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STUDY QUESTION What is the recommended management for couples presenting with unexplained infertility (UI), based on the best available evidence in the literature? SUMMARY ANSWER The evidence-based guideline on UI makes 52 recommendations on the definition, diagnosis, and treatment of UI. WHAT IS KNOWN ALREADY UI is diagnosed in the absence of any abnormalities of the female and male reproductive systems after 'standard' investigations. However, a consensual standardization of the diagnostic work-up is still lacking. The management of UI is traditionally empirical. The efficacy, safety, costs, and risks of treatment options have not been subjected to robust evaluation. STUDY DESIGN, SIZE, DURATION The guideline was developed according to the structured methodology for ESHRE guidelines. Following formulation of key questions by a group of experts, literature searches, and assessments were undertaken. Papers written in English and published up to 24 October 2022 were evaluated. PARTICIPANTS/MATERIALS, SETTING, METHODS Based on the available evidence, recommendations were formulated and discussed until consensus was reached within the guideline development group (GDG). Following stakeholder review of an initial draft, the final version was approved by the GDG and the ESHRE Executive Committee. MAIN RESULTS AND THE ROLE OF CHANCE This guideline aims to help clinicians provide the best care for couples with UI. As UI is a diagnosis of exclusion, the guideline outlined the basic diagnostic procedures that couples should/could undergo during an infertility work-up, and explored the need for additional tests. The first-line treatment for couples with UI was deemed to be IUI in combination with ovarian stimulation. The place of additional and alternative options for treatment of UI was also evaluated. The GDG made 52 recommendations on diagnosis and treatment for couples with UI. The GDG formulated 40 evidence-based recommendations—of which 29 were formulated as strong recommendations and 11 as weak—10 good practice points and two research only recommendations. Of the evidence-based recommendations, none were supported by high-quality evidence, one by moderate-quality evidence, nine by low-quality evidence, and 31 by very low-quality evidence. To support future research in UI, a list of research recommendations was provided. LIMITATIONS, REASONS FOR CAUTION Most additional diagnostic tests and interventions in couples with UI have not been subjected to robust evaluation. For a large proportion of these tests and treatments, evidence was very limited and of very low quality. More evidence is required, and the results of future studies may result in the current recommendations being revised. WIDER IMPLICATIONS OF THE FINDINGS The guideline provides clinicians with clear advice on best practice in the care of couples with UI, based on the best evidence currently available. In addition, a list of research recommendations is provided to stimulate further studies in the field. The full guideline and a patient leaflet are available in www.eshre.eu/guideline/UI. STUDY FUNDING/COMPETING INTEREST(S) The guideline was developed by ESHRE, who funded the guideline meetings, literature searches, and dissemination of the guideline in collaboration with the Monash University led Australian NHMRC Centre of Research Excellence in Women's Health in Reproductive Life (CREWHIRL). The guideline group members did not receive any financial incentives; all work was provided voluntarily. D.R. reports honoraria from IBSA and Novo Nordisk. B.A. reports speakers' fees from Merck, Gedeon Richter, Organon and Intas Pharma; is part of the advisory board for Organon Turkey and president of the Turkish Society of Reproductive Medicine. S.B. reports speakers' fees from Merck, Organon, Ferring, the Ostetric and Gynaecological Society of Singapore and the Taiwanese Society for Reproductive Medicine; editor and contributing author, Reproductive Medicine for the MRCOG, Cambridge University Press; is part of the METAFOR and CAPE trials data monitoring committee. E.B. reports research grants from Roche diagnostics, Gedeon Richter and IBSA; speaker's fees from Merck, Ferring, MSD, Roche Diagnostics, Gedeon Richter, IBSA; E.B. is also a part of an Advisory Board of Ferring Pharmaceuticals, MSD, Roche Diagnostics, IBSA, Merck, Abbott and Gedeon Richter. M.M. reports consulting fees from Mojo Fertility Ltd. R.J.N. reports research grant from Australian National Health and Medical Research Council (NHMRC); consulting fees from Flinders Fertility Adelaide, VinMec Hospital Hanoi Vietnam; speaker's fees from Merck Australia, Cadilla Pharma India, Ferring Australia; chair clinical advisory committee Westmead Fertility and research institute MyDuc Hospital Vietnam. T.P. is a part of the Research Council of Finland and reports research grants from Roche Diagnostics, Novo Nordics and Sigrid Juselius foundation; consulting fees from Roche Diagnostics and organon; speaker's fees from Gedeon Richter, Roche, Exeltis, Organon, Ferring and Korento patient organization; is a part of NFOG, AE-PCOS society and several Finnish associations. S.S.R. reports research grants from Roche Diagnostics, Organon, Theramex; consulting fees from Ferring Pharmaceuticals, MSD and Organon; speaker's fees from Ferring Pharmaceuticals, MSD/Organon, Besins, Theramex, Gedeon Richter; travel support from Gedeon Richter; S.S.R. is part of the Data Safety Monitoring Board of TTRANSPORT and deputy of the ESHRE Special Interest Group on Safety and Quality in ART; stock or stock options from IVI Lisboa, Clínica de Reprodução assistida Lda; equipment/medical writing/gifts from Roche Diagnostics and Ferring Pharmaceuticals. S.K.S. reports speakers' fees from Merck, Ferring, MSD, Pharmasure. HRV reports consulting and travel fees from Ferring Pharmaceuticals. The other authors have nothing to disclose. DISCLAIMER This guideline represents the views of ESHRE, which were achieved after careful consideration of the scientific evidence available at the time of preparation. In the absence of scientific evidence on certain aspects, a consensus between the relevant ESHRE stakeholders has been obtained. Adherence to these clinical practice guidelines does not guarantee a successful or specific outcome, nor does it establish a standard of care. Clinical practice guidelines do not replace the need for application of clinical judgment to each individual presentation, nor variations based on locality and facility type. ESHRE makes no warranty, express or implied, regarding the clinical practice guidelines and specifically excludes any warranties of merchantability and fitness for a particular use or purpose. (Full disclaimer available at www.eshre.eu/guidelines.) [ABSTRACT FROM AUTHOR]

