Role of intracellular stochasticity in biofilm growth. Insights from population balance modeling

Current examining methods and mathematical models of horizontal transfer of antibiotic resistance genes in the environment

The increasing prevalence of antibiotic resistance genes (ARGs) in the environment has garnered significant attention due to their health risk to human beings. Horizontal gene transfer (HGT) is considered as an important way for ARG dissemination. There are four general routes of HGT, including conjugation, transformation, transduction and vesiduction. Selection of appropriate examining methods is crucial for comprehensively understanding characteristics and mechanisms of different HGT ways. Moreover, combined with the results obtained from different experimental methods, mathematical models could be established and serve as a powerful tool for predicting ARG transfer dynamics and frequencies. However, current reviews of HGT for ARG spread mainly focus on its influencing factors and mechanisms, overlooking the important roles of examining methods and models. This review, therefore, delineated four pathways of HGT, summarized the strengths and limitations of current examining methods, and provided a comprehensive summing-up of mathematical models pertaining to three main HGT ways of conjugation, transformation and transduction. Finally, deficiencies in current studies were discussed, and proposed the future perspectives to better understand and assess the risks of ARG dissemination through HGT.

Probing transient memory of cellular states using single-cell lineages

The inherent stochasticity in the gene product levels can drive single cells within an isoclonal population to different phenotypic states. The dynamic nature of this intercellular variation, where individual cells can transition between different states over time, makes it a particularly hard phenomenon to characterize. We reviewed recent progress in leveraging the classical Luria-Delbrück experiment to infer the transient heritability of the cellular states. Similar to the original experiment, individual cells were first grown into cell colonies, and then, the fraction of cells residing in different states was assayed for each colony. We discuss modeling approaches for capturing dynamic state transitions in a growing cell population and highlight formulas that identify the kinetics of state switching from the extent of colony-to-colony fluctuations. The utility of this method in identifying multi-generational memory of the both expression and phenotypic states is illustrated across diverse biological systems from cancer drug resistance, reactivation of human viruses, and cellular immune responses. In summary, this fluctuation-based methodology provides a powerful approach for elucidating cell-state transitions from a single time point measurement, which is particularly relevant in situations where measurements lead to cell death (as in single-cell RNA-seq or drug treatment) or cause an irreversible change in cell physiology.

The switch of DNA states filtering the extrinsic noise in the system of frequency modulation

There is a special node, which the large noise of the upstream element may not always lead to a broad distribution of downstream elements. This node is DNA, with upstream element TF and downstream elements mRNA and proteins. By applying the stochastic simulation algorithm (SSA) on gene circuits inspired by the fim operon in Escherichia coli, we found that cells exchanged the distribution of the upstream transcription factor (TF) for the transitional frequency of DNA. Then cells do an inverse transform, which exchanges the transitional frequency of DNA for the distribution of downstream products. Due to this special feature, DNA in the system of frequency modulation is able to reset the noise. By probability generating function, we know the ranges of parameter values that grant such an interesting phenomenon.

The common misuse of noise decomposition as applied to genetic systems

The noise-decomposition technique is applied in several fields, including genetic systems, optical images, recording, and navigation. In genetic systems, noise decomposition is usually achieved by using two reporters [Elowitz M.B., Levine A.J., Siggia E.D., Swain P·S., 2002. Stochastic gene expression in a single cell. Science 297, 1183-6.]. A reporter is a protein with fluorescence, an RNA hybridized with a fluorescent probe, or any other detectable intracellular component. If a reporter is constructed in addition to the original reporter, the system's stochasticity may change. Such phenomena became severe for genes in plasmids with a high copy number. By SSA (stochastic simulation algorithm), we observed an approximately 50% increment in the coefficient of variation while introducing additional reporters. Besides, if two reporters respond to the upstream element at a different time, the trunk noise (or extrinsic noise) cannot be accurately determined. This is because the "calculative trunk noise" changes along with the delay, though the real trunk noise does not. For RNA reporters, a 5-min transcriptional delay caused a calculative trunk noise that was 90% less than the real trunk noise. Fortunately, this problem is negligible when the degradation rate constant is low, and it is usually true in the case of the protein reporters. One can check the lifespan of the reporter before applying the noise-decomposition technique.

