A comprehensive study on flocculation of anionic dyes using the bioflocculant produced by Bacillus thuringiensis: Kinetics, affecting factors, and perspectives.

Bioflocculants have received more and more attention as alternatives to chemical flocculants because of their innocuousness, environmental friendliness, and high effectiveness. This study aims to investigate various factors that influence the performance of the novel bioflocculant produced by Bacillus thuringiensis (BF-TWB10) and analyze its adsorption kinetics to optimize its flocculation performance for real applications. The best-fit kinetic model was pseudo-second order with R2 = 0.999. The effects of pretreatment temperature, pH, and the presence of cations on flocculation were assessed. Further investigations of flocculation, including zeta potential analysis and particle size analysis, were also conducted. Thermal pretreatment of BF-TWB10 or the presence of divalent cations could stimulate the decolorization efficiency of the bioflocculant. BF-TWB10 manifested outstanding dye removal performances with over 90% for all tested anionic dyes at pH 2 and 3. Its decolorization efficiency on anionic dyes decreased with the increase of pH values. Zeta potential analysis revealed that the electrostatic repulsion between anionic dyes decreased after the addition of BT-TWB10 and further diminished by adjusting the reaction mixture to pH 2 before flocculation, suggesting the occurrence of adsorption bridging and charge neutralization. These findings proposed that BF-TWB10 might be a promising bioflocculant for the removal of dyes in textile wastewater. PRACTITIONER POINTS: Bioflocculant BF-TWB10 shows outstanding performance in flocculation. Adsorption process follows pseudo-second-order kinetic model. Flocculation process is pH-responsive. High-temperature pretreatment or divalent cations enhance its flocculation performance. The analyses suggest the occurrence of charge neutralization and adsorption bridging.

Dimerization induces bimodality in protein number distributions.

We examined gene expression with DNA switching between two states, active and inactive. Subpopulations emerge from mechanisms that do not arise from trivial transcriptional heterogeneity. Although the RNA demonstrates a unimodal distribution, dimerization intriguingly causes protein bimodality. No control loop or deterministic bistability are present. In such a situation, increasing the degradation rate of the protein does not lead to bimodality. The bimodality is achieved through the interplay between the protein monomer and the formation of protein dimer. We applied Stochastic Simulation Algorithm (SSA) and found that cells spontaneously change states at the protein level. While sweeping parameters, decreasing the rate constant of dimerization severely impairs the bimodality. We also examined the influence of DNA switching. To have bimodality, the system requires a proper ratio of DNA in the active state to the inactive state. In addition to bimodality of the monomer, tetramerization also causes the bimodality of the dimer.

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.

Author Correction: The Reaction of Dimerization by Itself Reduces the Noise Intensity of the Protein Monomer.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Exposure to One Antibiotic Leads to Acquisition of Resistance to Another Antibiotic via Quorum Sensing Mechanisms.

The vancomycin-resistant Enterococci (VRE) have progressively become a severe medical problem. Although clinics have started to reduce vancomycin prescription, vancomycin resistance has not been contained. We found that the transfer of vancomycin resistance in Enterococcus faecalis increased more than 30-fold upon treatment by streptomycin. Notably, treatment with an antibiotic caused the bacteria to become resistant to another. The response was even stronger in the well-studied plasmid pCF10 and the number of transconjugants increased about 100,000-fold. We tested four different antibiotics, and all of them induced conjugal response. Through a mathematical model based on gene regulation, we found a plausible explanation. Via quorum sensing, the change of the cell density triggers the conjugation. Moreover, we searched for generality and found a similar strategy in Bacillus subtilis. The outcome of the present study suggests that even common antibiotics must not be overused.

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.

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.

On speeding up stochastic simulations by parallelization of random number generation.