Introduction: The 2024 Australian evidence-based guideline for unexplained infertility provides clinicians with evidence-based recommendations for the optimal diagnostic workup for infertile couples to establish the diagnosis of unexplained infertility and optimal therapeutic approach to treat couples diagnosed with unexplained infertility in the Australian health care setting. The guideline recommendations were adapted for the Australian context from the rigorous, comprehensive European Society of Human Reproduction and Embryology (ESHRE) 2023 Evidence-based guideline: unexplained infertility, using the ADAPTE process and have been approved by the Australian National Health and Medical Research Council., Main Recommendations: The guideline includes 40 evidence-based recommendations, 21 practice points and three research recommendations addressing: definition - defining infertility and frequency of intercourse, infertility and age, female and male factor infertility; diagnosis - ovulation, ovarian reserve, tubal factor, uterine factor, laparoscopy, cervical/vaginal factor, male factor, additional testing for systemic conditions; and treatment - expectant management, active treatment, mechanical-surgical procedures, alternative therapeutic approaches, quality of life. CHANGES IN ASSESSMENT AND MANAGEMENT RESULTING FROM THE GUIDELINE: This guideline refines the definition of unexplained infertility and addresses basic diagnostic procedures for infertility assessment not considered in previous guidelines on unexplained infertility. For therapeutic approaches, consideration of evidence quality, efficacy, safety and, in the Australian setting, feasibility, acceptability, cost, implementation and ultimately recommendation strength were integrated across multidisciplinary expertise and consumer perspectives in adapting recommendations to the Australian context by using the Grading of Recommendations, Assessment, Development and Evaluation (GRADE) framework, which had not been used in past guidelines on unexplained infertility to formulate recommendations. The Australian process also included an established data integrity check to ensure evidence could be trusted to guide practice. Practice points were added and expanded to consider the Australian setting. No evidence-based recommendations were underpinned by high quality evidence, with most having low or very low quality evidence. In this context, research recommendations were made including those for the Australian context. The full guideline and technical report are publicly available online and can be accessed at https://www.monash.edu/medicine/mchri/infertility and are supported by extensive translation resources, including the free patient ASKFertility mobile application (https://www.askfertility.org/)., (© 2024 The Author(s). Medical Journal of Australia published by John Wiley & Sons Australia, Ltd on behalf of AMPCo Pty Ltd.)

