Kyung Hyuk Kim

Network topology and parameter estimation: from experimental design methods to gene regulatory network kinetics using a community based approach

BackgroundAccurate estimation of parameters of biochemical models is required to characterize the dynamics of molecular processes. This problem is intimately linked to identifying the most informative experiments for accomplishing such tasks. While significant progress has been made, effective experimental strategies for parameter identification and for distinguishing among alternative network topologies remain unclear. We approached these questions in an unbiased manner using a unique community-based approach in the context of the DREAM initiative (Dialogue for Reverse Engineering Assessment of Methods). We created an in silico test framework under which participants could probe a network with hidden parameters by requesting a range of experimental assays; results of these experiments were simulated according to a model of network dynamics only partially revealed to participants.ResultsWe proposed two challenges; in the first, participants were given the topology and underlying biochemical structure of a 9-gene regulatory network and were asked to determine its parameter values. In the second challenge, participants were given an incomplete topology with 11 genes and asked to find three missing links in the model. In both challenges, a budget was provided to buy experimental data generated in silico with the model and mimicking the features of different common experimental techniques, such as microarrays and fluorescence microscopy. Data could be bought at any stage, allowing participants to implement an iterative loop of experiments and computation.ConclusionsA total of 19 teams participated in this competition. The results suggest that the combination of state-of-the-art parameter estimation and a varied set of experimental methods using a few datasets, mostly fluorescence imaging data, can accurately determine parameters of biochemical models of gene regulation. However, the task is considerably more difficult if the gene network topology is not completely defined, as in challenge 2. Importantly, we found that aggregating independent parameter predictions and network topology across submissions creates a solution that can be better than the one from the best-performing submission.

Fan-out in gene regulatory networks.

BackgroundIn synthetic biology, gene regulatory circuits are often constructed by combining smaller circuit components. Connections between components are achieved by transcription factors acting on promoters. If the individual components behave as true modules and certain module interface conditions are satisfied, the function of the composite circuits can in principle be predicted.ResultsIn this paper, we investigate one of the interface conditions: fan-out. We quantify the fan-out, a concept widely used in electrical engineering, to indicate the maximum number of the downstream inputs that an upstream output transcription factor can regulate. The fan-out is shown to be closely related to retroactivity studied by Del Vecchio, et al. An efficient operational method for measuring the fan-out is proposed and shown to be applied to various types of module interfaces. The fan-out is also shown to be enhanced by self-inhibitory regulation on the output. The potential role of an inhibitory regulation is discussed.ConclusionsThe proposed estimation method for fan-out not only provides an experimentally efficient way for quantifying the level of modularity in gene regulatory circuits but also helps characterize and design module interfaces, enabling the modular construction of gene circuits.

Fluctuation theorems for a molecular refrigerator

We study the stochastic dynamics of Brownian particles in a heat bath and subject to an active feedback control by an external, Maxwells demon-like agent. The agent uses the information of the velocity of a particle and reduces its thermal agitation by applying a force. The entropy of the particle and the heat bath as a whole, thus, reduces. Entropy pumping [Phys. Rev. Lett. 93, 120602 (2004)] quantifies the entropy reduction. We discover that the entropy pumping has a dual role of work and heat contributing to free energy changes and entropy production of the open-system with the feedback control. Generalized Jarzynski equality and fluctuation theorems for work functional and entropy production are developed with the presence of the entropy pumping.

Entropy production of Brownian macromolecules with inertia.

We investigate the nonequilibrium steady-state thermodynamics of single Brownian macromolecules with inertia under feedback control in an isothermal ambient fluid. With the control being represented by a velocity-dependent external force, we find such an open system can have a negative entropy production rate, and we develop a mesoscopic theory consistent with the second law. We propose an equilibrium condition and define a class of external force, which includes the transverse Lorentz force, leading to equilibrium.

Adjusting Phenotypes by Noise Control

Genetically identical cells can show phenotypic variability. This is often caused by stochastic events that originate from randomness in biochemical processes involving in gene expression and other extrinsic cellular processes. From an engineering perspective, there have been efforts focused on theory and experiments to control noise levels by perturbing and replacing gene network components. However, systematic methods for noise control are lacking mainly due to the intractable mathematical structure of noise propagation through reaction networks. Here, we provide a numerical analysis method by quantifying the parametric sensitivity of noise characteristics at the level of the linear noise approximation. Our analysis is readily applicable to various types of noise control and to different types of system; for example, we can orthogonally control the mean and noise levels and can control system dynamics such as noisy oscillations. As an illustration we applied our method to HIV and yeast gene expression systems and metabolic networks. The oscillatory signal control was applied to p53 oscillations from DNA damage. Furthermore, we showed that the efficiency of orthogonal control can be enhanced by applying extrinsic noise and feedback. Our noise control analysis can be applied to any stochastic model belonging to continuous time Markovian systems such as biological and chemical reaction systems, and even computer and social networks. We anticipate the proposed analysis to be a useful tool for designing and controlling synthetic gene networks.

