Differential control of active and silent phases in relaxation models of neuronal rhythms

Rhythmic bursting activity, found in many biological systems, serves a variety of important functions. Such activity is composed of episodes, or bursts (the active phase, AP) that are separated by quiescent periods (the silent phase, SP). Here, we use mean field, firing rate models of excitatory neural network activity to study how AP and SP durations depend on two critical network parameters that control network connectivity and cellular excitability. In these models, the AP and SP correspond to the network's underlying bistability on a fast time scale due to rapid recurrent excitatory connectivity. Activity switches between the AP and SP because of two types of slow negative feedback: synaptic depression—which has a divisive effect on the network input/output function, or cellular adaptation—a subtractive effect on the input/output function. We show that if a model incorporates the divisive process (regardless of the presence of the subtractive process), then increasing cellular excitability will speed up the activity, mostly by decreasing the silent phase. Reciprocally, if the subtractive process is present, increasing the excitatory connectivity will slow down the activity, mostly by lengthening the active phase. We also show that the model incorporating both slow processes is less sensitive to parameter variations than the models with only one process. Finally, we note that these network models are formally analogous to a type of cellular pacemaker and thus similar results apply to these cellular pacemakers. Action Editor: Misha Tsodyks     

Stochastic modeling of gene positive autoregulation networks involving signal molecules

Positive autoregulation in gene regulation networks has been shown in the past to exhibit stochastic behavior, including stochastic bistability, in which an initially uniform cell population develops into two distinct subpopulations. However, positive autoregulation is often mediated by signal molecules, which have not been considered in prior stochastic analysis of these networks. Here we propose both a full model of such a network that includes a signal molecule, and a simplified model in which the signal molecules have been eliminated through the use of two simplifications. The simplified model is amenable to direct mathematical analysis that shows that stochastic bistability is possible. We use stochastic Petri networks for simulating both types of models. The simulation results show that 1), the stochastic behavior of the two models is similar; and 2), that the analytical steady-state distribution of the simplified model matches well the transient results at times equal to that of a cell generation. A discussion of the simplifications we used in the context of the results indicates the importance of the signal molecule number as a factor determining the presence of bistability. This is further supported from a deterministic steady-state analysis of the full model that is shown to be a useful indicator of potential stochastic bistability. We use the regulation of SdiA in Escherichia coli as an example, due to the importance of this protein and of the signal molecule, a bacterial autoinducer, that is involved. However, the use of kinetic parameter values representing typical cellular activities make the conclusions applicable to other signal-mediated positive autoregulation networks as well.     

In silico evolved lac operons exhibit bistability for artificial inducers, but not for lactose

Bistability in the lac operon of Escherichia coli has been widely studied, both experimentally and theoretically. Experimentally, bistability has been observed when E. coli is induced by an artificial, nonmetabolizable, inducer. However, if the lac operon is induced with lactose, the natural inducer, bistability has not been demonstrated. We derive an analytical expression that can predict the occurrence of bistability both for artificial inducers and lactose. We find very different conditions for bistability in the two cases. Indeed, for artificial inducers bistability is predicted, but for lactose the condition for bistability is much more difficult to satisfy. Moreover, we demonstrate that in silico evolution of the lac operon generates an operon that avoids bistability with respect to lactose, but does exhibit bistability with respect to artificial inducers. The activity of this evolved operon strikingly resembles the experimentally observed activity of the operon. Thus our computational experiments suggest that the wild-type lac operon, which regulates lactose metabolism, is not a bistable switch. Nevertheless, for engineering purposes, this operon can be used as a bistable switch with artificial inducers.     

Structural and regulatory evolution of cellular electrophysiological systems

SUMMARY Cellular electrophysiological systems, like developmental systems, appear to evolve primarily by means of regulatory evolution. It is suggested that electrophysiological systems share two key features with developmental systems that account for this dependence on regulatory evolution. For both systems, structural evolution has the potential to create significant problems of pleiotropy and both systems are predominantly computational in nature. It is concluded that the relative balance of physical and computational tasks that a biological system has to perform, combined with the probability that these tasks may have to change significantly during the course of evolution, will be major factors in determining the relative mix of regulatory and structural evolution that is observed for a given system. Physiological systems that directly interface with the environment will almost always perform some low-level physical task. In the majority of cases this will require evolution of protein function in order for the tasks themselves to evolve. For complex physiological systems a large fraction of their function will be devoted to high-level control functions that are predominantly computational in nature. In most cases regulatory evolution will be sufficient in order for these computational tasks to evolve.     

