47 results found
Thomas P, Shahrezaei V, 2021, Coordination of gene expression noise with cell size: analytical results for agent-based models of growing cell populations, Journal of the Royal Society Interface, Vol: 18, Pages: 1-16, ISSN: 1742-5662
The chemical master equation and the Gillespie algorithm are widely used to model the reaction kinetics inside living cells. It is thereby assumed that cell growth and division can be modelled through effective dilution reactions and extrinsic noise sources. We here re-examine these paradigms through developing an analytical agent-based framework of growing and dividing cells accompanied by an exact simulation algorithm, which allows us to quantify the dynamics of virtually any intracellular reaction network affected by stochastic cell size control and division noise. We find that the solution of the chemical master equation—including static extrinsic noise—exactly agrees with the agent-based formulation when the network under study exhibits stochastic concentration homeostasis, a novel condition that generalizes concentration homeostasis in deterministic systems to higher order moments and distributions. We illustrate stochastic concentration homeostasis for a range of common gene expression networks. When this condition is not met, we demonstrate by extending the linear noise approximation to agent-based models that the dependence of gene expression noise on cell size can qualitatively deviate from the chemical master equation. Surprisingly, the total noise of the agent-based approach can still be well approximated by extrinsic noise models.
Beltran T, Shahrezaei V, Katju V, et al., 2020, Epimutations driven by small RNAs arise frequently but most have limited duration in Caenorhabditis elegans, Nature Ecology and Evolution, Vol: 4, Pages: 1539-1548, ISSN: 2397-334X
Epigenetic regulation involves changes in gene expression independent of DNA sequence variation that are inherited through cell division. In addition to a fundamental role in cell differentiation, some epigenetic changes can also be transmitted transgenerationally through meiosis. Epigenetic alterations (epimutations) could thus contribute to heritable variation within populations and be subject to evolutionary processes such as natural selection and drift. However, the rate at which epimutations arise and their typical persistence are unknown, making it difficult to evaluate their potential for evolutionary adaptation. Here, we perform a genome-wide study of epimutations in a metazoan organism. We use experimental evolution to characterize the rate, spectrum and stability of epimutations driven by small silencing RNAs in the model nematode Caenorhabditis elegans. We show that epimutations arise spontaneously at a rate approximately 25 times greater than DNA sequence changes and typically have short half-lives of two to three generations. Nevertheless, some epimutations last at least ten generations. Epimutations mediated by small RNAs may thus contribute to evolutionary processes over a short timescale but are unlikely to bring about long-term divergence in the absence of selection.
Bertaux F, von Kugelgen J, Marguerat S, et al., 2020, A bacterial size law revealed by a coarse-grained model of cell physiology, PLOS COMPUTATIONAL BIOLOGY, Vol: 16, ISSN: 1553-734X
Rodosthenous T, Shahrezaei V, Evangelou M, 2020, Integrating multi-OMICS data through sparse Canonical Correlation Analysis for the prediction of complex traits: A comparison study, Bioinformatics, Vol: 36, Pages: 4616-4625, ISSN: 1367-4803
MotivationRecent developments in technology have enabled researchers to collect multiple OMICS datasets for the same individuals. The conventional approach for understanding the relationships between the collected datasets and the complex trait of interest would be through the analysis of each OMIC dataset separately from the rest, or to test for associations between the OMICS datasets. In this work we show that integrating multiple OMICS datasets together, instead of analysing them separately, improves our understanding of their in-between relationships as well as the predictive accuracy for the tested trait. Several approaches have been proposed for the integration of heterogeneous and high-dimensional (p ≫ n) data, such as OMICS. The sparse variant of Canonical Correlation Analysis (CCA) approach is a promising one that seeks to penalise the canonical variables for producing sparse latent variables while achieving maximal correlation between the datasets. Over the last years, a number of approaches for implementing sparse CCA (sCCA) have