Biol. Bull. 204: 174-179. (April 2003)
© 2003 Marine Biological Laboratory
Modeling Microbial Consortiums as Distributed Metabolic Networks
Joseph J. Vallino*
Ecosystems Center, Marine Biological Laboratory, Woods Hole, Massachusetts 02543
* E-mail: jvallino{at}mbl.edu
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Abstract
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Biogeochemistry is the study of how living systems in combination with abiotic reactions process and cycle mass and energy on local, regional, and global scales (Schlesinger, 1997). Understanding how these biogeochemical cycles function and respond to perturbations has become increasingly important, as anthropogenic impacts have significantly altered many of these cycles (Galloway and Cowling, 2002; Houghton et al., 2002). Biogeochemistry is strongly governed by microbial processes, and it appears to closely follow thermodynamic constraints in that electron acceptor (O2, NO3-, SO42-, etc.) utilization closely follows a priori expectations based on energetics (Vallino et al., 1996; Hoehler et al., 1998; Jakobsen and Postma, 1999; Amend and Shock, 2001). Consortiums of microorganisms seem to have evolved to exploit chemical potentials wherever they exist in the environment, as manifested by the recent discovery of anaerobic methane oxidation by sulfate (Boetius et al., 2000) or sulfide oxidation by nitrate (Schulz et al., 1999). Three and a half billion years of natural selection have produced living systems capable of degrading most chemical potentials. We may therefore ask: If all ecosystem niche space is filled, is the biogeochemistry we observe in the environment dependent on the organisms that occupy that environment, or is the biogeochemistry determined by fundamental forces, with the evolution of living systems being the implementation of those forces? Recent developments in nonequilibrium thermodynamics (NET) are beginning to support the latter alternative, and advances in genomics are allowing us to explore microbial consortiums in detail. Taking advantage of ideas being suggested by NET, we have developed a modeling framework that views microbial consortiums as an inter-species distributed metabolic network. When combined with experimental observations, the model should help us test hypotheses that govern how living systems function.
The main challenge to understanding microbial biogeochemistry is understanding the complex, but mostly cooperative, metabolism that develops among organisms that orchestrate biogeochemical cycles. Consider, for example, the metabolism found in the rumen of ruminant organisms such as cows (Madigan et al., 2000). The ecosystem of the rumen develops dozens of functional groups consisting of hundreds of species that degrade cellulose and starch to many intermediate organic acids and alcohols, as well as to CO2, methane, and hydrogen. Many of these organisms cannot survive without the presence of others. For instance, ethanol fermentation to acetate and H2 is unfavorable due to the accumulation of H2, which is also toxic to many organisms. However, if the fermenting organisms are coupled with methanogens (i.e., syntrophy), the overall reactions can proceed, and are very efficient (Jackson and McInerney, 2002). Furthermore, these systems are controllable, hence predictable, as the host organism is able to utilize a food source that it is not capable of digesting without the organisms in its rumen. What governs the development of this biochemistry? Interestingly, no one organism conducts all these biochemical transformations. Instead, the overall metabolism of the system is distributed across hundreds of different microbial species. Yet the system is well coordinated due to multiple levels of organization and multiple levels of proliferation, not by Darwinian selection (Caldwell et al., 1997). Can this enigmatic coordination be explained by nonequilibrium thermodynamics?
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Nonequilibrium Thermodynamics
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The application of thermodynamics to living systems dates back to Schrödinger (1944) and his examination of the creation of order from disorder. Although at first it appears that living systems violate the second law of thermodynamics in that they synthesize order from disorder, Schrödinger solved this problem by turning to nonequilibrium thermodynamics (NET). In an open system, energy flux from outside the system can reduce the system’s internal entropy, which is offset by an equal or greater increase in entropy outside the system. Since Schrödinger, many investigators have extended the application of NET to living systems (Prigogine, 1955; Margalef, 1968; Morowitz, 1968) with many recent advances (Allen, 1985; Johnson, 1988; Schneider, 1988; Wiley, 1988; Choi et al., 1999; Jorgensen et al., 2000; Toussaint and Schneider, 1988). Schneider and Kay (1994) succinctly describe the current restatement of the Second Law:
Thermodynamic systems exhibiting temperature, pressure and chemical equilibrium resist movement away from their equilibrium states. When moved away from a local equilibrium state a system will behave in a way which opposes the applied gradients and moves it back to its local equilibrium attractor. The stronger the applied gradient, the greater the effect of the equilibrium attractor on the system. The more a system is moved from equilibrium, the more sophisticated its mechanisms for resisting being moved from equilibrium. If dynamic and/or kinetic conditions permit, self-organization processes are to be expected. This behaviour is not sensible from a classical second law perspective, but is what is expected given the restated second law. No longer is the emergence of coherent self-organizing structures a surprise, but rather it is an expected response of a system as it attempts to resist and dissipate externally applied gradients which would move the system away from equilibrium.
