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1.  Inferring causal metabolic signals that regulate the dynamic TORC1-dependent transcriptome 
Molecular Systems Biology  2015;11(4):802.
Cells react to nutritional cues in changing environments via the integrated action of signaling, transcriptional, and metabolic networks. Mechanistic insight into signaling processes is often complicated because ubiquitous feedback loops obscure causal relationships. Consequently, the endogenous inputs of many nutrient signaling pathways remain unknown. Recent advances for system-wide experimental data generation have facilitated the quantification of signaling systems, but the integration of multi-level dynamic data remains challenging. Here, we co-designed dynamic experiments and a probabilistic, model-based method to infer causal relationships between metabolism, signaling, and gene regulation. We analyzed the dynamic regulation of nitrogen metabolism by the target of rapamycin complex 1 (TORC1) pathway in budding yeast. Dynamic transcriptomic, proteomic, and metabolomic measurements along shifts in nitrogen quality yielded a consistent dataset that demonstrated extensive re-wiring of cellular networks during adaptation. Our inference method identified putative downstream targets of TORC1 and putative metabolic inputs of TORC1, including the hypothesized glutamine signal. The work provides a basis for further mechanistic studies of nitrogen metabolism and a general computational framework to study cellular processes.
PMCID: PMC4422559  PMID: 25888284
causal inference; network motifs; nutrient signaling; target of rapamycin pathway
2.  Transcriptional regulation is insufficient to explain substrate-induced flux changes in Bacillus subtilis 
Regulation of enzyme expression is one key mechanism by which cells control their metabolic programs. In this work, a quantitative analysis of metabolism in a model bacterium under different conditions shows that expression alone cannot explain the majority of the observed metabolic changes.
Most enzymes are indeed highly expressed in conditions where they are more active.Quantitatively, however, the observed changes in expression between conditions do not match the changes in activity for most enzymes.A good quantitative match is only observed for enzymes involved in the TCA cycle.Metabolomics reveals that increased substrate availability explains only a few instances of changes in activity.
One of the key ways in which microbes are thought to regulate their metabolism is by modulating the availability of enzymes through transcriptional regulation. However, the limited success of efforts to manipulate metabolic fluxes by rewiring the transcriptional network has cast doubt on the idea that transcript abundance controls metabolic fluxes. In this study, we investigate control of metabolic flux in the model bacterium Bacillus subtilis by quantifying fluxes, transcripts, and metabolites in eight metabolic states enforced by different environmental conditions. We find that most enzymes whose flux switches between on and off states, such as those involved in substrate uptake, exhibit large corresponding transcriptional changes. However, for the majority of enzymes in central metabolism, enzyme concentrations were insufficient to explain the observed fluxes—only for a number of reactions in the tricarboxylic acid cycle were enzyme changes approximately proportional to flux changes. Surprisingly, substrate changes revealed by metabolomics were also insufficient to explain observed fluxes, leaving a large role for allosteric regulation and enzyme modification in the control of metabolic fluxes.
PMCID: PMC4039378  PMID: 24281055
central carbon metabolism; metabolic flux; transcriptional regulation
3.  Near-optimal experimental design for model selection in systems biology 
Bioinformatics  2013;29(20):2625-2632.
Motivation: Biological systems are understood through iterations of modeling and experimentation. Not all experiments, however, are equally valuable for predictive modeling. This study introduces an efficient method for experimental design aimed at selecting dynamical models from data. Motivated by biological applications, the method enables the design of crucial experiments: it determines a highly informative selection of measurement readouts and time points.
Results: We demonstrate formal guarantees of design efficiency on the basis of previous results. By reducing our task to the setting of graphical models, we prove that the method finds a near-optimal design selection with a polynomial number of evaluations. Moreover, the method exhibits the best polynomial-complexity constant approximation factor, unless P = NP. We measure the performance of the method in comparison with established alternatives, such as ensemble non-centrality, on example models of different complexity. Efficient design accelerates the loop between modeling and experimentation: it enables the inference of complex mechanisms, such as those controlling central metabolic operation.
