Optimal spatial allocation of enzymes as an investment problem

Given a limited number of molecular components, cells face various allocation problems demanding decisions on how to distribute their resources. For instance, cells decide which enzymes to produce at what quantity, but also where to position them. Here we focus on the spatial allocation problem of how to distribute enzymes such as to maximize the total reaction flux produced by them in a system with given geometry and boundary conditions. So far, such distributions have been studied by computational optimization, but a deeper theoretical understanding was lacking. We derive an optimal allocation principle, which demands that the available enzymes are distributed such that the marginal flux returns at each occupied position are equal. This ‘homogeneous marginal returns criterion’ (HMR criterion) corresponds to a portfolio optimization criterion in a scenario where each investment globally feeds back onto all payoffs. The HMR criterion allows us to analytically understand and characterize a localization-delocalization transition in the optimal enzyme distribution that was previously observed numerically. In particular, our analysis reveals the generality of the transition, and produces a practical test for the optimality of enzyme localization by comparing the reaction flux to the influx of substrate. Based on these results, we devise an additive construction algorithm, which builds up optimal enzyme arrangements systematically rather than by trial and error. Taken together, our results reveal a common principle in allocation problems from biology and economics, which can also serve as a design principle for synthetic biomolecular systems.

La6Cd0.75Ga2Q11.5Cl2.5 (Q = S and Se): Two New Nonlinear Optical Chalcohalides with Large Laser-Induced Damage Threshold (LIDT)

Two new chalcohalides La6Cd0.75Ga2Q11.5Cl2.5 (Q = S and Se) with mixed-anionic functional groups were synthesized by high temperature reaction using LaCl3 as reaction-flux. Both compounds crystalize in the non-centrosymmetric space...

Regulation of reaction fluxes via enzyme sequestration and co-clustering

Experimental observations suggest that cells change the intracellular localization of key enzymes to regulate the reaction fluxes in enzymatic networks. In particular, cells appear to use sequestration and co-clustering of enzymes as spatial regulation strategies. These strategies should be equally useful to achieve rapid flux regulation in synthetic biomolecular systems. Here, we leverage a theoretical model to analyse the capacity of enzyme sequestration and co-clustering to control the reaction flux in a branch of a reaction–diffusion network. We find that in both cases, the response of the system is determined by two dimensionless parameters, the ratio of total activities of the competing enzymes and the ratio of diffusion to reaction timescales. Using these dependencies, we determine the parameter range for which sequestration and co-clustering can yield a biologically significant regulatory effect. Based on the known kinetic parameters of enzymes, we conclude that sequestration and co-clustering represent a viable regulation strategy for a large fraction of metabolic enzymes, and suggest design principles for reaction flux regulation in natural or synthetic systems.

Signaling architectures that transmit unidirectional information despite retroactivity

A signaling pathway transmits information from an upstream system to downstream systems, ideally in a unidirectional fashion. A key obstacle to unidirectional transmission is retroactivity, the additional reaction flux that affects a system once its species interact with those of downstream systems. This raises the fundamental question of whether signaling pathways have developed specialized architectures that overcome retroactivity and transmit unidirectional signals. Here, we propose a general procedure based on mathematical analysis that provides an answer to this question. Using this procedure, we analyze the ability of a variety of signaling architectures to transmit one-way (from upstream to downstream) signals, as key biological parameters are tuned. We find that single stage phosphorylation and phosphotransfer systems that transmit signals from a kinase show a stringent design trade-off that hampers their ability to overcome retroactivity. Interestingly, cascades of these architectures, which are highly represented in nature, can overcome this trade-off and thus enable unidirectional transmission. By contrast, phosphotransfer systems, and single and double phosphorylation cycles that transmit signals from a substrate are unable to mitigate retroactivity effects, even when cascaded, and hence are not well suited for unidirectional information transmission. Our results identify signaling architectures that, allowing unidirectional transmission of signals, embody modular processes that conserve their input/output behavior across multiple contexts. These findings can be used to decompose natural signal transduction networks into modules, and, at the same time, they establish a library of devices that can be used in synthetic biology to facilitate modular circuit design.

Atomic decomposition of conceptual DFT descriptors: application to proton transfer reactions

We present an atomic decomposition of the molecular energy, reaction force and reaction flux, which is based on Bader's atoms-in-molecules theory.