Biochemical Networks Research Articles

A mathematically rigorous algorithm to define, compute and assess relevance of the probable dissociation constants in characterizing a biochemical network

Metabolism results from enzymatic- and non-enzymatic interactions of several molecules, is easily parameterized with the dissociation constant and occurs via biochemical networks. The dissociation constant is an empirically determined parameter and cannot be used directly to investigate in silico models of biochemical networks. Here, we develop and present an algorithm to define, compute and assess the relevance of the probable dissociation constant for every reaction of a biochemical network. The reactants and reactions of this network are modelled by a stoichiometry number matrix. The algorithm computes the null space and then serially generates subspaces by combinatorially summing the spanning vectors that are non-trivial and unique. This is done until the terms of each row either monotonically diverge or form an alternating sequence whose terms can be partitioned into subsets with almost the same number of oppositely signed terms. For a selected null space-generated subspace the algorithm utilizes several statistical and mathematical descriptors to select and bin terms from each row into distinct outcome-specific subsets. The terms of each subset are summed, mapped to the real-valued open interval 0,∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left(0,\\infty \\right)$$\\end{document} and used to populate a reaction-specific outcome vector. The p1-norm for this vector is then the probable dissociation constant for this reaction. These steps are continued until every reaction of a modelled network is unambiguously annotated. The assertions presented are complemented by computational studies of a biochemical network for aerobic glycolysis. The fundamental premise of this work is that every row of a null space-generated subspace is a valid reaction and can therefore, be modelled as a reaction-specific sequence vector with a dimension that corresponds to the cardinality of the subspace after excluding all trivial- and redundant-vectors. A major finding of this study is that the row-wise sum or the sum of the terms contained in each reaction-specific sequence vector is mapped unambiguously to a positive real number. This means that the probable dissociation constants, for all reactions, can be directly computed from the stoichiometry number matrix and are suitable indicators of outcome for every reaction of the modelled biochemical network. Additionally, we find that the unambiguous annotation for a biochemical network will require a minimum number of iterations and will determine computational complexity.

MetaLo: metabolic analysis of Logical models extracted from molecular interaction maps.

Molecular interaction maps (MIMs) are static graphical representations depicting complex biochemical networks that can be formalized using one of the Systems Biology Graphical Notation languages. Regardless of their extensive coverage of various biological processes, they are limited in terms of dynamic insights. However, MIMs can serve as templates for developing dynamic computational models. We present MetaLo, an open-source Python package that enables the coupling of Boolean models inferred from process description MIMs with generic core metabolic networks. MetaLo provides a framework to study the impact of signaling cascades, gene regulation processes, and metabolic flux distribution of central energy production pathways. MetaLo computes the Boolean model's asynchronous asymptotic behavior, through the identification of trap-spaces, and extracts metabolic constraints to contextualize the generic metabolic network. MetaLo is able to handle large-scale Boolean models and genome-scale metabolic models without requiring kinetic information or manual tuning. The framework behind MetaLo enables in depth analysis of the regulatory model, and may allow tackling a lack of omics data in poorly addressed biological fields to contextualize generic metabolic networks along with improper automatic reconstructions of cell- and/or disease-specific metabolic networks. MetaLo is available at https://pypi.org/project/metalo/ under the terms of the GNU General Public License v3.

Compartmental exchange regulates steady states and stochastic switching of a phosphorylation network

The phosphoregulation of proteins with multiple phosphorylation sites is governed by biochemical reaction networks that can exhibit multistable behavior. However, the behavior of such networks is typically studied in a single reaction volume, while cells are spatially organized into compartments that can exchange proteins. In this work, we use stochastic simulations to study the impact of compartmentalization on a two-site phosphorylation network. We characterize steady states and fluctuation-driven transitions between them as a function of the rate of protein exchange between two compartments. Surprisingly, the average time spent in a state before stochastically switching to another depends nonmonotonically on the protein exchange rate, with the most frequent switching occurring at intermediate exchange rates. At sufficiently small exchange rates, the state of the system and mean switching time are controlled largely by fluctuations in the balance of enzymes in each compartment. This leads to negatively correlated states in the compartments. For large exchange rates, the two compartments behave as a single effective compartment. However, when the compartmental volumes are unequal, the behavior differs from a single compartment with the same total volume. These results demonstrate that exchange of proteins between distinct compartments can regulate the emergent behavior of a common signaling motif.

