Generalized Michaelis-Menten rate law with time-varying molecular concentrations.

The Michaelis-Menten (MM) rate law has been the dominant paradigm of modeling biochemical rate processes for over a century with applications in biochemistry, biophysics, cell biology, systems biology, and chemical engineering. The MM rate law and its remedied form stand on the assumption that the concentration of the complex of interacting molecules, at each moment, approaches an equilibrium (quasi-steady state) much faster than the molecular concentrations change. Yet, this assumption is not always justified. Here, we relax this quasi-steady state requirement and propose the generalized MM rate law for the interactions of molecules with active concentration changes over time. Our approach for time-varying molecular concentrations, termed the effective time-delay scheme (ETS), is based on rigorously estimated time-delay effects in molecular complex formation. With particularly marked improvements in protein-protein and protein-DNA interaction modeling, the ETS provides an analytical framework to interpret and predict rich transient or rhythmic dynamics (such as autogenously-regulated cellular adaptation and circadian protein turnover), which goes beyond the quasi-steady state assumption.

The Boltzmann fair division for distributive justice.

Fair division is a significant, long-standing problem and is closely related to social and economic justice. The conventional division methods such as cut-and-choose are hardly applicable to real-world problems because of their complexity and unrealistic assumptions about human behaviors. Here we propose a fair division method from a completely different perspective, using the Boltzmann division. The mathematical model of the Boltzmann division was developed for both homogeneous and heterogeneous cake-cutting problems, and the realistic human factors (contributions, needs, and preferences) of the multiple participating players could be successfully integrated. The Boltzmann division was then optimized by maximizing the players' total utility. We show that the Boltzmann fair division is a division method favorable to the socially disadvantaged or underprivileged, and it is drastically simple yet highly versatile and can be easily fine-tuned to directly apply to a variety of social, economic, and political division problems.

Backward simulation for inferring hidden biomolecular kinetic profiles.

Our backward simulation (BS) is an approach to infer the dynamics of individual components in ordinary differential equation (ODE) models, given the information on relatively downstream components or their sums. Here, we demonstrate the use of BS to infer protein synthesis rates with a given profile of protein concentrations over time in a circadian system. This protocol can also be applied to a wide range of problems with undetermined dynamics at the upstream levels. For complete details on the use and execution of this protocol, please refer to Lim et al. (2021).

Cost-effective circadian mechanism: rhythmic degradation of circadian proteins spontaneously emerges without rhythmic post-translational regulation.

Circadian protein oscillations are maintained by the lifelong repetition of protein production and degradation in daily balance. It comes at the cost of ever-replayed, futile protein synthesis each day. This biosynthetic cost with a given oscillatory protein profile is relievable by a rhythmic, not constant, degradation rate that selectively peaks at the right time of day but remains low elsewhere, saving much of the gross protein loss and of the replenishing protein synthesis. Here, our mathematical modeling reveals that the rhythmic degradation rate of proteins with circadian production spontaneously emerges under steady and limited activity of proteolytic mediators and does not necessarily require rhythmic post-translational regulation of previous focus. Additional (yet steady) post-translational modifications in a proteolytic pathway can further facilitate the degradation's rhythmicity in favor of the biosynthetic cost saving. Our work is supported by animal and plant circadian data, offering a generic mechanism for potentially widespread, time-dependent protein turnover.

Photoacoustic Tomography Opening New Paradigms in Biomedical Imaging.

After the emergence of the ultrasound, X-ray CT, PET, and MRI, photoacoustic tomography (PAT) is now in the phase of its exponential growth, with its expected full maturation being another form of mainstream clinical imaging modality. By combining the high contrast benefit of optical imaging and the high-resolution deep imaging capability of ultrasound, PAT can provide unprecedented anatomical image contrasts at clinically relevant depths as well as enable the use of a variety of functional and molecular imaging information, which is not possible with conventional imaging modalities. With these strengths, PAT has achieved numerous breakthroughs in various biomedical applications and also provided new technical platforms that may be able to resolve unmet issues in clinics. In this chapter, we provide an overview of the development of PAT technology for several major biomedical applications and provide an approximate projection of the future of PAT.