This paper adds to the tool kit of stochastic simulations based on a very simple idea. Applicable to both SSA and Tau-leap algorithms, it can notably reduce computational times. Stochastic simulations are based on computing sample paths based on the generation of random numbers with either exactly stipulated distribution functions as in SSA (Gillespie, 1977) or in the method of interval of quiescence (Shah et al., 1977) or distribution functions featuring approximations designed to promote efficiency (as in Tau-leap algorithms (Cao et al., 2006; Tian and Burrage, 2004; Peng et al., 2007; Gillespie, 2001; Ramkrishna et al., 2014) where a leap condition with the parameter epsilon is used). The usual strategy involves sequential computation of a large number of sample paths over a bounded time interval which is covered by a set of discrete time subintervals obtained by random number generation. The strategy here departs from the foregoing by parallelizing the generation of random subintervals for the set of sample paths until all sample paths have been computed for the stated time interval. The advantage of this procedure lies in the fact that the time for initiation of the random number generator has been notably reduced. Many examples are demonstrated from SSA as well as Tau-leap algorithms to establish that the advantage of the approach is much more than conceptual.

New "Tau-Leap" Strategy for Accelerated Stochastic Simulation.

The "Tau-Leap" strategy for stochastic simulations of chemical reaction systems due to Gillespie and co-workers has had considerable impact on various applications. This strategy is reexamined with Chebyshev's inequality for random variables as it provides a rigorous probabilistic basis for a measured τ-leap thus adding significantly to simulation efficiency. It is also shown that existing strategies for simulation times have no probabilistic assurance that they satisfy the τ-leap criterion while the use of Chebyshev's inequality leads to a specified degree of certainty with which the τ-leap criterion is satisfied. This reduces the loss of sample paths which do not comply with the τ-leap criterion. The performance of the present algorithm is assessed, with respect to one discussed by Cao et al. (J. Chem. Phys.2006, 124, 044109), a second pertaining to binomial leap (Tian and Burrage J. Chem. Phys.2004, 121, 10356; Chatterjee et al. J. Chem. Phys.2005, 122, 024112; Peng et al. J. Chem. Phys.2007, 126, 224109), and a third regarding the midpoint Poisson leap (Peng et al., 2007; Gillespie J. Chem. Phys.2001, 115, 1716). The performance assessment is made by estimating the error in the histogram measured against that obtained with the so-called stochastic simulation algorithm. It is shown that the current algorithm displays notably less histogram error than its predecessor for a fixed computation time and, conversely, less computation time for a fixed accuracy. This computational advantage is an asset in repetitive calculations essential for modeling stochastic systems. The importance of stochastic simulations is derived from diverse areas of application in physical and biological sciences, process systems, and economics, etc. Computational improvements such as those reported herein are therefore of considerable significance.

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

There is increasing recognition that stochasticity involved in gene regulatory processes may help cells enhance the signal or synchronize expression for a group of genes. Thus the validity of the traditional deterministic approach to modeling the foregoing processes cannot be without exception. In this study, we identify a frequently encountered situation, i.e., the biofilm, which has in the past been persistently investigated with intracellular deterministic models in the literature. We show in this paper circumstances in which use of the intracellular deterministic model appears distinctly inappropriate. In Enterococcus faecalis, the horizontal gene transfer of plasmid spreads drug resistance. The induction of conjugation in planktonic and biofilm circumstances is examined here with stochastic as well as deterministic models. The stochastic model is formulated with the Chemical Master Equation (CME) for planktonic cells and Reaction-Diffusion Master Equation (RDME) for biofilm. The results show that although the deterministic model works well for the perfectly-mixed planktonic circumstance, it fails to predict the averaged behavior in the biofilm, a behavior that has come to be known as stochastic focusing. A notable finding from this work is that the interception of antagonistic feedback loops to signaling, accentuates stochastic focusing. Moreover, interestingly, increasing particle number of a control variable could lead to an even larger deviation. Intracellular stochasticity plays an important role in biofilm and we surmise by implications from the model, that cell populations may use it to minimize the influence from environmental fluctuation.

Antagonistic self-sensing and mate-sensing signaling controls antibiotic-resistance transfer.

