Discreteness-induced transitions in multibody reaction systems

A decrease in system size can induce qualitatively different behavior compared to the macroscopic behavior of the corresponding large-size system. The mechanisms of this transition, which is known as the small-size transition, can be attributed to either a relative increase in the noise intensity or to the discreteness of the state space due to the small system size. The former mechanism has been intensively investigated using several toy and realistic models. However, the latter has rarely been analyzed and is sometimes confused with the former, because a toy model that extracts the essence of the discreteness-induced transition mechanism is lacking. In this work, we propose a one- and three-body reaction system as a minimal model of the discreteness-induced transition and derive the conditions under which this transition occurs in more complex systems. This work enriches our understanding of the influence of small system size on system behavior.

Fluctuation Relations of Fitness and Information in Population Dynamics

Phenotype switching with and without sensing environment is a common strategy of organisms to survive in a fluctuating environment. Understanding the evolutionary advantages of switching and sensing requires a quantitative evaluation of their fitness gain and its fluctuation together with the conditions for the switching and sensing strategies being adapted to a given environment. In this work, by using a pathwise formulation of the population dynamics, we show that the optimal switching strategy is characterized by a consistency condition for time-forward and backward path probabilities. The formulation also clarifies the underlying information-theoretic aspect of selection as a passive information compression. The loss of fitness by a suboptimal strategy is also shown to satisfy a fluctuation relation, which provides us with the information on how environmental fluctuation impacts the advantages of the optimal strategy. These results are naturally extended to the situation that organisms can use an environmental signal by actively sensing the environment. The fluctuation relations of the fitness gain by sensing are derived in which the multivariate mutual information among the phenotype, the environment, and the signal plays the role to quantify the relevant information in the signal for the fitness gain.

In vivo oriented modeling with consideration of intracellular crowding

In vivo reaction space is constrained by complex structures which are made of entwined cytoskeletons and organelles; this create the difference between in vivo and in vitro in respect of molecular mobility, and it may affect reaction processes. Our motivation is to reveal the background mechanisms of the properties of molecular behaviors in vivo by numerical approach. For this object, we reassembled a pseudo-intracellular environment in 3D lattice space, and executed Monte Carlo simulation. By changing the relative amount of non-reactive obstacles in the simulation space, we tested the effect of the level of crowdedness to the molecular mobility and reaction processes. Our results showed that molecules demonstrated anomalous diffusion correlating to the restriction level of the reaction space. Reaction processes also showed distinct characteristics, that is increase of reaction rate at the beginning of reactions, with the decrease of the reaction rate at later time frame of reactions. Our results suggested that the anomalous behaviors at singe molecule level in vivo could bring an essential difference to the reaction processes and the results.

Positive and Negative Regulatory Mechanisms for Fine-Tuning Cellularity and Functions of Medullary Thymic Epithelial Cells

Self-tolerant T cells and regulatory T cells develop in the thymus. A wide variety of cell-cell interactions in the thymus is required for the differentiation, proliferation, and repertoire selection of T cells. Various secreted and cell surface molecules expressed in thymic epithelial cells (TECs) mediate these processes. Moreover, cytokines expressed by cells of hematopoietic origin regulate the cellularity of TECs. Tumor necrosis factor (TNF) family RANK ligand, lymphotoxin, and CD40 ligand, expressed in T cells and innate lymphoid cells (ILCs), promote the differentiation and proliferation of medullary TECs (mTECs) that play critical roles in the induction of immune tolerance. A recent study suggests that interleukin-22 (IL-22) produced by ILCs promotes regeneration of TECs after irradiation. Intriguingly, tumor growth factor-β and osteoprotegerin limit cellularity of mTECs, thereby attenuating regulatory T cell generation. We will review recent insights into the molecular basis for cell-cell interactions regulating differentiation and proliferation of mTECs and also discuss about a perspective on use of mathematical models for understanding this complicated system.

