Global view of bionetwork dynamics: adaptive landscape

Based on recent work, I will give a nontechnical brief review of a powerful quantitative concept in biology, adaptive landscape, ini- tially proposed by S. Wright over 70 years ago, reintroduced by one of the founders of molecular biology and by others in different bio- logical contexts, but apparently forgotten by modem biologists for many years. Nevertheless, this concept finds an increasingly important role in the development of systems biology and bionetwork dynamics modeling, from phage lambda genetic switch to endogenous net- work for cancer genesis and progression. It is an ideal quantification to describe the robustness and stability of bionetworks. Here, I will first introduce five landmark proposals in biology on this concept, to demonstrate an important common thread in theoretical biology. Then I will discuss a few recent results, focusing on the studies showing theoretical consistency of adaptive landscape. From the perspec- tive of a working scientist and of what is needed logically for a dynamical theory when confronting empirical data, the adaptive landscape is useful both metaphorically and quantitatively, and has captured an essential aspect of biological dynamical processes. Though at the theoretical level the adaptive landscape must exist and it can be used across hierarchical boundaries in biology, many associated issues are indeed vague in their initial formulations and their quantitative realizations are not easy, and are good research topics for quantitative biologists. I will discuss three types of open problems associated with the adaptive landscape in a broader perspective.     

Calculating biological behaviors of epigenetic states in the phage λ life cycle

The biology and behavior of bacteriophage regulation have been the focus of classical investigations of molecular control of gene expression. Both qualitative and quantitative aspects of this behavior have been systematically characterized experimentally. Complete understanding of the robustness and stability of the genetic circuitry for the lysis-lysogeny switch remains an unsolved puzzle. It is an excellent test case for our understanding of biological behavior of an integrated network based on its physical, chemical, DNA, protein, and functional properties. We have used a new approach to non-linear dynamics to formulate a new mathematical model, performed a theoretical study on the phage life cycle, and solved the crucial part of this puzzle. We find a good quantitative agreement between the theoretical calculation and published experimental observations in the protein number levels, the lysis frequency in the lysogen culture, and the lysogenization frequency for mutants of O_R. We also predict the desired robustness for the genetic switch. We believe that this is the first successful example in the quantitative calculation of robustness and stability of the phage regulatory network, one of the simplest and most well-studied regulatory systems.     

Study of microorganism genome DNA by atomic force microscopy

The potential of atomic force microscopy (AFM) for the investigation of peculiarities of microorganisms genome structure is demonstrated. AFM images of phage lambda DNA linear molecules and supercoiled mica in buffer solution was imaged in air. New experimental method of DNA stretching based on using amino-modified mica with a decreased surface density of active amino-groups is proposed. Stretched molecules of phage lambda DNA were imaged by AFM.     

Genetic screen for monitoring severe acute respiratory syndrome coronavirus 3C-like protease

A novel coronavirus (SCoV) is the etiological agent of severe acute respiratory syndrome. Site-specific proteolysis plays a critical role in regulating a number of cellular and viral processes. Since the main protease of SCoV, also termed 3C-like protease, is an attractive target for drug therapy, we have developed a safe, simple, and rapid genetic screen assay to monitor the activity of the SCoV 3C-like protease. This genetic system is based on the bacteriophage lambda regulatory circuit, in which the viral repressor cI is specifically cleaved to initiate the lysogenic-to-lytic switch. A specific target for the SCoV 3C-like protease, P1/P2 (SAVLQ/SGFRK), was inserted into the lambda phage cI repressor. The target specificity of the SCoV P1/P2 repressor was evaluated by coexpression of this repressor with a chemically synthesized SCoV 3C-like protease gene construct. Upon infection of Escherichia coli cells containing the two plasmids encoding the cI. SCoV P1/P2-cro and the beta-galactosidase-SCoV 3C-like protease constructs, lambda phage replicated up to 2,000-fold more efficiently than in cells that did not express the SCoV 3C-like protease. This simple and highly specific assay can be used to monitor the activity of the SCoV 3C-like protease, and it has the potential to be used for screening specific inhibitors.     

Modelling the stability of Stx lysogens

Shiga-toxin-converting bacteriophages (Stx phages) are temperate phages of Escherichia coli, and can cause severe human disease. The spread of shiga toxins by Stx phages is directly linked to lysogen stability because toxins are only synthesized and released once the lytic cycle is initiated. Lysogens of Stx phages are known to be less stable than those of the related lambda phage; this is often described in terms of a 'hair-trigger' molecular switch from lysogeny to lysis. We have developed a mathematical model to examine whether known differences in operator regions and binding affinities between Stx phages and lambda phage can account for the lower stability of Stx lysogens. The Stx phage 933W has only two binding sites in its left operator region (compared to three in phage lambda), but this has a minimal effect on 933W lysogen stability. However, the relatively weak binding affinity between repressor molecules and the second binding site in the right operator is found to significantly reduce the stability of its lysogens, and may account for the hair-trigger nature of the switch. Reduced lysogen stability can lead to increased frequency of genetic recombination in bacterial genomes. The development of the mathematical model has considerable utility in understanding the behaviour and evolution of the molecular switch, with implications for phage-related diseases.     