Elucidating the role of metal ions in carbonic anhydrase catalysis.

Why metalloenzymes often show dramatic changes in their catalytic activity when subjected to chemically similar but non-native metal substitutions is a long-standing puzzle. Here, we report on the catalytic roles of metal ions in a model metalloenzyme system, human carbonic anhydrase II (CA II). Through a comparative study on the intermediate states of the zinc-bound native CA II and non-native metal-substituted CA IIs, we demonstrate that the characteristic metal ion coordination geometries (tetrahedral for Zn2+, tetrahedral to octahedral conversion for Co2+, octahedral for Ni2+, and trigonal bipyramidal for Cu2+) directly modulate the catalytic efficacy. In addition, we reveal that the metal ions have a long-range (~10 Å) electrostatic effect on restructuring water network in the active site. Our study provides evidence that the metal ions in metalloenzymes have a crucial impact on the catalytic mechanism beyond their primary chemical properties.

Publisher Correction: Large-scale metabolic interaction network of the mouse and human gut microbiota.

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

Large-scale metabolic interaction network of the mouse and human gut microbiota.

The role of our gut microbiota in health and disease is largely attributed to the collective metabolic activities of the inhabitant microbes. A system-level framework of the microbial community structure, mediated through metabolite transport, would provide important insights into the complex microbe-microbe and host-microbe chemical interactions. This framework, if adaptable to both mouse and human systems, would be useful for mechanistic interpretations of the vast amounts of experimental data from gut microbiomes in murine animal models, whether humanized or not. Here, we constructed a literature-curated, interspecies network of the mammalian gut microbiota for mouse and human hosts, called NJC19. This network is an extensive data resource, encompassing 838 microbial species (766 bacteria, 53 archaea, and 19 eukaryotes) and 6 host cell types, interacting through 8,224 small-molecule transport and macromolecule degradation events. Moreover, we compiled 912 negative associations between organisms and metabolic compounds that are not transportable or degradable by those organisms. Our network may facilitate experimental and computational endeavors for the mechanistic investigations of host-associated microbial communities.

Serum albumin and osmolality inhibit Bdellovibrio bacteriovorus predation in human serum.

We evaluated the bactericidal activity of Bdellovibrio bacteriovorus, strain HD100, within blood sera against bacterial strains commonly associated with bacteremic infections, including E. coli, Klebsiella pneumoniae and Salmonella enterica. Tests show that B. bacteriovorus HD100 is not susceptible to serum complement or its bactericidal activity. After a two hour exposure to human sera, the prey populations decreased 15- to 7,300-fold due to the serum complement activity while, in contrast, the B. bacteriovorus HD100 population showed a loss of only 33%. Dot blot analyses showed that this is not due to the absence of antibodies against this predator. Predation in human serum was inhibited, though, by both the osmolality and serum albumin. The activity of B. bacteriovorus HD100 showed a sharp transition between 200 and 250 mOsm/kg, and was progressively reduced as the osmolality increased. Serum albumin also acted to inhibit predation by binding to and coating the predatory cells. This was confirmed via dot blot analyses and confocal microscopy. The results from both the osmolality and serum albumin tests were incorporated into a numerical model describing bacterial predation of pathogens. In conclusion, both of these factors inhibit predation and, as such, they limit its effectiveness against pathogenic prey located within sera.

Selected heterozygosity at cis-regulatory sequences increases the expression homogeneity of a cell population in humans.