been proposed, where they differ on their objective functions, iterative algorithm for obtaining the sparse latent variables and make different assumptions about the original datasets.ResultsThrough a comparative study we have explored the performance of the conventional CCA proposed by Parkhomenko et al. (2009), penalised matrix decomposition CCA proposed by Witten and Tibshirani (2009) and its extension proposed by Suo et al. (2017). The aforementioned methods were modified to allow for different penalty functions. Although sCCA is an unsupervised learning approach for understanding of the in-between relationships, we have twisted the problem as a supervised learning one and investigated how the computed latent variables can be used for predicting complex traits. The approaches were extended to allow for multiple (more than two) datasets where the trait was included as one of the input datasets. Both ways have shown improvement
Sun X-M, Bowman A, Priestman M, et al., 2020, Size-Dependent Increase in RNA Polymerase II Initiation Rates Mediates Gene Expression Scaling with Cell Size., Curr Biol, Vol: 30, Pages: 1217-1230.e7
Cell size varies during the cell cycle and in response to external stimuli. This requires the tight coordination, or "scaling," of mRNA and protein quantities with the cell volume in order to maintain biomolecule concentrations and cell density. Evidence in cell populations and single cells indicates that scaling relies on the coordination of mRNA transcription rates with cell size. Here, we use a combination of single-molecule fluorescence in situ hybridization (smFISH), time-lapse microscopy, and mathematical modeling in single fission yeast cells to uncover the precise molecular mechanisms that control transcription rates scaling with cell size. Linear scaling of mRNA quantities is apparent in single fission yeast cells during a normal cell cycle. Transcription of both constitutive and periodic genes is a Poisson process with transcription rates scaling with cell size and without evidence for transcriptional off states. Modeling and experimental data indicate that scaling relies on the coordination of RNA polymerase II (RNAPII) transcription initiation rates with cell size and that RNAPII is a limiting factor. We show using real-time quantitative imaging that size increase is accompanied by a rapid concentration-independent recruitment of RNAPII onto chromatin. Finally, we find that, in multinucleated cells, scaling is set at the level of single nuclei and not the entire cell, making the nucleus a determinant of scaling. Integrating our observations in a mechanistic model of RNAPII-mediated transcription, we propose that scaling of gene expression with cell size is the consequence of competition between genes for limiting RNAPII.
Sun X-M, Bowman A, Priestman M, et al., 2020, Size-dependent increase in RNA Polymerase II initiation rates mediates gene expression scaling with cell size, Current Biology, Vol: 30, Pages: 1217-1230.e7, ISSN: 0960-9822
Cell size varies during the cell cycle and in response to external stimuli. This requires the tight coordination, or “scaling”, of mRNA and protein quantities with the cell volume in order to maintain biomolecules concentrations and cell density. Evidence in cell populations and single cells indicates that scaling relies on the coordination of mRNA transcription rates with cell size. Here we use a combination of single-molecule fluorescence in situ hybridisation (smFISH), time-lapse microscopy and mathematical modelling in single fission yeast cells to uncover the precise molecular mechanisms that control transcription rates scaling with cell size. Linear scaling of mRNA quantities is apparent in single fission yeast cells during a normal cell cycle. Transcription rates of both constitutive and regulated genes scale with cell size without evidence for transcriptional bursting. Modelling and experimental data indicate that scaling relies on the coordination of RNAPII transcription initiation rates with cell size and that RNAPII is a limiting factor. We show using real-time quantitative imaging that size increase is accompanied by a rapid concentration independent recruitment of RNAPII onto chromatin. Finally, we find that in multinucleated cells, scaling is set at the level of single nuclei and not the entire cell, making the nucleus the transcriptional scaling unit. Integrating our observations in a mechanistic model of RNAPII mediated transcription, we propose that scaling of gene expression with cell size is the consequence of competition between genes for limiting RNAPII.
