Probing gene expression in live cells, one protein molecule at a time

Modelling Population-Level Hes1 Dynamics: Insights from a Multi-framework Approach

Mathematical models of living cells have been successively refined with advancements in experimental techniques. A main concern is striking a balance between modelling power and the tractability of the associated mathematical analysis. In this work we model the dynamics for the transcription factor Hairy and enhancer of split-1 (Hes1), whose expression oscillates during neural development, and which critically enables stable fate decision in the embryonic brain. We design, parametrise, and analyse a detailed spatial model using ordinary differential equations (ODEs) over a grid capturing both transient oscillatory behaviour and fate decision on a population-level. We also investigate the relationship between this ODE model and a more realistic grid-based model involving intrinsic noise using mostly directly biologically motivated parameters. While we focus specifically on Hes1 in neural development, the approach of linking deterministic and stochastic grid-based models shows promise in modelling various biological processes taking place in a cell population. In this context, our work stresses the importance of the interpretability of complex computational models into a framework which is amenable to mathematical analysis.

Multimodal Nanoplasmonic and Fluorescence Imaging for Simultaneous Monitoring of Single-Cell Secretory and Intracellular Dynamics

Current imaging technologies are limited in their capability to simultaneously capture intracellular and extracellular dynamics in a spatially and temporally resolved manner. This study presents a multimodal imaging system that integrates nanoplasmonic sensing with multichannel fluorescence imaging to concomitantly analyze intracellular and extracellular processes in space and time at the single-cell level. Utilizing a highly sensitive gold nanohole array biosensor, the system provides label-free and real-time monitoring of extracellular secretion, while implementing nanoplasmonic-compatible multichannel fluorescence microscopy enables to visualize the interconnected intracellular activities. Combined with deep-learning-assisted image processing, this integrated approach allows multiparametric and simultaneous study of various cellular constituents in hundreds of individual cells with subcellular spatial and minute-level temporal resolution over extended periods of up to 20 h. The system's utility is demonstrated by characterizing a range of secreted biomolecules and fluorescence toolkits across three distinct applications: visualization of secretory behaviors along with subcellular organelles and metabolic processes, concurrent monitoring of protein expression and secretion, and assessment of cell cycle phases alongside their corresponding secretory profiles. By offering comprehensive insights, the multifunctional approach is expected to enhance holistic readouts of biological systems, facilitating new discoveries in both fundamental and translational sciences.

Optimisation of gene expression noise for cellular persistence against lethal events

Bacterial cell persistence, crucial for survival under adverse conditions like antibiotic exposure, is intrinsically linked to stochastic fluctuations in gene expression. Certain genes, while inhibiting growth under normal circumstances, confer tolerance to antibiotics at elevated expression levels. The occurrence of antibiotic events lead to instantaneous cellular responses with varied survival probabilities correlated with gene expression levels. Notably, cells with lower protein concentrations face higher mortality rates. This study aims to elucidate an optimal strategy for protein expression conducive to cellular survival. Through comprehensive mathematical analysis, we determine the optimal burst size and frequency that maximise cell proliferation. Furthermore, we explore how the optimal expression distribution changes as the cost of protein expression to growth escalates. Our model reveals a hysteresis phenomenon, characterised by discontinuous transitions between deterministic and stochastic optima. Intriguingly, stochastic optima possess a noise floor, representing the minimal level of fluctuations essential for optimal cellular resilience.

Attractor Landscape Analysis Reveals a Reversion Switch in the Transition of Colorectal Tumorigenesis

A cell fate change such as tumorigenesis incurs critical transition. It remains a longstanding challenge whether the underlying mechanism can be unraveled and a molecular switch that can reverse such transition is found. Here a systems framework, REVERT, is presented with which can reconstruct the core molecular regulatory network model and a reversion switch based on single-cell transcriptome data over the transition process is identified. The usefulness of REVERT is demonstrated by applying it to single-cell transcriptome of patient-derived matched organoids of colon cancer and normal colon. REVERT is a generic framework that can be applied to investigate various cell fate transition phenomena.

Bone-derived nanoparticles (BNPs) enhance osteogenic differentiation via Notch signaling

Mesenchymal stem cell (MSC)-based bone tissue regeneration has gained significant attention due to the excellent differentiation capacity and immunomodulatory activity of MSCs. Enhancing osteogenesis regulation is crucial for improving the therapeutic efficacy of MSC-based regeneration. By utilizing the regenerative capacity of bone ECM and the functionality of nanoparticles, we recently engineered bone-based nanoparticles (BNPs) from decellularized porcine bones. The effects of internalization of BNPs on MSC viability, proliferation, and osteogenic differentiation were first investigated and compared at different time points. The phenotypic behaviors, including cell number, proliferation, and differentiation were characterized and compared. By incorporating a LNA/DNA nanobiosensor and MSC live cell imaging, we monitored and compared Notch ligand delta-like 4 (Dll4) expression dynamics in the cytoplasm and nucleus during osteogenic differentiation. Pharmacological interventions are used to inhibit Notch signaling to examine the mechanisms involved. The results suggest that Notch inhibition mediates the osteogenic process, with reduced expression of early and late stage differentiation markers (ALP and calcium mineralization). The internalization of BNPs led to an increase in Dll4 expression, exhibiting a time-dependent pattern that aligned with enhanced cell proliferation and differentiation. Our findings indicate that the observed changes in BNP-treated cells during osteogenic differentiation could be associated with elevated levels of Dll4 mRNA expression. In summary, this study provides new insights into MSC osteogenic differentiation and the molecular mechanisms through which BNPs stimulate this process. The results indicate that BNPs influence osteogenesis by modulating Notch ligand Dll4 expression, demonstrating a potential link between Notch signaling and the proteins present in BNPs.

Exact distributions of threshold crossing times of proteins under post-transcriptional regulation by small RNAs

The timings of several cellular events like cell lysis, cell division, or pore formation in endosomes are regulated by the time taken for the relevant proteins to cross a threshold in number or concentration. Since protein synthesis is stochastic, the threshold crossing time is a first passage problem. The exact distributions of these first passage processes have been obtained recently for unregulated and autoregulated genes. Many proteins are however regulated by post-transcriptional regulation, controlled by small noncoding RNAs (sRNAs). Certain mathematical models of gene expression with post-transcriptional sRNA regulation have been recently exactly mapped to models without sRNA regulation. Utilizing this mapping and the exact distributions, we calculate exact results on fluctuations (full distribution, all cumulants, and characteristic times) of protein threshold crossing times in the presence of sRNA regulation. We derive two interesting predictions from these exact results. We show that the size of the fluctuation of the threshold crossing times have a nonmonotonic U-shaped behavior as a function of the rates of binding and unbinding of the sRNA-mRNA complex. Thus there are optimal parameters that minimize noise. Furthermore, the fluctuations in models with sRNA regulation may be higher or lower compared to the model without regulation, depending on the mean protein burst size.

