Modeling network dynamics: the lac operon, a case study

The unreasonable effectiveness of equilibrium gene regulation through the cell cycle

Systems like the prototypical lac operon can reliably hold repression of transcription upon DNA replication across cell cycles with just 10 repressor molecules per cell and behave as if they were at equilibrium. The origin of this phenomenology is still an unresolved question. Here, we develop a general theory to analyze strong perturbations in quasi-equilibrium systems and use it to quantify the effects of DNA replication in gene regulation. We find a scaling law linking actual with predicted equilibrium transcription via a single kinetic parameter. We show that even the lac operon functions beyond the physical limits of naive regulation through compensatory mechanisms that suppress non-equilibrium effects. Synthetic systems without adjuvant activators, such as the cAMP receptor protein (CRP), lack this reliability. Our results provide a rationale for the function of CRP, beyond just being a tunable activator, as a mitigator of cell cycle perturbations.

Exploring gene regulation and biological processes in insects: Insights from omics data using gene regulatory network models

Gene regulatory network (GRN) comprises complicated yet intertwined gene-regulator relationships. Understanding the GRN dynamics will unravel the complexity behind the observed gene expressions. Insect gene regulation is often complicated due to their complex life cycles and diverse ecological adaptations. The main interest of this review is to have an update on the current mathematical modelling methods of GRNs to explain insect science. Several popular GRN architecture models are discussed, together with examples of applications in insect science. In the last part of this review, each model is compared from different aspects, including network scalability, computation complexity, robustness to noise and biological relevancy.

Transcription-replication interactions reveal bacterial genome regulation

Organisms determine the transcription rates of thousands of genes through a few modes of regulation that recur across the genome1. In bacteria, the relationship between the regulatory architecture of a gene and its expression is well understood for individual model gene circuits2,3. However, a broader perspective of these dynamics at the genome scale is lacking, in part because bacterial transcriptomics has hitherto captured only a static snapshot of expression averaged across millions of cells4. As a result, the full diversity of gene expression dynamics and their relation to regulatory architecture remains unknown. Here we present a novel genome-wide classification of regulatory modes based on the transcriptional response of each gene to its own replication, which we term the transcription-replication interaction profile (TRIP). Analysing single-bacterium RNA-sequencing data, we found that the response to the universal perturbation of chromosomal replication integrates biological regulatory factors with biophysical molecular events on the chromosome to reveal the local regulatory context of a gene. Whereas the TRIPs of many genes conform to a gene dosage-dependent pattern, others diverge in distinct ways, and this is shaped by factors such as intra-operon position and repression state. By revealing the underlying mechanistic drivers of gene expression heterogeneity, this work provides a quantitative, biophysical framework for modelling replication-dependent expression dynamics.

Monitoring lineages of growing and dividing bacteria reveals an inducible memory of mar operon expression

In Gram negative bacteria, the multiple antibiotic resistance or mar operon, is known to control the expression of multi-drug efflux genes that protect bacteria from a wide range of drugs. As many different chemical compounds can induce this operon, identifying the parameters that govern the dynamics of its induction is crucial to better characterize the processes of tolerance and resistance. Most experiments have assumed that the properties of the mar transcriptional network can be inferred from population measurements. However, measurements from an asynchronous population of cells can mask underlying phenotypic variations of single cells. We monitored the activity of the mar promoter in single Escherichia coli cells in linear micro-colonies and established that the response to a steady level of inducer was most heterogeneous within individual colonies for an intermediate value of inducer. Specifically, sub-lineages defined by contiguous daughter-cells exhibited similar promoter activity, whereas activity was greatly variable between different sub-lineages. Specific sub-trees of uniform promoter activity persisted over several generations. Statistical analyses of the lineages suggest that the presence of these sub-trees is the signature of an inducible memory of the promoter state that is transmitted from mother to daughter cells. This single-cell study reveals that the degree of epigenetic inheritance changes as a function of inducer concentration, suggesting that phenotypic inheritance may be an inducible phenotype.

Rethinking (again) Hardy-Weinberg and genetic drift in undergraduate biology

Designing effective curricula is challenging. Content decisions can impact both learning outcomes and student engagement. As an example consider the place of Hardy-Weinberg equilibria (HWE) and genetic drift calculations in introductory biology courses, as discussed by Masel (2012). Given that population genetics, "a fairly arcane speciality", can be difficult to grasp, there is little justification for introducing introductory students to HWE calculations. It is more useful to introduce them to the behavior of alleles in terms of basic features of biological systems, and that in the absence of selection recessive alleles are no "weaker" or preferentially lost from a population than are dominant alleles. On the other hand, stochastic behaviors, such as genetic drift, are ubiquitous in biological systems and often play functionally significant roles; they can be introduced to introductory students in mechanistic and probabilistic terms. Specifically, genetic drift emerges from the stochastic processes involved in meiotic chromosome segregation and recombination. A focus on stochastic processes may help counteract naive bio-deterministic thinking and can reinforce, for students, the value of thinking quantitatively about biological processes.

Functional Clustering of Metabolically Related Genes Is Conserved across Dikarya

Transcriptional regulation is vital for organismal survival, with many layers and mechanisms collaborating to balance gene expression. One layer of this regulation is genome organization, specifically the clustering of functionally related, co-expressed genes along the chromosomes. Spatial organization allows for position effects to stabilize RNA expression and balance transcription, which can be advantageous for a number of reasons, including reductions in stochastic influences between the gene products. The organization of co-regulated gene families into functional clusters occurs extensively in Ascomycota fungi. However, this is less characterized within the related Basidiomycota fungi despite the many uses and applications for the species within this clade. This review will provide insight into the prevalence, purpose, and significance of the clustering of functionally related genes across Dikarya, including foundational studies from Ascomycetes and the current state of our understanding throughout representative Basidiomycete species.