Ordered distributive double phosphorylation is a recurrent motif in intracellular signaling and control. It is either sequential (where the site phosphorylated last is dephosphorylated first) or cyclic (where the site phosphorylated first is dephosphorylated first). Sequential distributive double phosphorylation has been extensively studied and an inequality involving only the catalytic constants of kinase and phosphatase is known to be sufficient for multistationarity. As multistationarity is necessary for bistability it has been argued that these constants enable bistability. Here we show for cyclic distributive double phosphorylation that if its catalytic constants satisfy an analogous inequality, then Hopf bifurcations and hence sustained oscillations can occur. Hence we argue that in distributive double phosphorylation (sequential or distributive) the catalytic constants enable non-trivial dynamics. In fact, if the rate constant values in a network of cyclic distributive double phosphorylation satisfy this inequality, then a network of sequential distributive double phosphorylation with the same rate constant values will show multistationarity-albeit for different values of the total concentrations. For cyclic distributive double phosphorylation we further describe a procedure to generate rate constant values where Hopf bifurcations and hence sustained oscillations can occur. This may, for example, allow for an efficient sampling of oscillatory regions in parameter space. Our analysis is greatly simplified by the fact that it is possible to reduce the network of cyclic distributive double phosphorylation to what we call a network with a single extreme ray. We summarize key properties of these networks., (© 2024. The Author(s).)