A Simple and Low-cost Preliminary Quantification of Target Membrane Protein in Single Cells

To study the heterogeneity of target membrane proteins in single cells with cellular integrity, we proposed a simple and low-cost method to obtain the copy number of the membrane proteins. HeLa cells were labeled by FITC affinity bodies specifically targeting HER2 membrane proteins. The immunolabeled HeLa cells were quantified by a laboratory-built laser induced fluorescence detector. A series of fluorescent microspheres with known number of FITC molecules on the surface were used to establish the calibration curve, instead of the standard fluorescent solutions, because the morphology of the microspheres was similar to the cells, and the distribution of FITC on the spheres were similar to the distribution of HER2 on the HeLa. The fluorescence intensity of the cells was converted to the molecule number of HER2 by the calibration curve. A capillary electrophoresis system was used to drive the microspheres and cells through the detection window. The copy number of HER2 in HeLa cells ranged from 4,036 to 1,224,920 ± 100 (2.5-97.5%), and the median of copy numbers were 104,438 ± 100 per cell. This method for measuring low-abundance membrane proteins can be utilized for the initial exploration of proteomics in ordinary laboratories.

Genome-wide single-cell and single-molecule footprinting of transcription factors with deaminase

Decades of research have established that mammalian transcription factors (TFs) bind to each gene's regulatory regions and cooperatively control tissue specificity, timing, and intensity of gene transcription. Mapping the combination of TF binding sites genome wide is critically important for understanding functional genomics. Here, we report a technique to measure TFs' binding sites on the human genome with a near single-base resolution by footprinting with deaminase (FOODIE) on a single-molecule and single-cell basis. Single-molecule sequencing reads after enzymatic deamination allow detection of the TF binding fraction on a particular footprint and the binding cooperativity of any two adjacent TFs, which can be either positive or negative. As a newcomer of single-cell genomics, single-cell FOODIE enables the detection of cell-type-specific TF footprints in a pure cell population in a heterogeneous tissue, such as the brain. We found that genes carrying out a certain biological function together in a housing-keeping correlated gene module (CGM) or a tissues-specific CGM are coordinated by shared TFs in the gene's promoters and enhancers, respectively. Scalable and cost-effective, FOODIE allows us to create an open FOODIE database for cell lines, with applicability to human tissues and clinical samples.

Sequestration of gene products by decoys enhances precision in the timing of intracellular events

Expressed gene products often interact ubiquitously with binding sites at nucleic acids and macromolecular complexes, known as decoys. The binding of transcription factors (TFs) to decoys can be crucial in controlling the stochastic dynamics of gene expression. Here, we explore the impact of decoys on the timing of intracellular events, as captured by the time taken for the levels of a given TF to reach a critical threshold level, known as the first passage time (FPT). Although nonlinearity introduced by binding makes exact mathematical analysis challenging, employing suitable approximations and reformulating FPT in terms of an alternative variable, we analytically assess the impact of decoys. The stability of the decoy-bound TFs against degradation impacts FPT statistics crucially. Decoys reduce noise in FPT, and stable decoy-bound TFs offer greater timing precision with less expression cost than their unstable counterparts. Interestingly, when both bound and free TFs decay at the same rate, decoy binding does not directly alter FPT noise. We verify these results by performing exact stochastic simulations. These results have important implications for the precise temporal scheduling of events involved in the functioning of biomolecular clocks, development processes, cell-cycle control, and cell-size homeostasis.

DNA packaging by molecular motors: from bacteriophage to human chromosomes

Dense packaging of genomic DNA is crucial for organismal survival, as DNA length always far exceeds the dimensions of the cells that contain it. Organisms, therefore, use sophisticated machineries to package their genomes. These systems range across kingdoms from a single ultra-powerful rotary motor that spools the DNA into a bacteriophage head, to hundreds of thousands of relatively weak molecular motors that coordinate the compaction of mitotic chromosomes in eukaryotic cells. Recent technological advances, such as DNA proximity-based sequencing approaches, polymer modelling and in vitro reconstitution of DNA loop extrusion, have shed light on the biological mechanisms driving DNA organization in different systems. Here, we discuss DNA packaging in bacteriophage, bacteria and eukaryotic cells, which, despite their extreme variation in size, structure and genomic content, all rely on the action of molecular motors to package their genomes.

Event horizon kinetic Monte Carlo

In this study, we present a novel approach for modeling the dynamics of stochastic processes. The fundamental concept involves constructing a stochastic Markov chain comprising states separated by more than one stochastic event. Initially, the method explores the network of neighboring states connected by stochastic events. This exploration results in a "horizon" of events leading to a set of "boundary" states at the periphery of each local network. Subsequently, the next member in the Markov chain is selected from the "boundary" states based on the probability of reaching each of the "boundary" states for the first time. Meanwhile, the simulation clock is updated according to the time required to reach the boundary for the first time. This can be achieved using an analytical approach, where the probability of reaching each boundary state for the first time is estimated using absorbing conditions for all boundary states in the analytical solution of a master equation describing the local network of states around each current state. The proposed method is demonstrated in modeling the dynamics in networks of stochastic reactions but can be easily applied in any stochastic system whose dynamics can be expressed via the solution of a master equation. It is expected to enhance the efficiency of event-driven Monte Carlo simulations, originally introduced by Gillespie and widely regarded as the gold standard in the field, especially in cases where the presence of events is characterized by different timescales.

Ribosome External Electric Field Regulates Metabolic Enzyme Activity: The RAMBO Effect

Ribosomes bind to many metabolic enzymes and change their activity. A general mechanism for ribosome-mediated amplification of metabolic enzyme activity, RAMBO, was formulated and elucidated for the glycolytic enzyme triosephosphate isomerase, TPI. The RAMBO effect results from a ribosome-dependent electric field-substrate dipole interaction energy that can increase or decrease the ground state of the reactant and product to regulate catalytic rates. NMR spectroscopy was used to determine the interaction surface of TPI binding to ribosomes and to measure the corresponding kinetic rates in the absence and presence of intact ribosome particles. Chemical cross-linking and mass spectrometry revealed potential ribosomal protein binding partners of TPI. Structural results and related changes in TPI energetics and activity show that the interaction between TPI and ribosomal protein L11 mediate the RAMBO effect.

Analysis of Fluorescent Proteins for Observing Single Gene Locus in a Live and Fixed Escherichia coli Cell

Fluorescent proteins (FPs) are essential tools for advanced microscopy techniques such as super-resolution imaging, single-particle tracking, and quantitative single-molecule counting. Various FPs fused to DNA-binding proteins have been used to observe the subcellular location and movement of specific gene loci in living and fixed bacterial cells. However, quantitative assessments of the properties of FPs for gene locus measurements are still lacking. Here, we assessed various FPs to observe specific gene loci in live and fixed Escherichia coli cells using a fluorescent repressor-operator binding system (FROS), tet operator-Tet repressor proteins (TetR). Tsr-fused FPs were used to assess the intensity and photostability of various FPs (five red FPs: mCherry2, FusionRed, mRFP, mCrimson3, and dKatushka; and seven yellow FPs: SYFP2, Venus, mCitrine, YPet, mClover3, mTopaz, and EYFP) at the single-molecule level in living cells. These FPs were then used for gene locus measurements using FROS. Our results indicate that TetR-mCrimson3 (red) and TetR-EYFP (yellow) had better properties for visualizing gene loci than the other TetR-FPs. Furthermore, fixation procedures affected the clustering of diffusing TetR-FPs and altered the locations of the TetR-FP foci. Fixation with formaldehyde consistently disrupted proper DNA locus observations using TetR-FPs. Notably, the foci measured using TetR-mCrimson3 remained close to their original positions in live cells after glyoxal fixation. This in vivo study provides a cell-imaging guide for the use of FPs for gene-locus observation in E. coli and a scheme for evaluating the use of FPs for other cell-imaging purposes.