Dissipative systems need not always operate at an optimum (Ulanowicz, 1997), because perturbations can reduce system organization, which will result in slower gradient degradation. For example, a perturbation of significant magnitude can destabilize the rumen microbial system and kill the host organism. If the feed changes abruptly from cellulose (grasses) to starch (grains), the organization of the microbial system can collapse due to a rapid increase in the bacteria that produce lactic acid, thus causing acidosis. Interestingly, if the feed is gradually changed, destabilization does not occur. Such phenomena are the essence of self-organization, which occurs in many autocatalytic systems (Ulanowicz, 1997).
Simple examples of the restated second law abound. For example, a chamber of gas isolated from any energy gradients soon reaches equilibrium in which the gas molecules are uniformly distributed (i.e., its highest entropy state). If the chamber is placed within a thermal gradient, the molecular gas distribution is no longer uniform, but shows increased order since a higher density of molecules will reside near the cold end of the chamber. Hence, the thermal gradient has lowered the internal entropy of the chamber. Once more, if the thermal gradient is sufficiently strong, a density-driven circulation will develop, further increasing system order, while reducing system entropy. This self-organization can also be seen in hurricanes, which are the organized structures that develop to facilitate degradation of the thermal gradient that has built up between the atmosphere and ocean over the summer. In an analogous manner, living systems are the organized structures that develop to degrade incoming solar radiation and chemical potential. Indeed, by examining emitted thermal radiation, Schneider and Kay (1994) have found that mature forests degrade incoming solar radiation more effectively than early successional forests or arid land.
The observation that ecosystem function may be governed by laws that transcend Darwinian selection is not new. Many theories related to, or derived from, NET have been developed to describe objective functions living systems tend to follow; however, the choice of an appropriate objective function still remains controversial. This is understandable, since current theories of NET apply only to linear approximations in the neighborhood of an equilibrium (Onsager, 1931; Prigogine, 1978). Theories for systems far from equilibrium are still under development. As a result, objective functions that ecosystems might track are numerous, and include optimizations of exergy (Jørgensen, 1994; Nielsen, 1995, Jorgensen et al., 2000) emergy (Odum, 1983), ascendancy (Ulanowicz, 1986), power (Odum and Pinkerton, 1955; Odum, 1971), biomass to maintenance (Margalef, 1968), thermodynamic efficiency (Nielsen and Ulanowicz, 2000), or entropy (Prigogine and Nicolis, 1971). As NET theories develop, perhaps many of these observations and theories will be collapsed or falsified.
Our objective is to develop a modeling framework that can be used to test these various objective hypotheses, but we must first have a basis for the model. Johnson (1988) argues that the rotational pattern of the earth converts the rectilinear energy output of the sun into a pulsed energy input to the earth, which induces cyclical energy flows, resonance, and time delays. This allows the energy of the system to be pumped up before it decays back towards ground state. Metabolically, this is what we see. Autotrophs use incoming solar radiation to create chemical potential in the form of redox gradients. Material at equilibrium, H2O and CO2, is pumped into a high-energy state by its conversion to O2 (oxidizing) and glucose (reducing). Heterotrophs return this redox gradient to ground state in a cyclical manner. Real ecosystem biogeochemistry is more complex when we include abiotic reactions, anaerobic environments, alternate electron acceptors and donors, nutrient constraints, and transport limitations. Nevertheless, it is the buildup and decay of redox potential via a distributed metabolism that forms the cornerstone of our approach. We focus on microbial systems because these systems exhibit the greatest degree of metabolic capacity, are responsible for the majority of biogeochemistry on earth, display fast dynamics that allows for practical experiments, and are less susceptible to loss of diversity.
