- Email: [email protected]
Finding the Optimal Tradeoffs
Cell Systems
Previews Finding the Optimal Tradeoffs Shibin Mathew,1,2 Amy E. Thurber,1,2,3 and Suzanne Gaudet1,2,* 1Department
of Cancer Biology and Center for Cancer Systems Biology, Dana-Farber Cancer Institute, Boston, MA 02215, USA of Genetics, Harvard Medical School, Boston, MA 02115, USA 3Department of Molecular Biology and Microbiology, Tufts University School of Medicine, Boston, MA 02111, USA *Correspondence: [email protected] http://dx.doi.org/10.1016/j.cels.2017.02.002 2Department
Computational analyses of a half-million circuit topologies provide a rationale for why certain fold-change detection topologies are more prevalent in nature. Immersed in the age of high-throughput data collection, it becomes easier to generate extensive hairball-like networks describing molecular and functional interactions, but it remains challenging to understand the biological meaning of the connections. The concept of network motifs has informed us on the origins of certain complex phenotypes seen in biological systems by breaking down networks into basic blocks with interpretable input-output relationships. In this issue of Cell Systems, Miri Adler, Uri Alon, and colleagues present analyses that help to explain why particular versions of these basic blocks may have evolved. Network motifs are patterns of connections found within a network at a frequency significantly greater than would be expected in a similarly sized random network (Shen-Orr et al., 2002; Figure 1A). Because a specific motif has the same parameter-dependent information-processing functions across all networks, the properties of a network are determined by the motifs it contains and the same motifs can be found within networks with similar information-processing objectives (Milo et al., 2002). For example, the concept of network motifs has allowed us to understand how two cyclical systems, the cell cycle and circadian rhythm, both rely on mechanistically similar oscillators (Lander, 2010) that are built on interacting positive and negative feedback motifs (Tyson et al., 2003). One network property or informationprocessing objective that has been observed in several biological systems is fold-change detection (FCD), or scale invariance, whereby a system responds to relative changes, instead of absolute value, of input signal (Skataric and Sontag, 2012). Inherently, FCD systems also show adaptation, responding only tran-
siently to a continuous stimulus. By avoiding saturation of response, scale invariance greatly increases the dynamic range over which a signal can be detected. This is notably displayed in C. elegans odorant detection as these worms are able to detect and move toward an odorant as the concentration increases over many orders of magnitude (Larsch et al., 2015). Finally, FCD can also impart greater robustness to variability in the concentration of signaling proteins (Shoval et al., 2010; Skataric and Sontag, 2012). Interestingly, only two FCD network motif topologies have been identified so far in biological networks: incoherent type 1 feed forward loops (I1-FFLs) and non-linear integral feedback loops (NLIFLs) (Figure 1B; Shoval et al., 2010). Why are these two topologies repeatedly used by nature? Do other FCD motif topologies exist, and if so, could they bring other functional advantages? Adler et al. (2017) address these questions with an extensive screen and analysis of motif topologies that show FCD. By comparing tradeoffs between functional features of these topologies, such as speed and efficiency of information transmission, they show why evolution may have favored those found in nature. Comparing large numbers of network topologies, even topologies with small number of nodes, has long been a challenge, limiting the scale of prior network motif topology analyses. As the number of parameters increases (Figure 1A), the problem becomes extremely computationally expensive. Now, Adler et al. have developed an elegant mathematical solution relying on S-system description of dynamical systems (Savageau and Voit, 1987). Using the S-system, nonlinear reaction kinetics are systematically