Larrouy-Maumus G, Shahrezaei V, tang W, et al., 2020, Discrimination of bovine milk from non-dairy milk by lipids fingerprinting using routine matrix-assisted laser desorption ionization mass spectrometry, Scientific Reports, Vol: 10, ISSN: 2045-2322
An important sustainable development goal for any country is to ensure food security by producing a sufficient and safe food supply. This is the case for bovine milk where addition of non-dairy milks such as vegetables (e.g., soya or coconut) has become a common source of adulteration and fraud. Conventionally, gas chromatography techniques are used to detect key lipids (e.g., triacylglycerols) has an effective read-out of assessing milks origins and to detect foreign milks in bovine milks. However, such approach requires several sample preparation steps and a dedicated laboratory environment, precluding a high throughput process. To cope with this need, here, we aimed to develop a novel and simple method without organic solvent extractions for the detection of bovine and non-dairy milks based on lipids fingerprint by routine MALDI-TOF mass spectrometry (MS). The optimized method relies on the simple dilution of milks in water followed by MALDI-TOF MS analyses in the positive linear ion mode and using a matrix consisting of a 9:1 mixture of 2,5-dihydroxybenzoic acid and 2-hydroxy-5-methoxybenzoic acid (super-DHB) solubilized at 10 mg/mL in 70% ethanol. This sensitive, inexpensive, and rapid method has potential for use in food authenticity applications.
Tang W, Bertaux F, Thomas P, et al., 2020, bayNorm: Bayesian gene expression recovery, imputation and normalisation for single cell RNA-sequencing data, Bioinformatics, Vol: 36, Pages: 1174-1181, ISSN: 1367-4803
Motivation:Normalisation of single cell RNA sequencing (scRNA-seq) data is a prerequisite to theirinterpretation. The marked technical variability, high amounts of missing observations and batch effecttypical of scRNA-seq datasets make this task particularly challenging. There is a need for an efficient andunified approach for normalisation, imputation and batch effect correction.Results:Here, we introduce bayNorm, a novel Bayesian approach for scaling and inference of scRNA-seq counts. The method’s likelihood function follows a binomial model of mRNA capture, while priorsare estimated from expression values across cells using an empirical Bayes approach. We first validateour assumptions by showing this model can reproduce different statistics observed in real scRNA-seqdata. We demonstrate using publicly-available scRNA-seq datasets and simulated expression data thatbayNorm allows robust imputation of missing values generating realistic transcript distributions that matchsingle molecule FISH measurements. Moreover, by using priors informed by dataset structures, bayNormimproves accuracy and sensitivity of differential expression analysis and reduces batch effect comparedto other existing methods. Altogether, bayNorm provides an efficient, integrated solution for global scalingnormalisation, imputation and true count recovery of gene expression measurements from scRNA-seqdata.Availability:The R package “bayNorm” is available at https://github.com/WT215/bayNorm. The code foranalysing data in this paper is available at https://github.com/WT215/bayNorm_papercode.Contact:email@example.com or firstname.lastname@example.orgSupplementary information:Supplementary data are available atBioinformaticsonline.
Brugger SP, Angelescu I, Abi-Dargham A, et al., 2020, Heterogeneity of Striatal Dopamine Function in Schizophrenia: Meta-analysis of Variance, BIOLOGICAL PSYCHIATRY, Vol: 87, Pages: 215-224, ISSN: 0006-3223
Ciechonska M, Sturrock M, Grob A, et al., 2019, Ohm’s Law for increasing fitness gene expression with selection pressure
<jats:title>Abstract</jats:title><jats:p>Natural selection relies on genotypic and phenotypic adaptation in response to fluctuating environmental conditions and is the key to predicting and preventing drug resistance. Whereas classic persistence is all-or-nothing, here we show for the first time that an antibiotic resistance gene displays linear dose-responsive selection for increased expression in proportion to rising antibiotic concentration in <jats:italic>E. coli</jats:italic>. Furthermore, we observe the general nature of an instantaneous phenotypic selection process upon bactericidal and bacteriostatic antibiotic treatment, as well as an amino acid synthesis pathway enzyme under a range of auxotrophic conditions. To explain this phenomenon, we propose an analogy to Ohm’s law in electricity (V=IR) where fitness pressure acts similarly to voltage (V), gene expression to current (I), and resistance (R) to cellular machinery constraints. Lastly, mathematical modelling approaches reveal that the emergent gene expression mechanism requires variation in mRNA and protein production within an isogenic population, and cell ‘memory’ from positive feedbacks between growth and expression of any fitness-inducing gene.</jats:p>