Sensitivity summation theorems for stochastic biochemical reaction systems

We investigate how stochastic reaction processes are affected by external perturbations. We describe an extension of the deterministic metabolic control analysis (MCA) to the stochastic regime. We introduce stochastic sensitivities for mean and covariance values of reactant concentrations and reaction fluxes and show that there exist MCA-like summation theorems among these sensitivities. The summation theorems for flux variances is shown to depend on the size of the measurement time window () within which reaction events are counted for measuring a single flux. It is found that the degree of the -dependency can become significant for processes involving multi-time-scale dynamics and is estimated by introducing a new measure of time-scale separation. This -dependency is shown to be closely related to the power-law scaling observed in flux fluctuations in various complex networks.

Dynamic screening in a two-species asymmetric exclusion process

The dynamic scaling properties of the one-dimensional Burgers equation are expected to change with the inclusion of additional conserved degrees of freedom. We study this by means of one-dimensional (1D) driven lattice gas models that conserve both mass and momentum. The most elementary version of this is the Arndt-Heinzel-Rittenberg (AHR) process, which is usually presented as a two-species diffusion process, with particles of opposite charge hopping in opposite directions and with a variable passing probability. From the hydrodynamics perspective this can be viewed as two coupled Burgers equations, with the number of positive and negative momentum quanta individually conserved. We determine the dynamic scaling dimension of the AHR process from the time evolution of the two-point correlation functions, and find numerically that the dynamic critical exponent is consistent with simple Kardar-Parisi-Zhang- (KPZ) type scaling. We establish that this is the result of perfect screening of fluctuations in the stationary state. The two-point correlations decay exponentially in our simulations and in such a manner that in terms of quasiparticles, fluctuations fully screen each other at coarse grained length scales. We prove this screening rigorously using the analytic matrix product structure of the stationary state. The proof suggests the existence of a topological invariant. The process remains in the KPZ universality class but only in the sense of a factorization, as (KPZ)2. The two Burgers equations decouple at large length scales due to the perfect screening.

In search of noise-induced bimodality

Many biological studies are carried out on large populations of cells, often in order to obtain enough material to make measurements. However, we now know that noise is endemic in biological systems and this results in cell-to-cell variability in what appears to be a population of identical cells. Although often neglected, this noise can have a dramatic effect on system responses to environmental cues with significant and often counter-intuitive biological outcomes. A recent study in BMC Systems Biology provides an example of this, documenting a bimodal distribution of activated extracellular signal-regulated kinase in a population of cells exposed to epidermal growth factor and demonstrating that the observed bimodality of the response is induced purely by noise.See research article: http://www.biomedcentral.com/1752-0509/6/109

Controlling E. coli Gene Expression Noise

Intracellular protein copy numbers show significant cell-to-cell variability within an isogenic population due to the random nature of biological reactions. Here we show how the variability in copy number can be controlled by perturbing gene expression. Depending on the genetic network and host, different perturbations can be applied to control variability. To understand more fully how noise propagates and behaves in biochemical networks we developed stochastic control analysis (SCA) which is a sensitivity-based analysis framework for the study of noise control. Here we apply SCA to synthetic gene expression systems encoded on plasmids that are transformed into Escherichia coli. We show that (1) dual control of transcription and translation efficiencies provides the most efficient way of noise-versus-mean control. (2) The expressed proteins follow the gamma distribution function as found in chromosomal proteins. (3) One of the major sources of noise, leading to the cell-to-cell variability in protein copy numbers, is related to bursty translation. (4) By taking into account stochastic fluctuations in autofluorescence, the correct scaling relationship between the noise and mean levels of the protein copy numbers was recovered for the case of weak fluorescence signals.

Toward Modularity in Synthetic Biology: Design Patterns and Fan-out

Modularity is a concept that is widely used in biological science with various interpretations. In this chapter we will first give a general overview of modularity in biology, and later focus on modularity in synthetic biology. In engineering, a module is a component whose intrinsic functionality is independent of its surrounding milieu. In biology, however, modularity is less clear-cut; for example, modules can be classified by network interactions or by functional distinctiveness such as the reuse of protein domains. In synthetic biology the question of modularity is more closely related to engineering where functional independence is important. One way of defining synthetic modules is by specifying a generic pattern of regulations that results in desired functionalities, which we term a design pattern. In this perspective, connections between modules are described by the regulatory links, which are represented by molecular reactions. Under these reactions, the output of an upstream module – the concentration of regulating molecules – is sequestered by the input of the downstream module. This sequestration can cause changes in the upstream module function. We quantify the maximally tolerable load from the downstream input, which we term gene circuit fan-out. We provide an efficient and practical way of estimating the fan-out by experiment.