Balancing acts of two HEAT subunits of condensin I support dynamic assembly of chromosome axes

Condensin I is a five-subunit protein complex that plays a central role in mitotic chromosome assembly and segregation in eukaryotes. To dissect its mechanism of action, we reconstituted wild-type and mutant complexes from recombinant subunits and tested their abilities to assemble chromosomes in Xenopus egg cell-free extracts depleted of endogenous condensins. We find that ATP binding and hydrolysis by SMC subunits have distinct contributions to the action of condensin I and that continuous ATP hydrolysis is required for structural maintenance of chromosomes. Mutant complexes lacking either one of two HEAT subunits produce abnormal chromosomes with highly characteristic defects and have contrasting structural effects on chromosome axes preassembled with the wild-type complex. We propose that balancing acts of the two HEAT subunits support dynamic assembly of chromosome axes under the control of the SMC ATPase cycle, thereby governing construction of rod-shaped chromosomes in eukaryotic cells.

Experimental and theoretical bases for mechanisms of antigen discrimination by T cells

Interaction only within specific molecules is a requisite for accurate operations of a biochemical reaction in a cell where bulk of background molecules exist. While structural specificity is a well-established mechanism for specific interaction, biophysical and biochemical experiments indicate that the mechanism is not sufficient for accounting for the antigen discrimination by T cells. In addition, the antigen discrimination by T cells also accompanies three intriguing properties other than the specificity: sensitivity, speed, and concentration compensation. In this work, we review experimental and theoretical works on the antigen discrimination by focusing on these four properties and show future directions towards understanding of the fundamental principle for molecular discrimination.

Pathwise thermodynamic structure in population dynamics

We reveal thermodynamic structure in population dynamics with phenotype switching. Mean fitness for a population of organisms is determined by a thermodynamic variational principle described by the large deviation of phenotype-switching dynamics. Owing to this variational principle, a response relation of the mean fitness with respect to changes of environments and phenotype-switching dynamics is represented as a thermodynamic differential form. Furthermore, we discuss the strength of the selection by using the difference between time-forward and time-backward (retrospective) processes.

Improved and robust detection of cell nuclei from four dimensional fluorescence images

Segmentation-free direct methods are quite efficient for automated nuclei extraction from high dimensional images. A few such methods do exist but most of them do not ensure algorithmic robustness to parameter and noise variations. In this research, we propose a method based on multiscale adaptive filtering for efficient and robust detection of nuclei centroids from four dimensional (4D) fluorescence images. A temporal feedback mechanism is employed between the enhancement and the initial detection steps of a typical direct method. We estimate the minimum and maximum nuclei diameters from the previous frame and feed back them as filter lengths for multiscale enhancement of the current frame. A radial intensity-gradient function is optimized at positions of initial centroids to estimate all nuclei diameters. This procedure continues for processing subsequent images in the sequence. Above mechanism thus ensures proper enhancement by automated estimation of major parameters. This brings robustness and safeguards the system against additive noises and effects from wrong parameters. Later, the method and its single-scale variant are simplified for further reduction of parameters. The proposed method is then extended for nuclei volume segmentation. The same optimization technique is applied to final centroid positions of the enhanced image and the estimated diameters are projected onto the binary candidate regions to segment nuclei volumes.Our method is finally integrated with a simple sequential tracking approach to establish nuclear trajectories in the 4D space. Experimental evaluations with five image-sequences (each having 271 3D sequential images) corresponding to five different mouse embryos show promising performances of our methods in terms of nuclear detection, segmentation, and tracking. A detail analysis with a sub-sequence of 101 3D images from an embryo reveals that the proposed method can improve the nuclei detection accuracy by 9 over the previous methods, which used inappropriate large valued parameters. Results also confirm that the proposed method and its variants achieve high detection accuracies ( 98 mean F-measure) irrespective of the large variations of filter parameters and noise levels.