A review of changes at the phenotypic, physiological, biochemical, and molecular levels of plants due to high temperatures.

This review summarizes the physiological, biochemical, and molecular regulatory network changes in plants in response to high temperature. With the continuous rise in temperature, high temperature has become an important issue limiting global plant growth and development, affecting the phenotype and physiological and biochemical processes of plants and seriously restricting crop yield and tree growth speed. As sessile organisms, plants inevitably encounter high temperatures and improve their heat tolerance by activating molecular networks related to heat stress, such as signal transduction, synthesis of metabolites, and gene expression. Heat tolerance is a polygenic trait regulated by a variety of genes, transcription factors, proteins, and metabolites. Therefore, this review summarizes the changes in physiological, biochemical and molecular regulatory networks in plants under high-temperature conditions to lay a foundation for an in-depth understanding of the mechanisms involved in plant heat tolerance responses.

Bifunctional enzyme provides absolute concentration robustness in multisite covalent modification networks.

Biochemical covalent modification networks exhibit a remarkable suite of steady state and dynamical properties such as multistationarity, oscillations, ultrasensitivity and absolute concentration robustness. This paper focuses on conditions required for a network of this type to have a species with absolute concentration robustness. We find that the robustness in a substrate is endowed by its interaction with a bifunctional enzyme, which is an enzyme that has different roles when isolated versus when bound as a substrate-enzyme complex. When isolated, the bifunctional enzyme promotes production of more molecules of the robust species while when bound, the same enzyme facilitates degradation of the robust species. These dual actions produce robustness in the large class of covalent modification networks. For each network of this type, we find the network conditions for the presence of robustness, the species that has robustness, and its robustness value. The unified approach of simultaneously analyzing a large class of networks for a single property, i.e. absolute concentration robustness, reveals the underlying mechanism of the action of bifunctional enzyme while simultaneously providing a precise mathematical description of bifunctionality.

DNA Reaction System That Acquires Classical Conditioning.

Biochemical reaction networks can exhibit plastic adaptation to alter their functions in response to environmental changes. This capability is derived from the structure and dynamics of the reaction networks and the functionality of the biomolecule. This plastic adaptation in biochemical reaction systems is essentially related to memory and learning capabilities, which have been studied in DNA computing applications for the past decade. However, designing DNA reaction systems with memory and learning capabilities using the dynamic properties of biochemical reactions remains challenging. In this study, we propose a basic DNA reaction system design that acquires classical conditioning, a phenomenon underlying memory and learning, as a typical learning task. Our design is based on a simple mechanism of five DNA strand displacement reactions and two degradative reactions. The proposed DNA circuit can acquire or lose a new function under specific conditions, depending on the input history formed by repetitive stimuli, by exploiting the dynamic properties of biochemical reactions induced by different input timings.

A data-driven approach for timescale decomposition of biochemical reaction networks.