Tang W, Ranganathan N, Shahrezaei V, et al., 2019, MALDI-TOF mass spectrometry on intact bacteria combined with a refined analysis framework allows accurate classification of MSSA and MRSA., PLoS ONE, Vol: 14, Pages: 1-16, ISSN: 1932-6203
Fast and reliable detection coupled with accurate data-processing and analysis of antibiotic-resistant bacteria is essential in clinical settings. In this study, we use MALDI-TOF on intact cells combined with a refined analysis framework to demonstrate discrimination between methicillin-susceptible (MSSA) and methicillin-resistant (MRSA) Staphylococcus aureus. By combining supervised and unsupervised machine learning methods, we firstly show that the mass spectroscopy data contains strong signal for the clustering of MSSA and MRSA. Then we concentrate on applying supervised learning to extract and verify the important features. A new workflow is proposed that allows for extracting a fixed set of reference peaks so that any new data can be aligned to it and hence consistent feature matrices can be obtained. Also note that by doing so we are able to examine the robustness of the important features that have been found. We also show that appropriate size of the benchmark data, appropriate alignment of the testing data and use of an optimal set of features via feature selection results in prediction accuracy over 90%. In summary, as proof-of-principle, our integrated experimental and bioinformatics study suggests a novel intact cell MALDI-TOF to be of great promise for fast and reliable detection of MRSA strains.
Dyer NP, Shahrezaei V, Hebenstreit D, 2019, LiBiNorm: an htseq-count analogue with improved normalisation of Smart-seq2 data and library preparation diagnostics, PeerJ, Vol: 7, Pages: 1-13, ISSN: 2167-8359
Protocols for preparing RNA sequencing (RNA-seq) libraries, most prominently“Smart-seq” variations, introduce global biases that can have a significant impact on thequantification of gene expression levels. This global bias can lead to drastic over- orunder-representation of RNA in non-linear length-dependent fashion due to enzymaticreactions during cDNA production. It is currently not corrected by any RNA-seqsoftware, which mostly focus on local bias in coverage along RNAs. This paper describesLiBiNorm, a simple command line program that mimics the popular htseq-countsoftware and allows diagnostics, quantification, and global bias removal. LiBiNormoutputs gene expression data that has been normalized to correct for global biasintroduced by the Smart-seq2 protocol. In addition, it produces data and several plotsthat allow insights into the experimental history underlying library preparation. TheLiBiNorm package includes an R script that allows visualization of the main results.LiBiNorm is the first software application to correct for the global bias that is introducedby the Smart-seq2 protocol. It is freely downloadable at http://www2.warwick.ac.uk/fac/sci/lifesci/research/libinorm.
Saint M, Bertaux F, Tang W, et al., 2019, Single-cell imaging and RNA sequencing reveal patterns of gene expression heterogeneity during fission yeast growth and adaptation, Nature Microbiology, Vol: 4, Pages: 480-491, ISSN: 2058-5276
Phenotypic cell-to-cell variability is a fundamental determinant of microbial fitness that contributes to stress adaptation and drug resistance. Gene expression heterogeneity underpins this variability but is challenging to study genome-wide. Here we examine the transcriptomes of >2,000 single fission yeast cells exposed to various environmental conditions by combining imaging, single-cell RNA sequencing and Bayesian true count recovery. We identify sets of highly variable genes during rapid proliferation in constant culture conditions. By integrating single-cell RNA sequencing and cell-size data, we provide insights into genes that are regulated during cell growth and division, including genes whose expression does not scale with cell size. We further analyse the heterogeneity of gene expression during adaptive and acute responses to changing environments. Entry into the stationary phase is preceded by a gradual, synchronized adaptation in gene regulation that is followed by highly variable gene expression when growth decreases. Conversely, sudden and acute heat shock leads to a stronger, coordinated response and adaptation across cells. This analysis reveals that the magnitude of global gene expression heterogeneity is regulated in response to different physiological conditions within populations of a unicellular eukaryote.
