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.     

A physical analogy of the genetic toggle switch.

We show that there is a physical analogy between a stochastic model of a genetic toggle switch system and a thermostated particle moving in a potential field, derived from the probability distribution of the toggle switch. This result suggests that one can actually simulate the dynamics of a more complex gene network by considering an ensemble of thermostated particles moving in a potential field, derived from the stationary distribution of the chemical stochastic model describing the gene network.     

Epigenes: design and construction of new hereditary units

A plasmid digene construction designed before [Tchuraev, R.N. (1982) J. Gen. Biol. 43, 79-87] has been realised, including feedback by repressing proteins with given trigger regime of gene functioning. Experimental tests of the expected epigene properties of the obtained pECPI recombinant plasmid involving lacI and cI(857) regulatory genes have shown a phenomenon of steady inheritance of two alternative epigenotypes lacI(1)cI(0) and lacI(0)cI(1), as well as an external toggle switch through metabolitic and temperature signals from one inherited functional state of the cyclic digene system into another. Thus, we have constructed a hereditary unit of a specific kind, namely, a two-component stationary epigene with preset properties.     

Simulating Genetic Circuits in Bacterial Populations with Growth Heterogeneity

We computationally study genetic circuits in bacterial populations with heterogeneities in the growth rate. To that end, we present a stochastic simulation method for gene circuits in populations of cells and propose an efficient implementation that we call the “Next Family Method”. Within this approach, we implement different population setups, specifically Chemostat-type growth and growth in an ideal Mother Machine and show that the population structure and its statistics are different for the different setups whenever there is growth heterogeneity. Such dependence on the population setup is demonstrated, in the case of bistable systems with different growth rates in the stable states, to have distinctive signatures on quantities including the distributions of protein concentration and growth rates, and hysteresis curves. Applying this method to a bistable antibiotic resistance circuit, we find that as a result of the different statistics in different population setups, the estimated minimal inhibitory concentration of the antibiotic becomes dependent on the population setup in which it is measured.     

A computational method for the investigation of multistable systems and its application to genetic switches

Background

Genetic switches exhibit multistability, form the basis of epigenetic memory, and are found in natural decision making systems, such as cell fate determination in developmental pathways. Synthetic genetic switches can be used for recording the presence of different environmental signals, for changing phenotype using synthetic inputs and as building blocks for higher-level sequential logic circuits. Understanding how multistable switches can be constructed and how they function within larger biological systems is therefore key to synthetic biology.

Results

Here we present a new computational tool, called StabilityFinder, that takes advantage of sequential Monte Carlo methods to identify regions of parameter space capable of producing multistable behaviour, while handling uncertainty in biochemical rate constants and initial conditions. The algorithm works by clustering trajectories in phase space, and iteratively minimizing a distance metric. Here we examine a collection of models of genetic switches, ranging from the deterministic Gardner toggle switch to stochastic models containing different positive feedback connections. We uncover the design principles behind making bistable, tristable and quadristable switches, and find that rate of gene expression is a key parameter. We demonstrate the ability of the framework to examine more complex systems and examine the design principles of a three gene switch. Our framework allows us to relax the assumptions that are often used in genetic switch models and we show that more complex abstractions are still capable of multistable behaviour.

Conclusions

Our results suggest many ways in which genetic switches can be enhanced and offer designs for the construction of novel switches. Our analysis also highlights subtle changes in correlation of experimentally tunable parameters that can lead to bifurcations in deterministic and stochastic systems. Overall we demonstrate that StabilityFinder will be a valuable tool in the future design and construction of novel gene networks.

     

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.     

