On BIOCHAM Symbolic Computation Pipeline for Compiling Mathematical Functions into Biochemistry

Chemical reaction networks (CRNs) are a standard formalism used in chemistry and biology to reason about the dynamics of molecular interaction networks. In their interpretation by ordinary differential equations, CRNs provide a Turing-complete model of analog computation, in the sense that any computable function over the reals can be computed by a finite number of molecular species with a continuous CRN which approximates the result of that function in one of its components in arbitrary precision. The proof of that result is based on a previous result of Bournez et al. on the Turing-completeness of polynomial ordinary differential equations with polynomial initial conditions (PIVP). It uses an encoding of real variables by two non-negative variables for concentrations, and a transformation to an equivalent quadratic PIVP (i.e. with degrees at most 2) for restricting ourselves to at most bimolecular reactions. In this paper, we study the theoretical and practical complexities of the quadratic transformation. We show that both problems of minimizing either the number of variables (i.e., molecular species) or the number of monomials (i.e. elementary reactions) in a quadratic transformation of a PIVP are NP-hard. We present an encoding of those problems in MAX-SAT and show the practical complexity of this algorithm on a benchmark of quadratization problems inspired from CRN design problems.

Chemical Reaction Networks (CRNs) provide a useful abstraction of molecular interaction networks in which molecular structures as well as mass conservation principles are abstracted away to focus on the main dynamical properties of the network structure. In their interpretation by ordinary differential equations, we say that a CRN with distinguished input and output species computes a positive real function \(f:\mathbb {R}_{+}\rightarrow \mathbb {R}_{+}\), if for any initial concentration x of the input species, the concentration of the output molecular species stabilizes at concentration f(x). The Turing-completeness of that notion of chemical analog computation has been established by proving that any computable real function can be computed by a CRN over a finite set of molecular species. Rate-independent CRNs form a restricted class of CRNs of high practical value since they enjoy a form of absolute robustness in the sense that the result is completely independent of the reaction rates and depends solely on the input concentrations. The functions computed by rate-independent CRNs have been characterized mathematically as the set of piecewise linear functions from input species. However, this does not provide a mean to decide whether a given CRN is rate-independent. In this paper, we provide graphical conditions on the Petri Net structure of a CRN which entail the rate-independence property either for all species or for some output species. We show that in the curated part of the Biomodels repository, among the 590 reaction models tested, 2 reaction graphs were found to satisfy our rate-independence conditions for all species, 94 for some output species, among which 29 for some non-trivial output species. Our graphical conditions are based on a non-standard use of the Petri net notions of place-invariants and siphons which are computed by constraint programming techniques for efficiency reasons.

Whereas germline-inherited whole-chromosome aneuploidy has long been known to cause miscarriages and developmental abnormalities, somatically acquired aneuploidies have been observed in cancer cells and more recently also in cells of the normal liver and brain. Furthermore, aneuploidy is being increasingly reported in clinical isolates of pathogenic microbes such as fungi and parasites. Whereas many efforts have been devoted to the dissection of the molecular mechanisms that lead to aneuploidy, we have only recently started to investigate how aneuploidy alters the phenotypic makeup of a cell. Here we review recent evidence supporting the idea that aneuploidy is a large-effect mutation that introduces large changes in the cellular phenome. From a systems biology perspective, this can be explained by the extensive changes that aneuploidy brings about in both the transcriptome and the proteome of a cell. We further provide an evolutionary perspective on how aneuploidy-induced phenotypic variation may contribute to the exacerbation of human pathologies such as cancer and infectious diseases, by conferring selectable traits such as increased virulence and drug resistance.

Reaction networks and kinetics of biochemical systems

MotivationNeurodegenerative diseases (NDs), including amyotrophic lateral sclerosis, Parkinson's disease, Alzheimer's disease, and Huntington's disease, occur as a result of neurodegenerative processes. Thus, it has been increasingly appreciated that many neurodegenerative conditions overlap at multiple levels. However, traditional clinicopathological correlation approaches to better classify a disease have met with limited success. Discovering this overlap offers hope for therapeutic advances that could ameliorate many ND simultaneously. In parallel, in the last decade, systems biology approaches have become a reliable choice in complex disease analysis for gaining more delicate biological insights and have enabled the comprehension of the higher order functions of the biological systems.ResultsToward this orientation, we developed a systems biology approach for the identification of common links and pathways of ND, based on well-established and novel topological and functional measures. For this purpose, a molecular pathway network was constructed, using molecular interactions and relations of four main neurodegenerative diseases (Alzheimer's disease, Parkinson's disease, amyotrophic lateral sclerosis, and Huntington's disease). Our analysis captured the overlapped subregions forming molecular subpathways fully enriched in these four NDs. Also, it exported molecules that act as bridges, hubs, and key players for neurodegeneration concerning either their topology or their functional role.ConclusionUnderstanding these common links and central topologies under the perspective of systems biology and network theory and greater insights are provided to uncover the complex neurodegeneration processes.