Uhia I, Priestman M, Joyce G, et al., 2018, Analysis of ParAB dynamics in mycobacteria shows active movement of ParB and differential inheritance of ParA, PLoS ONE, Vol: 13, Pages: 1-20, ISSN: 1932-6203
Correct chromosomal segregation, coordinated with cell division, is crucial for bacterial survival, but despite extensive studies, the mechanisms underlying this remain incompletely understood in mycobacteria. We report a detailed investigation of the dynamic interactions between ParA and ParB partitioning proteins in Mycobacterium smegmatis using microfluidics and time-lapse fluorescence microscopy to observe both proteins simultaneously. During growth and division, ParB presents as a focused fluorescent spot that subsequently splits in two. One focus moves towards a higher concentration of ParA at the new pole, while the other moves towards the old pole. We show ParB movement is in part an active process that does not rely on passive movement associated with cell growth. In some cells, another round of ParB segregation starts before cell division is complete, consistent with initiation of a second round of chromosome replication. ParA fluorescence distribution correlates with cell size, and in sister cells, the larger cell inherits a local peak of concentrated ParA, while the smaller sister inherits more homogeneously distributed protein. Cells which inherit more ParA grow faster than their sister cell, raising the question of whether inheritance of a local concentration of ParA provides a growth advantage. Alterations in levels of ParA and ParB were also found to disturb cell growth.
Bertaux F, Marguerat S, Shahrezaei V, 2018, Division rate, cell size and proteome allocation: impact on gene expression noise and implications for the dynamics of genetic circuits, ROYAL SOCIETY OPEN SCIENCE, Vol: 5, ISSN: 2054-5703
The cell division rate, size and gene expression programmes change in response to external conditions. These global changes impact on average concentrations of biomolecule and their variability or noise. Gene expression is inherently stochastic, and noise levels of individual proteins depend on synthesis and degradation rates as well as on cell-cycle dynamics. We have modelled stochastic gene expression inside growing and dividing cells to study the effect of division rates on noise in mRNA and protein expression. We use assumptions and parameters relevant to Escherichia coli, for which abundant quantitative data are available. We find that coupling of transcription, but not translation rates to the rate of cell division can result in protein concentration and noise homeostasis across conditions. Interestingly, we find that the increased cell size at fast division rates, observed in E. coli and other unicellular organisms, buffers noise levels even for proteins with decreased expression at faster growth. We then investigate the functional importance of these regulations using gene regulatory networks that exhibit bi-stability and oscillations. We find that network topology affects robustness to changes in division rate in complex and unexpected ways. In particular, a simple model of persistence, based on global physiological feedback, predicts increased proportion of persister cells at slow division rates. Altogether, our study reveals how cell size regulation in response to cell division rate could help controlling gene expression noise. It also highlights that understanding circuits' robustness across growth conditions is key for the effective design of synthetic biological systems.
Shahrezaei V, Robertson B, Thomas P, et al., 2017, Mycobacteria modify their cell size control under sub-optimal carbon sources, Frontiers in Cell and Developmental Biology, Vol: 5, ISSN: 2296-634X
The decision to divide is the most important one that any cell must make. Recent single cell studies suggest that most bacteria follow an “adder” model of cell size control, incorporating a fixed amount of cell wall material before dividing. Mycobacteria, including the causative agent of tuberculosis Mycobacterium tuberculosis, are known to divide asymmetrically resulting in heterogeneity in growth rate, doubling time, and other growth characteristics in daughter cells. The interplay between asymmetric cell division and adder size control has not been extensively investigated. Moreover, the impact of changes in the environment on growth rate and cell size control have not been addressed for mycobacteria. Here, we utilize time-lapse microscopy coupled with microfluidics to track live Mycobacterium smegmatis cells as they grow and divide over multiple generations, under a variety of growth conditions. We demonstrate that, under optimal conditions, M. smegmatis cells robustly follow the adder principle, with constant added length per generation independent of birth size, growth rate, and inherited pole age. However, the nature of the carbon source induces deviations from the adder model in a manner that is dependent on pole age. Understanding how mycobacteria maintain cell size homoeostasis may provide crucial targets for the development of drugs for the treatment of tuberculosis, which remains a leading cause of global mortality.