Availability: Toolbox ‘NearOED’ available with source code under GPL on the Machine Learning Open Source Software Web site (
Supplementary information: Supplementary data are available at Bioinformatics online.
PMCID: PMC3789540  PMID: 23900189
4.  Modular, rule-based modeling for the design of eukaryotic synthetic gene circuits 
BMC Systems Biology  2013;7:42.
The modular design of synthetic gene circuits via composable parts (DNA segments) and pools of signal carriers (molecules such as RNA polymerases and ribosomes) has been successfully applied to bacterial systems. However, eukaryotic cells are becoming a preferential host for new synthetic biology applications. Therefore, an accurate description of the intricate network of reactions that take place inside eukaryotic parts and pools is necessary. Rule-based modeling approaches are increasingly used to obtain compact representations of reaction networks in biological systems. However, this approach is intrinsically non-modular and not suitable per se for the description of composable genetic modules. In contrast, the Model Description Language (MDL) adopted by the modeling tool ProMoT is highly modular and it enables a faithful representation of biological parts and pools.
We developed a computational framework for the design of complex (eukaryotic) gene circuits by generating dynamic models of parts and pools via the joint usage of the BioNetGen rule-based modeling approach and MDL. The framework converts the specification of a part (or pool) structure into rules that serve as inputs for BioNetGen to calculate the part’s species and reactions. The BioNetGen output is translated into an MDL file that gives a complete description of all the reactions that take place inside the part (or pool) together with a proper interface to connect it to other modules in the circuit. In proof-of-principle applications to eukaryotic Boolean circuits with more than ten genes and more than one thousand reactions, our framework yielded proper representations of the circuits’ truth tables.
For the model-based design of increasingly complex gene circuits, it is critical to achieve exact and systematic representations of the biological processes with minimal effort. Our computational framework provides such a detailed and intuitive way to design new and complex synthetic gene circuits.
PMCID: PMC3680069  PMID: 23705868
Composable parts; Pools of signal carriers; Gene circuit modular design; Rule-based modeling
5.  A specialized ODE integrator for the efficient computation of parameter sensitivities 
BMC Systems Biology  2012;6:46.
Dynamic mathematical models in the form of systems of ordinary differential equations (ODEs) play an important role in systems biology. For any sufficiently complex model, the speed and accuracy of solving the ODEs by numerical integration is critical. This applies especially to systems identification problems where the parameter sensitivities must be integrated alongside the system variables. Although several very good general purpose ODE solvers exist, few of them compute the parameter sensitivities automatically.
We present a novel integration algorithm that is based on second derivatives and contains other unique features such as improved error estimates. These features allow the integrator to take larger time steps than other methods. In practical applications, i.e. systems biology models of different sizes and behaviors, the method competes well with established integrators in solving the system equations, and it outperforms them significantly when local parameter sensitivities are evaluated. For ease-of-use, the solver is embedded in a framework that automatically generates the integrator input from an SBML description of the system of interest.
For future applications, comparatively ‘cheap’ parameter sensitivities will enable advances in solving large, otherwise computationally expensive parameter estimation and optimization problems. More generally, we argue that substantially better computational performance can be achieved by exploiting characteristics specific to the problem domain; elements of our methods such as the error estimation could find broader use in other, more general numerical algorithms.
PMCID: PMC3522561  PMID: 22607742
Dynamical models; ordinary differential equations; parameter sensitivities; integration
6.  System-Level Insights into Yeast Metabolism by Thermodynamic Analysis of Elementary Flux Modes 
PLoS Computational Biology  2012;8(3):e1002415.