A Practicable Method of Tuning the Noise Intensity at Protein Level

The expression of genes is inevitably subject to intracellular noise. Noise, for some regulatory networks, is constructive but detrimental to many others. The intensity of the noise is a determinant factor and the method of tuning it is of great value. In this study, we illustrated that the transcriptional delay in an incoherent feedforward loop (FFL) grants the target protein modulation the intensity of noise. Remarkably, for a wide range, the coefficient of variation (COV) of the target protein appeared to be about linear to the time span of the transcriptional delay. Without a noise-buffering method, the COV of the target protein is 0.455. While applying incoherent FFL, the COV reduced to 0.236. Then, it changed from 0.236 to 0.630 as the transcriptional delay raised from 0 to 1000 seconds. If we further increased the delay out of the linear range, the COV finally reached 0.779. In addition, we incorporated the distribution of the transcriptional delay in the delay stochastic simulation algorithm. This distribution is based on the experimental observation in the literature. The outcome suggested that the distributed delay slightly improved the ability of tuning noise. In conclusion, we demonstrated a noise-tuning method that altered only the intensity of noise without changing the deterministic steady-state behaviors. It is ready to be applied to various systems in the field of synthetic biology.

The Reaction of Dimerization by Itself Reduces the Noise Intensity of the Protein Monomer

Because of the small particle number of intracellular species participating in genetic circuits, stochastic fluctuations are inevitable. This intracellular noise is detrimental to precise regulation. To maintain the proper function of a cell, some natural motifs attenuate the noise at the protein level. In many biological systems, the protein monomer is used as a regulator, but the protein dimer also exists. In the present study, we demonstrated that the dimerization reaction reduces the noise intensity of the protein monomer. Compared with two common noise-buffering motifs, the incoherent feedforward loop (FFL) and negative feedback control, the coefficient of variation (COV) in the case of dimerization was 25% less. Furthermore, we examined a system with direct interaction between proteins and other ligands. Both the incoherent FFL and negative feedback control failed to buffer the noise, but the dimerization was effective. Remarkably, the formation of only one protein dimer was sufficient to cause a 7.5% reduction in the COV.

The Insight into Protein-Ligand Interactions, a Novel Way of Buffering Protein Noise in Gene Expression

Random fluctuations are often considered detrimental in the context of gene regulation. Studies aimed at discovering the noise-buffering strategies are important. In this study, we demonstrated a novel design of attenuating noise at protein-level. The protein-ligand interaction dramatically reduced noise so that the coefficient of variation (COV) became roughly 1/3. Remarkably, in comparison to the other two noise-buffering methods, the negative feedback control and the incoherent feedforward loop, the COV of the target protein in the case of protein-ligand interaction appeared to be less than 1/2 of that of the other two methods. The high correlation of the target protein and the ligand grants the present method great ability to buffer noise. Further, it buffers noise at the stage after translation so it is also capable of attenuating the noise inherited from the process of translation.

Use of in-field bioreactors demonstrate groundwater filtration influences planktonic bacterial community assembly, but not biofilm composition