Study Question: What is the recommended management for couples presenting with unexplained infertility (UI), based on the best available evidence in the literature?, Summary Answer: The evidence-based guideline on UI makes 52 recommendations on the definition, diagnosis, and treatment of UI., What Is Known Already: UI is diagnosed in the absence of any abnormalities of the female and male reproductive systems after 'standard' investigations. However, a consensual standardization of the diagnostic work-up is still lacking. The management of UI is traditionally empirical. The efficacy, safety, costs, and risks of treatment options have not been subjected to robust evaluation., Study Design, Size, Duration: The guideline was developed according to the structured methodology for ESHRE guidelines. Following formulation of key questions by a group of experts, literature searches, and assessments were undertaken. Papers written in English and published up to 24 October 2022 were evaluated., Participants/materials, Setting, Methods: Based on the available evidence, recommendations were formulated and discussed until consensus was reached within the guideline development group (GDG). Following stakeholder review of an initial draft, the final version was approved by the GDG and the ESHRE Executive Committee., Main Results and the Role of Chance: This guideline aims to help clinicians provide the best care for couples with UI. As UI is a diagnosis of exclusion, the guideline outlined the basic diagnostic procedures that couples should/could undergo during an infertility work-up, and explored the need for additional tests. The first-line treatment for couples with UI was deemed to be IUI in combination with ovarian stimulation. The place of additional and alternative options for treatment of UI was also evaluated. The GDG made 52 recommendations on diagnosis and treatment for couples with UI. The GDG formulated 40 evidence-based recommendations-of which 29 were formulated as strong recommendations and 11 as weak-10 good practice points and two research only recommendations. Of the evidence-based recommendations, none were supported by high-quality evidence, one by moderate-quality evidence, nine by low-quality evidence, and 31 by very low-quality evidence. To support future research in UI, a list of research recommendations was provided., Limitations, Reasons for Caution: Most additional diagnostic tests and interventions in couples with UI have not been subjected to robust evaluation. For a large proportion of these tests and treatments, evidence was very limited and of very low quality. More evidence is required, and the results of future studies may result in the current recommendations being revised., Wider Implications of the Findings: The guideline provides clinicians with clear advice on best practice in the care of couples with UI, based on the best evidence currently available. In addition, a list of research recommendations is provided to stimulate further studies in the field. The full guideline and a patient leaflet are available in www.eshre.eu/guideline/UI., Study Funding/competing Interest(s): The guideline was developed by ESHRE, who funded the guideline meetings, literature searches, and dissemination of the guideline in collaboration with the Monash University led Australian NHMRC Centre of Research Excellence in Women's Health in Reproductive Life (CREWHIRL). The guideline group members did not receive any financial incentives; all work was provided voluntarily. D.R. reports honoraria from IBSA and Novo Nordisk. B.A. reports speakers' fees from Merck, Gedeon Richter, Organon and Intas Pharma; is part of the advisory board for Organon Turkey and president of the Turkish Society of Reproductive Medicine. S.B. reports speakers' fees from Merck, Organon, Ferring, the Ostetric and Gynaecological Society of Singapore and the Taiwanese Society for Reproductive Medicine; editor and contributing author, Reproductive Medicine for the MRCOG, Cambridge University Press; is part of the METAFOR and CAPE trials data monitoring committee. E.B. reports research grants from Roche diagnostics, Gedeon Richter and IBSA; speaker's fees from Merck, Ferring, MSD, Roche Diagnostics, Gedeon Richter, IBSA; E.B. is also a part of an Advisory Board of Ferring Pharmaceuticals, MSD, Roche Diagnostics, IBSA, Merck, Abbott and Gedeon Richter. M.M. reports consulting fees from Mojo Fertility Ltd. R.J.N. reports research grant from Australian National Health and Medical Research Council (NHMRC); consulting fees from Flinders Fertility Adelaide, VinMec Hospital Hanoi Vietnam; speaker's fees from Merck Australia, Cadilla Pharma India, Ferring Australia; chair clinical advisory committee Westmead Fertility and research institute MyDuc Hospital Vietnam. T.P. is a part of the Research Council of Finland and reports research grants from Roche Diagnostics, Novo Nordics and Sigrid Juselius foundation; consulting fees from Roche Diagnostics and organon; speaker's fees from Gedeon Richter, Roche, Exeltis, Organon, Ferring and Korento patient organization; is a part of NFOG, AE-PCOS society and several Finnish associations. S.S.R. reports research grants from Roche Diagnostics, Organon, Theramex; consulting fees from Ferring Pharmaceuticals, MSD and Organon; speaker's fees from Ferring Pharmaceuticals, MSD/Organon, Besins, Theramex, Gedeon Richter; travel support from Gedeon Richter; S.S.R. is part of the Data Safety Monitoring Board of TTRANSPORT and deputy of the ESHRE Special Interest Group on Safety and Quality in ART; stock or stock options from IVI Lisboa, Clínica de Reprodução assistida Lda; equipment/medical writing/gifts from Roche Diagnostics and Ferring Pharmaceuticals. S.K.S. reports speakers' fees from Merck, Ferring, MSD, Pharmasure. HRV reports consulting and travel fees from Ferring Pharmaceuticals. The other authors have nothing to disclose., Disclaimer: This guideline represents the views of ESHRE, which were achieved after careful consideration of the scientific evidence available at the time of preparation. In the absence of scientific evidence on certain aspects, a consensus between the relevant ESHRE stakeholders has been obtained. Adherence to these clinical practice guidelines does not guarantee a successful or specific outcome, nor does it establish a standard of care. Clinical practice guidelines do not replace the need for application of clinical judgment to each individual presentation, nor variations based on locality and facility type. ESHRE makes no warranty, express or implied, regarding the clinical practice guidelines and specifically excludes any warranties of merchantability and fitness for a particular use or purpose. (Full disclaimer available at www.eshre.eu/guidelines.)., (© The Author(s) 2023. Published by Oxford University Press on behalf of European Society of Human Reproduction and Embryology.)