One of the most obvious phenotypes of a cell is its metabolic activity, which is defined by the fluxes in the metabolic network. Although experimental methods to determine intracellular fluxes are well established, only a limited number of fluxes can be resolved. Especially in eukaryotes such as yeast, compartmentalization and the existence of many parallel routes render exact flux analysis impossible using current methods. To gain more insight into the metabolic operation of S. cerevisiae we developed a new computational approach where we characterize the flux solution space by determining elementary flux modes (EFMs) that are subsequently classified as thermodynamically feasible or infeasible on the basis of experimental metabolome data. This allows us to provably rule out the contribution of certain EFMs to the in vivo flux distribution. From the 71 million EFMs in a medium size metabolic network of S. cerevisiae, we classified 54% as thermodynamically feasible. By comparing the thermodynamically feasible and infeasible EFMs, we could identify reaction combinations that span the cytosol and mitochondrion and, as a system, cannot operate under the investigated glucose batch conditions. Besides conclusions on single reactions, we found that thermodynamic constraints prevent the import of redox cofactor equivalents into the mitochondrion due to limits on compartmental cofactor concentrations. Our novel approach of incorporating quantitative metabolite concentrations into the analysis of the space of all stoichiometrically feasible flux distributions allows generating new insights into the system-level operation of the intracellular fluxes without making assumptions on metabolic objectives of the cell.
Author Summary
Fluxes in metabolic pathways are a highly informative aspect of an organism's phenotype. The experimental determination of such fluxes is well established and has proven very useful. To address some of the limitations of experimental flux analysis, such as when the cell is divided in multiple compartments, stoichiometric modeling provides a valuable addition. The approach that we take is based on stoichiometric modeling where we consider the thermodynamic feasibility of many different possible routes through the metabolic network of Saccharomyces cerevisiae using experimentally determined metabolite concentrations. We show that next to conclusions on single biochemical reactions in the metabolic network, we obtain system-level insights on thermodynamically infeasible flux patterns. We found that the compartmental concentrations of and NADH are the causes for the system-level infeasibilities. With the current advances in quantitative metabolomics and biochemical thermodynamics, we envision that the presented method will help gaining more insight into complex metabolic systems.
PMCID: PMC3296127  PMID: 22416224
7.  Automatic Design of Digital Synthetic Gene Circuits 
PLoS Computational Biology  2011;7(2):e1001083.
De novo computational design of synthetic gene circuits that achieve well-defined target functions is a hard task. Existing, brute-force approaches run optimization algorithms on the structure and on the kinetic parameter values of the network. However, more direct rational methods for automatic circuit design are lacking. Focusing on digital synthetic gene circuits, we developed a methodology and a corresponding tool for in silico automatic design. For a given truth table that specifies a circuit's input–output relations, our algorithm generates and ranks several possible circuit schemes without the need for any optimization. Logic behavior is reproduced by the action of regulatory factors and chemicals on the promoters and on the ribosome binding sites of biological Boolean gates. Simulations of circuits with up to four inputs show a faithful and unequivocal truth table representation, even under parametric perturbations and stochastic noise. A comparison with already implemented circuits, in addition, reveals the potential for simpler designs with the same function. Therefore, we expect the method to help both in devising new circuits and in simplifying existing solutions.
Author Summary
Synthetic Biology is a novel discipline that aims at the construction of new biological systems able to perform specific tasks. Following the example of electrical engineering, most of the synthetic systems so far realized look like circuits where smaller DNA-encoded components are interconnected by the exchange of different kinds of molecules. According to this modular approach, we developed, in a previous work, a tool for the visual design of new genetic circuits whose components are displayed on the computer screen and connected through hypothetical wires where molecules flow. Here, we present an extension of this tool that automatically computes the structure of a digital gene circuit–where the inputs and the output take only 0/1 values–by applying procedures commonly used in electrical engineering to biology. In this way, our method generalizes and simplifies the design of genetic circuits far more complex than the ones so far realized. Moreover, different from other currently used methods, our approach limits the use of optimization procedures and drastically reduces the computational time necessary to derive the circuit structure. Future improvements can be achieved by exploiting some more biological mechanisms able to mimic Boolean behavior, without a substantial growth of the algorithmic complexity.