Stochastic Gene Expression in Proliferating Cells: Differing Noise Intensity in Single-Cell and Population Perspectives

Random fluctuations (noise) in gene expression can be studied from two complementary perspectives: following expression in a single cell over time or comparing expression between cells in a proliferating population at a given time. Here, we systematically investigated scenarios where both perspectives lead to different levels of noise in a given gene product. We first consider a stable protein, whose concentration is diluted by cellular growth, and the protein inhibits growth at high concentrations, establishing a positive feedback loop. For a stochastic model with molecular bursting of gene products, we analytically predict and contrast the steady-state distributions of protein concentration in both frameworks. Although positive feedback amplifies the noise in expression, this amplification is much higher in the population framework compared to following a single cell over time. We also study other processes that lead to different noise levels even in the absence of such dilution-based feedback. When considering randomness in the partitioning of molecules between daughters during mitosis, we find that in the single-cell perspective, the noise in protein concentration is independent of noise in the cell cycle duration. In contrast, partitioning noise is amplified in the population perspective by increasing randomness in cell-cycle time. Overall, our results show that the commonly used single-cell framework that does not account for proliferating cells can, in some cases, underestimate the noise in gene product levels. These results have important implications for studying the inter-cellular variation of different stress-related expression programs across cell types that are known to inhibit cellular growth.

Probing the modulation in facilitated diffusion guided by DNA-protein interactions in target search processes

Many fundamental biophysical processes involving gene regulation and gene editing rely, at the molecular level, on an intricate methodology of searching and locating the precise target base pair sequence on the genome by specific binding proteins. A unique mechanism, known as 'facilitated diffusion', which is a combination of 1D sliding along with 3D movement, is considered to be the key step for such events. This also explains the relatively much shorter timescale of the target searching process, compared to other diffusion-controlled biophysical processes. In this work, we aim to probe the modulation of target search dynamics of a protein moiety by estimating the rate of the target search process, and the statistics of the search rounds and timescales accomplished by the 1D and 3D motions, based on first passage time (FPT) calculations. This is studied with its characteristics getting influenced by various given conditions such as, when the DNA is rigid or flexible, and when the target is placed at different locations on the DNA. The current theoretical framework includes a Brownian dynamics simulation setup adopting a straightforward coarse-grained model for a diffusing protein on DNA. Moreover, this theoretical analysis provides insights into the complex target search dynamics by highlighting the significance of the chain dynamics in the mechanistic details of the facilitated diffusion process.

Imaging spatiotemporal translation regulation in vivo

Translation is regulated spatiotemporally to direct protein synthesis when and where it is needed. RNA localization and local translation have been observed in various subcellular compartments, allowing cells to rapidly and finely adjust their proteome post-transcriptionally. Local translation on membrane-bound organelles is important to efficiently synthesize proteins targeted to the organelles. Protein-RNA phase condensates restrict RNA spatially in membraneless organelles and play essential roles in translation regulation and RNA metabolism. In addition, the temporal translation kinetics not only determine the amount of protein produced, but also serve as an important checkpoint for the quality of ribosomes, mRNAs, and nascent proteins. Translation imaging provides a unique capability to study these fundamental processes in the native environment. Recent breakthroughs in imaging enabled real-time visualization of translation of single mRNAs, making it possible to determine the spatial distribution and key biochemical parameters of in vivo translation dynamics. Here we reviewed the recent advances in translation imaging methods and their applications to study spatiotemporal translation regulation in vivo.

A genetic circuit on a single DNA molecule as an autonomous dissipative nanodevice

Realizing genetic circuits on single DNA molecules as self-encoded dissipative nanodevices is a major step toward miniaturization of autonomous biological systems. A circuit operating on a single DNA implies that genetically encoded proteins localize during coupled transcription-translation to DNA, but a single-molecule measurement demonstrating this has remained a challenge. Here, we use a genetically encoded fluorescent reporter system with improved temporal resolution and observe the synthesis of individual proteins tethered to a DNA molecule by transient complexes of RNA polymerase, messenger RNA, and ribosome. Against expectations in dilute cell-free conditions where equilibrium considerations favor dispersion, these nascent proteins linger long enough to regulate cascaded reactions on the same DNA. We rationally design a pulsatile genetic circuit by encoding an activator and repressor in feedback on the same DNA molecule. Driven by the local synthesis of only several proteins per hour and gene, the circuit dynamics exhibit enhanced variability between individual DNA molecules, and fluctuations with a broad power spectrum. Our results demonstrate that co-expressional localization, as a nonequilibrium process, facilitates single-DNA genetic circuits as dissipative nanodevices, with implications for nanobiotechnology applications and artificial cell design.

Antibiotic dose and nutrient availability differentially drive the evolution of antibiotic resistance and persistence

Effective treatment of bacterial infections proves increasingly challenging due to the emergence of bacterial variants that endure antibiotic exposure. Antibiotic resistance and persistence have been identified as two major bacterial survival mechanisms, and several studies have shown a rapid and strong selection of resistance or persistence mutants under repeated drug treatment. Yet, little is known about the impact of the environmental conditions on resistance and persistence evolution and the potential interplay between both phenotypes. Based on the distinct growth and survival characteristics of resistance and persistence mutants, we hypothesized that the antibiotic dose and availability of nutrients during treatment might play a key role in the evolutionary adaptation to antibiotic stress. To test this hypothesis, we combined high-throughput experimental evolution with a mathematical model of bacterial evolution under intermittent antibiotic exposure. We show that high nutrient levels during antibiotic treatment promote selection of high-level resistance, but that resistance mainly emerges independently of persistence when the antibiotic concentration is sufficiently low. At higher doses, resistance evolution is facilitated by the preceding or concurrent selection of persistence mutants, which ensures survival of populations in harsh conditions. Collectively, our experimental data and mathematical model elucidate the evolutionary routes toward increased bacterial survival under different antibiotic treatment schedules, which is key to designing effective antibiotic therapies.