Delay differential equations are used as a model when the effect of past states has to be taken into account. In this work we consider delay models of chemical reaction networks with mass action kinetics. We obtain a sufficient condition for absolute delay stability of equilibrium concentrations, i.e., local asymptotic stability independent of the delay parameters. Several interesting examples on sequestration networks with delays are presented., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 Elsevier Inc. All rights reserved.)

Protein phosphorylation cycles are important mechanisms of the post translational modification of a protein and as such an integral part of intracellular signaling and control. We consider the sequential phosphorylation and dephosphorylation of a protein at two binding sites. While it is known that proteins where phosphorylation is processive and dephosphorylation is distributive admit oscillations (for some value of the rate constants and total concentrations) it is not known whether or not this is the case if both phosphorylation and dephosphorylation are distributive. We study simplified mass action models of sequential and distributive phosphorylation and show that for each of those there do not exist rate constants and total concentrations where a Hopf bifurcation occurs. To arrive at this result we use convex parameters to parametrize the steady state and Hurwitz matrices.

The commercial asset value of sequestered forest carbon is based on protocols employed globally; however, their scientific basis has not been validated. We review and analyze commercial forest carbon protocols, claimed to have reduced net greenhouse gas emissions, issued by the California Air Resources Board and validated by the Climate Action Reserve (CARB-CAR). CARB-CAR forest carbon offsets, based on forest mensuration and model simulation, are compared to a global database of directly measured forest carbon sequestration, or net ecosystem exchange (NEE) of forest CO 2 . NEE is a meteorologically based method integrating CO 2 fluxes between the atmosphere, forest and soils and is independent of the CARB-CAR methodology. Annual carbon accounting results for CAR681 are compared with NEE for the Ameriflux site, Howland Forest Maine, USA, (Ho-1), the only site where both methods were applied contemporaneously, invalidating CARB-CAR protocol offsets. We then test the null hypothesis that CARB-CAR project population data fall within global NEE population values for natural and managed forests measured in the field; net annual gC m -2 yr -1 are compared for both protocols. Irrespective of geography, biome and project type, the CARB-CAR population mean is significantly different from the NEE population mean at the 95% confidence interval, rejecting the null hypothesis. The CARB-CAR population exhibits standard deviation ∼5× that of known interannual NEE ranges, is overcrediting biased, incapable of detecting forest transition to net positive CO 2 emissions, and exceeds the 5% CARB compliance limit for invalidation. Exclusion of CO 2 efflux via soil and ecosystem respiration precludes a valid net carbon accounting result for CARB-CAR and related protocols, consistent with our findings. Protocol invalidation risk extends to vendors and policy platforms such as the United Nations Program on Reducing Emissions from Deforestation and Forest Degradation (REDD+) and the Paris Agreement. We suggest that CARB-CAR and related protocols include NEE methodology for commercial forest carbon offsets to standardize methods, ensure in situ molecular specificity, verify claims of carbon emission reduction and harmonize carbon protocols for voluntary and compliance markets worldwide., Competing Interests: Bruno D.V. Marino is an Academic Editor for PeerJ. Bruno D.V. Marino and Aaron Doucett are unpaid associates of Planetary Emissions Management Inc., (©2019 Marino et al.)

This work investigates the emergence of oscillations in one of the simplest cellular signaling networks exhibiting oscillations, namely the dual-site phosphorylation and dephosphorylation network (futile cycle), in which the mechanism for phosphorylation is processive, while the one for dephosphorylation is distributive (or vice versa). The fact that this network yields oscillations was shown recently by Suwanmajo and Krishnan. Our results, which significantly extend their analyses, are as follows. First, in the three-dimensional space of total amounts, the border between systems with a stable versus unstable steady state is a surface defined by the vanishing of a single Hurwitz determinant. Second, this surface consists generically of simple Hopf bifurcations. Next, simulations suggest that when the steady state is unstable, oscillations are the norm. Finally, the emergence of oscillations via a Hopf bifurcation is enabled by the catalytic and association constants of the distributive part of the mechanism; if these rate constants satisfy two inequalities, then the system generically admits a Hopf bifurcation. Our proofs are enabled by the Routh-Hurwitz criterion, a Hopf bifurcation criterion due to Yang, and a monomial parametrization of steady states.