PMCID: PMC3048778  PMID: 21399700
8.  Modeling the Drosophila melanogaster Circadian Oscillator via Phase Optimization 
Journal of biological rhythms  2008;23(6):525-537.
The circadian clock, which coordinates daily physiological behaviors of most organisms, maintains endogenous (approximately 24 h) cycles and simultaneously synchronizes to the 24-h environment due to its inherent robustness to environmental perturbations coupled with a sensitivity to specific environmental stimuli. In this study, the authors develop a detailed mathematical model that characterizes the Drosophila melanogaster circadian network. This model incorporates the transcriptional regulation of period, time-less, vrille, PAR-domain protein 1, and clock gene and protein counterparts. The interlocked positive and negative feedback loops that arise from these clock components are described primarily through mass-action kinetics (with the exception of regulated gene expression) and without the use of explicit time delays. System parameters are estimated via a genetic algorithm-based optimization of a cost function that relies specifically on circadian phase behavior since amplitude measurements are often noisy and do not account for the unique entrainment features that define circadian oscillations. Resulting simulations of this 29-state ordinary differential equation model comply with fitted wild-type experimental data, demonstrating accurate free-running (23.24-h periodic) and entrained (24-h periodic) circadian dynamics. This model also predicts unfitted mutant phenotype behavior by illustrating short and long periodicity, robust oscillations, and arrhythmicity. This mechanistic model also predicts light-induced circadian phase resetting (as described by the phase-response curve) that are in line with experimental observations.
PMCID: PMC2675948  PMID: 19060261
circadian rhythms; phase; positive/negative feedback
9.  Precise Regulation of Gene Expression Dynamics Favors Complex Promoter Architectures 
PLoS Computational Biology  2009;5(1):e1000279.
Promoters process signals through recruitment of transcription factors and RNA polymerase, and dynamic changes in promoter activity constitute a major noise source in gene expression. However, it is barely understood how complex promoter architectures determine key features of promoter dynamics. Here, we employ prototypical promoters of yeast ribosomal protein genes as well as simplified versions thereof to analyze the relations among promoter design, complexity, and function. These promoters combine the action of a general regulatory factor with that of specific transcription factors, a common motif of many eukaryotic promoters. By comprehensively analyzing stationary and dynamic promoter properties, this model-based approach enables us to pinpoint the structural characteristics underlying the observed behavior. Functional tradeoffs impose constraints on the promoter architecture of ribosomal protein genes. We find that a stable scaffold in the natural design results in low transcriptional noise and strong co-regulation of target genes in the presence of gene silencing. This configuration also exhibits superior shut-off properties, and it can serve as a tunable switch in living cells. Model validation with independent experimental data suggests that the models are sufficiently realistic. When combined, our results offer a mechanistic explanation for why specific factors are associated with low protein noise in vivo. Many of these findings hold for a broad range of model parameters and likely apply to other eukaryotic promoters of similar structure.
Author Summary
Combinatorial regulation of gene expression is an important mechanism for signal integration in prokaryotes and eukaryotes. Typically, this regulation is established by transcription factors that bind to DNA or to other regulatory proteins. Modifications of the DNA structure provide another layer of control, for instance, in gene silencing. However, it is barely understood how complex promoter architectures determine key features of promoter dynamics such as gene expression levels and noise. Here, we employ realistic mathematical models for prototypical promoters of yeast ribosomal protein genes as well as simplified versions thereof to analyze the relations among promoter design, complexity, and function. By comprehensively analyzing stationary and dynamic promoter properties, we find that functional tradeoffs impose constraints on the promoter architecture. More specifically, a stable configuration in the natural design results in low transcriptional noise and strong co-regulation of target genes in the presence of gene silencing. Combined, our results offer a mechanistic explanation for why specific factors are associated with low protein noise in vivo. We expect that many of these findings apply to other promoters of similar structure.
