A systematic molecular circuit design method for gene networks under biochemical time delays and molecular noises

Polymerase-Based Signal Delay for Temporally Regulating DNA Involved Reactions, Programming Dynamic Molecular Systems, and Biomimetic Sensing

Complex temporal molecular signals play a pivotal role in the intricate biological pathways of living organisms, and cells exhibit the ability to transmit and receive information by intricately managing the temporal dynamics of their signaling molecules. Although biomimetic molecular networks are successfully engineered outside of cells, the capacity to precisely manipulate temporal behaviors remains limited. In this study, the catalysis activity of isothermal DNA polymerase (DNAP) through combined use of molecular dynamics simulation analysis and fluorescence assays is first characterized. DNAP-driven delay in signal strand release ranged from 100 to 102 min, which is achieved through new strategies including the introduction of primer overhangs, utilization of inhibitory reagents, and alteration of DNA template lengths. The results provide a deeper insight into the underlying mechanisms of temporal control DNAP-mediated primer extension and DNA strand displacement reactions. Then, the regulated DNAP catalysis reactions are applied in temporal modulation of downstream DNA-involved reactions, the establishment of dynamic molecular signals, and the generation of barcodes for multiplexed detection of target genes. The utility of DNAP-based signal delay as a dynamic DNA nanotechnology extends beyond theoretical concepts and achieves practical applications in the fields of cell-free synthetic biology and bionic sensing.

Systematic Design of a Metal Ion Biosensor: A Multi-Objective Optimization Approach

With the recent industrial expansion, heavy metals and other pollutants have increasingly contaminated our living surroundings. Heavy metals, being non-degradable, tend to accumulate in the food chain, resulting in potentially damaging toxicity to organisms. Thus, techniques to detect metal ions have gradually begun to receive attention. Recent progress in research on synthetic biology offers an alternative means for metal ion detection via the help of promoter elements derived from microorganisms. To make the design easier, it is necessary to develop a systemic design method for evaluating and selecting adequate components to achieve a desired detection performance. A multi-objective (MO) H₂/H_∞ performance criterion is derived here for design specifications of a metal ion biosensor to achieve the H₂ optimal matching of a desired input/output (I/O) response and simultaneous H_∞ optimal filtering of intrinsic parameter fluctuations and external cellular noise. According to the two design specifications, a Takagi-Sugeno (T-S) fuzzy model is employed to interpolate several local linear stochastic systems to approximate the nonlinear stochastic metal ion biosensor system so that the multi-objective H₂/H_∞ design of the metal ion biosensor can be solved by an associated linear matrix inequality (LMI)-constrained multi-objective (MO) design problem. The analysis and design of a metal ion biosensor with optimal I/O response matching and optimal noise filtering ability then can be achieved by solving the multi-objective problem under a set of LMIs. Moreover, a multi-objective evolutionary algorithm (MOEA)-based library search method is employed to find adequate components from corresponding libraries to solve LMI-constrained MO H₂/H_∞ design problems. It is a useful tool for the design of metal ion biosensors, particularly regarding the tradeoffs between the design factors under consideration.

A Unifying Mathematical Framework for Genetic Robustness, Environmental Robustness, Network Robustness and their Trade-offs on Phenotype Robustness in Biological Networks. Part III: Synthetic Gene Networks in Synthetic Biology

Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties that are observed in biological systems at many different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be large enough to confer: intrinsic robustness for tolerating intrinsic parameter fluctuations; genetic robustness for buffering genetic variations; and environmental robustness for resisting environmental disturbances. Network robustness is needed so phenotype stability of biological network can be maintained, guaranteeing phenotype robustness. Synthetic biology is foreseen to have important applications in biotechnology and medicine; it is expected to contribute significantly to a better understanding of functioning of complex biological systems. This paper presents a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation for synthetic gene networks in synthetic biology. Further, from the unifying mathematical framework, we found that the phenotype robustness criterion for synthetic gene networks is the following: if intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness, then the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in synthetic biology can also be investigated through corresponding phenotype robustness criteria from the systematic point of view. Finally, a robust synthetic design that involves network evolution algorithms with desired behavior under intrinsic parameter fluctuations, genetic variations, and environmental disturbances, is also proposed, together with a simulation example.

A checkpoints capturing timing-robust Boolean model of the budding yeast cell cycle regulatory network

Background

Cell cycle process of budding yeast (Saccharomyces cerevisiae) consists of four phases: G1, S, G2 and M. Initiated by stimulation of the G1 phase, cell cycle returns to the G1 stationary phase through a sequence of the S, G2 and M phases. During the cell cycle, a cell verifies whether necessary conditions are satisfied at the end of each phase (i.e., checkpoint) since damages of any phase can cause severe cell cycle defect. The cell cycle can proceed to the next phase properly only if checkpoint conditions are met. Over the last decade, there have been several studies to construct Boolean models that capture checkpoint conditions. However, they mostly focused on robustness to network perturbations, and the timing robustness has not been much addressed. Only recently, some studies suggested extension of such models towards timing-robust models, but they have not considered checkpoint conditions.

Results

To construct a timing-robust Boolean model that preserves checkpoint conditions of the budding yeast cell cycle, we used a model verification technique, ‘model checking’. By utilizing automatic and exhaustive verification of model checking, we found that previous models cannot properly capture essential checkpoint conditions in the presence of timing variations. In particular, such models violate the M phase checkpoint condition so that it allows a division of a budding yeast cell into two before the completion of its full DNA replication and synthesis. In this paper, we present a timing-robust model that preserves all the essential checkpoint conditions properly against timing variations. Our simulation results show that the proposed timing-robust model is more robust even against network perturbations and can better represent the nature of cell cycle than previous models.