described using first-order ordinary differential equations that all have the same structure (Savageau and Voit, 1987). The S-system is thus mathematically tractable and can be solved much more efficiently. In addition, Adler et al. used dimensionality reduction to reduce the number of parameters required to describe each topology. This allowed them to screen a wide class of three-node circuits to identify all topologies that give rise to FCD. By using analytically solvable equations to model these circuits, they were able to screen through a space of a half-million topologies (a prior effort had analyzed 16,000 topologies [Skataric and Sontag, 2012]) and found that only 0.1% of these circuits show FCD. Overall, the small fraction of topologies exhibiting FCD still constitutes >600 distinct three-node circuits—a large number, considering that only two have been identified experimentally. What do those two topologies offer that is unique? Although all FCD circuits were found to show exact adaptation and therefore have the same ultimate steadystate response, different topologies can exhibit very different transient responses (Figure 1C). This led Adler et al. to investigate potential advantages of differing transient responses of the FCD circuits. Considering a group of dynamic tasks (like response amplitude, response time or ‘‘speed,’’ and noise resistance) that are thought to be important for circuits to transmit information robustly and effectively, they found that not all tasks could be simultaneously optimized. In fact, it is possible to find the set of circuits that allow the best possible tradeoffs between selected dynamic tasks; this set forms the ‘‘front,’’ or outer boundary, of a multiobjective optimization (Figure 1D). This front, known as the Pareto front, is a set
Cell Systems 4, February 22, 2017 ª 2017 Elsevier Inc. 149
Cell Systems
Previews A
C
D
150 Cell Systems 4, February 22, 2017
B
Figure 1. A Search for Optimal FCD Network Motifs (A) Diagram showing possible connections within a three-node motif, including positive (blue) and negative (red) regulation of activity (solid) or synthesis or degradation (dashed). (B) Diagrams of the topology of two FCD network motifs, an incoherent type 1 feedforward loop (I1-FFL) and a non-linear integral feedback loop (NLIFL). (C) Schematic of the time course of response (quantified by motif output) for two FCD network motifs. All FCD motifs show adaptation with a return to baseline in the steady state (dark orange region), but they differ in the transient regime (lightorange region). Here, we illustrate how transient response can differ in speed (defined as 1/t, the time to center of mass of the response curve [dot]) and amplitude. (D) Schematic of a Pareto front showing optimal tradeoffs between two tasks. Motifs lying on the front (I1-FFL and motif 2) have reached an optimal tradeoff between task 1 and 2, while any internal motif is suboptimal, with room for improvement in both tasks.
of solutions for which each individual task cannot be improved without sacrificing other objectives, thus the optimal tradeoff. Adler et al. found that the experimentally observed I1FFL and NLIFL FCD circuits are on the Pareto front of task pairs like speed versus amplitude and noise resistance versus amplitude, suggesting why these circuits have been selected for by evolution. Nevertheless, a few other topologies were also found to lie on Pareto fronts, and Adler et al. speculate that these are likely to exist in biological systems unless they are suboptimal for a yet unexplored but necessary task. So how conclusive is the exploration of optimal FCD circuits conducted by Adler and colleagues? Complex systems have multiple competing essential tasks, and these systems should evolve toward operating points where all these goals are optimally attained. Yet, because of the complex nature of interactions between different tasks, the optimal operating solution for one goal may not be optimal for others, hence the need for tradeoffs. This can be said for all biological systems, not only FCD circuits (Hart et al., 2015). Still, these statements have a corollary: for us to know what nature’s optimal tradeoffs are, we must know its objectives. Therefore, although a Pareto analysis-based optimal network motif selection is anchored in sound theory, it is by necessity ad hoc, dependent on prior knowledge of the system under study. In the future, we may be able to use this logic in reverse: investigating which
Cell Systems
Previews Pareto front a system lies on could inform us about which tasks it needs to achieve well. Going back to where we started, as hairball-like high-dimensional datasets become more and more complete, they can perhaps help us identify the objectives, or tasks, for which a system has been optimized. Indeed, the set of connections described in these hairballs have arisen via the sampling of a large phenotypic space where tradeoffs have been made, and the topologies chosen should outline the Pareto fronts of the relevant sets of tasks or goals (Hart et al., 2015). It will be fascinating in the future to consider how combinations of network motifs perform together and how they might arise from an evolutionary
perspective. Do systems’ tasks acquire new meanings when network motifs work together; are there higher-level tradeoffs? When considering biological systems as dynamic entities that are optimized over evolutionary timescales to perform certain tasks, we still have a lot to learn.