Understanding the dynamics of biological systems in evolving environments is a challenge due to their scale and complexity. Here, we present a computational framework for the timescale decomposition of biochemical reaction networks to distill essential patterns from their intricate dynamics. This approach identifies timescale hierarchies, concentration pools, and coherent structures from time-series data, providing a system-level description of reaction networks at physiologically important timescales. We apply this technique to kinetic models of hypothetical and biological pathways, validating it by reproducing analytically characterized or previously known concentration pools of these pathways. Moreover, by analyzing the timescale hierarchy of the glycolytic pathway, we elucidate the connections between the stoichiometric and dissipative structures of reaction networks and the temporal organization of coherent structures. Specifically, we show that glycolysis is a cofactor-driven pathway, the slowest dynamics of which are described by a balance between high-energy phosphate bond and redox trafficking. Overall, this approach provides more biologically interpretable characterizations of network dynamics than large-scale kinetic models, thus facilitating model reduction and personalized medicine applications. IMPORTANCE Complex interactions within interconnected biochemical reaction networks enable cellular responses to a wide range of unpredictable environmental perturbations. Understanding how biological functions arise from these intricate interactions has been a long-standing problem in biology. Here, we introduce a computational approach to dissect complex biological systems' dynamics in evolving environments. This approach characterizes the timescale hierarchies of complex reaction networks, offering a system-level understanding at physiologically relevant timescales. Analyzing various hypothetical and biological pathways, we show how stoichiometric properties shape the way energy is dissipated throughout reaction networks. Notably, we establish that glycolysis operates as a cofactor-driven pathway, where the slowest dynamics are governed by a balance between high-energy phosphate bonds and redox trafficking. This approach enhances our understanding of network dynamics and facilitates the development of reduced-order kinetic models with biologically interpretable components.

Pattern recognition in the nucleation kinetics of non-equilibrium self-assembly

Inspired by biology’s most sophisticated computer, the brain, neural networks constitute a profound reformulation of computational principles1–3. Analogous high-dimensional, highly interconnected computational architectures also arise within information-processing molecular systems inside living cells, such as signal transduction cascades and genetic regulatory networks4–7. Might collective modes analogous to neural computation be found more broadly in other physical and chemical processes, even those that ostensibly play non-information-processing roles? Here we examine nucleation during self-assembly of multicomponent structures, showing that high-dimensional patterns of concentrations can be discriminated and classified in a manner similar to neural network computation. Specifically, we design a set of 917 DNA tiles that can self-assemble in three alternative ways such that competitive nucleation depends sensitively on the extent of colocalization of high-concentration tiles within the three structures. The system was trained in silico to classify a set of 18 grayscale 30 × 30 pixel images into three categories. Experimentally, fluorescence and atomic force microscopy measurements during and after a 150 hour anneal established that all trained images were correctly classified, whereas a test set of image variations probed the robustness of the results. Although slow compared to previous biochemical neural networks, our approach is compact, robust and scalable. Our findings suggest that ubiquitous physical phenomena, such as nucleation, may hold powerful information-processing capabilities when they occur within high-dimensional multicomponent systems.

Engineering a dual-loop molecular circuit with buffering capability to solve molecular information tasks.

Molecular circuits, as an effective strategy for implementing artificial biochemical networks, have been widely constructed to process molecular-level information tasks both in vivo and in vitro. However, the complex and diverse structures of molecular devices, along with inflexible signal output methods, pose significant challenges for molecular circuits to handle complex molecular information tasks. In response to the growing field of molecular circuits, we design an exonuclease-driven fan-out molecular device (FMD) with a programmable cascade approach capable of receiving uniform signal types and transmitting multifunctional signals. Combined with the buffering reaction proposed here, the approach expands the dynamic properties of biochemical networks. Unlike the conventional delay strategy, the buffering process not only withstands transient changes in transmission signals, but also delays the transmission of lossless signals. Furthermore, we construct a dual-loop molecular circuit with adjustable buffering modes, thereby enabling signal amplification, time delay, and a differentiated output. Finally, we develop a method to obtain the colorimetric output of dual pulse signals driven by a dual-loop molecular circuit with buffering and hence precisely classify multiple signals. This work promises programmable and multifunctional molecular circuits in nanomachines, molecular computing, and biomedical applications.

Transcriptional bursting dynamics in gene expression.