Using in-field bioreactors, we investigated the influence of exogenous microorganisms in groundwater planktonic and biofilm microbial communities as part of the Integrated Field Research Challenge (IFRC). After an acclimation period with source groundwater, bioreactors received either filtered (0.22 μM filter) or unfiltered well groundwater in triplicate and communities were tracked routinely for 23 days after filtration was initiated. To address geochemical influences, the planktonic phase was assayed periodically for protein, organic acids, physico-/geochemical measurements and bacterial community (via 16S rRNA gene sequencing), while biofilms (i.e. microbial growth on sediment coupons) were targeted for bacterial community composition at the completion of the experiment (23 d). Based on Bray-Curtis distance, planktonic bacterial community composition varied temporally and between treatments (filtered, unfiltered bioreactors). Notably, filtration led to an increase in the dominant genus, Zoogloea relative abundance over time within the planktonic community, while remaining relatively constant when unfiltered. At day 23, biofilm communities were more taxonomically and phylogenetically diverse and substantially different from planktonic bacterial communities; however, the biofilm bacterial communities were similar regardless of filtration. These results suggest that although planktonic communities were sensitive to groundwater filtration, bacterial biofilm communities were stable and resistant to filtration. Bioreactors are useful tools in addressing questions pertaining to microbial community assembly and succession. These data provide a first step in understanding how an extrinsic factor, such as a groundwater inoculation and flux of microbial colonizers, impact how microbial communities assemble in environmental systems.

Inhibitors Alter the Stochasticity of Regulatory Proteins to Force Cells to Switch to the Other State in the Bistable System

The cellular behaviors under the control of genetic circuits are subject to stochastic fluctuations, or noise. The stochasticity in gene regulation, far from a nuisance, has been gradually appreciated for its unusual function in cellular activities. In this work, with Chemical Master Equation (CME), we discovered that the addition of inhibitors altered the stochasticity of regulatory proteins. For a bistable system of a mutually inhibitory network, such a change of noise led to the migration of cells in the bimodal distribution. We proposed that the consumption of regulatory protein caused by the addition of inhibitor is not the only reason for pushing cells to the specific state; the change of the intracellular stochasticity is also the main cause for the redistribution. For the level of the inhibitor capable of driving 99% of cells, if there is no consumption of regulatory protein, 88% of cells were guided to the specific state. It implied that cells were pushed, by the inhibitor, to the specific state due to the change of stochasticity.

Driving Cells to the Desired State in a Bimodal Distribution through Manipulation of Internal Noise with Biologically Practicable Approaches

The stochastic nature of gene regulatory networks described by Chemical Master Equation (CME) leads to the distribution of proteins. A deterministic bistability is usually reflected as a bimodal distribution in stochastic simulations. Within a certain range of the parameter space, a bistable system exhibits two stable steady states, one at the low end and the other at the high end. Consequently, it appears to have a bimodal distribution with one sub-population (mode) around the low end and the other around the high end. In most cases, only one mode is favorable, and guiding cells to the desired state is valuable. Traditionally, the population was redistributed simply by adjusting the concentration of the inducer or the stimulator. However, this method has limitations; for example, the addition of stimulator cannot drive cells to the desired state in a common bistable system studied in this work. In fact, it pushes cells only to the undesired state. In addition, it causes a position shift of the modes, and this shift could be as large as the value of the mode itself. Such a side effect might damage coordination, and this problem can be avoided by applying a new method presented in this work. We illustrated how to manipulate the intensity of internal noise by using biologically practicable methods and utilized it to prompt the population to the desired mode. As we kept the deterministic behavior untouched, the aforementioned drawback was overcome. Remarkably, more than 96% of cells has been driven to the desired state. This method is genetically applicable to biological systems exhibiting a bimodal distribution resulting from bistability. Moreover, the reaction network studied in this work can easily be extended and applied to many other systems.

The Plasmidome of Firmicutes: Impact on the Emergence and the Spread of Resistance to Antimicrobials