Transcription-replication interactions reveal principles of bacterial genome regulation

Organisms determine the transcription rates of thousands of genes through a few modes of regulation that recur across the genome1. These modes interact with a changing cellular environment to yield highly dynamic expression patterns2. In bacteria, the relationship between a gene's regulatory architecture and its expression is well understood for individual model gene circuits3,4. However, a broader perspective of these dynamics at the genome-scale is lacking, in part because bacterial transcriptomics have hitherto captured only a static snapshot of expression averaged across millions of cells5. As a result, the full diversity of gene expression dynamics and their relation to regulatory architecture remains unknown. Here we present a novel genome-wide classification of regulatory modes based on each gene's transcriptional response to its own replication, which we term the Transcription-Replication Interaction Profile (TRIP). We found that the response to the universal perturbation of chromosomal replication integrates biological regulatory factors with biophysical molecular events on the chromosome to reveal a gene's local regulatory context. While the TRIPs of many genes conform to a gene dosage-dependent pattern, others diverge in distinct ways, including altered timing or amplitude of expression, and this is shaped by factors such as intra-operon position, repression state, or presence on mobile genetic elements. Our transcriptome analysis also simultaneously captures global properties, such as the rates of replication and transcription, as well as the nestedness of replication patterns. This work challenges previous notions of the drivers of expression heterogeneity within a population of cells, and unearths a previously unseen world of gene transcription dynamics.

Estimating and Assessing Differential Equation Models with Time-Course Data

Ordinary differential equation (ODE) models are widely used to describe chemical or biological processes. This Article considers the estimation and assessment of such models on the basis of time-course data. Due to experimental limitations, time-course data are often noisy, and some components of the system may not be observed. Furthermore, the computational demands of numerical integration have hindered the widespread adoption of time-course analysis using ODEs. To address these challenges, we explore the efficacy of the recently developed MAGI (MAnifold-constrained Gaussian process Inference) method for ODE inference. First, via a range of examples we show that MAGI is capable of inferring the parameters and system trajectories, including unobserved components, with appropriate uncertainty quantification. Second, we illustrate how MAGI can be used to assess and select different ODE models with time-course data based on MAGI's efficient computation of model predictions. Overall, we believe MAGI is a useful method for the analysis of time-course data in the context of ODE models, which bypasses the need for any numerical integration.

Mechanistic aspects of IPTG (isopropylthio-β-galactoside) transport across the cytoplasmic membrane of Escherichia coli-a rate limiting step in the induction of recombinant protein expression

Coupling transcription of a cloned gene to the lac operon with induction by isopropylthio-β-galactoside (IPTG) has been a favoured approach for recombinant protein expression using Escherichia coli as a heterologous host for more than six decades. Despite a wealth of experimental data gleaned over this period, a quantitative relationship between extracellular IPTG concentration and consequent levels of recombinant protein expression remains surprisingly elusive across a broad spectrum of experimental conditions. This is because gene expression under lac operon regulation is tightly correlated with intracellular IPTG concentration due to allosteric regulation of the lac repressor protein (lacY). An in-silico mathematical model established that uptake of IPTG across the cytoplasmic membrane of E. coli by simple diffusion was negligible. Conversely, lacY mediated active transport was a rapid process, taking only some seconds for internal and external IPTG concentrations to equalize. Optimizing kcat and KM parameters by targeted mutation of the galactoside binding site in lacY could be a future strategy to improve the performance of recombinant protein expression. For example, if kcat were reduced whilst KM was increased, active transport of IPTG across the cytoplasmic membrane would be reduced, thereby lessening the metabolic burden on the cell and expediating accumulation of recombinant protein. The computational model described herein is made freely available and is amenable to optimize recombinant protein expression in other heterologous hosts.

ONE-SENTENCE SUMMARY

A computational model made freely available to optimize recombinant protein expression in Escherichia coli other heterologous hosts.

A scalable, open-source implementation of a large-scale mechanistic model for single cell proliferation and death signaling

Mechanistic models of how single cells respond to different perturbations can help integrate disparate big data sets or predict response to varied drug combinations. However, the construction and simulation of such models have proved challenging. Here, we developed a python-based model creation and simulation pipeline that converts a few structured text files into an SBML standard and is high-performance- and cloud-computing ready. We applied this pipeline to our large-scale, mechanistic pan-cancer signaling model (named SPARCED) and demonstrate it by adding an IFNγ pathway submodel. We then investigated whether a putative crosstalk mechanism could be consistent with experimental observations from the LINCS MCF10A Data Cube that IFNγ acts as an anti-proliferative factor. The analyses suggested this observation can be explained by IFNγ-induced SOCS1 sequestering activated EGF receptors. This work forms a foundational recipe for increased mechanistic model-based data integration on a single-cell level, an important building block for clinically-predictive mechanistic models.

Eigenvalue sensitivity-based analysis for evaluation of biological network stability versus disturbances

Network modeling is an effective tool for understanding the properties of complex systems. Networks are widely used to help us gain insight into biological systems. In this way, the cell, gene, and protein are denoted as nodes, and the connection elements are regarded as links or edges. In this paper, a novel stochastic strategy is developed for identifying the most influential edges on the stability of biological networks. Regarding the principles of networks and control-theory basics like Jacobian and eigenvalue sensitivity-based analysis, a new criterion is proposed, called "random sensitivity index matrix" (RSIM). RSIM evaluates the eigenvalue sensitivity of all edges in a network in the presents of stochastic disturbances based on the Monte Carlo algorithm. Through the values of RSIM elements, the sensitive edges are identifiable. In addition, the contribution of each edge in network instability has been compared through different percentages of disturbances. Different percentages of disturbances did not change the results. The performance of the proposed method was verified by simulation results for Lac (lactose) operon and MAPK (Mitogen-activated protein kinases) as two sample biological networks.

Organic Bioelectronic Devices for Metabolite Sensing

Electrochemical detection of metabolites is essential for early diagnosis and continuous monitoring of a variety of health conditions. This review focuses on organic electronic material-based metabolite sensors and highlights their potential to tackle critical challenges associated with metabolite detection. We provide an overview of the distinct classes of organic electronic materials and biorecognition units used in metabolite sensors, explain the different detection strategies developed to date, and identify the advantages and drawbacks of each technology. We then benchmark state-of-the-art organic electronic metabolite sensors by categorizing them based on their application area (in vitro, body-interfaced, in vivo, and cell-interfaced). Finally, we share our perspective on using organic bioelectronic materials for metabolite sensing and address the current challenges for the devices and progress to come.