Information decoding in microscopic biological processes

The cellular and intracellular dynamics are intrinsically stochastic and dynamic. However, whole biological system such as a cell or our body can function very robustly and stably even though they are composed of these stochastic reactions. To account for this riddling relation between macroscopic robustness and microscopic stochasticity, I propose a mechanism that information relevant for stable and reliable operation of a biological system is embedded in apparently stochastic and noisy behavior of their components. To show validity of this possibility, I demonstrates that information can actually be decoded from apparently noisy signal when it is processed by an appropriate dynamics derived by Bayes' rule. Next, I investigate biological relevance of this possibility by showing that several intracellular networks can implement this decoding dynamics. Finally, by focusing its dynamical properties, I show the mechanism how the derived dynamics can separate information and noise.

Single cell visualization of yeast gene expression shows correlation of epigenetic switching between multiple heterochromatic regions through multiple generations

A single-cell method allows the assessment of relationships between the dynamic epigenetic behavior of yeast heterochromatin boundaries over multiple generations.

Differences in gene expression between individual cells can be mediated by epigenetic regulation; thus, methods that enable detailed analyses of single cells are crucial to understanding this phenomenon. In this study, genomic silencing regions of Saccharomyces cerevisiae that are subject to epigenetic regulation, including the HMR, HML, and telomere regions, were investigated using a newly developed single cell analysis method. This method uses fluorescently labeled proteins to track changes in gene expression over multiple generations of a single cell. Epigenetic control of gene expression differed depending on the specific silencing region at which the reporter gene was inserted. Correlations between gene expression at the HMR-left and HMR-right regions, as well as the HMR-right and HML-right regions, were observed in the single-cell level; however, no such correlations involving the telomere region were observed. Deletion of the histone acetyltransferase GCN5 gene from a yeast strain carrying a fluorescent reporter gene at the HMR-left region reduced the frequency of changes in gene expression over a generation. The results presented here suggest that epigenetic control within an individual cell is reversible and can be achieved via regulation of histone acetyltransferase activity.

Although eukaryotic gene repression usually acts on individual genes, cells can also repress larger chromosomal regions via the establishment of a high order chromatin structure called heterochromatin. Once initiated, heterochromatin spreads until halted by a boundary, and in this study we focus on how this boundary is formed. Because the mechanism is epigenetic and can differ from cell to cell, we wanted to assess the dynamics of the process by tracking individual cells over multiple generations. Here we develop a novel method employing protein fluorescence to monitor gene expression at the boundaries of several yeast heterochromatic regions simultaneously. This allows us to assess whether different boundaries within a single cell fluctuate in concert or independently of each other. In addition, we use histone modification mutants to probe the specific types of epigenetic regulation responsible for fluctuations in heterochromatin boundary positioning. Using this method, we show that epigenetic gene expression within individual cells is reversible and that this process is regulated by histone acetylation state. Future work will identify connections between variation in boundary positioning and novel transcription control systems.

Physiological Intracellular Crowdedness is Defined by the Perimeter-to-Area Ratio of Sub-Cellular Compartments

The intracellular environment is known to be a crowded and inhomogeneous space. Such an in vivo environment differs from a well-diluted, homogeneous environment for biochemical reactions. However, the effects of both crowdedness and the inhomogeneity of environment on the behavior of a mobile particle have not yet been investigated sufficiently. As described in this paper, we constructed artificial reaction spaces with fractal models, which are assumed to be non-reactive solid obstacles in a reaction space with crevices that function as operating ranges for mobile particles threading the space. Because of the homogeneity of the structures of artificial reaction spaces, the models succeeded in reproducing the physiological fractal dimension of solid structures with a smaller number of non-reactive obstacles than in the physiological condition. This incomplete compatibility was mitigated when we chose a suitable condition of a perimeter-to-area ratio of the operating range to our model. Our results also show that a simulation space is partitioned into convenient reaction compartments as an in vivo environment with the exact amount of solid structures estimated from TEM images. The characteristics of these compartments engender larger mean square displacement of a mobile particle than that of particles in smaller compartments. Subsequently, the particles start to show confined particle-like behavior. These results are compatible with our previously presented results, which predicted that a physiological environment would produce quick response and slow exhaustion reactions.