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Thermodynamically Constrained Metabolic Biogeochemical Model
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A traditional reductionist biogeochemical model would include differential equations for growth of each microbial functional group, equations for Monod-type growth kinetics, and numerous conditional statements to direct the use of the various electron donor and acceptor resources that exist within the environment (Koelmans et al., 2001). While this approach has been useful for well-defined laboratory experiments with a few species growing on a limited number of well-defined substrates, it is not practical for extension to more diverse microbial ecosystems with numerous or ill-defined substrates. Reductionist-based biological models fail to incorporate the governing laws that define living systems (Lawton, 1999); the models are based solely on empirical observations. Consequently, these models are brittle and often fail as the system’s state changes significantly over time and space (Vallino, 2000).
To develop a robust model that can predict microbially governed biogeochemistry in spatially and temporally diverse environments, a more holistic, systems-based perspective must be taken. Our governing philosophy is that living systems synthesize and allocate metabolic capability in such a way as to optimally utilize available resources in the environment as governed by NET. What we seek to determine is the nature of the objective function that living systems tend to follow, and what causes living systems to diverge from this function.
This optimization-based approach was first developed in a thermodynamically constrained metabolic framework to examine bacterial utilization of dissolved organic matter (Vallino et al., 1996). However, this model still uses an organismal approach, in that the model tracks bacterial biomass. We increase the applicability of our modeling approach by removing emphasis on synthesizing bacterial biomass and placing it instead on synthesis of metabolic capability exhibited by the whole ecosystem. The model consists of a set of metabolic half-reactions that represents the major metabolic capability of a planktonic ecosystem (Table 1). But instead of synthesizing bacteria, reactions produce protein, chlorophyll, storage compounds, and other fundamental building materials observed in living systems (Fig. 1). These building materials represent those summed over all organisms in the ecosystem, not any one particular organism. Indeed, organisms are not directly modeled. Newly synthesized protein is then allocated to those metabolic reactions that optimize the specified objective criteria, while enzymes no longer in use can be degraded back into constituent amino acids (Fig. 1). A linear programming (LP) problem is used to determine the reaction rates (ri) and enzyme concentrations (Ei) that maximize a given objective function, subject to fundamental constraints, such as energy, redox, composition, kinetics, and light-capturing capabilities (Table 2). Although the model does not distinguish species in a classic sense, it does from a functional perspective. As environmental conditions change, so do allocations of resources to metabolic reactions. Real systems accomplish this same objective via relative changes in species abundances and magnitude of gene expression.
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Figure 1. Conceptualization of the metabolic biogeochemistry model. Half reactions lead to production of protein (and other building-block constituents), which is then allocated to reactions governed by an optimization function. Abiotic reactions are incorporated with standard kinetics.
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As an example of the model, we simulate a marine phytoplankton bloom, where metabolic reactions associated with ammonium (NH4+) and nitrate (NO3-) uptake, N2-fixation, carbon dioxide (CO2) fixation, and biomass synthesis (protein and chlorophyll) are included in the model (Table 1). The optimization goal chosen was maximizing the rate of biomass synthesis, though others could be formulated. Resources made available were 5 µM NH4+, 5 µM NO3-, atmospheric N2, and light. The model simulation proceeds by preferentially consuming NH4+ over NO3- (Fig. 2a,b), which is evident by the allocation of protein (in the form of enzyme) to NH4+ uptake (Fig. 3a), but not to NO3- uptake nor N2 fixation (Fig. 3b,c). There is also a strong initial allocation of protein to chlorophyll synthesis (Figs. 2d, 3d), but this protein is rapidly reallocated after 0.5 d due to diminished returns on the investment in light harvesting capacity (i.e., chlorophyll), which saturates at high chlorophyll concentration (Fig. 3d). As NH4+ becomes exhausted (Fig. 2a), protein is reallocated from NH4+ to NO3- uptake (Fig. 3a, b). Subsequently, as NO3- becomes depleted (Fig 2b), protein is allocated to N2 fixation (Fig. 3c).
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Figure 2. Metabolic model. Changes in resource concentrations of (a) ammonium and (b) nitrate, and accumulation of biological structure (c) protein and (d) chlorophyll over the course of the simulation.
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Figure 3. Reaction rates (solid line) and allocation of protein (enzyme concentration, dashed line) for reactions involving (a) ammonium uptake, (b) nitrate uptake, (c) N2 fixation, and (d) chlorophyll synthesis during the course of the simulation. Abbreviations: Glc, glucose; AA, amino acids, Chl, chlorophyll.