Larsch, J., Flavell, S.W., Liu, Q., Gordus, A., Albrecht, D.R., and Bargmann, C.I. (2015). Cell Rep. 12, 1748–1760. Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., and Alon, U. (2002). Science 298, 824–827. Savageau, M.A., and Voit, E.O. (1987). Math. Biosci. 87, 83–115. Shen-Orr, S.S., Milo, R., Mangan, S., and Alon, U. (2002). Nat. Genet. 31, 64–68.
REFERENCES Adler, M., Szekely, P., Mayo, A., and Alon, U. (2017). Cell Syst. 4, this issue, 171–181.
Shoval, O., Goentoro, L., Hart, Y., Mayo, A., Sontag, E., and Alon, U. (2010). Proc. Natl. Acad. Sci. USA 107, 15995–16000.
Hart, Y., Sheftel, H., Hausser, J., Szekely, P., BenMoshe, N.B., Korem, Y., Tendler, A., Mayo, A.E., and Alon, U. (2015). Nat. Methods 12, 233–235, 3, 235.
Skataric, M., and Sontag, E.D. (2012). PLoS Comput. Biol. 8, e1002748.
Lander, A.D. (2010). BMC Biol. 8, 40.
Tyson, J.J., Chen, K.C., and Novak, B. (2003). Curr. Opin. Cell Biol. 15, 221–231.
Synthetic Gene Circuits Learn to Classify Andriy Didovyk1,2 and Lev S. Tsimring1,2,* 1BioCircuits
Institute, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA 92093, USA Diego Center for Systems Biology, 9500 Gilman Dr., La Jolla, CA 92093, USA *Correspondence: [email protected] http://dx.doi.org/10.1016/j.cels.2017.02.001 2San
An efficient computational algorithm is developed to design microRNA-based synthetic cell classifiers and to optimize their performance. Classification and pattern recognition problems are traditionally the domain of computer science. Typically, a classification system is built to choose one of a finite repertoire of outputs based on the analysis of multiple inputs. Such classifiers are usually designed and trained using sophisticated machine-learning algorithms. In recent years, synthetic biologists have begun to explore the possibilities of engineering living cells to perform classification tasks. There are many important potential applications of this approach—from building automated water quality monitoring systems to identifying abnormal cells in situ in living organisms. Designing a synthetic gene circuit for a particular task is usually done by trial and error and requires laborious manual parameter tuning to achieve acceptable performance. In this issue of Cell Systems, Yaakov Benenson and his
collaborators (Mohammadi et al., 2017) put forth a computational workflow to streamline and automate this tedious and highly non-trivial process (Figure 1). They use this workflow to design a classifier gene circuit that responds to complex microRNA (miRNA) expression patterns for recognition and selective targeting of pathological cell types. For a synthetic gene circuit with sufficiently complex functions, the choice of optimal topology may not be obvious, thus calling for a systematic automated approach to find it. Overall, a complete gene circuit design is a two-step process. One must decide on a circuit topology (discrete optimization) and also select biochemical parameters that optimize the circuit performance (continuous optimization). In general, these two tasks are not independent of each other, since different circuit topologies may yield
optimal performance at different values of parameters. Franc¸ois and Hakim (2004) were, to our knowledge, the first who proposed a computational evolutionary algorithm for the automatic design of gene networks with desired properties. They illustrated the feasibility of this approach by generating robust bistable switch and oscillator circuits in silico. However, evolutionary algorithms operating on comprehensive mathematical models of synthetic gene circuits were computationally costly and only applicable to designing relatively small networks. To alleviate this problem, Marchisio and Stelling (2011) developed an algorithm that could efficiently design large logical gene networks, i.e., networks where inputs and the output only take ‘‘0’’ or ‘‘1’’ values. Classifiers form an important class of synthetic gene circuits with potentially
Cell Systems 4, February 22, 2017 ª 2017 Elsevier Inc. 151
Previews Finding the Optimal Tradeoffs Shibin Mathew,1,2 Amy E. Thurber,1,2,3 and Suzanne Gaudet1,2,* 1Department
of Cancer Biology and Center for Cancer Systems Biology, Dana-Farber Cancer Institute, Boston, MA 02215, USA of Genetics, Harvard Medical School, Boston, MA 02115, USA 3Department of Molecular Biology and Microbiology, Tufts University School of Medicine, Boston, MA 02111, USA *Correspondence: [email protected] http://dx.doi.org/10.1016/j.cels.2017.02.002 2Department
