Matthew D. Johnston

Carbon payback times for crop-based biofuel expansion in the tropics: the effects of changing yield and technology

Biofuels from land-rich tropical countries may help displace foreign petroleum imports for many industrialized nations, providing a possible solution to the twin challenges of energy security and climate change. But concern is mounting that crop-based biofuels will increase net greenhouse gas emissions if feedstocks are produced by expanding agricultural lands. Here we quantify the ‘carbon payback time’ for a range of biofuel crop expansion pathways in the tropics. We use a new, geographically detailed database of crop locations and yields, along with updated vegetation and soil biomass estimates, to provide carbon payback estimates that are more regionally specific than those in previous studies. Using this cropland database, we also estimate carbon payback times under different scenarios of future crop yields, biofuel technologies, and petroleum sources. Under current conditions, the expansion of biofuels into productive tropical ecosystems will always lead to net carbon emissions for decades to centuries, while expanding into degraded or already cultivated land will provide almost immediate carbon savings. Future crop yield improvements and technology advances, coupled with unconventional petroleum supplies, will increase biofuel carbon offsets, but clearing carbon-rich land still requires several decades or more for carbon payback. No foreseeable changes in agricultural or energy technology will be able to achieve meaningful carbon benefits if crop-based biofuels are produced at the expense of tropical forests. S Supplementary data are available from stacks.iop.org/ERL/3/034001

Resetting global expectations from agricultural biofuels

Aggressive renewable energy policies have helped the biofuels industry grow at a rate few could have predicted. However, while discourse on the energy balance and environmental impacts of agricultural biofuel feedstocks are common, the potential they hold for additional production has received considerably less attention. Here we present a new biofuel yield analysis based on the best available global agricultural census data. These new data give us the first opportunity to consider geographically-specific patterns of biofuel feedstock production in different regions, across global, continental, national and sub-national scales. Compared to earlier biofuel yield tables, our global results show overestimates of biofuel yields by ~100% or more for many crops. To encourage the use of regionally-specific data for future biofuel studies, we calculated complete results for 20 feedstock crops for 238 countries, states, territories and protectorates.

A linear programming approach to weak reversibility and linear conjugacy of chemical reaction networks

A numerically effective procedure for determining weakly reversible chemical reaction networks that are linearly conjugate to a known reaction network is proposed in this paper. The method is based on translating the structural and algebraic characteristics of weak reversibility to logical statements and solving the obtained set of linear (in)equalities in the framework of mixed integer linear programming. The unknowns in the problem are the reaction rate coefficients and the parameters of the linear conjugacy transformation. The efficacy of the approach is shown through numerical examples.

Computing weakly reversible linearly conjugate chemical reaction networks with minimal deficiency

Mass-action kinetics is frequently used in systems biology to model the behavior of interacting chemical species. Many important dynamical properties are known to hold for such systems if their underlying networks are weakly reversible and have a low deficiency. In particular, the Deficiency Zero and Deficiency One Theorems guarantee strong regularity with regards to the number and stability of positive equilibrium states. It is also known that chemical reaction networks with distinct reaction structure can admit mass-action systems with the same qualitative dynamics. The theory of linear conjugacy encapsulates the cases where this relationship is captured by a linear transformation. In this paper, we propose a mixed-integer linear programming algorithm capable of determining the minimal deficiency weakly reversible reaction network which admits a mass-action system which is linearly conjugate to a given reaction network.

Stochastic analysis of biochemical reaction networks with absolute concentration robustness

It has recently been shown that structural conditions on the reaction network, rather than a ‘fine-tuning’ of system parameters, often suffice to impart ‘absolute concentration robustness’ (ACR) on a wide class of biologically relevant, deterministically modelled mass-action systems. We show here that fundamentally different conclusions about the long-term behaviour of such systems are reached if the systems are instead modelled with stochastic dynamics and a discrete state space. Specifically, we characterize a large class of models that exhibit convergence to a positive robust equilibrium in the deterministic setting, whereas trajectories of the corresponding stochastic models are necessarily absorbed by a set of states that reside on the boundary of the state space, i.e. the system undergoes an extinction event. If the time to extinction is large relative to the relevant timescales of the system, the process will appear to settle down to a stationary distribution long before the inevitable extinction will occur. This quasi-stationary distribution is considered for two systems taken from the literature, and results consistent with ACR are recovered by showing that the quasi-stationary distribution of the robust species approaches a Poisson distribution.