Finding the last bits of positional information

In a developing embryo, information about the position of cells is encoded in the concentrations of morphogen molecules. In the fruit fly, the local concentrations of just a handful of proteins encoded by the gap genes are sufficient to specify position with a precision comparable to the spacing between cells along the anterior-posterior axis. This matches the precision of downstream events such as the striped patterns of expression in the pair-rule genes, but is not quite sufficient to define unique identities for individual cells. We demonstrate theoretically that this information gap can be bridged if positional errors are spatially correlated, with correlation lengths ~ 20% of the embryo length. We then show experimentally that these correlations are present, with the required strength, in the fluctuating positions of the pair-rule stripes, and this can be traced back to the gap genes. Taking account of these correlations, the available information matches the information needed for unique cellular specification, within error bars of ~ 2%. These observation support a precisionist view of information flow through the underlying genetic networks, in which accurate signals are available from the start and preserved as they are transformed into the final spatial patterns.

Long non-coding RNA (lncRNA) MALAT1 in regulating osteogenic and adipogenic differentiation using a double-stranded gapmer locked nucleic acid nanobiosensor

Long non-coding RNAs (lncRNA) are non-protein coding RNA molecules that are longer than 200 nucleotides. The lncRNA molecule plays diverse roles in gene regulation, chromatin remodeling, and cellular processes, influencing various biological pathways. However, probing the complex dynamics of lncRNA in live cells is a challenging task. In this study, a double-stranded gapmer locked nucleic acid (ds-GapM-LNA) nanobiosensor is designed for visualizing the abundance and expression of lncRNA in live human bone-marrow-derived mesenchymal stem cells (hMSCs). The sensitivity, specificity, and stability were characterized. The results showed that this ds-GapM-LNA nanobiosensor has very good sensitivity, specificity, and stability, which allows for dissecting the regulatory roles of cellular processes during dynamic physiological events. By incorporating this nanobiosensor in living hMSC imaging, we elucidated lncRNA MALAT1 expression dynamics during osteogenic and adipogenic differentiation. The data reveal that lncRNA MALAT1 expression is correlated with distinct sub-stages of osteogenic and adipogenic differentiation.

Technologies for whole-cell modeling: Genome-wide reconstruction of a cell in silico

With advances in high-throughput, large-scale in vivo measurement and genome modification techniques at the single-nucleotide level, there is an increasing demand for the development of new technologies for the flexible design and control of cellular systems. Computer-aided design is a powerful tool to design new cells. Whole-cell modeling aims to integrate various cellular subsystems, determine their interactions and cooperative mechanisms, and predict comprehensive cellular behaviors by computational simulations on a genome-wide scale. It has been applied to prokaryotes, yeasts, and higher eukaryotic cells, and utilized in a wide range of applications, including production of valuable substances, drug discovery, and controlled differentiation. Whole-cell modeling, consisting of several thousand elements with diverse scales and properties, requires innovative model construction, simulation, and analysis techniques. Furthermore, whole-cell modeling has been extended to multiple scales, including high-resolution modeling at the single-nucleotide and single-amino acid levels and multicellular modeling of tissues and organs. This review presents an overview of the current state of whole-cell modeling, discusses the novel computational and experimental technologies driving it, and introduces further developments toward multihierarchical modeling on a whole-genome scale.

Diffusion-Controlled Reactions: An Overview

We review the milestones in the century-long development of the theory of diffusion-controlled reactions. Starting from the seminal work by von Smoluchowski, who recognized the importance of diffusion in chemical reactions, we discuss perfect and imperfect surface reactions, their microscopic origins, and the underlying mathematical framework. Single-molecule reaction schemes, anomalous bulk diffusions, reversible binding/unbinding kinetics, and many other extensions are presented. An alternative encounter-based approach to diffusion-controlled reactions is introduced, with emphasis on its advantages and potential applications. Some open problems and future perspectives are outlined.

Soft repression and chromatin modification by conserved transcriptional corepressors

Transcriptional regulation in eukaryotic cells involves the activity of multifarious DNA-binding transcription factors and recruited corepressor complexes. Together, these complexes interact with the core transcriptional machinery, chromatin, and nuclear environment to effect complex patterns of gene regulation. Much focus has been paid to the action of master regulatory switches that are key to developmental and environmental responses, as these genetic elements have important phenotypic effects. The regulation of widely-expressed metabolic control genes has been less well studied, particularly in cases in which physically-interacting repressors and corepressors have subtle influences on steady-state expression. This latter phenomenon, termed "soft repression" is a topic of increasing interest as genomic approaches provide ever more powerful tools to uncover the significance of this level of control. This review provides an oversight of classic and current approaches to the study of transcriptional repression in eukaryotic systems, with a specific focus on opportunities and challenges that lie ahead in the study of soft repression.

Inferring transcriptional bursting kinetics from single-cell snapshot data using a generalized telegraph model

Gene expression has inherent stochasticity resulting from transcription's burst manners. Single-cell snapshot data can be exploited to rigorously infer transcriptional burst kinetics, using mathematical models as blueprints. The classical telegraph model (CTM) has been widely used to explain transcriptional bursting with Markovian assumptions. However, growing evidence suggests that the gene-state dwell times are generally non-exponential, as gene-state switching is a multi-step process in organisms. Therefore, interpretable non-Markovian mathematical models and efficient statistical inference methods are urgently required in investigating transcriptional burst kinetics. We develop an interpretable and tractable model, the generalized telegraph model (GTM), to characterize transcriptional bursting that allows arbitrary dwell-time distributions, rather than exponential distributions, to be incorporated into the ON and OFF switching process. Based on the GTM, we propose an inference method for transcriptional bursting kinetics using an approximate Bayesian computation framework. This method demonstrates an efficient and scalable estimation of burst frequency and burst size on synthetic data. Further, the application of inference to genome-wide data from mouse embryonic fibroblasts reveals that GTM would estimate lower burst frequency and higher burst size than those estimated by CTM. In conclusion, the GTM and the corresponding inference method are effective tools to infer dynamic transcriptional bursting from static single-cell snapshot data.

Statistical Analysis of Random Motion and Energetic Behavior of Counting: Gibbs' Theory Revisited

Following a recently reformulated Gibbs' statistical chemical thermodynamic theory on discrete state space, we present a treatment on statistical measurements of random mechanical motions in continuous space. In particular, we show how the concept of temperature and an ideal gas/solution law arise from a statistical analysis of a collection of independent and identically distributed complex particles without relying on Newtonian mechanics, nor the very concept of mechanical energy. When sampling from an ergodic system, the data ad infinitum limit elucidates how the entropy function characterizes randomness among measurements with the emergence of a novel energetic representation for the statistics and an internal energy additivity. This generalization of Gibbs' theory is applicable to statistical measurements on single living cells and other complex biological organisms, one individual at a time.

Achieving Single-Molecule Tracking of Subcellular Regulation in Bacteria during Real-Time Environmental Perturbations

Bacteria rely on protein systems for regulation in response to external environmental signals. Single-molecule fluorescence imaging and tracking has elucidated the complex mechanism of these protein systems in a variety of bacteria. We recently investigated Vibrio cholerae, the Gram-negative bacterium responsible for the human cholera disease, and its regulation of the production of toxins and virulence factors through the membrane-localized transcription factors TcpP and ToxR. These experiments determined that TcpP and ToxR work cooperatively under steady-state conditions, but measurements of how these dynamical interactions change over the course of environmental perturbations were precluded by the traditional preparation of bacterial cells confined on agarose pads. Here, we address this gap in technology and access single-molecule dynamics during real-time changes by implementing two alternative sample preparations: microfluidic devices and chitosan-coated coverslips. We report the first demonstration of single-molecule tracking within live bacterial cells in a microfluidic device. Additionally, using the chitosan-coated coverslips, we show that real-time environmental changes impact TcpP-PAmCherry dynamics, activating a virulence condition in the bacteria about 45 min after dropping to pH 6 and about 20 min after inducing ToxR expression. These new technology advances open our ability for new experiments studying a variety of bacteria with single-molecule imaging and tracking during real-time environmental perturbations.