Integrated Strategies for Enhancing the Expression of the AqCoA Chitosanase in Pichia pastoris by Combined Optimization of Molecular Chaperones Combinations and Copy Numbers via a Novel Plasmid pMC-GAP

In our previous study, the chitosanase AqCoA and the chitooligosaccharides it produced were found to exhibit significant protective effects against fungal diseases. In this study, we enhanced the expression of AqCoA using the novel pMC-GAP that enables stable transformation of Escherichia coli, and built an integrated model based on the gene copy number, molecular chaperones, and protein production of AqCoA. In terms of gene dosage, the highest hydrolase activity was 0.32 U/ml in the strain with four copies, which was 1.78-fold higher than that of the strain with only one copy (0.18 U/ml). In addition, we found the chaperones such as PDI, ERO1, HAC1, YDJ1, SSE1, SSA4, and SSO2 improved protein expression. Furthermore, the PDI/ERO1, SSA4/SSE1, and YDJ1/SSO2 pairs synergistically increased the expression levels by 61%, 31%, and 42%, respectively. Finally, we investigated the combined effects of gene copy numbers and molecular chaperones on protein expression. The highest activity reached 2.32 U/ml in the strain with six integrated molecular chaperone expression cassettes and sixteen copies of the target gene, which was 13-fold higher than that of the control strain with only one copy (GAP-1AqCoA). Combined optimization of gene dosage and molecular chaperone combinations significantly increased the expression level of AqCoA, providing a powerful strategy to improve the expression of other heterologous proteins in P. pastoris.

All-or-none amyloid disassembly via chaperone-triggered fibril unzipping favors clearance of α-synuclein toxic species

α-synuclein aggregation is present in Parkinson's disease and other neuropathologies. Among the assemblies that populate the amyloid formation process, oligomers and short fibrils are the most cytotoxic. The human Hsc70-based disaggregase system can resolve α-synuclein fibrils, but its ability to target other toxic assemblies has not been studied. Here, we show that this chaperone system preferentially disaggregates toxic oligomers and short fibrils, while its activity against large, less toxic amyloids is severely impaired. Biochemical and kinetic characterization of the disassembly process reveals that this behavior is the result of an all-or-none abrupt solubilization of individual aggregates. High-speed atomic force microscopy explicitly shows that disassembly starts with the destabilization of the tips and rapidly progresses to completion through protofilament unzipping and depolymerization without accumulation of harmful oligomeric intermediates. Our data provide molecular insights into the selective processing of toxic amyloids, which is critical to identify potential therapeutic targets against increasingly prevalent neurodegenerative disorders.

Engineering of a new Escherichia coli strain efficiently metabolizing cellobiose with promising perspectives for plant biomass-based application design

The necessity to decrease our fossil energy dependence requests bioprocesses based on biomass degradation. Cellobiose is the main product released by cellulases when acting on the major plant cell wall polysaccharide constituent, the cellulose. Escherichia coli, one of the most common model organisms for the academy and the industry, is unable to metabolize this disaccharide. In this context, the remodeling of E. coli to catabolize cellobiose should thus constitute an important progress for the design of such applications. Here, we developed a robust E. coli strain able to metabolize cellobiose by integration of a small set of modifications in its genome. Contrary to previous studies that use adaptative evolution to achieve some growth on this sugar by reactivating E. coli cryptic operons coding for cellobiose metabolism, we identified easily insertable modifications impacting the cellobiose import (expression of a gene coding a truncated variant of the maltoporin LamB, modification of the expression of lacY encoding the lactose permease) and its intracellular degradation (genomic insertion of a gene encoding either a cytosolic β-glucosidase or a cellobiose phosphorylase). Taken together, our results provide an easily transferable set of mutations that confers to E. coli an efficient growth phenotype on cellobiose (doubling time of 2.2 ​h in aerobiosis) without any prior adaptation.

Characterization and computation of ancestors in reaction systems

In reaction systems, preimages and nth ancestors are sets of reactants leading to the production of a target set of products in either 1 or n steps, respectively. Many computational problems on preimages and ancestors, such as finding all minimum-cardinality nth ancestors, computing their size or counting them, are intractable. In this paper, we characterize all nth ancestors using a Boolean formula that can be computed in polynomial time. Once simplified, this formula can be exploited to easily solve all preimage and ancestor problems. This allows us to directly relate the difficulty of ancestor problems to the cost of the simplification so that new insights into computational complexity investigations can be achieved. In particular, we focus on two problems: (i) deciding whether a preimage/nth ancestor exists and (ii) finding a preimage/nth ancestor of minimal size. Our approach is constructive, it aims at finding classes of reactions systems for which the ancestor problems can be solved in polynomial time, in exact or approximate way.

Reconciling kinetic and thermodynamic models of bacterial transcription

The study of transcription remains one of the centerpieces of modern biology with implications in settings from development to metabolism to evolution to disease. Precision measurements using a host of different techniques including fluorescence and sequencing readouts have raised the bar for what it means to quantitatively understand transcriptional regulation. In particular our understanding of the simplest genetic circuit is sufficiently refined both experimentally and theoretically that it has become possible to carefully discriminate between different conceptual pictures of how this regulatory system works. This regulatory motif, originally posited by Jacob and Monod in the 1960s, consists of a single transcriptional repressor binding to a promoter site and inhibiting transcription. In this paper, we show how seven distinct models of this so-called simple-repression motif, based both on thermodynamic and kinetic thinking, can be used to derive the predicted levels of gene expression and shed light on the often surprising past success of the thermodynamic models. These different models are then invoked to confront a variety of different data on mean, variance and full gene expression distributions, illustrating the extent to which such models can and cannot be distinguished, and suggesting a two-state model with a distribution of burst sizes as the most potent of the seven for describing the simple-repression motif.

