Currently, our knowledge of essentially all biological systems is incomplete. A number of groups have recently used dual reporter methods to track identical genes in the same cell to measure the impact of noise on expression.
2003), or through genetic oscillators to incorporate analysis methods in the frequency domain (Ljung 1999). Hence, at least certain cellular design principles can be revealed by evaluating assumptions on cellular optimality principles. As an engineering system evolves to incorporate ancillary layers of stabilizing control, these layers often expose the system to novel points of fragility, thus leading to so-called spiralling complexity. MPA computes and uses the set of independent pathwaysgenerating rays in figure 3that uniquely describe the entire flux space; owing to the algorithmic complexity, it can currently only handle networks of moderate size. As a clear limitation, finding a unique global optimum in the estimation, or convergence of the algorithms cannot be guaranteed. In addition, there are qualitative phenomena that are intrinsic to such descriptions that arise in biological systems, as mentioned later. systems with additive responses to perturbations. Some simple examples of canonical regulatory constructs that yield specific classes of behaviour in gene networks include (Smolen et al. 2002): autoregulatory motif: in which, a regulator binds to the promotor region of its own gene. In particular, systems engineering methods are finding unique opportunities in characterizing the rich behaviour exhibited by biological systems. In, Wessels, L. F. A., Van Someren, E. P. & Reinders, M. J. T. 2001 A comparison of genetic network models. Apparently, some simplifying assumptions have to be made; for example, modules are coupled by information flow only, and mass flow is negligible (Kholodenko et al. The FIM allows flexibility in choosing the appropriate criterion for optimality depending on the goal of both robustness and model identification. 2000; Hasty et al. Some of the intrinsically dynamic features of biophysical networks have been analysed in a recent paper that shows the close relationship between dynamic measures of robustness and the abundance of particular network motifs for a wide range of organisms (Prill et al. 2000; Holter et al. Parametric sensitivity has found widespread application in the analysis and design of both scientific and engineering systems (Varma et al. Application areas in biology include stability analysis (Sontag 2001) and model discrimination by safely rejecting hypotheses on reaction mechanisms, thus, identifying crucial reaction steps (Conradi et al. 2002). In a more recent work, Arkin & co-workers (Samoilov et al.
Depending on whether model structure and parameters, or only the parameters have to be identified, the problems fall into the classes of mixed-integer nonlinear programs or nonlinear programs, respectively. 1999; Weaver et al. 2002; Zak et al. Instead of focusing on a single objective function, mathematical models and experimental data can be used to test hypotheses on optimality principles, given a specific cellular function to be fulfilled. Enter your email address below and we will send you the reset instructions. 
Rodriguez-Fernandez et al. Similarly, other approaches invoking principles of optimal control theory have opened new avenues for systems analysis in biology. 2003), network reconstruction (MacCarthy et al. In the case of Tian et al., cardiomyocytes were grown on these structures as a way to create a synthetic tissue structure that could be used to monitor the electrical activity of the cells on the scaffold. Doyle 1982; Skogestad & Postlethwaite 1996; Zhou 1998). 2002; Swain et al. In general, FBA has proven effective for simpler organisms, and when the steady-state assumption is valid. The probabilistic division of the initially homogeneous cell population into subpopulations corresponding to the two possible fate outcomes was shown to require stochastic description (and could not be described with a continuous deterministic model).
In the field of systems biology, sensitivity analysis has been employed in a number of applications, including optimized design of synthetic circuits (Feng et al. As an example, consider the exquisite timekeeping of circadian rhythm in neuronal cells. Newer approaches to systems identification aim at exploiting modularity in biological networks. Therefore, on longer time-scales, it can be regarded as being in quasi-steady state. (2002) for transcriptional control is a first step into this direction. Mathematically, most methods reconstruct the system matrix A, which corresponds to the Jacobian matrix J=f(x,p)/x, from the measured effects of (sufficiently small) perturbations.
Thus, the stoichiometric matrix N is fundamental, not only for SNA, but also for dynamic processes in reaction networks, in which the reaction rates r in equation (3.2) are time-dependent. 2004a). This renewed interest in discrete stochastic simulation has motivated a number of systems engineering developments for the analysis of, and more efficient computation of, stochastic models. The discrete stochastic system of interest is described by a CME (Gillespie 1977). systems described by differential (or differential-algebraic) equations. The noteworthy insight is that the complex networks, which underlie biological regulation, appear to be made of elementary systems components like a digital circuit. In other words, they showed that integral control is a necessary condition for robust perfect adaptation, and if the mechanism described in Barkai & Leibler (1997) is incorrect in some aspects, then some other fine-tuned structure must be present. At the TU level, a detailed mathematical treatment of transcriptional regulation is described in Barkai & Leibler (2000). 2000), protein correlation and dynamic deviation factors (You & Yin 2000), and robust statistics approaches (Thomas et al. Novel methods could also take known uncertainties associated with measurementssuch as experimentally determined characteristics of stochastic noise (see 3.3)explicitly into account. 2006) and closed-loop (i.e. The computational costs are modest, even for genome-scale models. 2001). 2004) rely on the FIM formalism. As with engineering systems, robust performance requires the precise specification of both a performance metric and the type/size of uncertainty.
2004). FET devices respond to electric potential charges at the surface of the device, or in this case the surface of the SiNW. Kevrekidis & co-workers have introduced so-called equation-free modelling approaches, which avoid the need for extensive Monte Carlo simulations. More specifically, the Fisher information matrix (FIM) F(p) (Emery & Nenarokomov 1998), for a point in parameter space p, links model and experiment via state sensitivities S(t)=x/p (see 3.4.1) and measurement covariance matrix for a discrete sampling time ti, C(ti). Notably, most of the examples discussed here involved new developments in theory to address challenges posed by biology; with respect to robustness as an important functional constraint, we will discuss these interfaces in more detail in 3.4.