Genome-wide inference reveals that feedback regulations constrain promoter-dependent transcriptional burst kinetics

Gene expression in mammalian cells is highly variable and episodic, resulting in a series of discontinuous bursts of mRNAs. A challenge is to understand how static promoter architecture and dynamic feedback regulations dictate bursting on a genome-wide scale. Although single-cell RNA sequencing (scRNA-seq) provides an opportunity to address this challenge, effective analytical methods are scarce. We developed an interpretable and scalable inference framework, which combined experimental data with a mechanistic model to infer transcriptional burst kinetics (sizes and frequencies) and feedback regulations. Applying this framework to scRNA-seq data generated from embryonic mouse fibroblast cells, we found Simpson's paradoxes, i.e. genome-wide burst kinetics exhibit different characteristics in two cases without and with distinguishing feedback regulations. We also showed that feedbacks differently modulate burst frequencies and sizes and conceal the effects of transcription start site distributions on burst kinetics. Notably, only in the presence of positive feedback, TATA genes are expressed with high burst frequencies and enhancer-promoter interactions mainly modulate burst frequencies. The developed inference method provided a flexible and efficient way to investigate transcriptional burst kinetics and the obtained results would be helpful for understanding cell development and fate decision.

Theoretical insights into the full description of DNA target search by subdiffusing proteins

DNA binding proteins (DBPs) diffuse in the cytoplasm to recognise and bind with their respective target sites on the DNA to initiate several biologically important processes. The first passage time distributions (FPTDs) of DBPs are useful in quantifying the timescales of the most-probable search paths in addition to the mean value of the distribution which, strikingly, are decades of order apart in time. However, extremely crowded in vivo conditions or the viscoelasticity of the cellular medium among other factors causes biomolecules to exhibit anomalous diffusion which is usually overlooked in most theoretical studies. We have obtained approximate analytical expressions of a general FPTD and the two characteristic timescales that are valid for any single subdiffusing protein searching for its target in vivo. Our results can be applied to single-particle tracking experiments of target search.

Development of single-molecule ubiquitination mediated fluorescence complementation to visualize protein ubiquitination dynamics in dendrites

The ubiquitination/proteasome system is important for the spatiotemporal control of protein synthesis and degradation at synapses, while dysregulation may underlie autism spectrum disorders (ASDs). However, methods allowing direct visualization of the subcellular localization and temporal dynamics of protein ubiquitination are lacking. Here we report the development of Single-Molecule Ubiquitin Mediated Fluorescence Complementation (SM-UbFC) as a method to visualize and quantify the dynamics of protein ubiquitination in dendrites of live neurons in culture. Using SM-UbFC, we demonstrate that the rate of PSD-95 ubiquitination is elevated in dendrites of FMR1 KO neurons compared with wild-type controls. We further demonstrate the rapid ubiquitination of the fragile X messenger ribonucleoprotein, FMRP, and the AMPA receptor subunit, GluA1, which are known to be key events in the regulation of synaptic protein synthesis and plasticity. SM-UbFC will be useful for future studies on the regulation of synaptic protein homeostasis.

Notch signaling and fluid shear stress in regulating osteogenic differentiation

Osteoporosis is a common bone and metabolic disease that is characterized by bone density loss and microstructural degeneration. Human bone marrow-derived mesenchymal stem cells (hMSCs) are multipotent progenitor cells with the potential to differentiate into various cell types, including osteoblasts, chondrocytes, and adipocytes, which have been utilized extensively in the field of bone tissue engineering and cell-based therapy. Although fluid shear stress plays an important role in bone osteogenic differentiation, the cellular and molecular mechanisms underlying this effect remain poorly understood. Here, a locked nucleic acid (LNA)/DNA nanobiosensor was exploited to monitor mRNA gene expression of hMSCs that were exposed to physiologically relevant fluid shear stress to examine the regulatory role of Notch signaling during osteogenic differentiation. First, the effects of fluid shear stress on cell viability, proliferation, morphology, and osteogenic differentiation were investigated and compared. Our results showed shear stress modulates hMSCs morphology and osteogenic differentiation depending on the applied shear and duration. By incorporating this LNA/DNA nanobiosensor and alkaline phosphatase (ALP) staining, we further investigated the role of Notch signaling in regulating osteogenic differentiation. Pharmacological treatment is applied to disrupt Notch signaling to investigate the mechanisms that govern shear stress induced osteogenic differentiation. Our experimental results provide convincing evidence supporting that physiologically relevant shear stress regulates osteogenic differentiation through Notch signaling. Inhibition of Notch signaling mediates the effects of shear stress on osteogenic differentiation, with reduced ALP enzyme activity and decreased Dll4 mRNA expression. In conclusion, our results will add new information concerning osteogenic differentiation of hMSCs under shear stress and the regulatory role of Notch signaling. Further studies may elucidate the mechanisms underlying the mechanosensitive role of Notch signaling in stem cell differentiation.

Probing Notch1-Dll4 signaling in regulating osteogenic differentiation of human mesenchymal stem cells using single cell nanobiosensor

Human mesenchymal stem cells (hMSCs) have great potential in cell-based therapies for tissue engineering and regenerative medicine due to their self-renewal and multipotent properties. Recent studies indicate that Notch1-Dll4 signaling is an important pathway in regulating osteogenic differentiation of hMSCs. However, the fundamental mechanisms that govern osteogenic differentiation are poorly understood due to a lack of effective tools to detect gene expression at single cell level. Here, we established a double-stranded locked nucleic acid (LNA)/DNA (LNA/DNA) nanobiosensor for gene expression analysis in single hMSC in both 2D and 3D microenvironments. We first characterized this LNA/DNA nanobiosensor and demonstrated the Dll4 mRNA expression dynamics in hMSCs during osteogenic differentiation. By incorporating this nanobiosensor with live hMSCs imaging during osteogenic induction, we performed dynamic tracking of hMSCs differentiation and Dll4 mRNA gene expression profiles of individual hMSC during osteogenic induction. Our results showed the dynamic expression profile of Dll4 during osteogenesis, indicating the heterogeneity of hMSCs during this dynamic process. We further investigated the role of Notch1-Dll4 signaling in regulating hMSCs during osteogenic differentiation. Pharmacological perturbation is applied to disrupt Notch1-Dll4 signaling to investigate the molecular mechanisms that govern osteogenic differentiation. In addition, the effects of Notch1-Dll4 signaling on hMSCs spheroids differentiation were also investigated. Our results provide convincing evidence supporting that Notch1-Dll4 signaling is involved in regulating hMSCs osteogenic differentiation. Specifically, Notch1-Dll4 signaling is active during osteogenic differentiation. Our results also showed that Dll4 is a molecular signature of differentiated hMSCs during osteogenic induction. Notch inhibition mediated osteogenic differentiation with reduced Alkaline Phosphatase (ALP) activity. Lastly, we elucidated the role of Notch1-Dll4 signaling during osteogenic differentiation in a 3D spheroid model. Our results showed that Notch1-Dll4 signaling is required and activated during osteogenic differentiation in hMSCs spheroids. Inhibition of Notch1-Dll4 signaling mediated osteogenic differentiation and enhanced hMSCs proliferation, with increased spheroid sizes. Taken together, the capability of LNA/DNA nanobiosensor to probe gene expression dynamics during osteogenesis, combined with the engineered 2D/3D microenvironment, enables us to study in detail the role of Notch1-Dll4 signaling in regulating osteogenesis in 2D and 3D microenvironment. These findings will provide new insights to improve cell-based therapies and organ repair techniques.