Sturrock M, Li S, Shahrezaei V, 2017, The influence of nuclear compartmentalisation on stochastic dynamics of self-repressing gene expression, Journal of Theoretical Biology, Vol: 424, Pages: 55-72, ISSN: 0022-5193
Gene expression is an inherently noisy process. This noise is generally thought to be deleterious as precise internal regulation of biochemical reactions is essential for cell growth and survival. Self-repression of gene expression, which is the simplest form of a negative feedback loop, is commonly believed to be employed by cellular systems to decrease the stochastic fluctuations in gene expression. When there is some delay in autoregulation, it is also believed that this system can generate oscillations. In eukaryotic cells, mRNAs that are synthesised in the nucleus must be exported to the cytoplasm to function in protein synthesis, whereas proteins must be transported into the nucleus from the cytoplasm to regulate the expression levels of genes. Nuclear transport thus plays a critical role in eukaryotic gene expression and regulation. Some recent studies have suggested that nuclear retention of mRNAs can control noise in mRNA expression. However, the effect of nuclear transport on protein noise and its interplay with negative feedback regulation is not completely understood. In this paper, we systematically compare four different simple models of gene expression. By using simulations and applying the linear noise approximation to the corresponding chemical master equations, we investigate the influence of nuclear import and export on noise in gene expression in a negative autoregulatory feedback loop. We first present results consistent with the literature, i.e., that negative feedback can effectively buffer the variability in protein levels, and nuclear retention can decrease mRNA noise levels. Interestingly we find that when negative feedback is combined with nuclear retention, an amplification in gene expression noise can be observed and is dependant on nuclear translocation rates. Finally, we investigate the effect of nuclear compartmentalisation on the ability of self-repressing genes to exhibit stochastic oscillatory dynamics.
Archer N, Walsh MD, Shahrezaei V, et al., 2016, Modeling Enzyme Processivity Reveals that RNA-Seq Libraries Are Biased in Characteristic and Correctable Ways, Cell Systems, Vol: 3, Pages: 467-479.E12, ISSN: 2405-4712
Experimental procedures for preparing RNA-seq and single-cell (sc) RNA-seq libraries are based on assumptions regarding their underlying enzymatic reactions. Here, we show that the fairness of these assumptions varies within libraries: coverage by sequencing reads along and between transcripts exhibits characteristic, protocol-dependent biases. To understand the mechanistic basis of this bias, we present an integrated modeling framework that infers the relationship between enzyme reactions during library preparation and the characteristic coverage patterns observed for different protocols. Analysis of new and existing (sc)RNA-seq data from six different library preparation protocols reveals that polymerase processivity is the mechanistic origin of coverage biases. We apply our framework to demonstrate that lowering incubation temperature increases processivity, yield, and (sc)RNA-seq sensitivity in all protocols. We also provide correction factors based on our model for increasing accuracy of transcript quantification in existing samples prepared at standard temperatures. In total, our findings improve our ability to accurately reflect in vivo transcript abundances in (sc)RNA-seq libraries.
Shahrezaei V, Marguerat S, 2015, Connecting growth with gene expression: of noise and numbers., Current Opinion in Microbiology, Vol: 25, Pages: 127-135, ISSN: 1879-0364
Growth is a dynamic process whereby cells accumulate mass. Growth rates of single cells are connected to RNA and protein synthesis rates, and therefore with biomolecule numbers. Noise in gene expression depends on these numbers, and is thus linked with cellular growth. Whether these global attributes of the cell participate in gene regulation is still largely unexplored. New experimental and modelling studies suggest that systemic variations in biomolecule numbers can coordinate cellular processes, including growth itself, through global regulatory feedback that acts in addition to genetic regulatory networks. Here, we review these findings and speculate on possible implications of this less appreciated layer of gene regulation for cellular physiology and adaptation to changing environments.
