Neutralizing noise in gene networks

A quantitative evaluation of topological motifs and their coupling in gene circuit state distributions

One of the major challenges in biology is to understand how gene interactions collaborate to determine overall functions of biological systems. Here, we present a new computational framework that enables systematic, high-throughput, and quantitative evaluation of how small transcriptional regulatory circuit motifs, and their coupling, contribute to functions of a dynamical biological system. We illustrate how this approach can be applied to identify four-node gene circuits, circuit motifs, and motif coupling responsible for various gene expression state distributions, including those derived from single-cell RNA sequencing data. We also identify seven major classes of four-node circuits from clustering analysis of state distributions. The method is applied to establish phenomenological models of gene circuits driving human neuron differentiation, revealing important biologically relevant regulatory interactions. Our study will shed light on a better understanding of gene regulatory mechanisms in creating and maintaining cellular states.

A redox-based electrogenetic CRISPR system to connect with and control biological information networks

Electronic information can be transmitted to cells directly from microelectronics via electrode-activated redox mediators. These transmissions are decoded by redox-responsive promoters which enable user-specified control over biological function. Here, we build on this redox communication modality by establishing an electronic eCRISPR conduit of information exchange. This system acts as a biological signal processor, amplifying signal reception and filtering biological noise. We electronically amplify bacterial quorum sensing (QS) signaling by activating LasI, the autoinducer-1 synthase. Similarly, we filter out unintended noise by inhibiting the native SoxRS-mediated oxidative stress response regulon. We then construct an eCRISPR based redox conduit in both E. coli and Salmonella enterica. Finally, we display eCRISPR based information processing that allows transmission of spatiotemporal redox commands which are then decoded by gelatin-encapsulated E. coli. We anticipate that redox communication channels will enable biohybrid microelectronic devices that could transform our abilities to electronically interpret and control biological function.

Identifying a Probabilistic Boolean Threshold Network From Samples

This paper studies the problem of exactly identifying the structure of a probabilistic Boolean network (PBN) from a given set of samples, where PBNs are probabilistic extensions of Boolean networks. Cheng et al. studied the problem while focusing on PBNs consisting of pairs of AND/OR functions. This paper considers PBNs consisting of Boolean threshold functions while focusing on those threshold functions that have unit coefficients. The treatment of Boolean threshold functions, and triplets and -tuplets of such functions, necessitates a deepening of the theoretical analyses. It is shown that wide classes of PBNs with such threshold functions can be exactly identified from samples under reasonable constraints, which include: 1) PBNs in which any number of threshold functions can be assigned provided that all have the same number of input variables and 2) PBNs consisting of pairs of threshold functions with different numbers of input variables. It is also shown that the problem of deciding the equivalence of two Boolean threshold functions is solvable in pseudopolynomial time but remains co-NP complete.

Stochastic noise reduction upon complexification: positively correlated birth-death type systems

Cell systems consist of a huge number of various molecules that display specific patterns of interactions, which have a determining influence on the cell׳s functioning. In general, such complexity is seen to increase with the complexity of the organism, with a concomitant increase of the accuracy and specificity of the cellular processes. The question thus arises how the complexification of systems - modeled here by simple interacting birth-death type processes - can lead to a reduction of the noise - described by the variance of the number of molecules. To gain understanding of this issue, we investigated the difference between a single system containing molecules that are produced and degraded, and the same system - with the same average number of molecules - connected to a buffer. We modeled these systems using Itō stochastic differential equations in discrete time, as they allow straightforward analytical developments. In general, when the molecules in the system and the buffer are positively correlated, the variance on the number of molecules in the system is found to decrease compared to the equivalent system without a buffer. Only buffers that are too noisy themselves tend to increase the noise in the main system. We tested this result on two model cases, in which the system and the buffer contain proteins in their active and inactive state, or protein monomers and homodimers. We found that in the second test case, where the interconversion terms are non-linear in the number of molecules, the noise reduction is much more pronounced; it reaches up to 20% reduction of the Fano factor with the parameter values tested in numerical simulations on an unperturbed birth-death model. We extended our analysis to two arbitrary interconnected systems, and found that the sum of the noise levels in the two systems generally decreases upon interconnection if the molecules they contain are positively correlated.