Frequency modulation of a bacterial quorum sensing response

In quorum sensing, bacteria secrete or release small molecules into the environment that, once they reach a certain threshold, trigger a behavioural change in the population. As the concentration of these so-called autoinducers is supposed to reflect population density, they were originally assumed to be continuously produced by all cells in a population. However, here we show that in the α-proteobacterium Sinorhizobium meliloti expression of the autoinducer synthase gene is realized in asynchronous stochastic pulses that result from scarcity and, presumably, low binding affinity of the key activator. Physiological cues modulate pulse frequency, and pulse frequency in turn modulates the velocity with which autoinducer levels in the environment reach the threshold to trigger the quorum sensing response. We therefore propose that frequency-modulated pulsing in S. meliloti represents the molecular mechanism for a collective decision-making process in which each cell's physiological state and need for behavioural adaptation is encoded in the pulse frequency with which it expresses the autoinducer synthase gene; the pulse frequencies of all members of the population are then integrated in the common pool of autoinducers, and only once this vote crosses the threshold, the response behaviour is initiated.

Can DyeCycling break the photobleaching limit in single-molecule FRET?

Biomolecular systems, such as proteins, crucially rely on dynamic processes at the nanoscale. Detecting biomolecular nanodynamics is therefore key to obtaining a mechanistic understanding of the energies and molecular driving forces that control biomolecular systems. Single-molecule fluorescence resonance energy transfer (smFRET) is a powerful technique to observe in real-time how a single biomolecule proceeds through its functional cycle involving a sequence of distinct structural states. Currently, this technique is fundamentally limited by irreversible photobleaching, causing the untimely end of the experiment and thus, a narrow temporal bandwidth of ≤ 3 orders of magnitude. Here, we introduce "DyeCycling", a measurement scheme with which we aim to break the photobleaching limit in smFRET. We introduce the concept of spontaneous dye replacement by simulations, and as an experimental proof-of-concept, we demonstrate the intermittent observation of a single biomolecule for one hour with a time resolution of milliseconds. Theoretically, DyeCycling can provide > 100-fold more information per single molecule than conventional smFRET. We discuss the experimental implementation of DyeCycling, its current and fundamental limitations, and specific biological use cases. Given its general simplicity and versatility, DyeCycling has the potential to revolutionize the field of time-resolved smFRET, where it may serve to unravel a wealth of biomolecular dynamics by bridging from milliseconds to the hour range.

Electronic Supplementary Material

Supplementary material is available for this article at 10.1007/s12274-022-4420-5 and is accessible for authorized users.

Synthesis, Characterization, Properties, and Novel Applications of Fluorescent Nanodiamonds

In the last few years, fluorescent nanodiamonds (FNDs)  have been developed significantly as a new member in the nanocarbon family. The surface of FNDs is embedded with some crystallographic defects containing color centres which surmount the properties of other fluorochromes including up conversion and down conversion nanoparticles, quantum dots, nano tubes, fullerenes, organic dyes, silica etc. Some of the intriguing properties like inevitable photostability, inherent bio-compatibility, outstanding optical and robust mechanical properties, excellent magnetic field, and electric field sensing potentiality make FNDs appealing to some benevolent applications in numerous fields like bio-imaging, delivering drugs, fighting cancer, spin electronics, imaging of magnetic structure at nanoscale and as promising nanometric temperature sensor. The structure of FNDs has certain point defects on the surface among which negatively charged nitrogen vacancy centre (NV^-) is the most investigated color centre. The production of NV^- fluorescence nanodiamonds is the most challenging task as substitution of carbon atoms is required to create vacancies by causing irradiation from an electron beam which is followed by high temperature annealing. Thus, this review points out the relative advantages of FNDs containing negatively charged nitrogen vacancy centres produced from HPHT method or CVD method with those nanodiamonds produced through detonation process or pulsed laser ablation (PLA) method. The steps involved in the fabrication of FNDs are described along with the major challenges and struggles underwent during the process in this review. This review also summarizes the recent developments made in the functionalization and applications predominantly made in the field of biological science and it is understood that depending on the defect color centres they can exhibit different emitted wavelengths ranging from UV-visible to near infrared with broad or narrow bandwidths. This review also highlights some of the fluorescent NDs that emit stable and strong red or green photoluminescence from the defect centers of NV^- which are implanted in the crystal lattice. This critical and extensive review will be useful for the further progress in this futuristic field of FNDs.

A Framework for Investigating Rules of Life by Establishing Zones of Influence

The incredible complexity of biological processes across temporal and spatial scales hampers defining common underlying mechanisms driving the patterns of life. However, recent advances in sequencing, big data analysis, machine learning, and molecular dynamics simulation have renewed the hope and urgency of finding potential hidden rules of life. There currently exists no framework to develop such synoptic investigations. Some efforts aim to identify unifying rules of life across hierarchical levels of time, space, and biological organization, but not all phenomena occur across all the levels of these hierarchies. Instead of identifying the same parameters and rules across levels, we posit that each level of a temporal and spatial scale and each level of biological organization has unique parameters and rules that may or may not predict outcomes in neighboring levels. We define this neighborhood, or the set of levels, across which a rule functions as the zone of influence. Here, we introduce the zone of influence framework and explain using three examples: (a) randomness in biology, where we use a Poisson process to describe processes from protein dynamics to DNA mutations to gene expressions, (b) island biogeography, and (c) animal coloration. The zone of influence framework may enable researchers to identify which levels are worth investigating for a particular phenomenon and reframe the narrative of searching for a unifying rule of life to the investigation of how, when, and where various rules of life operate.

Exact Distribution of Threshold Crossing Times for Protein Concentrations: Implication for Biological Timekeeping

Stochastic protein accumulation up to some concentration threshold sets the timing of many cellular physiological processes. Here we obtain the exact distribution of first threshold crossing times of protein concentration, in either Laplace or time domain, and its associated cumulants: mean, variance, and skewness. The distribution is asymmetric, and its skewness nonmonotonically varies with the threshold. We study lysis times of E. coli cells for holin gene mutants of bacteriophage-λ and find a good match with theory. Mutants requiring higher holin thresholds show more skewed lysis time distributions as predicted. The theory also predicts a linear relationship between infection delay time and host doubling time for lytic viruses, that has recently been experimentally observed.