PMCID: PMC2615112  PMID: 19180182
10.  Signaling cascades as cellular devices for spatial computations 
Journal of mathematical biology  2008;58(1-2):35-55.
Signaling networks usually include protein-modification cycles. Cascades of such cycles are the backbones of multiple signaling pathways. Protein gradients emerge from the spatial separation of opposing enzymes, such as kinases and phosphatases, or guanine nucleotide exchange factors (GEFs) and GTPase activating proteins (GAPs) for GTPase cycles. We show that different diffusivities of an active protein form and an inactive form leads to spatial gradients of protein abundance in the cytoplasm. For a cascade of cycles, using a discrete approximation of the space, we derive an analytical expression for the spatial gradients and show that it converges to an exact solution with decreasing the size of the quantization. Our results facilitate quantitative analysis of the dependence of spatial gradients on the network topology and reaction kinetics. We demonstrate how different cascade designs filter and process the input information to generate precise, complex spatial guidance for multiple GTPase effector processes. Thus, protein-modification cascades may serve as devices to compute complex spatial distributions of target proteins within intracellular space.
PMCID: PMC2574718  PMID: 18283462
Signaling networks; small GTPases; cascades; spatial gradients; spatial computations
11.  Circadian Phase Resetting via Single and Multiple Control Targets 
PLoS Computational Biology  2008;4(7):e1000104.
Circadian entrainment is necessary for rhythmic physiological functions to be appropriately timed over the 24-hour day. Disruption of circadian rhythms has been associated with sleep and neuro-behavioral impairments as well as cancer. To date, light is widely accepted to be the most powerful circadian synchronizer, motivating its use as a key control input for phase resetting. Through sensitivity analysis, we identify additional control targets whose individual and simultaneous manipulation (via a model predictive control algorithm) out-perform the open-loop light-based phase recovery dynamics by nearly 3-fold. We further demonstrate the robustness of phase resetting by synchronizing short- and long-period mutant phenotypes to the 24-hour environment; the control algorithm is robust in the presence of model mismatch. These studies prove the efficacy and immediate application of model predictive control in experimental studies and medicine. In particular, maintaining proper circadian regulation may significantly decrease the chance of acquiring chronic illness.
Author Summary
The robust timing, or phase, of the circadian clock is critical in directing and synchronizing molecular, cellular, and organismal behaviors. The clock's failure to maintain precision and adaption is associated with sleeping disorders, depression, and cancer. To better study and control the timing of circadian rhythms, we make use of systems theoretic tools such as sensitivity analysis and model predictive control (MPC). Sensitivity analysis is used to identify key driving mechanisms without having to fully understand or investigate the detailed mechanistic interconnections of the large complex circadian network. Contrary to intuition, sensitivity analysis of the circadian model highlights several non-photic control inputs (such as transcriptional regulation) that outperform light-based circadian phase resetting – light is known to accelerate protein degradation. Aside from targeting individual parameters as control inputs, our methods identify combinations of control targets that may further the efficiency of entrainment. We compare the phase resetting performance of our MPC algorithm among cases involving individual and multiple simultaneous control targets (in wild-type simulations). We then tailor the algorithm to correct continuously the phase mismatch that occurs in short and long period mutant phenotypes. Through use of the presented tools, our algorithm is robust in the presence of model mismatch and outperforms the natural in silico sun-cycle–based phase recovery strategy by nearly 3-fold.
PMCID: PMC2536509  PMID: 18795146
12.  Systems interface biology 
The field of systems biology has attracted the attention of biologists, engineers, mathematicians, physicists, chemists and others in an endeavour to create systems-level understanding of complex biological networks. In particular, systems engineering methods are finding unique opportunities in characterizing the rich behaviour exhibited by biological systems. In the same manner, these new classes of biological problems are motivating novel developments in theoretical systems approaches. Hence, the interface between systems and biology is of mutual benefit to both disciplines.
PMCID: PMC1664650  PMID: 16971329
systems biology; identification; constraints; optimality; stochastics; robustness

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