Computational analyses of a half-million circuit topologies provide a rationale for why certain fold-change detection topologies are more prevalent in nature. Immersed in the age of high-throughput data collection, it becomes easier to generate extensive hairball-like networks describing molecular and functional interactions, but it remains challenging to understand the biological meaning of the connections. The concept of network motifs has informed us on the origins of certain complex phenotypes seen in biological systems by breaking down networks into basic blocks with interpretable input-output relationships. In this issue of Cell Systems, Miri Adler, Uri Alon, and colleagues present analyses that help to explain why particular versions of these basic blocks may have evolved. Network motifs are patterns of connections found within a network at a frequency significantly greater than would be expected in a similarly sized random network (Shen-Orr et al., 2002; Figure 1A). Because a specific motif has the same parameter-dependent information-processing functions across all networks, the properties of a network are determined by the motifs it contains and the same motifs can be found within networks with similar information-processing objectives (Milo et al., 2002). For example, the concept of network motifs has allowed us to understand how two cyclical systems, the cell cycle and circadian rhythm, both rely on mechanistically similar oscillators (Lander, 2010) that are built on interacting positive and negative feedback motifs (Tyson et al., 2003). One network property or informationprocessing objective that has been observed in several biological systems is fold-change detection (FCD), or scale invariance, whereby a system responds to relative changes, instead of absolute value, of input signal (Skataric and Sontag, 2012). Inherently, FCD systems also show adaptation, responding only tran-
siently to a continuous stimulus. By avoiding saturation of response, scale invariance greatly increases the dynamic range over which a signal can be detected. This is notably displayed in C. elegans odorant detection as these worms are able to detect and move toward an odorant as the concentration increases over many orders of magnitude (Larsch et al., 2015). Finally, FCD can also impart greater robustness to variability in the concentration of signaling proteins (Shoval et al., 2010; Skataric and Sontag, 2012). Interestingly, only two FCD network motif topologies have been identified so far in biological networks: incoherent type 1 feed forward loops (I1-FFLs) and non-linear integral feedback loops (NLIFLs) (Figure 1B; Shoval et al., 2010). Why are these two topologies repeatedly used by nature? Do other FCD motif topologies exist, and if so, could they bring other functional advantages? Adler et al. (2017) address these questions with an extensive screen and analysis of motif topologies that show FCD. By comparing tradeoffs between functional features of these topologies, such as speed and efficiency of information transmission, they show why evolution may have favored those found in nature. Comparing large numbers of network topologies, even topologies with small number of nodes, has long been a challenge, limiting the scale of prior network motif topology analyses. As the number of parameters increases (Figure 1A), the problem becomes extremely computationally expensive. Now, Adler et al. have developed an elegant mathematical solution relying on S-system description of dynamical systems (Savageau and Voit, 1987). Using the S-system, nonlinear reaction kinetics are systematically
described using first-order ordinary differential equations that all have the same structure (Savageau and Voit, 1987). The S-system is thus mathematically tractable and can be solved much more efficiently. In addition, Adler et al. used dimensionality reduction to reduce the number of parameters required to describe each topology. This allowed them to screen a wide class of three-node circuits to identify all topologies that give rise to FCD. By using analytically solvable equations to model these circuits, they were able to screen through a space of a half-million topologies (a prior effort had analyzed 16,000 topologies [Skataric and Sontag, 2012]) and found that only 0.1% of these circuits show FCD. Overall, the small fraction of topologies exhibiting FCD still constitutes >600 distinct three-node circuits—a large number, considering that only two have been identified experimentally. What do those two topologies offer that is unique? Although