Information processing and integration with intracellular dynamics near critical point

Recent experimental observations suggest that cells can show relatively precise and reliable responses to external signals even though substantial noise is inevitably involved in the signals. An intriguing question is the way how cells can manage to do it. One possible way to realize such response for a cell is to evolutionary develop and optimize its intracellular signaling pathways so as to extract relevant information from the noisy signal. We recently demonstrated that certain intracellular signaling reactions could actually conduct statistically optimal information processing. In this paper, we clarify that such optimal reaction operates near bifurcation point. This result suggests that critical-like phenomena in the single-cell level may be linked to efficient information processing inside a cell. In addition, improving the performance of response in the single-cell level is not the only way for cells to realize reliable response. Another possible strategy is to integrate information of individual cells by cell-to-cell interaction such as quorum sensing. Since cell-to-cell interaction is a common phenomenon, it is equally important to investigate how cells can integrate their information by cell-to-cell interaction to realize efficient information processing in the population level. In this paper, we consider roles and benefits of cell-to-cell interaction by considering integrations of obtained information of individuals with the other cells from the viewpoint of information processing. We also demonstrate that, by introducing cell movement, spatial organizations can spontaneously emerge as a result of efficient responses of the population to external signals.

Automatic extraction of nuclei centroids of mouse embryonic cells from fluorescence microscopy images

Accurate identification of cell nuclei and their tracking using three dimensional (3D) microscopic images is a demanding task in many biological studies. Manual identification of nuclei centroids from images is an error-prone task, sometimes impossible to accomplish due to low contrast and the presence of noise. Nonetheless, only a few methods are available for 3D bioimaging applications, which sharply contrast with 2D analysis, where many methods already exist. In addition, most methods essentially adopt segmentation for which a reliable solution is still unknown, especially for 3D bio-images having juxtaposed cells. In this work, we propose a new method that can directly extract nuclei centroids from fluorescence microscopy images. This method involves three steps: (i) Pre-processing, (ii) Local enhancement, and (iii) Centroid extraction. The first step includes two variations: first variation (Variant-1) uses the whole 3D pre-processed image, whereas the second one (Variant-2) modifies the preprocessed image to the candidate regions or the candidate hybrid image for further processing. At the second step, a multiscale cube filtering is employed in order to locally enhance the pre-processed image. Centroid extraction in the third step consists of three stages. In Stage-1, we compute a local characteristic ratio at every voxel and extract local maxima regions as candidate centroids using a ratio threshold. Stage-2 processing removes spurious centroids from Stage-1 results by analyzing shapes of intensity profiles from the enhanced image. An iterative procedure based on the nearest neighborhood principle is then proposed to combine if there are fragmented nuclei. Both qualitative and quantitative analyses on a set of 100 images of 3D mouse embryo are performed. Investigations reveal a promising achievement of the technique presented in terms of average sensitivity and precision (i.e., 88.04% and 91.30% for Variant-1; 86.19% and 95.00% for Variant-2), when compared with an existing method (86.06% and 90.11%), originally developed for analyzing C. elegans images.