Neuronal network analyses: premises, promises and uncertainties

Neuronal networks assemble the cellular components needed for sensory, motor and cognitive functions. Any rational intervention in the nervous system will thus require an understanding of network function. Obtaining this understanding is widely considered to be one of the major tasks facing neuroscience today. Network analyses have been performed for some years in relatively simple systems. In addition to the direct insights these systems have provided, they also illustrate some of the difficulties of understanding network function. Nevertheless, in more complex systems (including human), claims are made that the cellular bases of behaviour are, or will shortly be, understood. While the discussion is necessarily limited, this issue will examine these claims and highlight some traditional and novel aspects of network analyses and their difficulties. This introduction discusses the criteria that need to be satisfied for network understanding, and how they relate to traditional and novel approaches being applied to addressing network function.     

Characterizing multistationarity regimes in biochemical reaction networks

Switch like responses appear as common strategies in the regulation of cellular systems. Here we present a method to characterize bistable regimes in biochemical reaction networks that can be of use to both direct and reverse engineering of biological switches. In the design of a synthetic biological switch, it is important to study the capability for bistability of the underlying biochemical network structure. Chemical Reaction Network Theory (CRNT) may help at this level to decide whether a given network has the capacity for multiple positive equilibria, based on their structural properties. However, in order to build a working switch, we also need to ensure that the bistability property is robust, by studying the conditions leading to the existence of two different steady states. In the reverse engineering of biological switches, knowledge collected about the bistable regimes of the underlying potential model structures can contribute at the model identification stage to a drastic reduction of the feasible region in the parameter space of search. In this work, we make use and extend previous results of the CRNT, aiming not only to discriminate whether a biochemical reaction network can exhibit multiple steady states, but also to determine the regions within the whole space of parameters capable of producing multistationarity. To that purpose we present and justify a condition on the parameters of biochemical networks for the appearance of multistationarity, and propose an efficient and reliable computational method to check its satisfaction through the parameter space.     

Dependence of the specific growth rate of Escherichia coli MI 30 on the ammonia concentration]

The transient behaviour of ammonium limited continuous cultures of E. coli ML 30 led to the hypothesis that the bistability of pyruvate formation primarily is caused by a bistability of the ammonia metabolism. Therefore, a function of mu([NH+4]) should be expected different from that of Monod type. Measurements of the specific growth rate during washout of continuous cultures at different ammonium concentrations and at such low cell concentrations that the changes in the ammonium concentration of the medium could be neglected, showed a complex function with a relative minimum near 2 mg/1NH+4. This function allows bistability of the ammonium concentration in an ammonium limited continuous culture. The results are discussed on the basis of the two systems of ammonia assimilation found in prokaryotic cells.     

哺乳动物细胞小干扰RNA库的建立和应用

双链小干扰RNA（siRNA）在多种类型细胞中介导特异性的基因沉默,这一现象的发现为深入研究单个基因的功能提供了重要的方法学基础,从而得到了广泛的应用.最近的文献报道了全基因组siRNA库的建立,为高通量基因功能分析和研究提供了新的方法,成为新的研究热点.小干扰RNA库可以用来筛选和研究介导细胞复杂表型和生物学过程的关键基因,通过建立一系列具有目的表型的细胞系,有可能对特定细胞信号调节通路进行更为全面的解析.本文综述了目前在siRNA建库方法方面的进展,并探讨了建立小干扰RNA库中的关键问题.     