D-optimal design aims to maximize the degree of informativeness in data by maximizing the determinant of the FIM, which corresponds to the area/volume of an information hyperellipsoid (Emery & Nenarokomov 1998). Figure 4 Standard M diagram for robustness analysis. FBA, however, has to reverse-engineer and operate with an essentially unknown objective function. 2006 and references therein). The approach was successful, for instance, in predicting the effects of gene deletions and the outcomes of convergent evolution in micro-organisms (Fong et al.
Hence, quantitative characteristics, which are usually incorporated through model parameters in deterministic models, are also required. The classical parametric sensitivity analysis applies to continuous deterministic systems, e.g. 2005), as well as the possibility of a unified mathematical framework (Cho et al. Figure 2 FIM and identification quality. O'Shea analyses eukaryotic systems with both cis- and trans-acting mutations to distinguish between the noise effects that are intrinsic to transcription as opposed to upstream processes that might ultimately influence expression (Raser & O'Shea 2004). 2003). It is suggested that such noise-induced mechanisms may be responsible for control of switch and cycle behaviour in regulatory networks. Other dynamic extensions of the FBA algorithm have been proposed in Mahadevan et al. [3] Due to the many properties unique to each nanomaterial, like size, conductivity, and construction, various applications have been achieved. In control engineering, a standard tool for robustness analysis is the structured singular value (SSV), which allows to determine whether a particular dynamical system, subject to a specified (structured) uncertainty, is able to remain stable or to achieve a particular performance metric (e.g. In the enzymatic futile cycle problem, the deterministic model gives no indication of multiplicity, yet the discrete stochastic model generates behaviours, including switching as well as oscillations, that indicate characteristics of bifurcation regimes. In the discrete stochastic setting, the states and outputs are random variables governed by a probability density function, which follows a chemical master equation (CME) (Gillespie 1976).
Several, qualitatively different approaches for biological systems have been proposed, which can be roughly classified into three categories: data-driven, approximative and mechanistic. 2003).
1995). Mechanistic models for a number of specific biological systems have been reported, including basic operons and regulons in E. coli (trp, lac and pho) and bacteriophage systems (T7 and ; e.g. One of the more important messages from the engineering robust control literature is the notion of performance, which requires a precise description in order to calculate the so-called robust performance. Such descriptions can find relevance in systems biology when the magnitude of the fluctuations in a stochastic system approaches the levels of the actual variables (e.g. 2003; Bansal et al. 1995). 2002). Likewise, Xiao Ma and others,[7] have discussed the electrical control on the binding/unbinding of thrombin from aptamers immobilized on electrodes. Optimal production pipelines for biomass components, with fast responses to environmental changes and minimal additional efforts for enzyme synthesis, were predicted in detail to employ wave-like gene expression programs, which was later confirmed experimentally (Klipp et al.
2005) have shown another example of a biological behaviour that is intrinsically stochastic in naturenamely the dynamic switching behaviour in a class of biochemical reactions (enzymatic futile cycles). Stability of the depicted system is equivalent to robust stability of the original problem, and if a feedback loop between suitably transformed input and output signals is closed, then an operator whose stability characteristics coincide with the attainment of robust performance in the original problem is obtained.Figure 4 Standard M diagram for robustness analysis.Download figureOpen in new tabDownload PowerPoint. Insufficient performance will lead to extinction, and better solutions are likely to survive. A Markov process is a random process in which the future probabilities are dependent only on the present value, and not on past values. They include singular value decomposition analysis of microarray data (Alter et al. Empirical or data-driven methods rely on large-scale datasets that can be generated, for instance, through microarray analysis for gene regulatory networks. Parameter estimation accuracies are central to measuring identifiability of mechanistic models. From a systems engineering perspective, another critical point is the potentially divergent qualitative behaviour between continuous-time and discrete-time models of corresponding order (Pearson 1999). Discrete stochastic modelling has recently gained popularity owing to its relevance in biological processes (McAdams & Arkin 1997; Arkin et al. We acknowledge the financial support to F.J.D. 2002; Shen-Orr et al. Consider the three dominant network motifs found in Escherichia coli (Shen-Orr et al. The assumptions in this work require a specific mechanism of fine-tuning of the network structure so as to produce integral feedback, which is sufficient to make adaptation perfectly robust to all remaining network parameters. Nanotechnology is a rapidly growing field that has allowed for the creation of many different possibilities for creating biointerfaces. from WWW-posted data) to yield data records with inconsistent sampling, experimental bias, etc. Given detailed knowledge of a biological architecture, mathematical models can be constructed to describe the behaviour of interconnected motifs or transcriptional units (TUs). The recurring themes include: (i) integrative viewpoints towards unravelling complex dynamical systems, and (ii) tight iterations between experiments, modelling and hypothesis generation (figure 1).Figure 1 Systems biology cycle. One can improve upon this by performing analyses in a neighbourhood of operating points, thus extending the region of validity of the method. The interface of discrete stochastic systems and biology has clearly led to new insights into stochastic phenomena in biological systems, and has also spurred the development of more efficient computational methods for stochastic simulation, as well as analysis methods for these models. The two problems are known as robust stability and robust performance, respectively, and there are standard software packages available to facilitate this computation (e.g.