Conclusions

To our knowledge this is the first work that rigorously examined the timing robustness of the cell cycle process of budding yeast with respect to checkpoint conditions using Boolean models. The proposed timing-robust model is the complete state-of-the-art model that guarantees no violation in terms of checkpoints known to date.

Robust design of biological circuits: evolutionary systems biology approach

Artificial gene circuits have been proposed to be embedded into microbial cells that function as switches, timers, oscillators, and the Boolean logic gates. Building more complex systems from these basic gene circuit components is one key advance for biologic circuit design and synthetic biology. However, the behavior of bioengineered gene circuits remains unstable and uncertain. In this study, a nonlinear stochastic system is proposed to model the biological systems with intrinsic parameter fluctuations and environmental molecular noise from the cellular context in the host cell. Based on evolutionary systems biology algorithm, the design parameters of target gene circuits can evolve to specific values in order to robustly track a desired biologic function in spite of intrinsic and environmental noise. The fitness function is selected to be inversely proportional to the tracking error so that the evolutionary biological circuit can achieve the optimal tracking mimicking the evolutionary process of a gene circuit. Finally, several design examples are given in silico with the Monte Carlo simulation to illustrate the design procedure and to confirm the robust performance of the proposed design method. The result shows that the designed gene circuits can robustly track desired behaviors with minimal errors even with nontrivial intrinsic and external noise.

On the Interplay between the Evolvability and Network Robustness in an Evolutionary Biological Network: A Systems Biology Approach

In the evolutionary process, the random transmission and mutation of genes provide biological diversities for natural selection. In order to preserve functional phenotypes between generations, gene networks need to evolve robustly under the influence of random perturbations. Therefore, the robustness of the phenotype, in the evolutionary process, exerts a selection force on gene networks to keep network functions. However, gene networks need to adjust, by variations in genetic content, to generate phenotypes for new challenges in the network's evolution, ie, the evolvability. Hence, there should be some interplay between the evolvability and network robustness in evolutionary gene networks. In this study, the interplay between the evolvability and network robustness of a gene network and a biochemical network is discussed from a nonlinear stochastic system point of view. It was found that if the genetic robustness plus environmental robustness is less than the network robustness, the phenotype of the biological network is robust in evolution. The tradeoff between the genetic robustness and environmental robustness in evolution is discussed from the stochastic stability robustness and sensitivity of the nonlinear stochastic biological network, which may be relevant to the statistical tradeoff between bias and variance, the so-called bias/variance dilemma. Further, the tradeoff could be considered as an antagonistic pleiotropic action of a gene network and discussed from the systems biology perspective.

Robust synchronization analysis in nonlinear stochastic cellular networks with time-varying delays, intracellular perturbations and intercellular noise

Naturally, a cellular network consisted of a large amount of interacting cells is complex. These cells have to be synchronized in order to emerge their phenomena for some biological purposes. However, the inherently stochastic intra and intercellular interactions are noisy and delayed from biochemical processes. In this study, a robust synchronization scheme is proposed for a nonlinear stochastic time-delay coupled cellular network (TdCCN) in spite of the time-varying process delay and intracellular parameter perturbations. Furthermore, a nonlinear stochastic noise filtering ability is also investigated for this synchronized TdCCN against stochastic intercellular and environmental disturbances. Since it is very difficult to solve a robust synchronization problem with the Hamilton-Jacobi inequality (HJI) matrix, a linear matrix inequality (LMI) is employed to solve this problem via the help of a global linearization method. Through this robust synchronization analysis, we can gain a more systemic insight into not only the robust synchronizability but also the noise filtering ability of TdCCN under time-varying process delays, intracellular perturbations and intercellular disturbances. The measures of robustness and noise filtering ability of a synchronized TdCCN have potential application to the designs of neuron transmitters, on-time mass production of biochemical molecules, and synthetic biology. Finally, a benchmark of robust synchronization design in Escherichia coli repressilators is given to confirm the effectiveness of the proposed methods.

Modelling biochemical networks with intrinsic time delays: a hybrid semi-parametric approach

Background

This paper presents a method for modelling dynamical biochemical networks with intrinsic time delays. Since the fundamental mechanisms leading to such delays are many times unknown, non conventional modelling approaches become necessary. Herein, a hybrid semi-parametric identification methodology is proposed in which discrete time series are incorporated into fundamental material balance models. This integration results in hybrid delay differential equations which can be applied to identify unknown cellular dynamics.

Results

The proposed hybrid modelling methodology was evaluated using two case studies. The first of these deals with dynamic modelling of transcriptional factor A in mammalian cells. The protein transport from the cytosol to the nucleus introduced a delay that was accounted for by discrete time series formulation. The second case study focused on a simple network with distributed time delays that demonstrated that the discrete time delay formalism has broad applicability to both discrete and distributed delay problems.

Conclusions

Significantly better prediction qualities of the novel hybrid model were obtained when compared to dynamical structures without time delays, being the more distinctive the more significant the underlying system delay is. The identification of the system delays by studies of different discrete modelling delays was enabled by the proposed structure. Further, it was shown that the hybrid discrete delay methodology is not limited to discrete delay systems. The proposed method is a powerful tool to identify time delays in ill-defined biochemical networks.