Design principles of a genetic alarm clock

Turning genes on and off is a mechanism by which cells and tissues make phenotypic decisions. Gene network motifs capable of supporting two or more steady states and thereby providing cells with a plurality of possible phenotypes are referred to as genetic switches. Modeled on the bases of naturally occurring genetic networks, synthetic biologists have successfully constructed artificial switches, thus opening a door to new possibilities for improvement of the known, but also the design of new synthetic genetic circuits. One of many obstacles to overcome in such efforts is to understand and hence control intrinsic noise which is inherent in all biological systems. For some motifs the noise is negligible; for others, fluctuations in the particle number can be comparable to its average. Due to their slowed dynamics, motifs with positive autoregulation tend to be highly sensitive to fluctuations of their chemical environment and are in general very noisy, especially during transition (switching). In this article we use stochastic simulations (Gillespie algorithm) to model such a system, in particular a simple bistable motif consisting of a single gene with positive autoregulation. Due to cooperativety, the dynamical behavior of this kind of motif is reminiscent of an alarm clock - the gene is (nearly) silent for some time after it is turned on and becomes active very suddenly. We investigate how these sudden transitions are affected by noise and show that under certain conditions accurate timing can be achieved. We also examine how promoter complexity influences the accuracy of this timing mechanism.

Metaxin deficiency alters mitochondrial membrane permeability and leads to resistance to TNF-induced cell killing

Metaxin, a mitochondrial outer membrane protein, is critical for TNF-induced cell death in L929 cells. Its deficiency, caused by retroviral insertion-mediated mutagenesis, renders L929 cells resistance to TNF killing. In this study, we further characterized metaxin deficiency-caused TNF resistance in parallel with Bcl-X(L) overexpression-mediated death resistance. We did not find obvious change in mitochondria membrane potential in metaxin-deficient (Met(mut)) and Bcl-X(L)-overexpressing cells, but we did find an increase in the release rate of the mitochondrial membrane potential probe rhodamine 123 (Rh123) that was preloaded into mitochondria. In addition, overexpression of a function-interfering mutant of metaxin (MetaΔTM/C) or Bcl-X(L) in MCF-7.3.28 cells also resulted in an acquired resistance to TNF killing and a faster rate of Rh123 release, indicating a close correlation between TNF resistance and higher rates of the dye release from the mitochondria. The release of Rh123 can be controlled by the mitochondrial membrane permeability transition (PT) pore, as targeting an inner membrane component of the PT pore by cyclosporin A (CsA) inhibited Rh123 release. However, metaxin deficiency and Bcl-X(L) overexpression apparently affect Rh123 release from a site(s) different from that of CsA, as CsA can overcome their effect. Though both metaxin and Bcl-X(L) appear to function on the outer mitochondrial membrane, they do not interact with each other. They may use different mechanisms to increase the permeability of Rh123, since previous studies have suggested that metaxin may influence certain outer membrane porins while Bcl-X(L) may form pores on the outer membrane. The alteration of the mitochondrial outer membrane properties by metaxin deficiency and Bcl-X(L) overexpression, as indicated by a quicker Rh123 release, may be helpful in maintaining mitochondrial integrity.

Multilayered control of gene expression by stress-activated protein kinases

Stress-activated protein kinases (SAPKs) are key elements for intracellular signalling networks that serve to respond and adapt to extracellular changes. Exposure of yeast to high osmolarity results in the activation of p38-related SAPK, Hog1, which is essential for reprogramming the gene expression capacity of the cell by regulation of several steps of the transcription process. At initiation, active Hog1 not only directly phosphorylates several transcription factors to alter their activities, but also associates at stress-responsive promoters through such transcription factors. Once at the promoters, Hog1 serves as a platform to recruit general transcription factors, chromatin-modifying activities and RNA Pol II. In addition, the SAPK pathway has a role in elongation. At the stress-responsive ORFs, Hog1 recruits the RSC chromatin-remodelling complex to modify nucleosome organization. Several SAPKs from yeast to mammals have maintained some of the regulatory abilities of Hog1. Thus, elucidating the control of gene expression by the Hog1 SAPK should help to understand how eukaryotic cells implement a massive and rapid change on their transcriptional capacity in response to adverse conditions.

Dynamic signaling in the Hog1 MAPK pathway relies on high basal signal transduction

Appropriate regulation of the Hog1 mitogen-activated protein kinase (MAPK) pathway is essential for cells to survive osmotic stress. Here, we show that the two sensing mechanisms upstream of Hog1 display different signaling properties. The Sho1 branch is an inducible nonbasal system, whereas the Sln1 branch shows high basal signaling that is restricted by a MAPK-mediated feedback mechanism. A two-dimensional mathematical model of the Snl1 branch, including high basal signaling and a Hog1-regulated negative feedback, shows that a system with basal signaling exhibits higher efficiency, with faster response times and higher sensitivity to variations in external signals, than would systems without basal signaling. Analysis of two other yeast MAPK pathways, the Fus3 and Kss1 signaling pathways, indicates that high intrinsic basal signaling may be a general property of MAPK pathways allowing rapid and sensitive responses to environmental changes.