Robustness and Coherence of a Three-Protein Circadian Oscillator: Landscape and Flux Perspectives

Three-protein circadian oscillations in cyanobacteria sustain for weeks. To understand how cellular oscillations function robustly in stochastic fluctuating environments, we used a stochastic model to uncover two natures of circadian oscillation: the potential landscape related to steady-state probability distribution of protein concentrations; and the corresponding flux related to speed of concentration changes which drive the oscillations. The barrier height of escaping from the oscillation attractor on the landscape provides a quantitative measure of the robustness and coherence for oscillations against intrinsic and external fluctuations. The difference between the locations of the zero total driving force and the extremal of the potential provides a possible experimental probe and quantification of the force from curl flux. These results, correlated with experiments, can help in the design of robust oscillatory networks.     

Analysis of noise in quorum sensing

Noise may play a pivotal role in gene circuit functionality, as demonstrated for the genetic switch in the bacterial phage lambda. Like the lambda switch, bacterial quorum sensing (QS) systems operate within a population and contain a bistable switching element, making it likely that noise plays a functional role in QS circuit operation. Therefore, a detailed analysis of the noise behavior of QS systems is needed. We have developed a set of tools generally applicable to the analysis of gene circuits, with an emphasis on investigations in the frequency domain (FD), that we apply here to the QS system in the marine bacterium Vibrio fischeri. We demonstrate that a tight coupling between exact stochastic simulation and FD analysis provides insights into the structure/function relationships in the QS circuit. Furthermore, we argue that a noise analysis is incomplete without consideration of the power spectral densities (PSDs) of the important molecular output signals. As an example we consider reversible reactions in the QS circuit, and show through analysis and exact stochastic simulation that these circuits make significant and dynamic modifications to the noise spectra. In particular, we demonstrate a "whitening" effect, which occurs as the noise is processed through these reversible reactions.     

The lambda switch: cI closes the gap in autoregulation

The bacteriophage lambda genetic switch is still yielding surprises. A recent study reveals that a long-range interaction involving proteins bound 2.4 kilobases away from one another on the phage genome mediates negative autoregulation, solving a long-standing puzzle concerning the regulation of lysogeny.     

Two-stage fermentation with bacteriophage lambda as an expression vector in Escherachia coli

The potential of bacteriophage lambda as an expression vector for a large scale production of cloned-gene proteins was evaluated in batch and continuous bioreactors using a temperature-sensitive mutant in the cl gene, which allows a simple manipulation of temperature as a means to control the phage in the lysogenic or lytic state. A temperature switch from 32 degrees C (or below) to 38 degrees C (or above) forces the phage to go from the lysogenic state to the lytic state. Temperature cycling and a two-reactor system were used for continuous cultures. For the latter the first reactor is maintained in the lysogenic state at a lower temperature to stably maintain the foreign DNA in the host cell, while the second reactor is maintained in the lytic state to force replication of the cloned-gene and overproduction of its products. The results are promising but suggest a greater potential for a mutant which lacks the Q gene which is responsible for host cell lysis and packaging of phage particles.     

Dynamical Scenarios for Chromosome Bi-orientation

Chromosome bi-orientation at the metaphase spindle is essential for precise segregation of the genetic material. The process is error-prone, and error-correction mechanisms exist to switch misaligned chromosomes to the correct, bi-oriented configuration. Here, we analyze several possible dynamical scenarios to explore how cells might achieve correct bi-orientation in an efficient and robust manner. We first illustrate that tension-mediated feedback between the sister kinetochores can give rise to a bistable switch, which allows robust distinction between a loose attachment with low tension and a strong attachment with high tension. However, this mechanism has difficulties in explaining how bi-orientation is initiated starting from unattached kinetochores. We propose four possible mechanisms to overcome this problem (exploiting molecular noise; allowing an efficient attachment of kinetochores already in the absence of tension; a trial-and-error oscillation; and a stochastic bistable switch), and assess their impact on the bi-orientation process. Based on our results and supported by experimental data, we put forward a trial-and-error oscillation and a stochastic bistable switch as two elegant mechanisms with the potential to promote bi-orientation both efficiently and robustly.     