Bistability and oscillations in chemical reaction networks

Bifurcation theory is one of the most widely used approaches for analysis of dynamical behaviour of chemical and biochemical reaction networks. Some of the interesting qualitative behaviour that are analyzed are oscillations and bistability (a situation where a system has at least two coexisting stable equilibria). Both phenomena have been identified as central features of many biological and biochemical systems. This paper, using the theory of stoichiometric network analysis (SNA) and notions from algebraic geometry, presents sufficient conditions for a reaction network to display bifurcations associated with these phenomena. The advantage of these conditions is that they impose fewer algebraic conditions on model parameters than conditions associated with standard bifurcation theorems. To derive the new conditions, a coordinate transformation will be made that will guarantee the existence of branches of positive equilibria in the system. This is particularly useful in mathematical biology, where only positive variable values are considered to be meaningful. The first part of the paper will be an extended introduction to SNA and algebraic geometry-related methods which are used in the coordinate transformation and set up of the theorems. In the second part of the paper we will focus on the derivation of bifurcation conditions using SNA and algebraic geometry. Conditions will be derived for three bifurcations: the saddle-node bifurcation, a simple branching point, both linked to bistability, and a simple Hopf bifurcation. The latter is linked to oscillatory behaviour. The conditions derived are sufficient and they extend earlier results from stoichiometric network analysis as can be found in (Aguda and Clarke in J Chem Phys 87:3461–3470, 1987; Clarke and Jiang in J Chem Phys 99:4464–4476, 1993; Gatermann et al. in J Symb Comput 40:1361–1382, 2005). In these papers some necessary conditions for two of these bifurcations were given. A set of examples will illustrate that algebraic conditions arising from given sufficient bifurcation conditions are not more difficult to interpret nor harder to calculate than those arising from necessary bifurcation conditions. Hence an increasing amount of information is gained at no extra computational cost. The theory can also be used in a second step for a systematic bifurcation analysis of larger reaction networks. We have added a dedication of the paper to K. Gatermann.     

Innovation at the intersection of synthetic and systems biology

The promises of modern biotechnology hinge upon the hope that we can understand microscopic cellular complexity and in doing so create novel function. In this regard, the fields of systems and synthetic biology are important for accelerating both our understanding of biological systems and our ability to quantitatively engineer cells. At the nexus of these two fields is a unique synergy that can help attain these goals. Thus, the next greatest advances in biology and biotechnology are arising at the intersection of the top-down systems approach and the bottom-up synthetic approach. Collectively, these developments enable the precise control of cellular state for systems studies and the discovery of novel parts, control strategies, and interactions for the design of robust synthetic function. This review seeks to highlight this activity as well as provide a perspective for future directions. Combining these efforts can provide novel insights into cellular function and lead to robust, novel synthetic design.     

Bistability in the activity of glutamine synthetase in ammonium-limiting chemostat cultures of Escherichia coli ML 30]

The approximative estimation of the function micron([NH+4]) in cultures of E. coli ML 30 had shown that bistability of the ammonium concentration in ammonium limited continuous cultures could be possible (BERGTER et al. 1977). This phenomenon suggested a bistability in the regulation of ammonia assimilation. Therefore, the activity of one key enzyme of the two ammonia assimilation systems was measured. The distribution of the activity of glutamine synthetase in ammonia limited continuous cultures after different transition states confirmed this suggestion.     

Protein folding in vivo: the importance of molecular chaperones

The contribution of the two major cytosolic chaperone systems, Hsp70 and the cylindrical chaperonins, to cellular protein folding has been clarified by a number of recent papers. These studies found that, in vivo, a significant fraction of newly synthesized polypeptides transit through these chaperone systems in both prokaryotic and eukaryotic cells. The identification and characterization of the cellular substrates of chaperones will be instrumental in understanding how proteins fold in vivo.     