Statistical physics of a model binary genetic switch with linear feedback

We study the statistical properties of a simple genetic regulatory network that provides heterogeneity within a population of cells. This network consists of a binary genetic switch in which stochastic flipping between the two switch states is mediated by a "flipping" enzyme. Feedback between the switch state and the flipping rate is provided by a linear feedback mechanism: the flipping enzyme is only produced in the on switch state and the switching rate depends linearly on the copy number of the enzyme. This work generalizes the model of Visco [Phys. Rev. Lett. 101, 118104 (2008)] to a broader class of linear feedback systems. We present a complete analytical solution for the steady-state statistics of the number of enzyme molecules in the on and off states, for the general case where the enzyme can mediate flipping in either direction. For this general case we also solve for the flip time distribution, making a connection to first passage and persistence problems in statistical physics. We show that the statistics are non-Poissonian, leading to a peak in the flip time distribution. The occurrence of such a peak is analyzed as a function of the parameter space. We present a relation between the flip time distributions measured for two relevant choices of initial condition. We also introduce a correlation measure and use this to show that this model can exhibit long-lived temporal correlations, thus providing a primitive form of cellular memory. Motivated by DNA replication as well as by evolutionary mechanisms involving gene duplication, we study the case of two switches in the same cell. This results in correlations between the two switches; these can be either positive or negative depending on the parameter regime.

Regulation by transcription factors in bacteria: beyond description

Transcription is an essential step in gene expression and its understanding has been one of the major interests in molecular and cellular biology. By precisely tuning gene expression, transcriptional regulation determines the molecular machinery for developmental plasticity, homeostasis and adaptation. In this review, we transmit the main ideas or concepts behind regulation by transcription factors and give just enough examples to sustain these main ideas, thus avoiding a classical ennumeration of facts. We review recent concepts and developments: cis elements and trans regulatory factors, chromosome organization and structure, transcriptional regulatory networks (TRNs) and transcriptomics. We also summarize new important discoveries that will probably affect the direction of research in gene regulation: epigenetics and stochasticity in transcriptional regulation, synthetic circuits and plasticity and evolution of TRNs. Many of the new discoveries in gene regulation are not extensively tested with wetlab approaches. Consequently, we review this broad area in Inference of TRNs and Dynamical Models of TRNs. Finally, we have stepped backwards to trace the origins of these modern concepts, synthesizing their history in a timeline schema.

Digital-analog hybrid control model for eukaryotic heat shock response illustrating the dynamics of heat shock protein 70 on exposure to thermal stress

We are introducing in this paper a digital-analog hybrid model approach for the study of a complete gene regulatory network; the heat shock response (HSR) network of eukaryotes. HSR is a crucial and widely studied cellular phenomenon occurring due to various stresses on the cell, and is characterised by the induction of heat shock genes resulting in the production of heat shock proteins (HSPs) which restores cellular homeostasis by maintaining protein integrity. We are proposing a model which incorporates simple digital and analog components which mimic the functioning of biological molecules involved in HSR and model their dynamics and behaviour. The simulation result of the circuit for the production of HSP70 has been found to be consistent with published experimental results. The qualitative behaviour of the HSR is expressed through a truth table. Through this novel approach, the authors have tried to develop a level of understanding of the interactions of the parts of the HSR system and of this system as a whole.

Consequences of deterministic and stochastic modeling of a promoter

For an engineered genetic oscillator, deterministic analysis indicates sustained oscillations and stochastic simulations show irregular or absent oscillations. Since the major difference is in the modeling of the promoters, we have performed a detailed analysis of a generic repressible promoter system. Deterministic, stochastic, thermodynamic, and hybrid models were developed for the promoter. The average behavior of the stochastic model converged to the thermodynamic model. The deterministic model is a special case of the thermodynamic model. The hybrid model could lock into the off state. Adding an unrelated background reaction allowed it to exit that state. Increasing the background rate allowed the hybrid model to converge to thermodynamic and stochastic model. Adding a background reaction to the stochastic oscillator simulation noticeably improved its performance.