Systems biology views a living organism as an interacting and dynamical network of genes, proteins, and biochemical reactions which give rise to the function and behavior of that organism, and is considered as a powerfully analytical approach to reveal the essential mechanisms of initiation and progression for complex diseases such as cancer, cardiovascular disease, and diabetes. The classical bio-medicine based on molecular biology, cell biology, genetics, and other experimental biology has made significant progress against diseases in general. However, the researchers on the biomedicine area still face the great challenge against the complex diseases, since the methodology of the classical experimental biology is mainly based on studying individual genes and proteins and treating organisms as simple and linear systems, which are not good enough to solve increasingly complicated problems of the diseases. Therefore, the methodologies and techniques of systems biology are strongly demanded for analyzing the molecular mechanisms of the complex diseases and providing new solutions to fight the complex diseases. The aim of this special issue is to collect the latest advances in developing new computational and experimental approaches to decipher the complexity of diseases or on providing the implications and explanations for disease mechanisms and therapeutic endeavors in drug research, from systems biology perspective. In this issue, there are two review papers, three research articles and two letters, which present recent research efforts in various aspects for understanding mechanisms of the complex diseases, including prostate cancer, ovarian cancer, liver cancer, diabetes, and neuronal

Quantifying effects of stochastic focusing and defocusing on noise propagation in biochemical reaction networks

With a view towards artificial cells, molecular communication systems, molecular multiagent systems and federated learning, we propose a novel reaction network scheme (termed the Baum–Welch (BW) reaction network) that learns parameters for hidden Markov models (HMMs). All variables including inputs and outputs are encoded by separate species. Each reaction in the scheme changes only one molecule of one species to one molecule of another. The reverse change is also accessible but via a different set of enzymes, in a design reminiscent of futile cycles in biochemical pathways. We show that every positive fixed point of the BW algorithm for HMMs is a fixed point of the reaction network scheme, and vice versa. Furthermore, we prove that the ‘expectation’ step and the ‘maximization’ step of the reaction network separately converge exponentially fast and compute the same values as the E-step and the M-step of the BW algorithm. We simulate example sequences, and show that our reaction network learns the same parameters for the HMM as the BW algorithm, and that the log-likelihood increases continuously along the trajectory of the reaction network.

Tumorigenesis is closely and highly associated with developmental biology. The present study aimed to discover and identify marker proteins strongly associated with the occurrence and development of non‑small cell lung cancer (NSCLC) in humans and to provide new ideas for investigating lung cancer markers by combining biological analyses of embryonic development. We established primary cultures for samples of tumor and control tissues from 9patients with NSCLC and collected conditioned medium (CM). Subsequently, we used liquid chromatography and linear ion trap (LTQ) mass spectrometry to isolate and identify proteins in CM samples. Data mining of free proteins was conducted using the analogous analysis strategy in systems biology to obtain important lung cancer‑associated proteins (plasma markers). Proteins with significant plasma enrichment in lung cancer patients were detected via enzyme‑linked immunosorbent assay (ELISA). We identified 987high‑confidence proteins and established a primary database of free proteins associated with lung cancer. Furthermore, 511high‑confidence proteins were present in CM from primary tissue cultures from at least 2of the 9examined cases of lung cancer. Analysis using Gene Set Enrichment Analysis (GSEA) software revealed significant enrichment for 197proteins from the CM of lung cancer samples in maternal‑placental interface expression profiles for a mid‑term placenta with strong invasiveness relative to RNA expression profiles for a human full‑term placenta after delivery. ELISA results demonstrated that hypoxanthine phosphoribosyltransferase1 (HPRT1) was associated with worse rates of disease‑free survival (DFS) and overall survival (OS). The biological behaviors of embryonic implantation are similar to those of tumor invasion and metastasis, and the information obtained regarding developmental biology could facilitate the interpretation of tumor invasion and metastasis. Therefore, similar biological behaviors combined with analyses at different molecular levels from the perspective of systems biology will provide new ideas for tumor research.