Construction of a genetic multiplexer to toggle between chemosensory pathways in Escherichia coli

Many applications require cells to switch between discrete phenotypic states. Here, we harness the FimBE inversion switch to flip a promoter, allowing expression to be toggled between two genes oriented in opposite directions. The response characteristics of the switch are characterized using two-color cytometry. This switch is used to toggle between orthogonal chemosensory pathways by controlling the expression of CheW and CheW*, which interact with the Tar (aspartate) and Tsr* (serine) chemoreceptors, respectively. CheW* and Tsr* each contain a mutation at their protein-protein interface such that they interact with each other. The complete genetic program containing an arabinose-inducible FimE controlling CheW/CheW* (and constitutively expressed tar/tsr*) is transformed into an Escherichia coli strain lacking all native chemoreceptors. This program enables bacteria to swim toward serine or aspartate in the absence or in the presence of arabinose, respectively. Thus, the program functions as a multiplexer with arabinose as the selector. This demonstrates the ability of synthetic genetic circuits to connect to a natural signaling network to switch between phenotypes.     

Mitochondria inheritance in yeast saccharomyces cerevisiae

The review is devoted to the main mechanisms of mitochondria inheritance in yeast Saccharonmyces cerevisiae. The genetic mechanisms of functionally active mitochondria inheritance in eukaryotic cells is one of the most relevant in modem researches. A great number of genetic diseases are associated with mitochondria dysfunction. Plasticity of eukaryotic cell metabolism according to the environmental changes is ensured by adequate mitochondria functioning by means of ATP synthesis coordination, reactive oxygen species accumulation, apoptosis regulation and is an important factor of cell adaptation to stress. Mitochondria participation in important for cell vitality processes masters the presence of accurate mechanisms of mitochondria functions regulation according to environment fluctuations. The mechanisms of mitochondria division and distribution are highly conserved. Baker yeast S. cerevisiae is an ideal model object for mitochondria researches due to energetic metabolism lability, ability to switch over respiration to fermentation, and petite-positive phenotype. Correction of metabolism according to the environmental changes is necessary for cell vitality. The influence of respiratory, carbon, amino acid and phosphate metabolism on mitochondria functions was shown. As far as the mechanisms that stabilize functions of mitochondria and mtDNA are highly conserve, we can project yeast regularities on higher eukaryotes systems. This makes it possible to approximate understanding the etiology and pathogenesis of a great number of human diseases.     

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.     

Speed and Diffusion of Kinesin-2 Are Competing Limiting Factors in Flagellar Length-Control Model

Flagellar length control in Chlamydomonas is a tractable model system for studying the general question of organelle size regulation. We have previously proposed that the diffusive return of the kinesin motor that powers intraflagellar transport can play a key role in length regulation. Here, we explore how the motor speed and diffusion coefficient for the return of kinesin-2 affect flagellar growth kinetics. We find that the system can exist in two distinct regimes, one dominated by motor speed and one by diffusion coefficient. Depending on length, a flagellum can switch between these regimes. Our results indicate that mutations can affect the length in distinct ways. We discuss our theory’s implication for flagellar growth influenced by beating and provide possible explanations for the experimental observation that a beating flagellum is usually longer than its immotile mutant. These results demonstrate how our simple model can suggest explanations for mutant phenotypes.     

Biochemical polymorphisms in muscle and liver extracts and in the serum of the rainbow trout Salmo gairdneri

The frequency of polymorphic phenotypes determined by starch gel electrophoresis from six enzyme systems was investigated on 664 rainbow trout (stock I) originating equally from six full-sib families. The enzyme systems studied were CA, AKP, G-6-PD, SOD, AEP, and 6-PGD.
On material deriving from six parental matings totalling 212 offspring (stock II) the mode of inheritance of the first four enzymes (AEP and 6-PGD were not polymorphic) and the additional systems IDH, PGM, Alb, and Psta, not analysed in stock I, were investigated.
The G-6-PD system showed no polymorphism in the family material. The CA, PGM, Alb, and Psta systems were easily identifiable. Their mode of inheritance with two alleles each can be considered as proven. For SOD three alleles, in four out of six possible progeny types, were found, for which the postulated mode of inheritance was confirmed.
For IDH the mode of inheritance found by Allendorff & Utter (1973) was confirmed. This pattern shows two disomic gene loci, one of which is monomorphic, while the other carries four different alleles.
The number of alleles and their mode of inheritance for the AEP system, which was not clearly identifiable, could not be elucidated.