Smith S, Shahrezaei V, 2015, General transient solution of the one-step master equation in one dimension, Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol: 91, Pages: 062119-1-062119-6, ISSN: 1063-651X
Exact analytical solutions of the master equation are limited to special cases and exact numerical methods areinefficient. Even the generic one-dimensional, one-step master equation has evaded exact solution, aside fromthe steady-state case. This type of master equation describes the dynamics of a continuous-time Markov processwhose range consists of positive integers and whose transitions are allowed only between adjacent sites. Thesolution of any master equation can be written as the exponential of a (typically huge) matrix, which requiresthe calculation of the eigenvalues and eigenvectors of the matrix. Here we propose a linear algebraic methodfor simplifying this exponential for the general one-dimensional, one-step process. In particular, we prove thatthe calculation of the eigenvectors is actually not necessary for the computation of exponential, thereby wedramatically cut the time of this calculation. We apply our new methodology to examples from birth-deathprocesses and biochemical networks. We show that the computational time is significantly reduced compared toexisting methods
Smith S, Shahrezaei V, 2015, General transient solution of the one-step master equation in one dimension., Phys Rev E Stat Nonlin Soft Matter Phys, Vol: 91
Exact analytical solutions of the master equation are limited to special cases and exact numerical methods are inefficient. Even the generic one-dimensional, one-step master equation has evaded exact solution, aside from the steady-state case. This type of master equation describes the dynamics of a continuous-time Markov process whose range consists of positive integers and whose transitions are allowed only between adjacent sites. The solution of any master equation can be written as the exponential of a (typically huge) matrix, which requires the calculation of the eigenvalues and eigenvectors of the matrix. Here we propose a linear algebraic method for simplifying this exponential for the general one-dimensional, one-step process. In particular, we prove that the calculation of the eigenvectors is actually not necessary for the computation of exponential, thereby we dramatically cut the time of this calculation. We apply our new methodology to examples from birth-death processes and biochemical networks. We show that the computational time is significantly reduced compared to existing methods.
In this work, we review progress made in understanding the molecular underpinnings of growth and division in mycobacteria, concentrating on work published since the last comprehensive review ( Hett and Rubin 2008). We have focused on exciting work making use of new time-lapse imaging technologies coupled with reporter-gene fusions and antimicrobial treatment to generate insights into how mycobacteria grow and divide in a heterogeneous manner. We try to reconcile the different observations reported, providing a model of how they might fit together. We also review the topic of mycobacterial spores, which has generated considerable discussion during the last few years. Resuscitation promoting factors, and regulation of growth and division, have also been actively researched, and we summarize progress in these areas.
Robb ML, Shahrezaei V, 2014, Stochastic Cellular Fate Decision Making by Multiple Infecting Lambda Phage, PLOS ONE, Vol: 9, ISSN: 1932-6203
Dushek O, Lellouch AC, Vaux DJ, et al., 2014, Biosensor Architectures for High-Fidelity Reporting of Cellular Signaling, Biophysical Journal, Vol: 107, Pages: 773-782, ISSN: 1542-0086
Understanding mechanisms of information processing in cellular signaling networks requires quantitative measurements of protein activities in living cells. Biosensors are molecular probes that have been developed to directly track the activity of specific signaling proteins and their use is revolutionizing our understanding of signal transduction. The use of biosensors relies on the assumption that their activity is linearly proportional to the activity of the signaling protein they have been engineered to track. We use mechanistic mathematical models of common biosensor architectures (single-chain FRET-based biosensors), which include both intramolecular and intermolecular reactions, to study the validity of the linearity assumption. As a result of the classic mechanism of zero-order ultrasensitivity, we find that biosensor activity can be highly nonlinear so that small changes in signaling protein activity can give rise to large changes in biosensor activity and vice versa. This nonlinearity is abolished in architectures that favor the formation of biosensor oligomers, but oligomeric biosensors produce complicated FRET states. Based on this finding, we show that high-fidelity reporting is possible when a single-chain intermolecular biosensor is used that cannot undergo intramolecular reactions and is restricted to forming dimers. We provide phase diagrams that compare various trade-offs, including observer effects, which further highlight the utility of biosensor architectures that favor intermolecular over intramolecular binding. We discuss challenges in calibrating and constructing biosensors and highlight the utility of mathematical models in designing novel probes for cellular signaling.