Vascular dementia is the second most common cause of dementia, with clinical features that depend on neural substrates affected by the vascular lesions. Like most neurological disorders, it involves alterations that range from the molecular level to neuronal networks. Such alterations begin as compensatory mechanisms that reshape every subsystem involved in the brain's homeostasis. Although there have been recent huge advances in understanding the pathophysiology of cognitive dysfunction, a suitable therapeutic approach to vascular dementia remains elusive. Pharmacological interventions have failed to sustainably improve cognitive function, and it is a well-known fact that there is a need to change the current view for providing neuroprotection and enhancing neurorecovery after stroke. Studies regarding cognitive training are also faced with the difficulty of drawing up protocols that can embrace a holistic approach in cognitively impaired patients. This review will present a brief synthesis of current results from basic research data and clinical studies regarding pharmacological and non-pharmacological interventions in vascular dementia and will offer an integrated view from the perspective of systems biology.

0499 Use of an integrated multi-omics approach to unlock advantage of natural products for tone management: San Bai Decoction as case study

Leaf herbivory on tea plants ( Camellia sinensis) by tea geometrids ( Ectropis oblique) severely threaten the yield and quality of tea. In previous work, we found that local defense response was induced in damaged leaves by geometrids at the transcriptome level. Here, we investigated the systemic response triggered in undamaged roots and the potential role of roots in response to leaf herbivory. Comparative transcriptome analysis and carbohydrate dynamics indicated that leaf herbivory activated systemic carbon reallocation to enhance resource investment for local secondary metabolism. The crucial role of jasmonic acid and the involvement of other potential hormone signals for local and systemic signaling networks were supported by phytohormone quantification and dynamic expression analysis of phytohormone-related genes. This work represents a deep understanding of the interaction of tea plants and geometrids from the perspective of systems biology and reveals that tea plants have evolved an intricate root-mediated resource-based resistance strategy to cope with geometrid attack.

Recent computational and experimental work suggests that functional modules underlie much of cellular physiology and are a useful unit of cellular organization from the perspective of systems biology. Because interactions among modules can give rise to higher-level properties that are essential to cellular function, a complete knowledge of these interactions is necessary for future work in systems biology, including in silico modeling and metabolic engineering. Here we present a computational method for the systematic identification and analysis of functional modules whose activity is coordinated at the level of transcription. We applied this method, Search for Pairwise Interactions (SPIN), to obtain a global view of functional module connectivity in Saccharomyces cerevisiae and to provide insight into the biological mechanisms underlying this coordination. We also examined this global network at higher resolution to obtain detailed information about the interactions of particular module pairs. For instance, our results reveal possible transcriptional coordination of glycolysis and lipid metabolism by the transcription factor Gcr1p, and further suggest that glycolysis and phosphoinositide signaling may regulate each other reciprocally.

Spontaneous ultra-weak photon emission in correlation to inflammatory metabolism and oxidative stress in a mouse model of collagen-induced arthritis

MotivationThe growing complexity of reaction-based models necessitates early detection and resolution of model errors. Considerable work has been done on the detection of mass balance errors, especially atomic mass analysis (AMA) (which compares the counts of atoms in the reactants and products) and Linear Programming analysis (which detects stoichiometric inconsistencies). This article extends model error checking to include: (i) certain structural errors in reaction networks and (ii) error isolation. First, we consider the balance of chemical structures (moieties) between reactants and products. This balance is expected in many biochemical reactions, but the imbalance of chemical structures cannot be detected if the analysis is done in units of atomic masses. Second, we improve on error isolation for stoichiometric inconsistencies by identifying a small number of reactions and/or species that cause the error. Doing so simplifies error remediation.ResultsWe propose two algorithms that address isolating structural errors in reaction networks. Moiety analysis finds imbalances of moieties using the same algorithm as AMA, but moiety analysis works in units of moieties instead of atomic masses. We argue for the value of checking moiety balance, and discuss two approaches to decomposing chemical species into moieties. Graphical Analysis of Mass Equivalence Sets (GAMES) provides isolation for stoichiometric inconsistencies by constructing explanations that relate errors in the structure of the reaction network to elements of the reaction network. We study the effectiveness of moiety analysis and GAMES on curated models in the BioModels repository. We have created open source codes for moiety analysis and GAMES.Availability and implementationOur project is hosted at https://github.com/ModelEngineering/SBMLLint, which contains examples, documentation, source code files and build scripts used to create SBMLLint. Our source code is licensed under the MIT open source license.Supplementary informationSupplementary data are available at Bioinformatics online.