BACKGROUND: Examples of heterozygote advantage in humans are scarce and limited to protein-coding sequences. Here, we attempt a genome-wide functional inference of advantageous heterozygosity at cis-regulatory regions. RESULTS: The single-nucleotide polymorphisms bearing the signatures of balancing selection are enriched in active cis-regulatory regions of immune cells and epithelial cells, the latter of which provide barrier function and innate immunity. Examples associated with ancient trans-specific balancing selection are also discovered. Allelic imbalance in chromatin accessibility and divergence in transcription factor motif sequences indicate that these balanced polymorphisms cause distinct regulatory variation. However, a majority of these variants show no association with the expression level of the target gene. Instead, single-cell experimental data for gene expression and chromatin accessibility demonstrate that heterozygous sequences can lower cell-to-cell variability in proportion to selection strengths. This negative correlation is more pronounced for highly expressed genes and consistently observed when using different data and methods. Based on mathematical modeling, we hypothesize that extrinsic noise from fluctuations in transcription factor activity may be amplified in homozygotes, whereas it is buffered in heterozygotes. While high expression levels are coupled with intrinsic noise reduction, regulatory heterozygosity can contribute to the suppression of extrinsic noise. CONCLUSIONS: This mechanism may confer a selective advantage by increasing cell population homogeneity and thereby enhancing the collective action of the cells, especially of those involved in the defense systems in humans.

Hypothetical biomolecular probe based on a genetic switch with tunable symmetry and stability.

BACKGROUND: Genetic switches are ubiquitous in nature, frequently associated with the control of cellular functions and developmental programs. In the realm of synthetic biology, it is of great interest to engineer genetic circuits that can change their mode of operation from monostable to bistable, or even to multistable, based on the experimental fine-tuning of readily accessible parameters. In order to successfully design robust, bistable synthetic circuits to be used as biomolecular probes, or understand modes of operation of such naturally occurring circuits, we must identify parameters that are key in determining their characteristics. RESULTS: Here, we analyze the bistability properties of a general, asymmetric genetic toggle switch based on a chemical-reaction kinetic description. By making appropriate approximations, we are able to reduce the system to two coupled differential equations. Their deterministic stability analysis and stochastic numerical simulations are in excellent agreement. Drawing upon this general framework, we develop a model of an experimentally realized asymmetric bistable genetic switch based on the LacI and TetR repressors. By varying the concentrations of two synthetic inducers, doxycycline and isopropyl ß-D-1-thiogalactopyranoside, we predict that it will be possible to repeatedly fine-tune the mode of operation of this genetic switch from monostable to bistable, as well as the switching rates over many orders of magnitude, in an experimental setting. Furthermore, we find that the shape and size of the bistability region is closely connected with plasmid copy number. CONCLUSIONS: Based on our numerical calculations of the LacI-TetR asymmetric bistable switch phase diagram, we propose a generic work-flow for developing and applying biomolecular probes: Their initial state of operation should be specified by controlling inducer concentrations, and dilution due to cellular division would turn the probes into memory devices in which information could be preserved over multiple generations. Additionally, insights from our analysis of the LacI-TetR system suggest that this particular system is readily available to be employed in this kind of probe.

Shedding light on microbial predator-prey population dynamics using a quantitative bioluminescence assay.

This study assessed the dynamics of predation by Bdellovibrio bacteriovorus HD 100. Predation tests with two different bioluminescent strains of Escherichia coli, one expressing a heat-labile bacterial luciferase and the other a heat-stable form, showed near identical losses from both, indicating that protein expression and stability are not responsible for the "shutting-off" of the prey bioluminescence (BL). Furthermore, it was found that the loss in the prey BL was not proportional with the predator-to-prey ratio (PPR), with significantly greater losses seen as this value was increased. This suggests that other factors also play a role in lowering the prey BL. The loss in BL, however, was very consistent within nine independent experiments to the point that we were able to reliably estimate the predator numbers within only 1 h when present at a PPR of 6 or higher, Using a fluorescent prey, we found that premature lysis of the prey occurs at a significant level and was more prominent as the PPR ratio increased. Based upon the supernatant fluorescent signal, even a relatively low PPR of 10-20 led to approximately 5% of the prey population being prematurely lysed within 1 h, while a PPR of 90 led to nearly 15% lysis. Consequently, we developed a modified Lotka-Volterra predator-prey model that accounted for this lysis and is able to reliably estimate the prey and bdelloplast populations for a wide range of PPRs.

Rewiring carbon catabolite repression for microbial cell factory.