Conjugation is one of the most common ways bacteria acquire antibiotic resistance, contributing to the emergence of multidrug-resistant "superbugs." Bacteria of the genus Enterococcus faecalis are highly antibiotic-resistant nosocomial pathogens that use the mechanism of conjugation to spread antibiotic resistance between resistance-bearing donor cells and resistance-deficient recipient cells. Here, we report a unique quorum sensing-based communication system that uses two antagonistic signaling molecules to regulate conjugative transfer of tetracycline-resistance plasmid pCF10 in E. faecalis. A "mate-sensing" peptide sex pheromone produced by recipient cells is detected by donor cells to induce conjugative genetic transfer. Using mathematical modeling and experimentation, we show that a second antagonistic "self-sensing" signaling peptide, previously known to suppress self-induction of donor cells, also serves as a classic quorum-sensing signal for donors that functions to reduce antibiotic-resistance transfer at high donor density. This unique form of quorum sensing may provide a means of limiting the spread of the plasmid and present opportunities to control antibiotic-resistance transfer through manipulation of intercellular signaling, with implications in the clinical setting.

MODELING OF GENE REGULATORY PROCESSES BY POPULATION MEDIATED SIGNALING. NEW APPLICATIONS OF POPULATION BALANCES.

Population balance modeling is considered for cell populations in gene regulatory processes in which one or more intracellular variables undergo stochastic dynamics as determined by Ito stochastic differential equations. This paper addresses formulation and computational issues with sample applications to the spread of drug resistance among bacterial cells. It is shown that predictions from population balances can display qualitative differences from those made with single cell models which are usually encountered in the literature. Such differences are deemed to be important.

Bistability versus bimodal distributions in gene regulatory processes from population balance.

In recent times, stochastic treatments of gene regulatory processes have appeared in the literature in which a cell exposed to a signaling molecule in its environment triggers the synthesis of a specific protein through a network of intracellular reactions. The stochastic nature of this process leads to a distribution of protein levels in a population of cells as determined by a Fokker-Planck equation. Often instability occurs as a consequence of two (stable) steady state protein levels, one at the low end representing the "off" state, and the other at the high end representing the "on" state for a given concentration of the signaling molecule within a suitable range. A consequence of such bistability has been the appearance of bimodal distributions indicating two different populations, one in the "off" state and the other in the "on" state. The bimodal distribution can come about from stochastic analysis of a single cell. However, the concerted action of the population altering the extracellular concentration in the environment of individual cells and hence their behavior can only be accomplished by an appropriate population balance model which accounts for the reciprocal effects of interaction between the population and its environment. In this study, we show how to formulate a population balance model in which stochastic gene expression in individual cells is incorporated. Interestingly, the simulation of the model shows that bistability is neither sufficient nor necessary for bimodal distributions in a population. The original notion of linking bistability with bimodal distribution from single cell stochastic model is therefore only a special consequence of a population balance model.

Convergent transcription confers a bistable switch in Enterococcus faecalis conjugation.

Convergent gene pairs with head-to-head configurations are widespread in both eukaryotic and prokaryotic genomes and are speculated to be involved in gene regulation. Here we present a unique mechanism of gene regulation due to convergent transcription from the antagonistic prgX/prgQ operon in Enterococcus faecalis controlling conjugative transfer of the antibiotic resistance plasmid pCF10 from donor cells to recipient cells. Using mathematical modeling and experimentation, we demonstrate that convergent transcription in the prgX/prgQ operon endows the system with the properties of a robust genetic switch through premature termination of elongating transcripts due to collisions between RNA polymerases (RNAPs) transcribing from opposite directions and antisense regulation between complementary counter-transcripts. Evidence is provided for the presence of truncated RNAs resulting from convergent transcription from both the promoters that are capable of sense-antisense interactions. A mathematical model predicts that both RNAP collision and antisense regulation are essential for a robust bistable switch behavior in the control of conjugation initiation by prgX/prgQ operons. Moreover, given that convergent transcription is conserved across species, the mechanism of coupling RNAP collision and antisense interaction is likely to have a significant regulatory role in gene expression.