Multiplexed characterization of rationally designed promoter architectures deconstructs combinatorial logic for IPTG-inducible systems

A crucial step towards engineering biological systems is the ability to precisely tune the genetic response to environmental stimuli. In the case of Escherichia coli inducible promoters, our incomplete understanding of the relationship between sequence composition and gene expression hinders our ability to predictably control transcriptional responses. Here, we profile the expression dynamics of 8269 rationally designed, IPTG-inducible promoters that collectively explore the individual and combinatorial effects of RNA polymerase and LacI repressor binding site strengths. We then fit a statistical mechanics model to measured expression that accurately models gene expression and reveals properties of theoretically optimal inducible promoters. Furthermore, we characterize three alternative promoter architectures and show that repositioning binding sites within promoters influences the types of combinatorial effects observed between promoter elements. In total, this approach enables us to deconstruct relationships between inducible promoter elements and discover practical insights for engineering inducible promoters with desirable characteristics.

Deciphering the regulatory genome of Escherichia coli, one hundred promoters at a time

Advances in DNA sequencing have revolutionized our ability to read genomes. However, even in the most well-studied of organisms, the bacterium Escherichia coli, for ≈65% of promoters we remain ignorant of their regulation. Until we crack this regulatory Rosetta Stone, efforts to read and write genomes will remain haphazard. We introduce a new method, Reg-Seq, that links massively parallel reporter assays with mass spectrometry to produce a base pair resolution dissection of more than a E. coli promoters in 12 growth conditions. We demonstrate that the method recapitulates known regulatory information. Then, we examine regulatory architectures for more than 80 promoters which previously had no known regulatory information. In many cases, we also identify which transcription factors mediate their regulation. This method clears a path for highly multiplexed investigations of the regulatory genome of model organisms, with the potential of moving to an array of microbes of ecological and medical relevance.

Emergence of cooperative bistability and robustness of gene regulatory networks

Gene regulatory networks (GRNs) are complex systems in which many genes regulate mutually to adapt the cell state to environmental conditions. In addition to function, the GRNs possess several kinds of robustness. This robustness means that systems do not lose their functionality when exposed to disturbances such as mutations or noise, and is widely observed at many levels in living systems. Both function and robustness have been acquired through evolution. In this respect, GRNs utilized in living systems are rare among all possible GRNs. In this study, we explored the fitness landscape of GRNs and investigated how robustness emerged in highly-fit GRNs. We considered a toy model of GRNs with one input gene and one output gene. The difference in the expression level of the output gene between two input states, "on" and "off", was considered as fitness. Thus, the determination of the fitness of a GRN was based on how sensitively it responded to the input. We employed the multicanonical Monte Carlo method, which can sample GRNs randomly in a wide range of fitness levels, and classified the GRNs according to their fitness. As a result, the following properties were found: (1) Highly-fit GRNs exhibited bistability for intermediate input between "on" and "off". This means that such GRNs responded to two input states by using different fixed points of dynamics. This bistability emerges necessarily as fitness increases. (2) These highly-fit GRNs were robust against noise because of their bistability. In other words, noise robustness is a byproduct of high fitness. (3) GRNs that were robust against mutations were not extremely rare among the highly-fit GRNs. This implies that mutational robustness is readily acquired through the evolutionary process. These properties are universal irrespective of the evolutionary pathway, because the results do not rely on evolutionary simulation.

The analysis of living systems can generate both knowledge and illusions

Life relies on phenomena that range from changes in molecules that occur within nanoseconds to changes in populations that occur over millions of years. Researchers have developed a vast range of experimental techniques to analyze living systems, but a given technique usually only works over a limited range of length or time scales. Therefore, gaining a full understanding of a living system usually requires the integration of information obtained at multiple different scales by two or more techniques. This approach has undoubtedly led to a much better understanding of living systems but, equally, the staggering complexity of these systems, the sophistication and limitations of the techniques available in modern biology, and the need to use two or more techniques, can lead to persistent illusions of knowledge. Here, in an effort to make better use of the experimental techniques we have at our disposal, I propose a broad classification of techniques into six complementary approaches: perturbation, visualization, substitution, characterization, reconstitution, and simulation. Such a taxonomy might also help increase the reproducibility of inferences and improve peer review.

Figure 1 Theory Meets Figure 2 Experiments in the Study of Gene Expression

It is tempting to believe that we now own the genome. The ability to read and rewrite it at will has ushered in a stunning period in the history of science. Nonetheless, there is an Achilles' heel exposed by all of the genomic data that has accrued: We still do not know how to interpret them. Many genes are subject to sophisticated programs of transcriptional regulation, mediated by DNA sequences that harbor binding sites for transcription factors, which can up- or down-regulate gene expression depending upon environmental conditions. This gives rise to an input-output function describing how the level of expression depends upon the parameters of the regulated gene-for instance, on the number and type of binding sites in its regulatory sequence. In recent years, the ability to make precision measurements of expression, coupled with the ability to make increasingly sophisticated theoretical predictions, has enabled an explicit dialogue between theory and experiment that holds the promise of covering this genomic Achilles' heel. The goal is to reach a predictive understanding of transcriptional regulation that makes it possible to calculate gene expression levels from DNA regulatory sequence. This review focuses on the canonical simple repression motif to ask how well the models that have been used to characterize it actually work. We consider a hierarchy of increasingly sophisticated experiments in which the minimal parameter set learned at one level is applied to make quantitative predictions at the next. We show that these careful quantitative dissections provide a template for a predictive understanding of the many more complex regulatory arrangements found across all domains of life.

Disentangling a complex response in cell reprogramming and probing the Waddington landscape by automatic construction of Petri nets

We analyzed the developmental switch to sporulation of a multinucleate Physarum polycephalum plasmodial cell, a complex response to phytochrome photoreceptor activation. Automatic construction of Petri nets representing finite state machines assembled from trajectories of differential gene expression in single cells revealed alternative, genotype-dependent interconnected developmental routes and identified reversible steps, metastable states, commitment points, and subsequent irreversible steps together with molecular signatures associated with cell fate decision and differentiation. Formation of cyclic transits identified by transition invariants in mutants that are locked in a proliferative state is remarkable considering the view that oncogenic alterations may cause the formation of cancer attractors. We conclude that the Petri net approach is useful to probe the Waddington landscape of cellular reprogramming, to disentangle developmental routes for the reconstruction of the gene regulatory network, and to understand how genetic alterations or physiological conditions reshape the landscape eventually creating new basins of attraction. Unraveling the complexity of pathogenesis, disease progression, drug response or the analysis of attractor landscapes in other complex systems of uncertain structure might be additional fields of application.