Gene transcription is a stochastic process that occurs in all organisms. Transcriptional bursting, a critical molecular dynamics mechanism, creates significant heterogeneity in mRNA and protein levels. This heterogeneity drives cellular phenotypic diversity. Currently, the lack of a comprehensive quantitative model limits the research on transcriptional bursting. This review examines various gene expression models and compares their strengths and weaknesses to guide researchers in selecting the most suitable model for their research context. We also provide a detailed summary of the key metrics related to transcriptional bursting. We compared the temporal dynamics of transcriptional bursting across species and the molecular mechanisms influencing these bursts, and highlighted the spatiotemporal patterns of gene expression differences by utilizing metrics such as burst size and burst frequency. We summarized the strategies for modeling gene expression from both biostatistical and biochemical reaction network perspectives. Single-cell sequencing data and integrated multiomics approaches drive our exploration of cutting-edge trends in transcriptional bursting mechanisms. Moreover, we examined classical methods for parameter estimation that help capture dynamic parameters in gene expression data, assessing their merits and limitations to facilitate optimal parameter estimation. Our comprehensive summary and review of the current transcriptional burst dynamics theories provide deeper insights for promoting research on the nature of cell processes, cell fate determination, and cancer diagnosis.

Natural products from the human microbiome: an emergent frontier in organic synthesis and drug discovery.

Often referred to as the "second genome", the human microbiome is at the epicenter of complex inter-habitat biochemical networks like the "gut-brain axis", which has emerged as a significant determinant of cognition, overall health and well-being, as well as resistance to antibiotics and susceptibility to diseases. As part of a broader understanding of the nexus between the human microbiome, diseases and microbial interactions, whether encoded secondary metabolites (natural products) play crucial signalling roles has been the subject of intense scrutiny in the recent past. A major focus of these activities involves harvesting the genomic potential of the human microbiome via bioinformatics guided genome mining and culturomics. Through these efforts, an impressive number of structurally intriguing antibiotics, with enhanced chemical diversity vis-à-vis conventional antibiotics have been isolated from human commensal bacteria, thereby generating considerable interest in their total synthesis and expanding their therapeutic space for drug discovery. These developments augur well for the discovery of new drugs and antibiotics, particularly in the context of challenges posed by mycobacterial resistance and emerging new diseases. The current landscape of various synthetic campaigns and drug discovery initiatives on antibacterial natural products from the human microbiome is captured in this review with an intent to stimulate further activities in this interdisciplinary arena among the new generation.

Evaluation of mutations on O6-methylguanine methyl transferase structure and its interactions: molecular dynamics simulation study

O6-methylguanine DNA methyl transferase (MGMT) is a significant vehicle for the cellular clearance of alkyl lesions, particularly the methyl group of the O-6 and O-4 positions of guanine and thymine, respectively. Many publications have studied the correlation between polymorphisms in MGMT and susceptibility to various cancers. In the present study, we investigated the consequence of L84F, common single-nucleotide polymorphism, K125E, site-specific mutagenesis, and L84F/K125E on conformation, stability, and behavior of MGMT in the free form and interaction with proliferating cell nuclear antigen (PCNA) and DNA as partners in the biochemical network by using molecular dynamics simulation method. Our results showed that all free variants of MGMT differed from the native form. However, among all free variants of MGMT, the L84F/K125E variant exhibited similar properties compared with the wild-type. In contrast, in complex modes, only amino acid residues of the L84F variant are involved in the interactions with PCNA and DNA somewhat differently relative to the wild-type. Furthermore, L84F SNP showed the highest binding free energy compared to other variants and native forms. These alterations in the amino acids and binding free energy of L84F relative to the native are the reasons for changing its region connection compared to the native form. Therefore, we propose conducting further investigations into the impact of inhibitors or chemotherapeutic agents to assess their effectiveness on MGMT variants compared to the wild-type, aiming to reduce the cost of cancer treatment that will depend on inhibiting native MGMT protein. Communicated by Ramaswamy H. Sarma

A neutral theory of plant carbon allocation.

