochemical systems. In this study, we report of the synthesis of a new zinc Schiff base complex, bis(N’-(pyridine-3-carboxaldehyde) isonicotinoylhydrazone) zinc(II), which has been characterized by physico-chemical methods. The X-ray single crystal structure of the complex has also been determined. The Schiff base ligand is bonded to the metal in a monodentate manner, coordinating through the pyridine N-atom, as shown from spectral studies. The crystal structure shows the zinc atom bonded to two Schiff bases and four aqua ligands, with each Schiff base ligand coordinating through its pyridine N-atom forming a distorted octahedral ZnN2O4 complex. Two water molecules and two nitrate ions found in the crystal structure link the different monomers through hydrogen bonding to form a layered supramolecular structure.

Mechanistic Modeling of Biochemical Systems Without a Priori Parameter Values Using the Design Space Toolbox v.3.0

Mechanistic models of biochemical systems provide a rigorous description of biological phenomena. They are indispensable to elucidate biological design principles. To date, mathematical analysis and characterization of these models remain a challenging endeavor. Here, we introduce the Design Space Toolbox v.3.0 (DST3), a software implementation of the Design Space formalism that enables mechanistic modeling of biological processes without requiring previous knowledge of the parameter values involved. This is achieved by making use of a phenotype-centric modeling approach, in which the system is first decomposed into a series of biochemical phenotypes. Parameter values realizing phenotypes of interest are predicted in a second step. DST3 represents the most generally applicable implementation of the Design Space formalism and offers unique advantages over earlier versions. By expanding the Design Space formalism and streamlining its distribution, DST3 represents a valuable tool for elucidating biological design principles and designing novel synthetic circuits.

Effects of Electromagnetic Fields over DNA in Tumor Diseases, Biophysical and Biochemical Model Systems

Studies were conducted with model systems of influence of Drossinakis with electromagnetic (e.m.) fields and infrared thermal field (ITF) (Ignatov, Mosin, Niggli, Drossinakis, 2013). The purpose of research is to analyze effects over DNA. In the report is carried out analysis of effects over water and physiological saline. Results are achieved with blood serum of hamsters and physiological processes in hamsters with tumors. The analyses with water are conducted using the methods Nonequilibrium Energy Spectrum (NES) and Differential Nonequilibrium Energy Spectrum (DNES) (Antonov, 1992; Ignatov, 1998). Experiments are carried out with the influence of tumor cells of a mouse in water. It is observed reduction of DNES spectrum according to the control sample of cells in healthy animals. (Antonov, 1992). Reduction is also observed in DNES spectrum in blood serum of people having oncological diseases, compared to the one of healthy people (Ignatov, 2012). Such a reduction is most prevalent in (-0.1387 eV; 8.95 µm; 1117 cm -1 ). In research of the effects of e.m. fields in water and blood serum from hamsters the range is (-0.08 – -0.14 eV) (8.9 –15.5µm) (645–1129 cm -1 ). Research is conducted for the effects over Graffi tumor that was implanted in hamsters (Toshkova, Ignatov, Zvetkova, Ignatov, Gluhchev, Drossinakis, 2019). Studies are conducted with pH and oxidation redox potential (ORP) effects of e.m. fields over physiological saline (Gluhchev, Ignatov, Drossinakis, 2019). Keywords: Infrared thermal field (ITF), electromagnetic fields (e.m. fields), experimental Graffi solid tumor, energy spectrum, NES and DNES methods. DOI : 10.7176/JMPB/56-03 Publication date :May 31 st 2019

(Invited) Biomedical Applications of Metal Nanoparticle-Decorated Carbon Nanostructures

Carbon nanotubes and graphene are highly sensitive to changes in the local chemical environment and serve as an ideal platform for the fabrication of label-free nanoelectronic sensors. We recently employed a series of metal nanoparticle functionalized carbon nanotube devices as cross-sensitive sensor arrays, demonstrating electronic “tongue” functions and ability to analyze different cell types. By combining analysis of sensor device characteristics with supervised machine learning algorithms, we have successfully discriminated among different analytes and accurately discerned the presence of specific analytes in the complex mixtures. Carbon nanostructures can also be used as nano-carriers for applications in medical therapeutics. To this end, we developed cup-shaped carbon nanostructures, which have an elliptical hollow space that can be corked by gold nanoparticles at the opening. To illustrate the potential of corked nanocups as drug delivery systems, loading with common fluorescent dyes, as well as chemotherapeutic drugs, was performed. By using Raman spectroscopy, we were able to demonstrate the loading and release of the cargo in biochemical model systems and tumor-associated cells. We recently demonstrated in vivo systemic nanodelivery of paclitaxel loaded gold nanoparticle-corked nanocups inhibited melanoma growth in mice with 25-30% of treated animals being tumor free after 2-3 weeks. Figure 1

Reversible Doi and Smoluchowski Kinetics for High-Order Reactions

In recent years, modeling of biochemical systems has attracted much attention. Traditionally, these systems have been modeled with differential equations. However, specific biological processes ten...