Computational Modelling of Metabolic Burden and Substrate Toxicity in Escherichia coli Carrying a Synthetic Metabolic Pathway

In our previous work, we designed and implemented a synthetic metabolic pathway for 1,2,3-trichloropropane (TCP) biodegradation in Escherichia coli. Significant effects of metabolic burden and toxicity exacerbation were observed on single cell and population levels. Deeper understanding of mechanisms underlying these effects is extremely important for metabolic engineering of efficient microbial cell factories for biotechnological processes. In this paper, we present a novel mathematical model of the pathway. The model addresses for the first time the combined effects of toxicity exacerbation and metabolic burden in the context of bacterial population growth. The model is calibrated with respect to the real data obtained with our original synthetically modified E. coli strain. Using the model, we explore the dynamics of the population growth along with the outcome of the TCP biodegradation pathway considering the toxicity exacerbation and metabolic burden. On the methodological side, we introduce a unique computational workflow utilising algorithmic methods of computer science for the particular modelling problem.

Molecular noise of innate immunity shapes bacteria-phage ecologies

Mathematical models have been used successfully at diverse scales of biological organization, ranging from ecology and population dynamics to stochastic reaction events occurring between individual molecules in single cells. Generally, many biological processes unfold across multiple scales, with mutations being the best studied example of how stochasticity at the molecular scale can influence outcomes at the population scale. In many other contexts, however, an analogous link between micro- and macro-scale remains elusive, primarily due to the challenges involved in setting up and analyzing multi-scale models. Here, we employ such a model to investigate how stochasticity propagates from individual biochemical reaction events in the bacterial innate immune system to the ecology of bacteria and bacterial viruses. We show analytically how the dynamics of bacterial populations are shaped by the activities of immunity-conferring enzymes in single cells and how the ecological consequences imply optimal bacterial defense strategies against viruses. Our results suggest that bacterial populations in the presence of viruses can either optimize their initial growth rate or their population size, with the first strategy favoring simple immunity featuring a single restriction modification system and the second strategy favoring complex bacterial innate immunity featuring several simultaneously active restriction modification systems.

Effects of Population Dynamics on Establishment of a Restriction-Modification System in a Bacterial Host

In vivo dynamics of protein levels in bacterial cells depend on both intracellular regulation and relevant population dynamics. Such population dynamics effects, e.g., interplay between cell and plasmid division rates, are, however, often neglected in modeling gene expression regulation. Including them in a model introduces additional parameters shared by the dynamical equations, which can significantly increase dimensionality of the parameter inference. We here analyse the importance of these effects, on a case of bacterial restriction-modification (R-M) system. We redevelop our earlier minimal model of this system gene expression regulation, based on a thermodynamic and dynamic system modeling framework, to include the population dynamics effects. To resolve the problem of effective coupling of the dynamical equations, we propose a "mean-field-like" procedure, which allows determining only part of the parameters at a time, by separately fitting them to expression dynamics data of individual molecular species. We show that including the interplay between kinetics of cell division and plasmid replication is necessary to explain the experimental measurements. Moreover, neglecting population dynamics effects can lead to falsely identifying non-existent regulatory mechanisms. Our results call for advanced methods to reverse-engineer intracellular regulation from dynamical data, which would also take into account the population dynamics effects.

Photocatalysis Enables Visible-Light Uncaging of Bioactive Molecules in Live Cells

The photo-manipulation of bioactive molecules provides unique advantages due to the high temporal and spatial precision of light. The first visible-light uncaging reaction by photocatalytic deboronative hydroxylation in live cells is now demonstrated. Using Fluorescein and Rhodamine derivatives as photocatalysts and ascorbates as reductants, transient hydrogen peroxides were generated from molecular oxygen to uncage phenol, alcohol, and amine functional groups on bioactive molecules in bacteria and mammalian cells, including neurons. This effective visible-light uncaging reaction enabled the light-inducible protein expression, the photo-manipulation of membrane potentials, and the subcellular-specific photo-release of small molecules.

Metabolite sensing and signaling in cell metabolism

Metabolite sensing is one of the most fundamental biological processes. During evolution, multilayered mechanisms developed to sense fluctuations in a wide spectrum of metabolites, including nutrients, to coordinate cellular metabolism and biological networks. To date, AMPK and mTOR signaling are among the best-understood metabolite-sensing and signaling pathways. Here, we propose a sensor-transducer-effector model to describe known mechanisms of metabolite sensing and signaling. We define a metabolite sensor by its specificity, dynamicity, and functionality. We group the actions of metabolite sensing into three different modes: metabolite sensor-mediated signaling, metabolite-sensing module, and sensing by conjugating. With these modes of action, we provide a systematic view of how cells sense sugars, lipids, amino acids, and metabolic intermediates. In the future perspective, we suggest a systematic screen of metabolite-sensing macromolecules, high-throughput discovery of biomacromolecule-metabolite interactomes, and functional metabolomics to advance our knowledge of metabolite sensing and signaling. Most importantly, targeting metabolite sensing holds great promise in therapeutic intervention of metabolic diseases and in improving healthy aging.

A simple, three-part model provides a systematic view of how cells sense sugars, lipids, amino acids and metabolic intermediates. Cells quickly and accurately perceive changes in intra- and extracellular molecules such as nutrients to respond to changing environments. Drawing on existing knowledge about AMPK and MTORC1 signaling, Yi-Ping Wang and Qun-Ying Lei at Fudan University in Shanghai propose a model in which three components: a sensor, transducer and effector enable metabolic sensing and signaling to proceed. The sensor detects the metabolite, and, through conjugation, conformational changes or protein–protein interactions, transmits this information to the transducer, which decides the appropriate response. The transducer then issues orders to effector proteins which coordinate the action. The future identification of novel metabolic sensors through systematic screening could lead to new therapeutic interventions for metabolic and age-related diseases.