Bistability and oscillations in the Huang-Ferrell model of MAPK signaling

Physicochemical models of signaling pathways are characterized by high levels of structural and parametric uncertainty, reflecting both incomplete knowledge about signal transduction and the intrinsic variability of cellular processes. As a result, these models try to predict the dynamics of systems with tens or even hundreds of free parameters. At this level of uncertainty, model analysis should emphasize statistics of systems-level properties, rather than the detailed structure of solutions or boundaries separating different dynamic regimes. Based on the combination of random parameter search and continuation algorithms, we developed a methodology for the statistical analysis of mechanistic signaling models. In applying it to the well-studied MAPK cascade model, we discovered a large region of oscillations and explained their emergence from single-stage bistability. The surprising abundance of strongly nonlinear (oscillatory and bistable) input/output maps revealed by our analysis may be one of the reasons why the MAPK cascade in vivo is embedded in more complex regulatory structures. We argue that this type of analysis should accompany nonlinear multiparameter studies of stationary as well as transient features in network dynamics.     

Dynamic regulation of myosin light chain phosphorylation by Rho-kinase

Myosin light chain (MLC) phosphorylation plays important roles in various cellular functions such as cellular morphogenesis, motility, and smooth muscle contraction. MLC phosphorylation is determined by the balance between activities of Rho-associated kinase (Rho-kinase) and myosin phosphatase. An impaired balance between Rho-kinase and myosin phosphatase activities induces the abnormal sustained phosphorylation of MLC, which contributes to the pathogenesis of certain vascular diseases, such as vasospasm and hypertension. However, the dynamic principle of the system underlying the regulation of MLC phosphorylation remains to be clarified. Here, to elucidate this dynamic principle whereby Rho-kinase regulates MLC phosphorylation, we developed a mathematical model based on the behavior of thrombin-dependent MLC phosphorylation, which is regulated by the Rho-kinase signaling network. Through analyzing our mathematical model, we predict that MLC phosphorylation and myosin phosphatase activity exhibit bistability, and that a novel signaling pathway leading to the auto-activation of myosin phosphatase is required for the regulatory system of MLC phosphorylation. In addition, on the basis of experimental data, we propose that the auto-activation pathway of myosin phosphatase occurs in vivo. These results indicate that bistability of myosin phosphatase activity is responsible for the bistability of MLC phosphorylation, and the sustained phosphorylation of MLC is attributed to this feature of bistability.     

Oscillations and bistability predicted by a model for a cyclical bienzymatic system involving the regulated isocitrate dehydrogenase reaction

We analyze the dynamics of a bienzymatic system consisting of isocitrate dehydrogenase (IDH, EC. 1.1.1.42), which transforms NADP+ into NADPH, and of diaphorase (DIA, EC 1.8.1.4), which catalyzes the reverse reaction. Experimental evidence as well as a theoretical model showed the possibility of a coexistence between two stable steady states in this reaction system G.M. Guidi et al. Biophys. J. 74 (1998) 1229-1240[, owing to the regulatory properties of IDH. Here we extend this analysis by considering the behavior of the model proposed for the IDH-DIA bienzymatic system in conditions where the system is open to an influx of its substrates isocitrate and NADP+ and to an efflux of all metabolic species. The analysis indicates that in addition to different modes of bistability (including mushrooms and isolas), sustained oscillations can be observed in such conditions. These results point to the isocitrate dehydrogenase reaction coupled to diaphorase as a suitable candidate for further experimental and theoretical studies of bistability and oscillations in biochemical systems. The results obtained in this particular bienzymatic system bear on other enzymatic systems possessing a cyclical nature, which are known to play significant roles in a variety of metabolic and cellular regulatory processes.     

Taking the example of computer systems engineering for the analysis of biological cell systems

In this paper, we discuss the potential for the use of engineering methods that were originally developed for the design of embedded computer systems, to analyse biological cell systems. For embedded systems as well as for biological cell systems, design is a feature that defines their identity. The assembly of different components in designs of both systems can vary widely. In contrast to the biology domain, the computer engineering domain has the opportunity to quickly evaluate design options and consequences of its systems by methods for computer aided design and in particular design space exploration. We argue that there are enough concrete similarities between the two systems to assume that the engineering methodology from the computer systems domain, and in particular that related to embedded systems, can be applied to the domain of cellular systems. This will help to understand the myriad of different design options cellular systems have. First we compare computer systems with cellular systems. Then, we discuss exactly what features of engineering methods could aid researchers with the analysis of cellular systems, and what benefits could be gained.