Theoretical aspects of cellular decision-making and information-processing

Microscopic biological processes have extraordinary complexity and variety at the sub-cellular, intra-cellular, and multi-cellular levels. In dealing with such complex phenomena, conceptual and theoretical frameworks are crucial, which enable us to understand seemingly different intra- and inter-cellular phenomena from unified viewpoints. Decision-making is one such concept that has attracted much attention recently. Since a number of cellular behavior can be regarded as processes to make specific actions in response to external stimuli, decision-making can cover and has been used to explain a broad range of different cellular phenomena [Balázsi et al. (Cell 144(6):910, 2011), Zeng et al. (Cell 141(4):682, 2010)]. Decision-making is also closely related to cellular information-processing because appropriate decisions cannot be made without exploiting the information that the external stimuli contain. Efficiency of information transduction and processing by intra-cellular networks determines the amount of information obtained, which in turn limits the efficiency of subsequent decision-making. Furthermore, information-processing itself can serve as another concept that is crucial for understanding of other biological processes than decision-making. In this work, we review recent theoretical developments on cellular decision-making and information-processing by focusing on the relation between these two concepts.

Dynamics of intracellular information decoding

A variety of cellular functions are robust even to substantial intrinsic and extrinsic noise in intracellular reactions and the environment that could be strong enough to impair or limit them. In particular, of substantial importance is cellular decision-making in which a cell chooses a fate or behavior on the basis of information conveyed in noisy external signals. For robust decoding, the crucial step is filtering out the noise inevitably added during information transmission. As a minimal and optimal implementation of such an information decoding process, the autocatalytic phosphorylation and autocatalytic dephosphorylation (aPadP) cycle was recently proposed. Here, we analyze the dynamical properties of the aPadP cycle in detail. We describe the dynamical roles of the stationary and short-term responses in determining the efficiency of information decoding and clarify the optimality of the threshold value of the stationary response and its information-theoretical meaning. Furthermore, we investigate the robustness of the aPadP cycle against the receptor inactivation time and intrinsic noise. Finally, we discuss the relationship among information decoding with information-dependent actions, bet-hedging and network modularity.

Perturbation analyses of intermolecular interactions

Conformational fluctuations of a protein molecule are important to its function, and it is known that environmental molecules, such as water molecules, ions, and ligand molecules, significantly affect the function by changing the conformational fluctuations. However, it is difficult to systematically understand the role of environmental molecules because intermolecular interactions related to the conformational fluctuations are complicated. To identify important intermolecular interactions with regard to the conformational fluctuations, we develop herein (i) distance-independent and (ii) distance-dependent perturbation analyses of the intermolecular interactions. We show that these perturbation analyses can be realized by performing (i) a principal component analysis using conditional expectations of truncated and shifted intermolecular potential energy terms and (ii) a functional principal component analysis using products of intermolecular forces and conditional cumulative densities. We refer to these analyses as intermolecular perturbation analysis (IPA) and distance-dependent intermolecular perturbation analysis (DIPA), respectively. For comparison of the IPA and the DIPA, we apply them to the alanine dipeptide isomerization in explicit water. Although the first IPA principal components discriminate two states (the α state and PPII (polyproline II) + β states) for larger cutoff length, the separation between the PPII state and the β state is unclear in the second IPA principal components. On the other hand, in the large cutoff value, DIPA eigenvalues converge faster than that for IPA and the top two DIPA principal components clearly identify the three states. By using the DIPA biplot, the contributions of the dipeptide-water interactions to each state are analyzed systematically. Since the DIPA improves the state identification and the convergence rate with retaining distance information, we conclude that the DIPA is a more practical method compared with the IPA. To test the feasibility of the DIPA for larger molecules, we apply the DIPA to the ten-residue chignolin folding in explicit water. The top three principal components identify the four states (native state, two misfolded states, and unfolded state) and their corresponding eigenfunctions identify important chignolin-water interactions to each state. Thus, the DIPA provides the practical method to identify conformational states and their corresponding important intermolecular interactions with distance information.

Connection between noise-induced symmetry breaking and an information-decoding function for intracellular networks

The biological function of noise-induced symmetry breaking (NISB) is still unclear even though it may potentially occur in noisy intracellular systems. In this work, I demonstrate that information decoding from a noisy signal is a potential biological function of NISB by revealing that NISB naturally emerges from an optimal information-decoding dynamics and that several intracellular networks can be identified with the information-decoding dynamics. I also propose a mean first passage time profile as a way to experimentally identify NISB.