Transcriptional precision and accuracy in development: from measurements to models and mechanisms

During development, genes are transcribed at specific times, locations and levels. In recent years, the emergence of quantitative tools has significantly advanced our ability to measure transcription with high spatiotemporal resolution in vivo. Here, we highlight recent studies that have used these tools to characterize transcription during development, and discuss the mechanisms that contribute to the precision and accuracy of the timing, location and level of transcription. We attempt to disentangle the discrepancies in how physicists and biologists use the term ‘precision' to facilitate interactions using a common language. We also highlight selected examples in which the coupling of mathematical modeling with experimental approaches has provided important mechanistic insights, and call for a more expansive use of mathematical modeling to exploit the wealth of quantitative data and advance our understanding of animal transcription.

Summary: This Review highlights how high-resolution quantitative tools and theoretical models have formed our current view of the mechanisms determining precision and accuracy in the timing, location and level of transcription in the Drosophila embryo.

Random positioning of nucleosomes enhances heritable bistability

Chromosomal regions are often dynamically modified by histones, leading to the uncertainty of nucleosome positions. Experiments have provided evidence for this randomness, but it is unclear how it impacts epigenetic heritability. Here, by analyzing a mechanic model at the molecular level, which considers three representative types of nucleosomes (unmodified, methylated, and acetylated) and dynamic nucleosome modifications, we find that in contrast to the equidistance partition of nucleosomes, random partition can significantly enhance heritable bistability. Moreover, the more "chaotic" the nucleosome positions are, the better the heritable bistability is, in contrast to the previous view. In both cases of nucleosome positioning, heritable bistability occurs only when the total nucleosome number is beyond a threshold, and it depends strongly on the allocation rate that enzymes regulate transitions between different nucleosome types. Thus, we conclude that random positioning of nucleosomes is an unneglectable factor impacting heritable bistability. A point worth mentioning is that our model established on a master equation can easily be extended to include other more complex processes underlying dynamic nucleosome modifications.

Phenotypic Evolution With and Beyond Genome Evolution

DNA does not make phenotypes on its own. In this volume entitled "Genes and Phenotypic Evolution," the present review draws the attention on the process of phenotype construction-including development of multicellular organisms-and the multiple interactions and feedbacks between DNA, organism, and environment at various levels and timescales in the evolutionary process. First, during the construction of an individual's phenotype, DNA is recruited as a template for building blocks within the cellular context and may in addition be involved in dynamical feedback loops that depend on the environmental and organismal context. Second, in the production of phenotypic variation among individuals, stochastic, environmental, genetic, and parental sources of variation act jointly. While in controlled laboratory settings, various genetic and environmental factors can be tested one at a time or in various combinations, they cannot be separated in natural populations because the environment is not controlled and the genotype can rarely be replicated. Third, along generations, genotype and environment each have specific properties concerning the origin of their variation, the hereditary transmission of this variation, and the evolutionary feedbacks. Natural selection acts as a feedback from phenotype and environment to genotype. This review integrates recent results and concrete examples that illustrate these three points. Although some themes are shared with recent calls and claims to a new conceptual framework in evolutionary biology, the viewpoint presented here only means to add flesh to the standard evolutionary synthesis.

Adapting to Adaptations: Behavioural Strategies that are Robust to Mutations and Other Organisational-Transformations

Genetic mutations, infection by parasites or symbionts, and other events can transform the way that an organism’s internal state changes in response to a given environment. We use a minimalistic computational model to support an argument that by behaving “interoceptively,” i.e. responding to internal state rather than to the environment, organisms can be robust to these organisational-transformations. We suggest that the robustness of interoceptive behaviour is due, in part, to the asymmetrical relationship between an organism and its environment, where the latter more substantially influences the former than vice versa. This relationship means that interoceptive behaviour can respond to the environment, the internal state and the interaction between the two, while exteroceptive behaviour can only respond to the environment. We discuss the possibilities that (i) interoceptive behaviour may play an important role of facilitating adaptive evolution (especially in the early evolution of primitive life) and (ii) interoceptive mechanisms could prove useful in efforts to create more robust synthetic life-forms.

The Design and Transformation of Biofundamentals: A Nonsurvey Introductory Evolutionary and Molecular Biology Course

Many introductory biology courses amount to superficial surveys of disconnected topics. Often, foundational observations and the concepts derived from them and students' ability to use these ideas appropriately are overlooked, leading to unrealistic expectations and unrecognized learning obstacles. The result can be a focus on memorization at the expense of the development of a meaningful framework within which to consider biological phenomena. About a decade ago, we began a reconsideration of what an introductory course should present to students and the skills they need to master. The original Web-based course's design presaged many of the recommendations of the Vision and Change report; in particular, a focus on social evolutionary mechanisms, stochastic (evolutionary and molecular) processes, and core ideas (cellular continuity, evolutionary homology, molecular interactions, coupled chemical reactions, and molecular machines). Inspired by insights from the Chemistry, Life, the Universe & Everything general chemistry project, we transformed the original Web version into a (freely available) book with a more unified narrative flow and a set of formative assessments delivered through the beSocratic system. We outline how student responses to course materials are guiding future course modifications, in particular a more concerted effort at helping students to construct logical, empirically based arguments, explanations, and models.

Simulation and prediction of protein production in fed-batch E. coli cultures: An engineering approach

An overall model describing the dynamic behavior of fed-batch E. coli processes for protein production has been built, calibrated and validated. Using a macroscopic approach, the model consists of three interconnected blocks allowing simulation of biomass, inducer and protein concentration profiles with time. The model incorporates calculation of the extra and intracellular inducer concentration, as well as repressor-inducer dynamics leading to a successful prediction of the product concentration. The parameters of the model were estimated using experimental data of a rhamnulose-1-phosphate aldolase-producer strain, grown under a wide range of experimental conditions. After validation, the model has successfully predicted the behavior of different strains producing two different proteins: fructose-6-phosphate aldolase and ω-transaminase. In summary, the presented approach represents a powerful tool for E. coli production process simulation and control.