Dynamical Scenarios for Chromosome Bi-orientation

Chromosome bi-orientation at the metaphase spindle is essential for precise segregation of the genetic material. The process is error-prone, and error-correction mechanisms exist to switch misaligned chromosomes to the correct, bi-oriented configuration. Here, we analyze several possible dynamical scenarios to explore how cells might achieve correct bi-orientation in an efficient and robust manner. We first illustrate that tension-mediated feedback between the sister kinetochores can give rise to a bistable switch, which allows robust distinction between a loose attachment with low tension and a strong attachment with high tension. However, this mechanism has difficulties in explaining how bi-orientation is initiated starting from unattached kinetochores. We propose four possible mechanisms to overcome this problem (exploiting molecular noise; allowing an efficient attachment of kinetochores already in the absence of tension; a trial-and-error oscillation; and a stochastic bistable switch), and assess their impact on the bi-orientation process. Based on our results and supported by experimental data, we put forward a trial-and-error oscillation and a stochastic bistable switch as two elegant mechanisms with the potential to promote bi-orientation both efficiently and robustly.     

Modeling of the Genetic Switch of Bacteriophage TP901-1: A Heteromer of CI and MOR Ensures Robust Bistability

The lytic-lysogenic switch of the temperate lactococcal phage TP901-1 is fundamentally different from that of phage lambda. In phage TP901-1, the lytic promoter P_L is repressed by CI, whereas repression of the lysogenic promoter P_R requires the presence of both of the antagonistic regulator proteins, MOR and CI. We model the central part of the switch and compare the two cases for P_R repression: the one where the two regulators interact only on the DNA and the other where the two regulators form a heteromer complex in the cytoplasm prior to DNA binding. The models are analyzed for bistability, and the predicted promoter repression folds are compared to experimental data. We conclude that the experimental data are best reproduced the latter case, where a heteromer complex forms in solution. We further find that CI sequestration by the formation of MOR:CI complexes in cytoplasm makes the genetic switch robust.     

Quantifying robustness and dissipation cost of yeast cell cycle network: the funneled energy landscape perspectives

We study the origin of robustness of yeast cell cycle cellular network through uncovering its underlying energy landscape. This is realized from the information of the steady-state probabilities by solving a discrete set of kinetic master equations for the network. We discovered that the potential landscape of yeast cell cycle network is funneled toward the global minimum, G1 state. The ratio of the energy gap between G1 and average versus roughness of the landscape termed as robustness ratio (RR) becomes a quantitative measure of the robustness and stability for the network. The funneled landscape is quite robust against random perturbations from the inherent wiring or connections of the network. There exists a global phase transition between the more sensitive response or less self-degradation phase leading to underlying funneled global landscape with large RR, and insensitive response or more self-degradation phase leading to shallower underlying landscape of the network with small RR. Furthermore, we show that the more robust landscape also leads to less dissipation cost of the network. Least dissipation and robust landscape might be a realization of Darwinian principle of natural selection at cellular network level. It may provide an optimal criterion for network wiring connections and design.     

Potential energy landscape and robustness of a gene regulatory network: toggle switch

Finding a multidimensional potential landscape is the key for addressing important global issues, such as the robustness of cellular networks. We have uncovered the underlying potential energy landscape of a simple gene regulatory network: a toggle switch. This was realized by explicitly constructing the steady state probability of the gene switch in the protein concentration space in the presence of the intrinsic statistical fluctuations due to the small number of proteins in the cell. We explored the global phase space for the system. We found that the protein synthesis rate and the unbinding rate of proteins to the gene were small relative to the protein degradation rate; the gene switch is monostable with only one stable basin of attraction. When both the protein synthesis rate and the unbinding rate of proteins to the gene are large compared with the protein degradation rate, two global basins of attraction emerge for a toggle switch. These basins correspond to the biologically stable functional states. The potential energy barrier between the two basins determines the time scale of conversion from one to the other. We found as the protein synthesis rate and protein unbinding rate to the gene relative to the protein degradation rate became larger, the potential energy barrier became larger. This also corresponded to systems with less noise or the fluctuations on the protein numbers. It leads to the robustness of the biological basins of the gene switches. The technique used here is general and can be applied to explore the potential energy landscape of the gene networks.     

Design and analysis of a robust genetic Muller C-element

This paper presents results on the design and analysis of a robust genetic Muller C-element. The Muller C-element is a standard logic gate commonly used to synchronize independent processes in most asynchronous electronic circuits. Synthetic biological logic gates have been previously demonstrated, but there remain many open issues in the design of sequential (state-holding) logic operations. Three designs are considered for the genetic Muller C-element: a majority gate, a toggle switch, and a speed-independent implementation. While the three designs are logically equivalent, each design requires different assumptions to operate correctly. The majority gate design requires the most timing assumptions, the speed-independent design requires the least, and the toggle switch design is a compromise between the two. This paper examines the robustness of these designs as well as the effects of parameter variation using stochastic simulation. The results show that robustness to timing assumptions does not necessarily increase reliability, suggesting that modifications to existing logic design tools are going to be necessary for synthetic biology. Parameter variation simulations yield further insights into the design principles necessary for building robust genetic gates. The results suggest that high gene count, cooperativity of at least two, tight repression, and balanced decay rates are necessary for robust gates. Finally, this paper presents a potential application of the genetic Muller C-element as a quorum-mediated trigger.