Translated Chemical Reaction Networks

Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems of polynomial ordinary differential equations. The steady states of these mass action systems have been analyzed via a variety of techniques, including stoichiometric network analysis, deficiency theory, and algebraic techniques (e.g., Gröbner bases). In this paper, we present a novel method for characterizing the steady states of mass action systems. Our method explicitly links a network’s capacity to permit a particular class of steady states, called toric steady states, to topological properties of a generalized network called a translated chemical reaction network. These networks share their reaction vectors with their source network but are permitted to have different complex stoichiometries and different network topologies. We apply the results to examples drawn from the biochemical literature.

Emissions and Air Quality Impacts of Truck-to-Rail Freight Modal Shifts in the Midwestern United States

We present an examination of the potential emissions and air quality benefits of shifting freight from truck to rail in the upper Midwestern United States. Using a novel, freight-specific emissions inventory (the Wisconsin Inventory of Freight Emissions, WIFE) and a three-dimensional Eulerian photochemical transport model (the Community Multiscale Air Quality Model, CMAQ), we quantify how specific freight mode choices impact ambient air pollution concentrations. Using WIFE, we developed two modal shift scenarios: one focusing on intraregional freight movements within the Midwest and a second on through-freight movements through the region. Freight truck and rail emissions inventories for each scenario were gridded to a 12 km × 12 km horizontal resolution as input to CMAQ, along with emissions from all other major sectors, and three-dimensional time-varying meteorology from the Weather Research and Forecasting model (WRF). The through-freight scenario reduced monthly mean (January and July) localized concentrations of nitrogen dioxide (NO2) by 28% (-2.33 ppbV) in highway grid cells, and reduced elemental carbon (EC) by 16% (-0.05 μg/m(3)) in highway grid cells. There were corresponding localized increases in railway grid cells of 25% (+0.83 ppbV) for NO2, and 22% (+0.05 μg/m(3)) for EC. The through-freight scenario reduced CO2 emissions 31% compared to baseline trucking. The through-freight scenario yields a July mean change in ground-level ambient PM2.5 and O3 over the central and eastern part of the domain (up to -3%).

A stratum approach to global stability of complex balanced systems

It has long been known that complex balanced mass-action systems exhibit a restrictive form of behaviour known as locally stable dynamics. This means that within each compatibility class – the forward invariant space where solutions lies – there is exactly one equilibrium concentration and that this concentration is locally asymptotically stable. It has also been conjectured that this stability extends globally to . That is to say, all solutions originating in approach the unique positive equilibrium concentration rather than or ∞. To date, however, no general proof of this conjecture has been found. In this article, we approach the problem of global stability for complex balanced systems through the methodology of dividing the positive orthant into regions called strata. This methodology has been previously applied to detailed balanced systems – a proper subset of complex balanced systems – to show that, within a stratum, trajectories are repelled from any face of adjacent to the stratum. Several known global stability results for detailed balanced systems are generalized to complex balanced systems.

A computational approach to persistence, permanence, and endotacticity of biochemical reaction systems

We introduce a mixed-integer linear programming (MILP) framework capable of determining whether a chemical reaction network possesses the property of being endotactic or strongly endotactic. The network property of being strongly endotactic is known to lead to persistence and permanence of chemical species under genetic kinetic assumptions, while the same result is conjectured but as yet unproved for general endotactic networks. The algorithms we present are the first capable of verifying endotacticity of chemical reaction networks for systems with greater than two constituent species. We implement the algorithms in the open-source online package CoNtRol and apply them to a large sample of networks from the European Bioinformatics Institute’s BioModels Database. We use strong endotacticity to establish for the first time the permanence of a well-studied circadian clock mechanism.

A Computational Approach to Steady State Correspondence of Regular and Generalized Mass Action Systems

It has been recently observed that the dynamical properties of mass action systems arising from many models of biochemical reaction networks can be characterized by considering the corresponding properties of a related generalized mass action system. The correspondence process known as network translation in particular has been shown to be useful in characterizing a system’s steady states. In this paper, we further develop the theory of network translation with particular focus on a subclass of translations known as improper translations. For these translations, we derive conditions on the network topology of the translated network which are sufficient to guarantee the original and translated systems share the same steady states. We then present a mixed-integer linear programming algorithm capable of determining whether a mass action system can be corresponded to a generalized system through the process of network translation.