Study Question: Can enzymatically dispersed testicular cells from adult men reassemble into seminiferous cord-like structures in vitro?, Summary Answer: Adult human testicular somatic cells reassembled into testicular cord-like structures via dynamic interactions of Sertoli and peritubular cells., What Is Known Already: In vitro approaches using dispersed single cell suspensions of human testes to generate seminiferous tubule structures and to initiate their functionality have as yet shown only limited success., Study Design, Size, Duration: Testes from 15 adult gender dysphoria patients (mean ± standard deviation age 35 ± 9.3 years) showing spermatogonial arrest became available for this study after sex-reassignment surgery. In vitro primary testicular somatic cell cultures were generated to explore the self-organizing ability of testicular somatic cells to form testis cords over a 2-week period. Morphological phenotype, protein marker expression and temporal dynamics of cell reassembly were analyzed., Participants/materials, Setting, Methods: Cell suspensions obtained by two-step enzymatic digestion were plated onto glass coverslips in 24-well plates. To obtain adherent somatic cells, the supernatant was discarded on Day 2. The culture of the attached cell population was continued. Reassembly into cord-like structures was analyzed daily by microscopic observations. Endpoints were qualitative changes in morphology. Cell types were characterized by phase-contrast microscopy and immunohistochemistry. Dynamics of cord formation were recorded by time-lapse microscopy., Main Results and the Role of Chance: Primary adult human testicular cells underwent sequential morphological changes including compaction and reaggregation resulting in round or elongated cord-like structures. Time-lapse video recordings within the first 4 days of culture revealed highly dynamic processes of migration and coalescence of reaggregated cells. The cellular movements were mediated by peritubular cells. Immunohistochemical analysis showed that both SRY-related high mobility box 9-positive Sertoli and α-smooth muscle actin-positive peritubular myoid cells interacted and contributed to cord-like structure formation., Large Scale Data: Not applicable., Limitations, Reasons for Caution: Owing to scarcity of normal human testicular tissue, testes from gender dysphoria patients were used in the study. The regressed status might influence the experimental responses of primary cells. We observed basic morphological features resembling in vivo testicular cords, however, the proof of functionality (e.g. support of germ cells) will need further studies., Wider Implications of the Findings: The proposed in vitro culture system may open opportunities for examination of testicular cell interactions during testicular tubulogenesis. Further refinement of our approach may enable initiation of ex vivo spermatogenesis., Study Funding/competing Interests: The work was supported by EU-FP7-PEOPLE-2013-ITN 603568: 'Growsperm'. No conflict of interests is declared., (© The Author 2017. Published by Oxford University Press on behalf of the European Society of Human Reproduction and Embryology. All rights reserved. For Permissions, please email: journals.permissions@oup.com)

Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative features, such as switching behaviour, bistability or oscillations. Mathematically, the latter question amounts to identifying parameter values associated with a given qualitative feature. We introduce a procedure to partition the parameter space of a parameterized system of ordinary differential equations into regions for which the system has a unique or multiple equilibria. The procedure is based on the computation of the Brouwer degree, and it creates a multivariate polynomial with parameter depending coefficients. The signs of the coefficients determine parameter regions with and without multistationarity. A particular strength of the procedure is the avoidance of numerical analysis and parameter sampling. The procedure consists of a number of steps. Each of these steps might be addressed algorithmically using various computer programs and available software, or manually. We demonstrate our procedure on several models of gene transcription and cell signalling, and show that in many cases we obtain a complete partitioning of the parameter space with respect to multistationarity.