Atypical cadherins Dachsous and Fat control dynamics of noncentrosomal microtubules in planar cell polarity

How global organ asymmetry and individual cell polarity are connected to each other is a central question in studying planar cell polarity (PCP). In the Drosophila wing, which develops PCP along its proximal-distal (P-D) axis, we previously proposed that the core PCP mediator Frizzled redistributes distally in a microtubule (MT)-dependent manner. Here, we performed organ-wide analysis of MT dynamics by introducing quantitative in vivo imaging. We observed MTs aligning along the P-D axis at the onset of redistribution and a small but significant excess of + ends-distal MTs in the proximal region of the wing. This characteristic alignment and asymmetry of MT growth was controlled by atypical cadherins Dachsous (Ds) and Fat (Ft). Furthermore, the action of Ft was mediated in part by PAR-1. All these data support the idea that the active reorientation of MT growth adjusts cell polarity along the organ axis.

Implementation of dynamic Bayesian decision making by intracellular kinetics

Decision making in a noisy and dynamically changing environment is a fundamental task for a cell. To choose appropriate decisions over time, a cell must be equipped with intracellular kinetics that can conduct dynamic and efficient decision making. By using the theory of sequential inference, I demonstrate that dynamic Bayesian decision making can be implemented by an intracellular kinetics with a dual positive feedback structure. I also show that the combination of linear instantaneous and nonlinear stationary sensitivities to the input dominantly contributes to decision making efficiency, and that the state-dependent sensitivity change further suppresses noisy response. The statistical principles underlying these two factors are further clarified to be a log-likelihood-dependent quantification of the input information and uncertainty-dependent sensitivity control.

Perturbational formulation of principal component analysis in molecular dynamics simulation

Conformational fluctuations of a molecule are important to its function since such intrinsic fluctuations enable the molecule to respond to the external environmental perturbations. For extracting large conformational fluctuations, which predict the primary conformational change by the perturbation, principal component analysis (PCA) has been used in molecular dynamics simulations. However, several versions of PCA, such as Cartesian coordinate PCA and dihedral angle PCA (dPCA), are limited to use with molecules with a single dominant state or proteins where the dihedral angle represents an important internal coordinate. Other PCAs with general applicability, such as the PCA using pairwise atomic distances, do not represent the physical meaning clearly. Therefore, a formulation that provides general applicability and clearly represents the physical meaning is yet to be developed. For developing such a formulation, we consider the conformational distribution change by the perturbation with arbitrary linearly independent perturbation functions. Within the second order approximation of the Kullback-Leibler divergence by the perturbation, the PCA can be naturally interpreted as a method for (1) decomposing a given perturbation into perturbations that independently contribute to the conformational distribution change or (2) successively finding the perturbation that induces the largest conformational distribution change. In this perturbational formulation of PCA, (i) the eigenvalue measures the Kullback-Leibler divergence from the unperturbed to perturbed distributions, (ii) the eigenvector identifies the combination of the perturbation functions, and (iii) the principal component determines the probability change induced by the perturbation. Based on this formulation, we propose a PCA using potential energy terms, and we designate it as potential energy PCA (PEPCA). The PEPCA provides both general applicability and clear physical meaning. For demonstrating its power, we apply the PEPCA to an alanine dipeptide molecule in vacuum as a minimal model of a nonsingle dominant conformational biomolecule. The first and second principal components clearly characterize two stable states and the transition state between them. Positive and negative components with larger absolute values of the first and second eigenvectors identify the electrostatic interactions, which stabilize or destabilize each stable state and the transition state. Our result therefore indicates that PCA can be applied, by carefully selecting the perturbation functions, not only to identify the molecular conformational fluctuation but also to predict the conformational distribution change by the perturbation beyond the limitation of the previous methods.