Delaney KR, Shahrezaei V, 2013, Uncaging calcium in neurons., Cold Spring Harb Protoc, Vol: 2013, Pages: 1115-1124
Changes in intracellular free calcium concentration (Δ[Ca(2+)]i) driving physiological events such as neurotransmitter release or Ca(2+)-dependent currents can be monitored using Ca(2+)-sensitive fluorescent dyes. Although these dyes can correlate Δ[Ca(2+)]i with a physiological event, they cannot directly test for causality between changes in [Ca(2+)]i and that event. Photolabile Ca(2+) chelators are Ca(2+)-binding molecules that can alter and, to a certain extent, control [Ca(2+)]i in an inducible manner and with temporal and spatial resolution that surpasses microinjection or ionophore application. Here we discuss the properties of caged Ca(2+) compounds as well as some practical considerations for their use in neuronal cells, where they have proven particularly effective.
Joyce G, Williams KJ, Robb M, et al., 2012, Cell Division Site Placement and Asymmetric Growth in Mycobacteria, PLOS One, Vol: 7, ISSN: 1932-6203
Mycobacteria are members of the actinomycetes that grow by tip extension and lack apparent homologues of the known cell division regulators found in other rod-shaped bacteria. Previous work using static microscopy on dividing mycobacteria led to the hypothesis that these cells can grow and divide asymmetrically, and at a wide range of sizes, in contrast to the cell growth and division patterns observed in the model rod-shaped organisms. In this study, we test this hypothesis using live-cell time-lapse imaging of dividing Mycobacterium smegmatis labelled with fluorescent PBP1a, to probe peptidoglycan synthesis and label the cell septum. We demonstrate that the new septum is placed accurately at mid-cell, and that the asymmetric division observed is a result of differential growth from the cell tips, with a more than 2-fold difference in growth rate between fast and slow growing poles. We also show that the division site is not selected at a characteristic cell length, suggesting this is not an important cue during the mycobacterial cell cycle.
Szomolay B, Shahrezaei V, 2012, Bell-shaped and ultrasensitive dose-response in phosphorylation-dephosphorylation cycles: the role of kinase-phosphatase complex formation, BMC Systems Biology, Vol: 6, Pages: 1-14, ISSN: 1752-0509
BackgroundPhosphorylation-dephosphorylation cycles (PDCs) mediated by kinases and phosphatases are common in cellular signalling. Kinetic modelling of PDCs has shown that these systems can exhibit a variety of input-output (dose-response) behaviors including graded response, ultrasensitivity and bistability. In addition to proteins, there are a class of lipids known as phosphoinositides (PIs) that can be phosphorylated. Experimental studies have revealed the formation of an antagonistic kinase-phosphatase complex in regulation of phosphorylation of PIs. However, the functional significance of this type of complex formation is not clear.ResultsWe first revisit the basic PDC and show that partial asymptotic phosphorylation of substrate limits ultrasensitivity. Also, substrate levels are changed one can obtain non-monotonic bell-shaped dose-response curves over a narrow range of parameters. Then we extend the PDC to include kinase-phosphatase complex formation. We report the possibility of robust bell-shaped dose-response for a specific class of the model with complex formation. Also, we show that complex formation can produce ultrasensitivity outside the Goldbeter-Koshland zero-order ultrasensitivity regime through a mechanism similar to competitive inhibition between an enzyme and its inhibitor.ConclusionsWe conclude that the novel PDC module studied here exhibits new dose-response behaviour. In particular, we show that the bell-shaped response could result in transient phosphorylation of substrate. We discuss the relevance of this result in the context of experimental observations on PI regulation in endosomal trafficking.
Schley D, Tanaka RJ, Leungchavaphongse K, et al., 2012, Modelling the influence of foot-and-mouth disease vaccine antigen stability and dose on the bovine immune response, PLOS One, Vol: 7, ISSN: 1932-6203
Dushek O, van der Merwe PA, Shahrezaei V, 2011, Ultrasensitivity in Multisite Phosphorylation of Membrane-Anchored Proteins, BIOPHYSICAL JOURNAL, Vol: 100, Pages: 1189-1197, ISSN: 0006-3495
Ollivier JF, Shahrezaei V, Swain PS, 2010, Scalable Rule-Based Modelling of Allosteric Proteins and Biochemical Networks, PLOS COMPUTATIONAL BIOLOGY, Vol: 6
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