all FCD circuits were found to show exact adaptation and therefore have the same ultimate steadystate response, different topologies can exhibit very different transient responses (Figure 1C). This led Adler et al. to investigate potential advantages of differing transient responses of the FCD circuits. Considering a group of dynamic tasks (like response amplitude, response time or ‘‘speed,’’ and noise resistance) that are thought to be important for circuits to transmit information robustly and effectively, they found that not all tasks could be simultaneously optimized. In fact, it is possible to find the set of circuits that allow the best possible tradeoffs between selected dynamic tasks; this set forms the ‘‘front,’’ or outer boundary, of a multiobjective optimization (Figure 1D). This front, known as the Pareto front, is a set
Cell Systems 4, February 22, 2017 ª 2017 Elsevier Inc. 149
Cell Systems
Previews A
C
D
150 Cell Systems 4, February 22, 2017
B
Figure 1. A Search for Optimal FCD Network Motifs (A) Diagram showing possible connections within a three-node motif, including positive (blue) and negative (red) regulation of activity (solid) or synthesis or degradation (dashed). (B) Diagrams of the topology of two FCD network motifs, an incoherent type 1 feedforward loop (I1-FFL) and a non-linear integral feedback loop (NLIFL). (C) Schematic of the time course of response (quantified by motif output) for two FCD network motifs. All FCD motifs show adaptation with a return to baseline in the steady state (dark orange region), but they differ in the transient regime (lightorange region). Here, we illustrate how transient response can differ in speed (defined as 1/t, the time to center of mass of the response curve [dot]) and amplitude. (D) Schematic of a Pareto front showing optimal tradeoffs between two tasks. Motifs lying on the front (I1-FFL and motif 2) have reached an optimal tradeoff between task 1 and 2, while any internal motif is suboptimal, with room for improvement in both tasks.
of solutions for which each individual task cannot be improved without sacrificing other objectives, thus the optimal tradeoff. Adler et al. found that the experimentally observed I1FFL and NLIFL FCD circuits are on the Pareto front of task pairs like speed versus amplitude and noise resistance versus amplitude, suggesting why these circuits have been selected for by evolution. Nevertheless, a few other topologies were also found to lie on Pareto fronts, and Adler et al. speculate that these are likely to exist in biological systems unless they are suboptimal for a yet unexplored but necessary task. So how conclusive is the exploration of optimal FCD circuits conducted by Adler and colleagues? Complex systems have multiple competing essential tasks, and these systems should evolve toward operating points where all these goals are optimally attained. Yet, because of the complex nature of interactions between different tasks, the optimal operating solution for one goal may not be optimal for others, hence the need for tradeoffs. This can be said for all biological systems, not only FCD circuits (Hart et al., 2015). Still, these statements have a corollary: for us to know what nature’s optimal tradeoffs are, we must know its objectives. Therefore, although a Pareto analysis-based optimal network motif selection is anchored in sound theory, it is by necessity ad hoc, dependent on prior knowledge of the system under study. In the future, we may be able to use this logic in reverse: investigating which
Cell Systems
Previews Pareto front a system lies on could inform us about which tasks it needs to achieve well. Going back to where we started, as hairball-like high-dimensional datasets become more and more complete, they can perhaps help us identify the objectives, or tasks, for which a system has been optimized. Indeed, the set of connections described in these hairballs have arisen via the sampling of a large phenotypic space where tradeoffs have been made, and the topologies chosen should outline the Pareto fronts of the relevant sets of tasks or goals (Hart et al., 2015). It will be fascinating in the future to consider how combinations of network motifs perform together and how they might arise from an evolutionary
perspective. Do systems’ tasks acquire new meanings when network motifs work together; are there higher-level tradeoffs? When considering biological systems as dynamic entities that are optimized over evolutionary timescales to perform certain tasks, we still have a lot to learn.