Strategy-Driven Exploration for Rule-Based Models of Biochemical Systems with PORGY.

This chapter presents PORGY-an interactive visual environment for rule-based modelling of biochemical systems. We model molecules and molecule interactions as port graphs and port graph rewrite rules, respectively. We use rewriting strategies to control which rules to apply, and where and when to apply them. Our main contributions to rule-based modelling of biochemical systems lie in the strategy language and the associated visual and interactive features offered by PORGY. These features facilitate an exploratory approach to test different ways of applying the rules while recording the model evolution, and tracking and plotting parameters. We illustrate PORGY's features with a study of the role of a scaffold protein in RAF/MEK/ERK signalling.

Using RuleBuilder to Graphically Define and Visualize BioNetGen-Language Patterns and Reaction Rules.

RuleBuilder is a tool for drawing graphs that can be represented by the BioNetGen language (BNGL), which is used to formulate mathematical, rule-based models of biochemical systems. BNGL provides an intuitive plain text, or string, representation of such systems, which is based on a graphical formalism. Reactions are defined in terms of graph-rewriting rules that specify the necessary intrinsic properties of the reactants, a transformation, and a rate law. Rules also contain contextual constraints that restrict application of the rule. In some cases, the specification of contextual constraints can be verbose, making a rule difficult to read. RuleBuilder is designed to ease the task of reading and writing individual reaction rules or other BNGL patterns required for model formulation. The software assists in the reading of existing models by converting BNGL strings of interest into a graph-based representation composed of nodes and edges. RuleBuilder also enables the user to construct de novo a visual representation of BNGL strings using drawing tools available in its interface. As objects are added to the drawing canvas, the corresponding BNGL string is generated on the fly, and objects are similarly drawn on the fly as BNGL strings are entered into the application. RuleBuilder thus facilitates construction and interpretation of rule-based models.

Molecular Filters for Noise Reduction

Living systems are inherently stochastic and operate in a noisy environment, yet despite all these uncertainties, they perform their functions in a surprisingly reliable way. The biochemical mechanisms used by natural systems to tolerate and control noise are still not fully understood, and this issue also limits our capacity to engineer reliable, quantitative synthetic biological circuits. We study how representative models of biochemical systems propagate and attenuate noise, accounting for intrinsic as well as extrinsic noise. We investigate three molecular noise-filtering mechanisms, study their noise-reduction capabilities and limitations, and show that nonlinear dynamics such as complex formation are necessary for efficient noise reduction. We further suggest that the derived molecular filters are widespread in gene expression and regulation and, particularly, that microRNAs can serve as such noise filters. To our knowledge, our results provide new insight into how biochemical networks control noise and could be useful to build robust synthetic circuits.

Griffin: A Tool for Symbolic Inference of Synchronous Boolean Molecular Networks

Boolean networks are important models of biochemical systems, located at the high end of the abstraction spectrum. A number of Boolean gene networks have been inferred following essentially the same method. Such a method first considers experimental data for a typically underdetermined “regulation” graph. Next, Boolean networks are inferred by using biological constraints to narrow the search space, such as a desired set of (fixed-point or cyclic) attractors. We describe Griffin, a computer tool enhancing this method. Griffin incorporates a number of well-established algorithms, such as Dubrova and Teslenko's algorithm for finding attractors in synchronous Boolean networks. In addition, a formal definition of regulation allows Griffin to employ “symbolic” techniques, able to represent both large sets of network states and Boolean constraints. We observe that when the set of attractors is required to be an exact set, prohibiting additional attractors, a naive Boolean coding of this constraint may be unfeasible. Such cases may be intractable even with symbolic methods, as the number of Boolean constraints may be astronomically large. To overcome this problem, we employ an Artificial Intelligence technique known as “clause learning” considerably increasing Griffin's scalability. Without clause learning only toy examples prohibiting additional attractors are solvable: only one out of seven queries reported here is answered. With clause learning, by contrast, all seven queries are answered. We illustrate Griffin with three case studies drawn from the Arabidopsis thaliana literature. Griffin is available at: http://turing.iimas.unam.mx/griffin.