How plants use the carbon they gain from photosynthesis remains a key area of study among plant ecologists. Although numerous theories have been presented throughout the years, the field lacks a clear null model. To fill this gap, I have developed the first null model, or neutral theory, of plant carbon allocation using probability theory, plant biochemistry and graph theory at the level of a leaf. Neutral theories have been used to establish a null hypothesis in molecular evolution and community assembly to describe how much of an ecological phenomenon can be described by chance alone. Here, the aim of a neutral theory of plant carbon allocation is to ask: how is carbon partitioned between sinks if one assumes plants do not prioritize certain sinks over others? Using the biochemical network of plant carbon metabolism, I show that, if allocation was strictly random, carbon is more likely to be allocated to storage, defense, respiration and finally growth. This 'neutral hierarchy' suggests that a sink's biochemical distance from photosynthesis plays an important role in carbon allocation patterns, highlighting the potentially adaptive role of this biochemical network for plant survival in variable environments. A brief simulation underscores that our ability to measure the carbon allocation from photosynthesis to a given sink is unreliable due to simple probabilistic rules. While neutral theory may not explain all patterns of carbon allocation, its utility is in the minimal assumptions and role as a null model against which future data should be tested.

Response to stress via underlying deep gene regulation networks

Exposure of cells to non‐optimal growth conditions or to any environment that reduces cell viability can be considered as a stress. In this paper, we are going to highlight the main factors that determine the danger of stress to a cell considered as a biochemical system. To this end, we introduce a new mathematical concept of biosystem stability, where we take into account a signal transduction by deep gene networks. Using this concept and known results on approximations by deep networks, we find asymptotic estimates of the size and the depth of gene regulation networks that define the stress response. We propose a new algorithm to find the gene network approximating a prescribed output. It allows us, with the help of Kolmogorov ‐entropy and the deep neural network theory, to estimate the number of genes involved in regulation of responses on a stress (for example, a heat shock). We show that the main factors that increase the sensitivity of the systems with respect to a stress are the number of biochemical network parameters affected by the stress and sensitivities of kinetic rates with respect to these parameters.

Multimolecular Competition Effect as a Modulator of Protein Localization and Biochemical Networks in Cell-Size Space.

Cells are small, closed spaces filled with various types of macromolecules. Although it is shown that the characteristics of biochemical reactions in vitro are quite different from those in living cells, the role of the co-existence of various macromolecules in cell-size space remains still elusive. Here, using a constructive approach, it is demonstrated that the co-existence of various macromolecules themselves has the ability to tune protein localization for spatiotemporal regulation and a biochemical reaction system in a cell-size space. Both experimental and theoretical analyses reveal that enhancement of interfacial effects by a large surface-area-to-volume ratio facilitates membrane localization of molecules in the cell-size space, and the interfacial effects are alleviated by competitive binding to lipid membranes among multiple proteins even if their membrane affinities are weak. These results indicate that competition for membrane binding among various macromolecules in the cell-size space plays a role in regulating the spatiotemporal molecular organization and biochemical reaction networks. These findings shed light on the importance of surrounding molecules for biochemical reactions using purified elements in small spaces.

On Persistence of Some $\mathcal {W}_{I}$-Endotactic Chemical Reaction Networks

Motivated by the concept of the endotactic network, a kind of special geometric structure in chemical reaction networks developed for persistence analysis, we propose a new notion, named <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {W}_{I}$</tex-math></inline-formula> -endotactic network. The corresponding network set is a larger class of set than the endotactic network, let alone the weakly reversible network. Based on an energy-like function, we prove that all 1-dimensional mass-action <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {W}_{I}$</tex-math></inline-formula> -endotactic networks are persistent. Further, we prove some higher dimensional network systems also to support persistence if the system is composed of a series of 1-dimensional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {W}_{I}$</tex-math></inline-formula> -endotactic networks. We discuss two cases for the sub-systems with and without intersecting species, and present the corresponding sufficient conditions to capture persistence. Finally, we use some examples including abstract and real biochemical reaction networks to illustrate our results.