Larsch, J., Flavell, S.W., Liu, Q., Gordus, A., Albrecht, D.R., and Bargmann, C.I. (2015). Cell Rep. 12, 1748–1760. Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., and Alon, U. (2002). Science 298, 824–827. Savageau, M.A., and Voit, E.O. (1987). Math. Biosci. 87, 83–115. Shen-Orr, S.S., Milo, R., Mangan, S., and Alon, U. (2002). Nat. Genet. 31, 64–68.
REFERENCES Adler, M., Szekely, P., Mayo, A., and Alon, U. (2017). Cell Syst. 4, this issue, 171–181.
Shoval, O., Goentoro, L., Hart, Y., Mayo, A., Sontag, E., and Alon, U. (2010). Proc. Natl. Acad. Sci. USA 107, 15995–16000.
Hart, Y., Sheftel, H., Hausser, J., Szekely, P., BenMoshe, N.B., Korem, Y., Tendler, A., Mayo, A.E., and Alon, U. (2015). Nat. Methods 12, 233–235, 3, 235.
Skataric, M., and Sontag, E.D. (2012). PLoS Comput. Biol. 8, e1002748.
Lander, A.D. (2010). BMC Biol. 8, 40.
Tyson, J.J., Chen, K.C., and Novak, B. (2003). Curr. Opin. Cell Biol. 15, 221–231.
Synthetic Gene Circuits Learn to Classify Andriy Didovyk1,2 and Lev S. Tsimring1,2,* 1BioCircuits
Institute, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA 92093, USA Diego Center for Systems Biology, 9500 Gilman Dr., La Jolla, CA 92093, USA *Correspondence: [email protected] http://dx.doi.org/10.1016/j.cels.2017.02.001 2San
An efficient computational algorithm is developed to design microRNA-based synthetic cell classifiers and to optimize their performance. Classification and pattern recognition problems are traditionally the domain of computer science. Typically, a classification system is built to choose one of a finite repertoire of outputs based on the analysis of multiple inputs. Such classifiers are usually designed and trained using sophisticated machine-learning algorithms. In recent years, synthetic biologists have begun to explore the possibilities of engineering living cells to perform classification tasks. There are many important potential applications of this approach—from building automated water quality monitoring systems to identifying abnormal cells in situ in living organisms. Designing a synthetic gene circuit for a particular task is usually done by trial and error and requires laborious manual parameter tuning to achieve acceptable performance. In this issue of Cell Systems, Yaakov Benenson and his
collaborators (Mohammadi et al., 2017) put forth a computational workflow to streamline and automate this tedious and highly non-trivial process (Figure 1). They use this workflow to design a classifier gene circuit that responds to complex microRNA (miRNA) expression patterns for recognition and selective targeting of pathological cell types. For a synthetic gene circuit with sufficiently complex functions, the choice of optimal topology may not be obvious, thus calling for a systematic automated approach to find it. Overall, a complete gene circuit design is a two-step process. One must decide on a circuit topology (discrete optimization) and also select biochemical parameters that optimize the circuit performance (continuous optimization). In general, these two tasks are not independent of each other, since different circuit topologies may yield
optimal performance at different values of parameters. Franc¸ois and Hakim (2004) were, to our knowledge, the first who proposed a computational evolutionary algorithm for the automatic design of gene networks with desired properties. They illustrated the feasibility of this approach by generating robust bistable switch and oscillator circuits in silico. However, evolutionary algorithms operating on comprehensive mathematical models of synthetic gene circuits were computationally costly and only applicable to designing relatively small networks. To alleviate this problem, Marchisio and Stelling (2011) developed an algorithm that could efficiently design large logical gene networks, i.e., networks where inputs and the output only take ‘‘0’’ or ‘‘1’’ values. Classifiers form an important class of synthetic gene circuits with potentially
Cell Systems 4, February 22, 2017 ª 2017 Elsevier Inc. 151