A parametric sensitivity analysis for periodic solutions of delay-differential equations is developed. Because phase shifts cause the sensitivity coefficients of a periodic orbit to diverge, we focus on sensitivities of the extrema, from which amplitude sensitivities are computed, and of the period. Delay-differential equations are often used to model gene expression networks. In these models, the parametric sensitivities of a particular genotype define the local geometry of the evolutionary landscape. Thus, sensitivities can be used to investigate directions of gradual evolutionary change. An oscillatory protein synthesis model whose properties are modulated by RNA interference is used as an example. This model consists of a set of coupled delay-differential equations involving three delays. Sensitivity analyses are carried out at several operating points. Comments on the evolutionary implications of the results are offered.

Dual phosphorylation of proteins is a principal component of intracellular signalling. Bistability is considered an important property of such systems and its origin is not yet completely understood. Theoretical studies have established parameter values for multistationarity and bistability for many types of proteins. However, up to now no formal criterion linking multistationarity and bistability to the parameter values characterizing dual phosphorylation has been established. Deciding whether an unclassified protein has the capacity for bistability, therefore requires careful numerical studies. Here, we present two general algebraic conditions in the form of inequalities. The first employs the catalytic constants, and if satisfied guarantees multistationarity (and hence the potential for bistability). The second involves the catalytic and Michaelis constants, and if satisfied guarantees uniqueness of steady states (and hence absence of bistability). Our method also allows for the direct computation of the total concentration values such that multistationarity occurs. Applying our results yields insights into the emergence of bistability in the ERK-MEK-MKP system that previously required a delicate numerical effort. Our algebraic conditions present a practical way to determine the capacity for bistability and hence will be a useful tool for examining the origin of bistability in many models containing dual phosphorylation.

Background: A biochemical mechanism with mass action kinetics can be represented as a directed bipartite graph (bipartite digraph), and modeled by a system of differential equations. If the differential equations (DE) model can give rise to some instability such as multistability or Turing instability, then the bipartite digraph contains a structure referred to as a critical fragment. In some cases the existence of a critical fragment indicates that the DE model can display oscillations for some parameter values. We have implemented a graph-theoretic method that identifies the critical fragments of the bipartite digraph of a biochemical mechanism., Results: GraTeLPy lists all critical fragments of the bipartite digraph of a given biochemical mechanism, thus enabling a preliminary analysis on the potential of a biochemical mechanism for some instability based on its topological structure. The correctness of the implementation is supported by multiple examples. The code is implemented in Python, relies on open software, and is available under the GNU General Public License., Conclusions: GraTeLPy can be used by researchers to test large biochemical mechanisms with mass action kinetics for their capacity for multistability, oscillations and Turing instability.

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented.

Systems biologists increasingly use network representations to investigate biochemical pathways and their dynamic behaviours. In this critical review, we discuss four commonly used network representations of chemical and biochemical pathways. We illustrate how some of these representations reduce network complexity but result in the ambiguous representation of biochemical pathways. We also examine the current theoretical approaches available to investigate the dynamic behaviour of chemical and biochemical networks. Finally, we describe how the critical chemical and biochemical pathways responsible for emergent dynamic behaviour can be identified using network mining and functional mapping approaches.

We describe a necessary condition for zero-eigenvalue Turing instability, i.e., Turing instability arising from a real eigenvalue changing sign from negative to positive, for general chemical reaction networks modeled with mass-action kinetics. The reaction mechanisms are represented by the species-reaction graph (SR graph), which is a bipartite graph with different nodes representing species and reactions. If the SR graph satisfies certain conditions, similar to the conditions for ruling out multiple equilibria in spatially homogeneous differential equations systems, then the corresponding mass-action reaction-diffusion system cannot exhibit zero-eigenvalue Turing instability for any parameter values. On the other hand, if the graph-theoretic condition for ruling out zero-eigenvalue Turing instability is not satisfied, then the corresponding model may display zero-eigenvalue Turing instability for some parameter values. The technique is illustrated with a model of a bifunctional enzyme.