A query-response causal analysis of reaction events in biochemical reaction networks

The stochastic kinetics of biochemical reaction networks is described by a chemical master equation (CME) and the underlying laws of mass action. Assuming network-free simulations of the rule-based models of biochemical reaction networks (BRNs), this paper departs from the usual analysis of network dynamics as the time-dependent distributions of chemical species counts, and instead considers statistically evaluating the sequences of reaction events generated from the stochastic simulations. The reaction event-time series can be used for reaction clustering, identifying rare events, and recognizing the periods of increased or steady-state activity. However, the main aim of this paper is to device an effective method for identifying causally and anti-causally related sub-sequences of reaction events using their empirical probabilities. This allows discovering some of the causal dynamics of BRNs as well as uncovering their short-term deterministic behaviors. In particular, it is proposed that the reaction sub-sequences that are conditionally nearly certain or nearly uncertain can be considered as being causally related. Moreover, since the time-ordering of reaction events is locally irrelevant, the reaction sub-sequences can be transformed into the reaction sets or multi-sets. The distance metrics can be then used to define the equivalences among the reaction events. The proposed method for identifying the causally related reaction sub-sequences has been implemented as a computationally efficient query-response mechanism. The method was evaluated for five models of genetic networks in seven defined numerical experiments. The models were simulated in BioNetGen using the open-source network-free simulator NFsim. This simulator had to be modified first to allow recording the traces of reaction events, and it is available in the Github repository, ploskot/nfsim_1.20. The generated event time-series were analyzed with Python and Matlab scripts. The whole process of data generation, analysis and visualization has been nearly fully automated using shell scripts. This demonstrates the opportunities for substantially increasing the research productivity by creating automated data generation and processing pipelines.

Basic pathway decomposition of biochemical reaction networks within growing cells

This contribution treats linear, steady-state dynamics for a metabolic network within a growing cell. Admissible steady-state reaction fluxes are assumed to form a pointed, convex, polyhedral, conical subset of the stoichiometric null-space. A solution of the problem is defined to consist of a linear basis for the stoichiometric null-space consisting of admissible fluxes called basic pathways. The algorithm used to construct the set of basic pathways scales as a polynomial of the system size in contrast to the NP-hard algorithms employed in the traditional notions of solution named extreme pathways, elementary flux modes, MEMos, and MinSpan, and that therefore suffer from the curse of dimensionality. The basic pathways approach is applied to a metabolic network consisting of a simplified version of the TCA cycle coupled to glycolysis highlighting that each basic pathway has a readily understood chemical interpretation. Generic admissible pathways are simply expressed in terms of basic pathways.

Design Principles for Biological Adaptation: A Systems and Control-Theoretic Treatment.

Establishing a mapping between (from and to) the functionality of interest and the underlying network structure (design principles) remains a crucial step toward understanding and design of bio-systems. Perfect adaptation is one such crucial functionality that enables every living organism to regulate its essential activities in the presence of external disturbances. Previous approaches to deducing the design principles for adaptation have either relied on computationally burdensome brute-force methods or rule-based design strategies detecting only a subset of all possible adaptive network structures. This chapter outlines a scalable and generalizable method inspired by systems theory that unravels an exhaustive set of adaptation-capable structures. We first use the well-known performance parameters to characterize perfect adaptation. These performance parameters are then mapped back to a few parameters (poles, zeros, gain) characteristic of the underlying dynamical system constituted by the rate equations. Therefore, the performance parameters evaluated for the scenario of perfect adaptation can be expressed as a set of precise mathematical conditions involving the system parameters. Finally, we use algebraic graph theory to translate these abstract mathematical conditions to certain structural requirements for adaptation. The proposed algorithm does not assume any particular dynamics and is applicable to networks of any size. Moreover, the results offer a significant advancement in the realm of understanding and designing complex biochemical networks.

Interrogating epigenetic mechanisms with chemically customized chromatin.

Genetic and genomic techniques have proven incredibly powerful for identifying and studying molecular players implicated in the epigenetic regulation of DNA-templated processes such as transcription. However, achieving a mechanistic understanding of how these molecules interact with chromatin to elicit a functional output is non-trivial, owing to the tremendous complexity of the biochemical networks involved. Advances in protein engineering have enabled the reconstitution of 'designer' chromatin containing customized post-translational modification patterns, which, when used in conjunction with sophisticated biochemical and biophysical methods, allow many mechanistic questions to be addressed. In this Review, we discuss how such tools complement established 'omics' techniques to answer fundamental questions on chromatin regulation, focusing on chromatin mark establishment and protein-chromatin interactions.