Carbon catabolite repression (CCR) is a key regulatory system found in most microorganisms that ensures preferential utilization of energy-efficient carbon sources. CCR helps microorganisms obtain a proper balance between their metabolic capacity and the maximum sugar uptake capability. It also constrains the deregulated utilization of a preferred cognate substrate, enabling microorganisms to survive and dominate in natural environments. On the other side of the same coin lies the tenacious bottleneck in microbial production of bioproducts that employs a combination of carbon sources in varied proportion, such as lignocellulose-derived sugar mixtures. Preferential sugar uptake combined with the transcriptional and/or enzymatic exclusion of less preferred sugars turns out one of the major barriers in increasing the yield and productivity of fermentation process. Accumulation of the unused substrate also complicates the downstream processes used to extract the desired product. To overcome this difficulty and to develop tailor-made strains for specific metabolic engineering goals, quantitative and systemic understanding of the molecular interaction map behind CCR is a prerequisite. Here we comparatively review the universal and strain-specific features of CCR circuitry and discuss the recent efforts in developing synthetic cell factories devoid of CCR particularly for lignocellulose- based biorefinery.

Microbial linguistics: perspectives and applications of microbial cell-to-cell communication.

Inter-cellular communication via diffusible small molecules is a defining character not only of multicellular forms of life but also of single-celled organisms. A large number of bacterial genes are regulated by the change of chemical milieu mediated by the local population density of its own species or others. The cell density-dependent "autoinducer" molecules regulate the expression of those genes involved in genetic competence, biofilm formation and persistence, virulence, sporulation, bioluminescence, antibiotic production, and many others. Recent innovations in recombinant DNA technology and micro-/nano-fluidics systems render the genetic circuitry responsible for cell-to-cell communication feasible to and malleable via synthetic biological approaches. Here we review the current understanding of the molecular biology of bacterial intercellular communication and the novel experimental protocols and platforms used to investigate this phenomenon. A particular emphasis is given to the genetic regulatory circuits that provide the standard building blocks which constitute the syntax of the biochemical communication network. Thus, this review gives focus to the engineering principles necessary for rewiring bacterial chemo-communication for various applications, ranging from population-level gene expression control to the study of host-pathogen interactions.

The art of reporter proteins in science: past, present and future applications.

Starting with the first publication of lacZ gene fusion in 1980, reporter genes have just entered their fourth decade. Initial studies relied on the simple fusion of a promoter or gene with a particular reporter gene of interest. Such constructs were then used to determine the promoter activity under specific conditions or within a given cell or organ. Although this protocol was, and still is, very effective, current research shows a paradigm shift has occurred in the use of reporter systems. With the advent of innovative cloning and synthetic biology techniques and microfluidic/nanodroplet systems, reporter genes and their proteins are now finding themselves used in increasingly intricate and novel applications. For example, researchers have used fluorescent proteins to study biofilm formation and discovered that microchannels develop within the biofilm. Furthermore, there has recently been a "fusion" of art and science; through the construction of genetic circuits and regulatory systems, researchers are using bacteria to "paint" pictures based upon external stimuli. As such, this review will discuss the past and current trends in reporter gene applications as well as some exciting potential applications and models that are being developed based upon these remarkable proteins.

Systems biology of microbial communities.

Microbes exist naturally in a wide range of environments in communities where their interactions are significant, spanning the extremes of high acidity and high temperature environments to soil and the ocean. We present a practical discussion of three different approaches for modeling microbial communities: rate equations, individual-based modeling, and population dynamics. We illustrate the approaches with detailed examples. Each approach is best fit to different levels of system representation, and they have different needs for detailed biological input. Thus, this set of approaches is able to address the operation and function of microbial communities on a wide range of organizational levels.

The fixation probability of rare mutators in finite asexual populations.