The role of log-normal dynamics in the evolution of biochemical pathways

The study of the scale-free topology in non-biological and biological networks and the dynamics that can explain this fascinating property of complex systems have captured the attention of the scientific community in the last years. Here, we analyze the biochemical pathways of three organisms (Methanococcus jannaschii, Escherichia coli, Saccharomyces cerevisiae) which are representatives of the main kingdoms Archaea, Bacteria and Eukaryotes during the course of the biological evolution. We can consider two complementary representations of the biochemical pathways: the enzymes network and the chemical compounds network. In this article, we propose a stochastic model that explains that the scale-free topology with exponent in the vicinity of gamma approximately 3/2 found across these three organisms is governed by the log-normal dynamics in the evolution of the enzymes network. Precisely, the fluctuations of the connectivity degree of enzymes in the biochemical pathways between evolutionary distant organisms follow the same conserved dynamical principle, which in the end is the origin of the stationary scale-free distribution observed among species, from Archaea to Eukaryotes. In particular, the log-normal dynamics guarantees the conservation of the scale-free distribution in evolving networks. Furthermore, the log-normal dynamics also gives a possible explanation for the restricted range of observed exponents gamma in the scale-free networks (i.e., gamma > or = 3/2). Finally, our model is also applied to the chemical compounds network of biochemical pathways and the Internet network.

"Essential noise" - enhancing variability of informational constraints benefits movement control: a comment on Waddington and Adams (2003)

This commentary proposes a dynamical systems perspective to re-interpret data from a group of international soccer players demonstrating that wearing textured insoles in soccer boots enhanced tactile information from the sole of the foot and increased movement discrimination capacity in ankle inversion sensitivity tests to levels similar to those in barefoot conditions. Theoretical arguments on the functional role of variability induced in the sensorimotor system by textured insoles, acting as a form of "essential noise" to enhance the accuracy of foot positioning are presented. It seems that, far from interfering with motor performance, variability can actually enhance perception of information to support motor performance. The addition of intermittent, intermediate levels of noise in a perceptual motor context may benefit performers by helping them to pick up information signals from background structure. Movement system variability is conceived as noise induced resonance benefiting the pick up of information to regulate behaviour. Variability can be functional in practical programmes to offset negative effects of losses in sensory sensitivity through ageing, disease, illness, or injury.

Quantitative analysis of signaling networks

The response of biological cells to environmental change is coordinated by protein-based signaling networks. These networks are to be found in both prokaryotes and eukaryotes. In eukaryotes, the signaling networks can be highly complex, some networks comprising of 60 or more proteins. The fundamental motif that has been found in all signaling networks is the protein phosphorylation/dephosphorylation cycle--the cascade cycle. At this time, the computational function of many of the signaling networks is poorly understood. However, it is clear that it is possible to construct a huge variety of control and computational circuits, both analog and digital from combinations of the cascade cycle. In this review, we will summarize the great versatility of the simple cascade cycle as a computational unit and towards the end give two examples, one prokaryotic chemotaxis circuit and the other, the eukaryotic MAPK cascade.

Identifying constraints that govern cell behavior: a key to converting conceptual to computational models in biology?

Cells must abide by a number of constraints. The environmental constrains of cellular behavior and physicochemical limitations affect cellular processes. To regulate and adapt their functions, cells impose constraints on themselves. Enumerating, understanding, and applying these constraints leads to a constraints-based modeling formalism that has been helpful in converting conceptual models to computational models in biology. The continued success of the constraints-based approach depends upon identification and incorporation of new constraints to more accurately define cellular capabilities. This review considers constraints in terms of environmental, physicochemical, and self-imposed regulatory and evolutionary constraints with the purpose of refining current constraints-based models of cell phenotype.

Bistability and switching in the lysis/lysogeny genetic regulatory network of bacteriophage λ

Bistability and switching are two important aspects of the genetic regulatory network of lambda phage. Positive and negative feedbacks are key regulatory mechanisms in this network. By the introduction of threshold values, the developmental pathway of lambda phage is divided into different stages. If the protein level reaches a threshold value, positive or negative feedback will be effective and regulate the process of development. Using this regulatory mechanism, we present a quantitative model to realize bistability and switching of lambda phage based on experimental data. This model gives descriptions of decisive mechanisms for different pathways in induction. A stochastic model is also introduced for describing statistical properties of switching in induction. A stochastic degradation rate is used to represent intrinsic noise in induction for switching the system from the lysogenic pathway to the lysis pathway. The approach in this paper represents an attempt to describe the regulatory mechanism in genetic regulatory network under the influence of intrinsic noise in the framework of continuous models.

