Iterative design of training data to control intricate enzymatic reaction networks.

Kinetic modeling of in vitro enzymatic reaction networks is vital to understand and control the complex behaviors emerging from the nonlinear interactions inside. However, modeling is severely hampered by the lack of training data. Here, we introduce a methodology that combines an active learning-like approach and flow chemistry to efficiently create optimized datasets for a highly interconnected enzymatic reactions network with multiple sub-pathways. The optimal experimental design (OED) algorithm designs a sequence of out-of-equilibrium perturbations to maximize the information about the reaction kinetics, yielding a descriptive model that allows control of the output of the network towards any cost function. We experimentally validate the model by forcing the network to produce different product ratios while maintaining a minimum level of overall conversion efficiency. Our workflow scales with the complexity of the system and enables the optimization of previously unobtainable network outputs.

Bottom-Up Construction of an Adaptive Enzymatic Reaction Network.

The reproduction of emergent behaviors in nature using reaction networks is an important objective in synthetic biology and systems chemistry. Herein, the first experimental realization of an enzymatic reaction network capable of an adaptive response is reported. The design is based on the dual activity of trypsin, which activates chymotrypsin while at the same time generating a fluorescent output from a fluorogenic substrate. Once activated, chymotrypsin counteracts the trypsin output by competing for the fluorogenic substrate and producing a non-fluorescent output. It is demonstrated that this network produces a transient fluorescent output under out-of-equilibrium conditions while the input signal persists. Importantly, in agreement with mathematical simulations, we show that optimization of the pulse-like response is an inherent trade-off between maximum amplitude and lowest residual fluorescence.

Molecular Engineering of Robustness and Resilience in Enzymatic Reaction Networks.

Living systems rely on complex networks of chemical reactions to control the concentrations of molecules in space and time. Despite the enormous complexity in biological networks, it is possible to identify network motifs that lead to functional outputs such as bistability or oscillations. One of the greatest challenges in chemistry is the creation of such functionality from chemical reactions. A key limitation is our lack of understanding of how molecular structure impacts on the dynamics of chemical reaction networks, preventing the design of networks that are robust (i.e., function in a large parameter space) and resilient (i.e., reach their out-of-equilibrium function rapidly). Here we demonstrate that reaction rates of individual reactions in the network can control the dynamics by which the system reaches limit cycle oscillations, thereby gaining information on the key parameters that govern the dynamics of these networks. We envision that these principles will be incorporated into the design of network motifs, enabling chemists to develop "molecular software" to create functional behavior in chemical systems.

Interactions Between phyB and PIF Proteins Alter Thermal Reversion Reactions in vitro.

The dynamic behavior of the plant red/far-red light photoreceptor phytochrome B (phyB) has been elucidated in natural and synthetic systems. Red light switches phyB from the inactive Pr state to the active Pfr state, a process that is reversed by far-red light. Alongside light signals, phyB activity is constrained by thermal reversion (that is prominent in the dark) and protein-protein interactions between phyB, other phytochrome molecules, and, among others, PHYTOCHROME INTERACTING FACTORs (PIFs). Requirements for phyB-PIF association have been well studied and are central to light-regulated synthetic tools. However, it is unknown whether PIF interactions influence transitions of phyB between different conformers. Here, we show that the in vitro thermal reversion of phyB involves multiple reactions. Thermal reversion of phyB in vitro is inhibited by PIF6, and this effect is observed at all temperatures tested. We analyzed our experimental data using a mathematical model containing multiple Pfr conformers, in accordance with previous findings. Remarkably, each Pfr conformer is differentially regulated by PIF6 and temperature. As a result, we speculate that in vivo phytochrome signaling networks may require similar levels of complexity to fine-tune responses to the external environment.

Unearthing the transition rates between photoreceptor conformers.

BACKGROUND: Obtaining accurate estimates of biological or enzymatic reaction rates is critical in understanding the design principles of a network and how biological processes can be experimentally manipulated on demand. In many cases experimental limitations mean that some enzymatic rates cannot be measured directly, requiring mathematical algorithms to estimate them. Here, we describe a methodology that calculates rates at which light-regulated proteins switch between conformational states. We focus our analysis on the phytochrome family of photoreceptors found in cyanobacteria, plants and many optogenetic tools. Phytochrome proteins change between active (P A ) and inactive (P I ) states at rates that are proportional to photoconversion cross-sections and influenced by light quality, light intensity, thermal reactions and dimerisation. This work presents a method that can accurately calculate these photoconversion cross-sections in the presence of multiple non-light regulated reactions. RESULTS: Our approach to calculating the photoconversion cross-sections comprises three steps: i) calculate the thermal reversion reaction rate(s); ii) develop search spaces from which all possible sets of photoconversion cross-sections exist, and; iii) estimate extinction coefficients that describe our absorption spectra. We confirm that the presented approach yields accurate results through the use of simulated test cases. Our test cases were further expanded to more realistic scenarios where noise, multiple thermal reactions and dimerisation are considered. Finally, we present the photoconversion cross-sections of an Arabidopsis phyB N-terminal fragment commonly used in optogenetic tools. CONCLUSIONS: The calculation of photoconversion cross-sections has implications for both photoreceptor and synthetic biologists. Our method allows, for the first time, direct comparisons of photoconversion cross-sections and response speeds of photoreceptors in different cellular environments and synthetic tools. Due to the generality of our procedure, as shown by the application to multiple test cases, the photoconversion cross-sections and quantum yields of any photoreceptor might now, in principle, be obtained.