Melanopsin-dependent photo-perturbation reveals desynchronization underlying the singularity of mammalian circadian clocks

Singularity behaviour in circadian clocks--the loss of robust circadian rhythms following exposure to a stimulus such as a pulse of bright light--is one of the fundamental but mysterious properties of clocks. To quantitatively perturb and accurately measure the dynamics of cellular clocks, we synthetically produced photo-responsiveness within mammalian cells by exogenously introducing the photoreceptor melanopsin and continuously monitoring the effect of photo-perturbation on the state of cellular clocks. Here we report that a critical light pulse drives cellular clocks into singularity behaviour. Our theoretical analysis consistently predicts and subsequent single-cell level observation directly proves that desynchronization of individual cellular clocks underlies singularity behaviour. Our theoretical framework also explains why singularity behaviours have been experimentally observed in various organisms, and it suggests that desynchronization is a plausible mechanism for the observable singularity of circadian clocks. Importantly, these in vitro and in silico findings are further supported by in vivo observations that desynchronization underlies the multicell-level amplitude decrease in the rat suprachiasmatic nucleus induced by critical light pulses.

An optimal number of molecules for signal amplification and discrimination in a chemical cascade

Understanding the information processing ability of signal transduction pathways is of great importance because of their crucial roles in triggering various cellular responses. Despite continuing theoretical investigation, some important aspects of signal transduction such as a transient response and its connection to stochasticity originating from a small number of molecules have not yet been well understood. It is, however, through these aspects that unexpected and nontrivial properties of the information processing emerge. In this article, we analyze the transient behavior of a simple signaling cascade by taking into account the stochasticity originating from the small number of molecules. We identify several properties of the signaling cascade that emerge as a result of the interplay between the stochasticity and transient dynamics of the cascade. We specifically demonstrate that each step of the cascade has an optimal number of signaling molecules at which the average signal amplitude becomes maximal. We further investigate the connection between a finite number of molecules and the ability of the cascade to discriminate between true and error signals, which cannot be inferred from deterministic descriptions. The implications of our results are discussed from both biological and mathematical viewpoints.

Feedback repression is required for mammalian circadian clock function

Direct evidence for the requirement of transcriptional feedback repression in circadian clock function has been elusive. Here, we developed a molecular genetic screen in mammalian cells to identify mutants of the circadian transcriptional activators CLOCK and BMAL1, which were uncoupled from CRYPTOCHROME (CRY)-mediated transcriptional repression. Notably, mutations in the PER-ARNT-SIM domain of CLOCK and the C terminus of BMAL1 resulted in synergistic insensitivity through reduced physical interactions with CRY. Coexpression of these mutant proteins in cultured fibroblasts caused arrhythmic phenotypes in population and single-cell assays. These data demonstrate that CRY-mediated repression of the CLOCK/BMAL1 complex activity is required for maintenance of circadian rhythmicity and provide formal proof that transcriptional feedback is required for mammalian clock function.

Evaluation of the performance of mechanisms for noise attenuation in a single-gene expression

Experiments of synthetic gene regulatory modules and theoretical studies have clarified the stochastic nature of gene expression. The establishment of methods to control the fluctuation in gene expression is an indispensable step to the synthesis of robust and reliable genetic modules. In this study, we evaluate the performances of several major mechanisms to attenuate the fluctuation in a single-gene expression; noise attenuation through the control of the ratio of the transcription rate to the translation one, the interaction between synthesized proteins and background molecules, and an autoregulatory negative feedback. We analytically derive the dependence of the noise intensity on the parameter values related to elementary reaction processes, optimal conditions to attenuate the noise, and the limitation of the attenuation for those mechanisms. Our results can be an important basis for selecting the most efficient combination of the components in the design and synthesis of robust and reliable genetic modules. Furthermore, the knowledge on the performances that we obtain can also play a role in understanding the design principle of the intracellular gene regulatory networks.