Next generation single-molecule techniques: Imaging, labeling, and manipulation in vitro and in cellulo

Owing to their unique abilities to manipulate, label, and image individual molecules in vitro and in cellulo, single-molecule techniques provide previously unattainable access to elementary biological processes. In imaging, single-molecule fluorescence resonance energy transfer (smFRET) and protein-induced fluorescence enhancement in vitro can report on conformational changes and molecular interactions, single-molecule pull-down (SiMPull) can capture and analyze the composition and function of native protein complexes, and single-molecule tracking (SMT) in live cells reveals cellular structures and dynamics. In labeling, the abilities to specifically label genomic loci, mRNA, and nascent polypeptides in cells have uncovered chromosome organization and dynamics, transcription and translation dynamics, and gene expression regulation. In manipulation, optical tweezers, integration of single-molecule fluorescence with force measurements, and single-molecule force probes in live cells have transformed our mechanistic understanding of diverse biological processes, ranging from protein folding, nucleic acids-protein interactions to cell surface receptor function.

Controlling gene expression timing through gene regulatory architecture

Gene networks typically involve the regulatory control of multiple genes with related function. This connectivity enables correlated control of the levels and timing of gene expression. Here we study how gene expression timing in the single-input module motif can be encoded in the regulatory DNA of a gene. Using stochastic simulations, we examine the role of binding affinity, TF regulatory function and network size in controlling the mean first-passage time to reach a fixed fraction of steady-state expression for both an auto-regulated TF gene and a target gene. We also examine how the variability in first-passage time depends on these factors. We find that both network size and binding affinity can dramatically speed up or slow down the response time of network genes, in some cases predicting more than a 100-fold change compared to that for a constitutive gene. Furthermore, these factors can also significantly impact the fidelity of this response. Importantly, these effects do not occur at “extremes” of network size or binding affinity, but rather in an intermediate window of either quantity.

Live Imaging of RNA Transport and Translation in Xenopus Retinal Axons

In neurons, specific mRNAs are transported into axons, where their local translation supports essential cellular functions. Over the years, our knowledge of the molecular mechanisms underlying axonal mRNA translation has rapidly expanded. However, tools to study mRNA localization and translation in real time with high spatial precision were not available until recently. Here, we present a live imaging approach to examine axonal mRNA trafficking and translation simultaneously in Xenopus retinal ganglion cells (RGCs), using in vitro synthesized fluorescently labeled mRNAs coupled with a genetically encoded protein tagging system to visualize synthesizing peptides at single-molecule resolution. We further describe the process of image analysis in detail, thus providing a methodology that can be used to investigate new research questions in the field.

Silent transcription intervals and translational bursting lead to diverse phenotypic switching

For complex process of gene expression, we use theoretical analysis and stochastic simulations to study the phenotypic diversity induced by silent transcription intervals and translational bursting.

Exact distributions for stochastic gene expression models with arbitrary promoter architecture and translational bursting

Gene expression in individual cells is inherently variable and sporadic, leading to cell-to-cell variability in mRNA and protein levels. Recent single-cell and single-molecule experiments indicate that promoter architecture and translational bursting play significant roles in controlling gene expression noise and generating the phenotypic diversity that life exhibits. To quantitatively understand the impact of these factors, it is essential to construct an accurate mathematical description of stochastic gene expression and find the exact analytical results, which is a formidable task. Here, we develop a stochastic model of bursty gene expression, which considers the complex promoter architecture governing the variability in mRNA expression and a general distribution characterizing translational burst. We derive the analytical expression for the corresponding protein steady-state distribution and all moment statistics of protein counts. We show that the total protein noise can be decomposed into three parts: the low-copy noise of protein due to probabilistic individual birth and death events, the noise due to stochastic switching between promoter states, and the noise resulting from translational busting. The theoretical results derived provide quantitative insights into the biochemical mechanisms of stochastic gene expression.

Decoding the Structural Dynamics and Conformational Alternations of DNA Secondary Structures by Single-Molecule FRET Microspectroscopy

In addition to the canonical double helix form, DNA is known to be extrapolated into several other secondary structural patterns involving themselves in inter- and intramolecular type hydrogen bonding. The secondary structures of nucleic acids go through several stages of multiple, complex, and interconvertible heterogeneous conformations. The journey of DNA through these conformers has significant importance and has been monitored thoroughly to establish qualitative and quantitative information about the transition between the unfolded, folded, misfolded, and partially folded states. During this structural interconversion, there always exist specific populations of intermediates, which are short-lived or sometimes even do not accumulate within a heterogeneous population and are challenging to characterize using conventional ensemble techniques. The single-molecule FRET(sm-FRET) microspectroscopic method has the advantages to overcome these limitations and monitors biological phenomena transpiring at a measurable high rate and balanced stochastically over time. Thus, tracing the time trajectory of a particular molecule enables direct measurement of the rate constant of each transition step, including the intermediates that are hidden in the ensemble level due to their low concentrations. This review is focused on the advantages of the employment of single-molecule Forster's resonance energy transfer (sm-FRET), which is worthwhile to access the dynamic architecture and structural transition of various secondary structures that DNA adopts, without letting the donor of one molecule to cross-talk with the acceptor of any other. We have emphasized the studies performed to explore the states of folding and unfolding of several nucleic acid secondary structures, for example, the DNA hairpin, Holliday junction, G-quadruplex, and i-motif.

Stochastic Simulations as a Tool for Assessing Signal Fidelity in Gene Expression in Synthetic Promoter Design

Simple Summary

Synthetic biology is an emerging discipline, offering new perspectives in many industrial fields, from pharma and row-material production to renewable energy. Developing synthetic biology applications is often a lengthy and expensive process with extensive and tedious trial-and-error runs. Computational models can direct the engineering of biological circuits in a computer-aided design setting. By providing a virtual lab environment, in silico models of synthetic circuits can contribute to a quantitative understanding of the underlying molecular pathways before a wet-lab implementation. Here, we illustrate this notion from the point of view of signal fidelity and noise relationship. Noise in gene expression can undermine signal fidelity with implications on the well-functioning of the engineered organisms. For our analysis, we use a specific biological circuit that regulates the gene expression in bacterial inorganic phosphate economy. Applications that use this circuit include those in pollutant detection and wastewater treatment. We provide computational models with different levels of molecular detail as virtual labs. We show that inherent fluctuations in the gene expression machinery can be predicted via stochastic simulations to introduce control in the synthetic promoter design process. Our analysis suggests that noise in the system can be alleviated by strong synthetic promoters with slow unbinding rates. Overall, we provide a recipe for the computer-aided design of synthetic promoter libraries with specific signal to noise characteristics.