A mutator is an allele that increases the mutation rate throughout the genome by disrupting some aspect of DNA replication or repair. Mutators that increase the mutation rate by the order of 100-fold have been observed to spontaneously emerge and achieve high frequencies in natural populations and in long-term laboratory evolution experiments with Escherichia coli. In principle, the fixation of mutator alleles is limited by (i) competition with mutations in wild-type backgrounds, (ii) additional deleterious mutational load, and (iii) random genetic drift. Using a multiple-locus model and employing both simulation and analytic methods, we investigate the effects of these three factors on the fixation probability Pfix of an initially rare mutator as a function of population size N, beneficial and deleterious mutation rates, and the strength of mutations s. Our diffusion-based approximation for Pfix successfully captures effects ii and iii when selection is fast compared to mutation (micro/s<<1). This enables us to predict the conditions under which mutators will be evolutionarily favored. Surprisingly, our simulations show that effect i is typically small for strong-effect mutators. Our results agree semiquantitatively with existing laboratory evolution experiments and suggest future experimental directions.

Genetic noise control via protein oligomerization.

BACKGROUND: Gene expression in a cell entails random reaction events occurring over disparate time scales. Thus, molecular noise that often results in phenotypic and population-dynamic consequences sets a fundamental limit to biochemical signaling. While there have been numerous studies correlating the architecture of cellular reaction networks with noise tolerance, only a limited effort has been made to understand the dynamic role of protein-protein interactions. RESULTS: We have developed a fully stochastic model for the positive feedback control of a single gene, as well as a pair of genes (toggle switch), integrating quantitative results from previous in vivo and in vitro studies. In particular, we explicitly account for the fast binding-unbinding kinetics among proteins, RNA polymerases, and the promoter/operator sequences of DNA. We find that the overall noise-level is reduced and the frequency content of the noise is dramatically shifted to the physiologically irrelevant high-frequency regime in the presence of protein dimerization. This is independent of the choice of monomer or dimer as transcription factor and persists throughout the multiple model topologies considered. For the toggle switch, we additionally find that the presence of a protein dimer, either homodimer or heterodimer, may significantly reduce its random switching rate. Hence, the dimer promotes the robust function of bistable switches by preventing the uninduced (induced) state from randomly being induced (uninduced). CONCLUSION: The specific binding between regulatory proteins provides a buffer that may prevent the propagation of fluctuations in genetic activity. The capacity of the buffer is a non-monotonic function of association-dissociation rates. Since the protein oligomerization per se does not require extra protein components to be expressed, it provides a basis for the rapid control of intrinsic or extrinsic noise. The stabilization of regulatory circuits and epigenetic memory in general is of direct implications to organism fitness. Our results also suggest possible avenues for the design of synthetic gene circuits with tunable robustness for a wide range of engineering purposes.

Lethality and synthetic lethality in the genome-wide metabolic network of Escherichia coli.

Recent genomic analyses on the cellular metabolic network show that reaction flux across enzymes are diverse and exhibit power-law behavior in its distribution. While intuition might suggest that the reactions with larger fluxes are more likely to be lethal under the blockade of its catalysing gene products or gene knockouts, we find, by in silico flux analysis, that the lethality rarely has correlations with the flux level owing to the widespread backup pathways innate in the genome-wide metabolism of Escherichia coli. Lethal reactions, of which the deletion generates cascading failure of following reactions up to the biomass reaction, are identified in terms of the Boolean network scheme as well as the flux balance analysis. The avalanche size of a reaction, defined as the number of subsequently blocked reactions after its removal, turns out to be a useful measure of lethality. As a means to elucidate phenotypic robustness to a single deletion, we investigate synthetic lethality in reaction level, where simultaneous deletion of a pair of nonlethal reactions leads to the failure of the biomass reaction. Synthetic lethals identified via flux balance and Boolean scheme are consistently shown to act in parallel pathways, working in such a way that the backup machinery is compromised.

Physical model for the gating mechanism of ionic channels.

We propose a physical model for the gating mechanism of ionic channels. First, we investigate the fluctuation-mediated interactions between two proteins imbedded in a cellular membrane and find that the interaction depends on their orientational configuration as well as the distance between them. The orientational dependence of interactions arises from the fact that the noncircular cross-sectional shapes of individual proteins constrain fluctuations of the membrane differently according to their orientational configuration. Then, we apply these interactions to ionic channels composed of four, five, and six proteins. As the gating stimulus creates the changes in the structural shape of proteins composing ionic channels, the orientational configuration of the ionic channels changes due to the free energy minimization, and ionic channels are open or closed according to the conformation thereof.