The phylum Firmicutes is one of the most abundant groups of prokaryotes in the microbiota of humans and animals and includes genera of outstanding relevance in biomedicine, health care, and industry. Antimicrobial drug resistance is now considered a global health security challenge of the 21st century, and this heterogeneous group of microorganisms represents a significant part of this public health issue.The presence of the same resistant genes in unrelated bacterial genera indicates a complex history of genetic interactions. Plasmids have largely contributed to the spread of resistance genes among Staphylococcus, Enterococcus, and Streptococcus species, also influencing the selection and ecological variation of specific populations. However, this information is fragmented and often omits species outside these genera. To date, the antimicrobial resistance problem has been analyzed under a "single centric" perspective ("gene tracking" or "vehicle centric" in "single host-single pathogen" systems) that has greatly delayed the understanding of gene and plasmid dynamics and their role in the evolution of bacterial communities.This work analyzes the dynamics of antimicrobial resistance genes using gene exchange networks; the role of plasmids in the emergence, dissemination, and maintenance of genes encoding resistance to antimicrobials (antibiotics, heavy metals, and biocides); and their influence on the genomic diversity of the main Gram-positive opportunistic pathogens under the light of evolutionary ecology. A revision of the approaches to categorize plasmids in this group of microorganisms is given using the 1,326 fully sequenced plasmids of Gram-positive bacteria available in the GenBank database at the time the article was written.

Effect of Intrinsic Noise on the Phenotype of Cell Populations Featuring Solution Multiplicity: An Artificial lac Operon Network Paradigm

Heterogeneity in cell populations originates from two fundamentally different sources: the uneven distribution of intracellular content during cell division, and the stochastic fluctuations of regulatory molecules existing in small amounts. Discrete stochastic models can incorporate both sources of cell heterogeneity with sufficient accuracy in the description of an isogenic cell population; however, they lack efficiency when a systems level analysis is required, due to substantial computational requirements. In this work, we study the effect of cell heterogeneity in the behaviour of isogenic cell populations carrying the genetic network of lac operon, which exhibits solution multiplicity over a wide range of extracellular conditions. For such systems, the strategy of performing solely direct temporal solutions is a prohibitive task, since a large ensemble of initial states needs to be tested in order to drive the system--through long time simulations--to possible co-existing steady state solutions. We implement a multiscale computational framework, the so-called "equation-free" methodology, which enables the performance of numerical tasks, such as the computation of coarse steady state solutions and coarse bifurcation analysis. Dynamically stable and unstable solutions are computed and the effect of intrinsic noise on the range of bistability is efficiently investigated. The results are compared with the homogeneous model, which neglects all sources of heterogeneity, with the deterministic cell population balance model, as well as with a stochastic model neglecting the heterogeneity originating from intrinsic noise effects. We show that when the effect of intrinsic source of heterogeneity is intensified, the bistability range shifts towards higher extracellular inducer concentration values.

Coarse-grained analysis of stochastically simulated cell populations with a positive feedback genetic network architecture

Among the different computational approaches modelling the dynamics of isogenic cell populations, discrete stochastic models can describe with sufficient accuracy the evolution of small size populations. However, for a systematic and efficient study of their long-time behaviour over a wide range of parameter values, the performance of solely direct temporal simulations requires significantly high computational time. In addition, when the dynamics of the cell populations exhibit non-trivial bistable behaviour, such an analysis becomes a prohibitive task, since a large ensemble of initial states need to be tested for the quest of possibly co-existing steady state solutions. In this work, we study cell populations which carry the lac operon network exhibiting solution multiplicity over a wide range of extracellular conditions (inducer concentration). By adopting ideas from the so-called "equation-free" methodology, we perform systems-level analysis, which includes numerical tasks such as the computation of coarse steady state solutions, coarse bifurcation analysis, as well as coarse stability analysis. Dynamically stable and unstable macroscopic (population level) steady state solutions are computed by means of bifurcation analysis utilising short bursts of fine-scale simulations, and the range of bistability is determined for different sizes of cell populations. The results are compared with the deterministic cell population balance model, which is valid for large populations, and we demonstrate the increased effect of stochasticity in small size populations with asymmetric partitioning mechanisms.

Population Balance Modeling: Current Status and Future Prospects

Population balance modeling is undergoing phenomenal growth in its applications, and this growth is accompanied by multifarious reviews. This review aims to fortify the model's fundamental base, as well as point to a variety of new applications, including modeling of crystal morphology, cell growth and differentiation, gene regulatory processes, and transfer of drug resistance. This is accomplished by presenting the many faces of population balance equations that arise in the foregoing applications.