Abstract

The design and development of synthetic biology applications in a workflow often involve connecting modular components. Whereas computer-aided design tools are picking up in synthetic biology as in other areas of engineering, the methods for verifying the correct functioning of living technologies are still in their infancy. Especially, fine-tuning for the right promoter strength to match the design specifications is often a lengthy and expensive experimental process. In particular, the relationship between signal fidelity and noise in synthetic promoter design can be a key parameter that can affect the healthy functioning of the engineered organism. To this end, based on our previous work on synthetic promoters for the E. coli PhoBR two-component system, we make a case for using chemical reaction network models for computational verification of various promoter designs before a lab implementation. We provide an analysis of this system with extensive stochastic simulations at a single-cell level to assess the signal fidelity and noise relationship. We then show how quasi-steady-state analysis via ordinary differential equations can be used to navigate between models with different levels of detail. We compare stochastic simulations with our full and reduced models by using various metrics for assessing noise. Our analysis suggests that strong promoters with low unbinding rates can act as control tools for filtering out intrinsic noise in the PhoBR context. Our results confirm that even simpler models can be used to determine promoters with specific signal to noise characteristics.

Noise suppression in stochastic genetic circuits using PID controllers

Inside individual cells, protein population counts are subject to molecular noise due to low copy numbers and the inherent probabilistic nature of biochemical processes. We investigate the effectiveness of proportional, integral and derivative (PID) based feedback controllers to suppress protein count fluctuations originating from two noise sources: bursty expression of the protein, and external disturbance in protein synthesis. Designs of biochemical reactions that function as PID controllers are discussed, with particular focus on individual controllers separately, and the corresponding closed-loop system is analyzed for stochastic controller realizations. Our results show that proportional controllers are effective in buffering protein copy number fluctuations from both noise sources, but this noise suppression comes at the cost of reduced static sensitivity of the output to the input signal. In contrast, integral feedback has no effect on the protein noise level from stochastic expression, but significantly minimizes the impact of external disturbances, particularly when the disturbance comes at low frequencies. Counter-intuitively, integral feedback is found to amplify external disturbances at intermediate frequencies. Next, we discuss the design of a coupled feedforward-feedback biochemical circuit that approximately functions as a derivate controller. Analysis using both analytical methods and Monte Carlo simulations reveals that this derivative controller effectively buffers output fluctuations from bursty stochastic expression, while maintaining the static input-output sensitivity of the open-loop system. In summary, this study provides a systematic stochastic analysis of biochemical controllers, and paves the way for their synthetic design and implementation to minimize deleterious fluctuations in gene product levels.

In the noisy cellular environment, biochemical species such as genes, RNAs and proteins that often occur at low molecular counts, are subject to considerable stochastic fluctuations in copy numbers over time. How cellular biochemical processes function reliably in the face of such randomness is an intriguing fundamental problem. Increasing evidence suggests that random fluctuations (noise) in protein copy numbers play important functional roles, such as driving genetically identical cells to different cell fates. Moreover, many disease states have been attributed to elevated noise levels in specific proteins. Here we systematically investigate design of biochemical systems that function as proportional, integral and derivative-based feedback controllers to suppress protein count fluctuations arising from bursty expression of the protein and external disturbance in protein synthesis. Our results show that different controllers are effective in buffering different noise components, and identify ranges of feedback gain for minimizing deleterious fluctuations in protein levels.

Single-molecule localisation microscopy: accounting for chance co-localisation between foci in bacterial cells

Using single-molecule fluorescence microscopes, individual biomolecules can be observed within live bacterial cells. Using differently coloured probes, physical associations between two different molecular species can be assessed through co-localisation measurements. However, bacterial cells are finite and small (~ 1 μm) relative to the resolution limit of optical microscopes (~ 0.25 μm). Furthermore, the images produced by optical microscopes are typically two-dimensional projections of three-dimensional objects. These limitations mean that a certain proportion of object pairs (molecules) will inevitably be assigned as being co-localised, even when they are distant at molecular distance scales (nm). What is this proportion? Here, we attack this problem, theoretically and computationally, by creating a model of the co-localisation expected purely due to chance. We thus consider a bacterial cell wherein objects are distributed at random and evaluate the co-localisation in a fashion that emulates an experimental analysis. We consider simplified geometries where we can most transparently investigate the effect of a finite size of the cell and the effect of probing a three-dimensional cell in only two dimensions. Coupling theory to simulations, we also study the co-localisation expected due to chance using parameters relevant to bacterial cells. Overall, we show that the co-localisation expected purely due to chance can be quite substantial and describe the parameters that it depends upon.

Reconstructing an epigenetic landscape using a genetic pulling approach

Cells use genetic switches to shift between alternate stable gene expression states, e.g., to adapt to new environments or to follow a developmental pathway. Conceptually, these stable phenotypes can be considered as attractive states on an epigenetic landscape with phenotypic changes being transitions between states. Measuring these transitions is challenging because they are both very rare in the absence of appropriate signals and very fast. As such, it has proved difficult to experimentally map the epigenetic landscapes that are widely believed to underly developmental networks. Here, we introduce a nonequilibrium perturbation method to help reconstruct a regulatory network's epigenetic landscape. We derive the mathematical theory needed and then use the method on simulated data to reconstruct the landscapes. Our results show that with a relatively small number of perturbation experiments it is possible to recover an accurate representation of the true epigenetic landscape. We propose that our theory provides a general method by which epigenetic landscapes can be studied. Finally, our theory suggests that the total perturbation impulse required to induce a switch between metastable states is a fundamental quantity in developmental dynamics.

Probing low-copy-number proteins in single living cells using single-cell plasmonic immunosandwich assays

Cellular heterogeneity is pervasive and of paramount importance in biology. Single-cell analysis techniques are indispensable for understanding the heterogeneity and functions of cells. Low-copy-number proteins (fewer than 1,000 molecules per cell) perform multiple crucial functions such as gene expression, cellular metabolism and cell signaling. The expression level of low-copy-number proteins of individual cells provides key information for the in-depth understanding of biological processes and diseases. However, the quantitative analysis of low-copy-number proteins in a single cell still remains challenging. To overcome this, we developed an approach called single-cell plasmonic immunosandwich assay (scPISA) for the quantitative measurement of low-copy-number proteins in single living cells. scPISA combines in vivo microextraction for specific enrichment of target proteins from cells and a state-of-the-art technique called plasmon-enhanced Raman scattering for ultrasensitive detection of low-copy-number proteins. Plasmon-enhanced Raman scattering detection relies on the plasmonic coupling effect (hot-spot) between silver-based plasmonic nanotags and a gold-based extraction microprobe, which dramatically enhances the signal intensity of the surface-enhanced Raman scattering of the nanotags and thereby enables sensitivity at the single-molecule level. scPISA is a straightforward and minimally invasive technique, taking only ~6-15 min (from in vivo extraction to Raman spectrum readout). It is generally applicable to all freely floating intracellular proteins provided that appropriate antibodies or alternatives (for example, molecularly imprinted polymers or aptamers) are available. The entire protocol takes ~4-7 d to complete, including material fabrication, single-cell manipulation, protein labeling, signal acquisition and data analysis.