Hox in hair growth and development

The evolutionarily conserved Hox gene family of transcriptional regulators has originally been known for specifying positional identities along the longitudinal body axis of bilateral metazoans, including mouse and man. It is believed that subsequent to this archaic role, subsets of Hox genes have been co-opted for patterning functions in phylogenetically more recent structures, such as limbs and epithelial appendages. Among these, the hair follicle is of particular interest, as it is the only organ undergoing cyclical phases of regression and regeneration during the entire life span of an organism. Furthermore, the hair follicle is increasingly capturing the attention of developmental geneticists, as this abundantly available miniature organ mimics key aspects of embryonic patterning and, in addition, presents a model for studying organ renewal. The first Hox gene shown to play a universal role in hair follicle development is Hoxc13, as both Hoxc13-deficient and overexpressing mice exhibit severe hair growth and patterning defects. Differential gene expression analyses in the skin of these mutants, as well as in vitro DNA binding studies performed with potential targets for HOXC13 transcriptional regulation in human hair, identified genes encoding hair-specific keratins and keratin-associated proteins (KAPs) as major groups of presumptive Hoxc13 downstream effectors in the control of hair growth. The Hoxc13 mutant might thus serve as a paradigm for studying hair-specific roles of Hoxc13 and other members of this gene family, whose distinct spatio-temporally restricted expression patterns during hair development and cycling suggest discrete functions in follicular patterning and hair cycle control. The main conclusion from a discussion of these potential roles vis-à-vis current expression data in mouse and man, and from the perspective of the results obtained with the Hoxc13 transgenic models, is that members of the Hox family are likely to fulfill essential roles of great functional diversity in hair that require complex transcriptional control mechanisms to ensure proper spatio-temporal patterns of Hox gene expression at homeostatic levels.

Increased noise as an effect of haploinsufficiency of the tumor-suppressor gene neurofibromatosis type 1 in vitro

In human diseases related to tumor-suppressor genes, it is suggested that only the complete loss of the protein results in specific symptoms such as tumor formation, whereas simple reduction of protein quantity to 50%, called haploinsufficiency, essentially does not affect cellular behavior. Using a model of gene expression, it was presumed that haploinsufficiency is related to an increased noise in gene expression also in vivo [Cook, D. L., Gerber, A. N. & Tapscott, S. J. (1998) Proc. Natl. Acad. Sci. USA 95, 15641-15646]. Here, we demonstrate that haploinsufficiency of the tumor-suppressor gene neurofibromatosis type 1 (NF1) results in an increased variation of dendrite formation in cultured NF1 melanocytes. These morphological differences between NF1 and control melanocytes can be described by a mathematical model in which the cell is considered to be a self-organized automaton. The model describes the adjustment of the cells to a set point and includes a noise term that allows for stochastic processes. It describes the experimental data of control and NF1 melanocytes. In the cells haploinsufficient for NF1 we found an altered signal-to-noise ratio detectable as increased variation in dendrite formation in two of three investigated morphological parameters. We also suggest that in vivo NF1 haploinsufficiency results in an increased noise in cellular regulation and that this effect of haploinsufficiency may be found also in other tumor suppressors.

Overexpression of Hoxc13 in differentiating keratinocytes results in downregulation of a novel hair keratin gene cluster and alopecia

Studying the roles of Hox genes in normal and pathological development of skin and hair requires identification of downstream target genes in genetically defined animal models. We show that transgenic mice overexpressing Hoxc13 in differentiating keratinocytes of hair follicles develop alopecia, accompanied by a progressive pathological skin condition that resembles ichthyosis. Large-scale analysis of differential gene expression in postnatal skin of these mice identified 16 previously unknown and 13 known genes as presumptive Hoxc13 targets. The majority of these targets are downregulated and belong to a subgroup of genes that encode hair-specific keratin-associated proteins (KAPs). Genomic mapping using a mouse hamster radiation hybrid panel showed these genes to reside in a novel KAP gene cluster on mouse chromosome 16 in a region of conserved linkage with human chromosome 21q22.11. Furthermore, data obtained by Hoxc13/lacZ reporter gene analysis in mice that overexpress Hoxc13 suggest negative autoregulatory feedback control of Hoxc13 expression levels, thus providing an entry point for elucidating currently unknown mechanisms that are required for regulating quantitative levels of Hox gene expression. Combined, these results provide a framework for understanding molecular mechanisms of Hoxc13 function in hair growth and development.