Cellular metabolic network analysis: discovering important reactions in Treponema pallidum

T. pallidum, the syphilis-causing pathogen, performs very differently in metabolism compared with other bacterial pathogens. The desire for safe and effective vaccine of syphilis requests identification of important steps in T. pallidum's metabolism. Here, we apply Flux Balance Analysis to represent the reactions quantitatively. Thus, it is possible to cluster all reactions in T. pallidum. By calculating minimal cut sets and analyzing topological structure for the metabolic network of T. pallidum, critical reactions are identified. As a comparison, we also apply the analytical approaches to the metabolic network of H. pylori to find coregulated drug targets and unique drug targets for different microorganisms. Based on the clustering results, all reactions are further classified into various roles. Therefore, the general picture of their metabolic network is obtained and two types of reactions, both of which are involved in nucleic acid metabolism, are found to be essential for T. pallidum. It is also discovered that both hubs of reactions and the isolated reactions in purine and pyrimidine metabolisms play important roles in T. pallidum. These reactions could be potential drug targets for treating syphilis.

PROKARYO: an illustrative and interactive computational model of the lactose operon in the bacterium Escherichia coli

Background

We are creating software for agent-based simulation and visualization of bio-molecular processes in bacterial and eukaryotic cells. As a first example, we have built a 3-dimensional, interactive computer model of an Escherichia coli bacterium and its associated biomolecular processes. Our illustrative model focuses on the gene regulatory processes that control the expression of genes involved in the lactose operon. Prokaryo, our agent-based cell simulator, incorporates cellular structures, such as plasma membranes and cytoplasm, as well as elements of the molecular machinery, including RNA polymerase, messenger RNA, lactose permease, and ribosomes.

Results

The dynamics of cellular ’agents’ are defined by their rules of interaction, implemented as finite state machines. The agents are embedded within a 3-dimensional virtual environment with simulated physical and electrochemical properties. The hybrid model is driven by a combination of (1) mathematical equations (DEQs) to capture higher-scale phenomena and (2) agent-based rules to implement localized interactions among a small number of molecular elements. Consequently, our model is able to capture phenomena across multiple spatial scales, from changing concentration gradients to one-on-one molecular interactions.

We use the classic gene regulatory mechanism of the lactose operon to demonstrate our model’s resolution, visual presentation, and real-time interactivity. Our agent-based model expands on a sophisticated mathematical E. coli metabolism model, through which we highlight our model’s scientific validity.

Conclusion

We believe that through illustration and interactive exploratory learning a model system like Prokaryo can enhance the general understanding and perception of biomolecular processes. Our agent-DEQ hybrid modeling approach can also be of value to conceptualize, illustrate, and—eventually—validate cell experiments in the wet lab.

Environmental perception and epigenetic memory: mechanistic insight through FLC

Chromatin plays a central role in orchestrating gene regulation at the transcriptional level. However, our understanding of how chromatin states are altered in response to environmental and developmental cues, and then maintained epigenetically over many cell divisions, remains poor. The floral repressor gene FLOWERING LOCUS C (FLC) in Arabidopsis thaliana is a useful system to address these questions. FLC is transcriptionally repressed during exposure to cold temperatures, allowing studies of how environmental conditions alter expression states at the chromatin level. FLC repression is also epigenetically maintained during subsequent development in warm conditions, so that exposure to cold may be remembered. This memory depends on molecular complexes that are highly conserved among eukaryotes, making FLC not only interesting as a paradigm for understanding biological decision-making in plants, but also an important system for elucidating chromatin-based gene regulation more generally. In this review, we summarize our understanding of how cold temperature induces a switch in the FLC chromatin state, and how this state is epigenetically remembered. We also discuss how the epigenetic state of FLC is reprogrammed in the seed to ensure a requirement for cold exposure in the next generation.

Determining the bistability parameter ranges of artificially induced lac operon using the root locus method

This paper employs the root locus method to conduct a detailed investigation of the parameter regions that ensure bistability in a well-studied gene regulatory network namely, lac operon of Escherichia coli (E. coli). In contrast to previous works, the parametric bistability conditions observed in this study constitute a complete set of necessary and sufficient conditions. These conditions were derived by applying the root locus method to the polynomial equilibrium equation of the lac operon model to determine the parameter values yielding the multiple real roots necessary for bistability. The lac operon model used was defined as an ordinary differential equation system in a state equation form with a rational right hand side, and it was compatible with the Hill and Michaelis-Menten approaches of enzyme kinetics used to describe biochemical reactions that govern lactose metabolism. The developed root locus method can be used to study the steady-state behavior of any type of convergent biological system model based on mass action kinetics. This method provides a solution to the problem of analyzing gene regulatory networks under parameter uncertainties because the root locus method considers the model parameters as variable, rather than fixed. The obtained bistability ranges for the lac operon model parameters have the potential to elucidate the appearance of bistability for E. coli cells in in vivo experiments, and they could also be used to design robust hysteretic switches in synthetic biology.

Stochastic parameter search for events

Background

With recent increase in affordability and accessibility of high-performance computing (HPC), the use of large stochastic models has become increasingly popular for its ability to accurately mimic the behavior of the represented biochemical system. One important application of such models is to predict parameter configurations that yield an event of scientific significance. Due to the high computational requirements of Monte Carlo simulations and dimensionality of parameter space, brute force search is computationally infeasible for most large models.

Results

We have developed a novel parameter estimation algorithm—Stochastic Parameter Search for Events (SParSE)—that automatically computes parameter configurations for propagating the system to produce an event of interest at a user-specified success rate and error tolerance. Our method is highly automated and parallelizable. In addition, computational complexity does not scale linearly with the number of unknown parameters; all reaction rate parameters are updated concurrently at the end of each iteration in SParSE. We apply SParSE to three systems of increasing complexity: birth-death, reversible isomerization, and Susceptible-Infectious-Recovered-Susceptible (SIRS) disease transmission. Our results demonstrate that SParSE substantially accelerates computation of the parametric solution hyperplane compared to uniform random search. We also show that the novel heuristic for handling over-perturbing parameter sets enables SParSE to compute biasing parameters for a class of rare events that is not amenable to current algorithms that are based on importance sampling.