Network conditions for Turing instability in biochemical systems with two biochemical species are well known and involve autocatalysis or self-activation. On the other hand general network conditions for potential Turing instabilities in large biochemical reaction networks are not well developed. A biochemical reaction network with any number of species where only one species moves is represented by a simple digraph and is modeled by a reaction-diffusion system with non-mass action kinetics. A graph-theoretic condition for potential Turing-Hopf instability that arises when a spatially homogeneous equilibrium loses its stability via a single pair of complex eigenvalues is obtained. This novel graph-theoretic condition is closely related to the negative cycle condition for oscillations in ordinary differential equation models and its generalizations, and requires the existence of a pair of subnetworks, each containing an even number of positive cycles. The technique is illustrated with a double-cycle Goodwin type model., (Copyright © 2012 Elsevier Inc. All rights reserved.)

Biochemical reaction models show a variety of dynamical behaviors, such as stable steady states, multistability, and oscillations. Biochemical reaction networks with generalized mass action kinetics are represented as directed bipartite graphs with nodes for species and reactions. The bipartite graph of a biochemical reaction network usually contains at least one cycle, i.e., a sequence of nodes and directed edges which starts and ends at the same species node. Cycles can be positive or negative, and it has been shown that oscillations can arise as a result of either a positive cycle or a negative cycle. In earlier work it was shown that oscillations associated with a positive cycle can arise from subnetworks with an odd number of positive cycles. In this article we formulate a similar graph-theoretic condition, which generalizes the negative cycle condition for oscillations. This new graph-theoretic condition for oscillations involves pairs of subnetworks with an even number of positive cycles. An example of a calcium reaction network with generalized mass action kinetics is discussed in detail.

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied.

Delay-differential equations are commonly used to model genetic regulatory systems with the delays representing transcription and translation times. Equations with delayed terms can also be used to represent other types of chemical processes. Here we analyze delayed mass-action systems, i.e. systems in which the rates of reaction are given by mass-action kinetics, but where the appearance of products may be delayed. Necessary conditions for delay-induced instability are presented in terms both of a directed graph (digraph) constructed from the Jacobian matrix of the corresponding ODE model and of a species-reaction bipartite graph which directly represents a chemical mechanism. Methods based on the bipartite graph are particularly convenient and powerful. The condition for a delay-induced instability in this case is the existence of a subgraph of the bipartite graph containing an odd number of cycles of which an odd number are negative.

A chemical mechanism is a model of a chemical reaction network consisting of a set of elementary reactions that express how molecules react with each other. In classical mass-action kinetics, a mechanism implies a set of ordinary differential equations (ODEs) which govern the time evolution of the concentrations. In this article, ODE models of chemical kinetics that have the potential for multiple positive equilibria or oscillations are studied. We begin by considering some methods of stability analysis based on the digraph of the Jacobian matrix. We then prove two theorems originally given by A. N. Ivanova which correlate the bifurcation structure of a mass-action model to the properties of a bipartite graph with nodes representing chemical species and reactions. We provide several examples of the application of these theorems.

The conditions for diffusion-driven (Turing) instabilities in systems with two reactive species are well known. General methods for detecting potential Turing bifurcations in larger reaction schemes are, on the other hand, not well developed. We prove a theorem for a graph-theoretic condition originally given by Volpert and Ivanova [Mathematical Modeling (Nauka, Moscow, 1987) (in Russian), p. 57] for Turing instabilities in a mass-action reaction-diffusion system involving n substances. The method is based on the representation of a reaction mechanism as a bipartite graph with two types of nodes representing chemical species and reactions, respectively. The condition for diffusion-driven instability is related to the existence of a structure in the graph known as a critical fragment. The technique is illustrated using a substrate-inhibited bifunctional enzyme mechanism which involves seven chemical species.