Conclusions

SParSE provides a novel, efficient, event-oriented parameter estimation method for computing parametric configurations that can be readily applied to any stochastic systems obeying chemical master equation (CME). Its usability and utility do not diminish with large systems as the algorithmic complexity for a given system is independent of the number of unknown reaction rate parameters.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-014-0126-y) contains supplementary material, which is available to authorized users.

Systems biophysics of gene expression

Gene expression is a process central to any form of life. It involves multiple temporal and functional scales that extend from specific protein-DNA interactions to the coordinated regulation of multiple genes in response to intracellular and extracellular changes. This diversity in scales poses fundamental challenges to the use of traditional approaches to fully understand even the simplest gene expression systems. Recent advances in computational systems biophysics have provided promising avenues to reliably integrate the molecular detail of biophysical process into the system behavior. Here, we review recent advances in the description of gene regulation as a system of biophysical processes that extend from specific protein-DNA interactions to the combinatorial assembly of nucleoprotein complexes. There is now basic mechanistic understanding on how promoters controlled by multiple, local and distal, DNA binding sites for transcription factors can actively control transcriptional noise, cell-to-cell variability, and other properties of gene regulation, including precision and flexibility of the transcriptional responses.

An objective function exploiting suboptimal solutions in metabolic networks

Background

Flux Balance Analysis is a theoretically elegant, computationally efficient, genome-scale approach to predicting biochemical reaction fluxes. Yet FBA models exhibit persistent mathematical degeneracy that generally limits their predictive power.

Results

We propose a novel objective function for cellular metabolism that accounts for and exploits degeneracy in the metabolic network to improve flux predictions. In our model, regulation drives metabolism toward a region of flux space that allows nearly optimal growth. Metabolic mutants deviate minimally from this region, a function represented mathematically as a convex cone. Near-optimal flux configurations within this region are considered equally plausible and not subject to further optimizing regulation. Consistent with relaxed regulation near optimality, we find that the size of the near-optimal region predicts flux variability under experimental perturbation.

Conclusion

Accounting for suboptimal solutions can improve the predictive power of metabolic FBA models. Because fluctuations of enzyme and metabolite levels are inevitable, tolerance for suboptimality may support a functionally robust metabolic network.

Evolution in microbes

This review presents a broad survey of experimental microbial evolution, covering diverse topics including trade-offs, epistasis, fluctuating conditions, spatial dynamics, cooperation, aging, and stochastic switching. Emphasis is placed on examples that highlight key conceptual points or address theoretical predictions. Experimental evolution is discussed from two points of view. First, population trajectories are described as adaptive walks on a fitness landscape, whose genetic structure can be probed by experiments. Second, populations are viewed from a physiological perspective, and their nongenetic heterogeneity is examined. Bringing together these two viewpoints remains a major challenge for the future.

The effect of LacI autoregulation on the performance of the lactose utilization system in Escherichia coli

The lactose operon of Escherichia coli is a paradigm system for quantitative understanding of gene regulation in prokaryotes. Yet, none of the many mathematical models built so far to study the dynamics of this system considered the fact that the Lac repressor regulates its own transcription by forming a transcriptional roadblock at the O3 operator site. Here we study the effect of autoregulation on intracellular LacI levels and also show that cAMP-CRP binding does not affect the efficiency of autoregulation. We built a mathematical model to study the role of LacI autoregulation in the lactose utilization system. Previously, it has been argued that negative autoregulation can significantly reduce noise as well as increase the speed of response. We show that the particular molecular mechanism, a transcriptional roadblock, used to achieve self-repression in the lac system does neither. Instead, LacI autoregulation balances two opposing states, one that allows quicker response to smaller pulses of external lactose, and the other that minimizes production costs in the absence of lactose.

Resolving Sample Traces in Complex Mixtures with Microarray Analyses

This chapter reviews the microarray technology and deal with the majority of aspects regarding microarrays. It focuses on today’s knowledge of separation techniques and methodologies of complex signal, i.e. samples. Overall, the chapter reviews the current knowledge on the topic of microarrays and presents the analyses and techniques used, which facilitate such approaches. It starts with the theoretical framework on microarray technology; second, the chapter gives a brief review on statistical methods used for microarray analyses, and finally, it contains a detailed review of the methods used for discriminating traces of nucleic acids within a complex mixture of samples.

Kinetic approaches to lactose operon induction and bimodality

The quasi-equilibrium approximation is acceptable when molecular interactions are fast enough compared to circuit dynamics, but is no longer allowed when cellular activities are governed by rare events. A typical example is the lactose operon (lac), one of the most famous paradigms of transcription regulation, for which several theories still coexist to describe its behaviors. The lac system is generally analyzed by using equilibrium constants, contradicting single-event hypotheses long suggested by Novick and Weiner (1957). Enzyme induction as an all-or-none phenomenon. Proc. Natl. Acad. Sci. USA 43, 553-566) and recently refined in the study of (Choi et al., 2008. A stochastic single-molecule event triggers phenotype switching of a bacterial cell. Science 322, 442-446). In the present report, a lac repressor (LacI)-mediated DNA immunoprecipitation experiment reveals that the natural LacI-lac DNA complex built in vivo is extremely tight and long-lived compared to the time scale of lac expression dynamics, which could functionally disconnect the abortive expression bursts and forbid using the standard modes of lac bistability. As alternatives, purely kinetic mechanisms are examined for their capacity to restrict induction through: (i) widely scattered derepression related to the arrival time variance of a predominantly backward asymmetric random walk and (ii) an induction threshold arising in a single window of derepression without recourse to nonlinear multimeric binding and Hill functions. Considering the complete disengagement of the lac repressor from the lac promoter as the probabilistic consequence of a transient stepwise mechanism, is sufficient to explain the sigmoidal lac responses as functions of time and of inducer concentration. This sigmoidal shape can be misleadingly interpreted as a phenomenon of equilibrium cooperativity classically used to explain bistability, but which has been reported to be weak in this system.