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Conclusions
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If nonequilibrium thermodynamics governs biogeochemistry, our metabolic modeling approach represents a more direct means of capturing ecosystem dynamics than classic, organismal-based approaches. The approach also predicts how whole-system genomic transcription and translation should proceed, which can be compared to actual systems using techniques currently being advanced in molecular biology. Because the metabolic ecosystem model is based on fundamental governing equations, it should prove more robust and have a greater operating range than organismal-based models.
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Acknowledgments
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This research has been supported by NSF grants OCE-9726921 and DEB-9815598 and the Mellon Foundation.
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Footnotes
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The paper was originally presented at a workshop titled Outcomes of Genome-Genome Interactions. The workshop, which was held at the J. Erik Jonsson Center of the National Academy of Sciences, Woods Hole, Massachusetts, from 1-3 May 2002, was sponsored by the Center for Advanced Studies in the Space Life Sciences at the Marine Biological Laboratory, and funded by the National Aeronautics and Space Administration under Cooperative Agreement NCC 2-1266
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Literature Cited
|
|---|
Allen, P. M. 1985. Ecology, thermodynamics, and self-organization: towards a new understanding of complexity. Can. Bull. Fish. Aquat. Sci. 213: 3–26.
Amend, J. P., and E. L. Shock. 2001. Energetics of overall metabolic reactions of thermophilic and hyperthermophilic Archaea and Bacteria. FEMS Microbiol. Rev. 25: 175–243.[ISI][Medline]
Boetius, A., K. Ravenschlag, C. J. Schuber, D. Rickert, F. Widdel, A. Gieseke, R. Amann, B. B. Jørgensen, U. Witte, and O. Pfannkuche. 2000. A marine microbial consortium apparently mediating anaerobic oxidation of methane. Nature 407: 623–626.
Caldwell, D. E., G. M. Wolfaardt, D. R. Korber, and J. R. Lawrence. 1997. Do bacterial communities transcend Darwinism? Adv. Microb. Ecol. 15: 105–191.
Choi, J. S., A. Mazumder, and R. I. C. Hansell. 1999. Measuring perturbation in a complicated, thermodynamic world. Ecol. Model. 117: 143–158.
Galloway, J. N., and E. B. Cowling. 2002. Reactive nitrogen and the world: two hundred years of change. Ambio 31: 64–71.[Medline]
Hoehler, T. M., M. J. Alperin, D. B. Albert, and C. S. Martens. 1998. Thermodynamic control on hydrogen concentrations in anoxic sediments. Geochim. Cosmochim. Acta 62: 1745–1756.
Houghton, J. T., Y. Ding, D. J. Griggs, M. Noguer, P. J. van der Linden, and D. Xiaosu. 2002. Climate Change 2001: The Scientific Basis: Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change (IPCC). Cambridge University Press, Cambridge, UK. Pp. 1–944.
Jackson, B. E., and M. J. McInerney. 2002. Anaerobic microbial metabolism can proceed close to thermodynamic limits. Nature 415: 454–456.[Medline]
Jakobsen, R., and D. Postma. 1999. Redox zoning, rates of sulfate reduction and interactions with Fe-reduction and methanogenesis in a shallow sandy aquifer, Romo, Denmark. Geochim. Cosmochim. Acta 63: 137–151.
Johnson, L. 1988. The thermodynamic origin of ecosystems: a tale of broken symmetry. Pp. 75–105 in Entropy, Information, and Evolution: New Perspectives on Physical and Biological Evolution, B. H. Weber, D. J. Depew, and J. D. Smith, eds. MIT Press, Cambridge, MA.
Jørgensen, S. E. 1994. Review and comparison of goal function in system ecology. Vie Milieu 44: 11–20.
Jorgensen, S. E., B. C. Patten, and M. Straskraba. 2000. Ecosystems emerging: 4. growth. Ecol. Model. 126: 249–284.
Koelmans, A. A., A. Van Der Heijde, L. M. Knijff, and R. H. Aalderin. 2001. Integrated modelling of eutrophication and organic contaminant fate and effects in aquatic ecosystems. A review. Water Res. 35: 3517–3536.[Medline]
Lawton, J. H. 1999. Are there general laws in ecology? Oikos 84: 177–192.
Madigan, M. T., J. M. Martinko, and J. Parker. 2000. Brock Biology of Microorganisms, 9th ed. Prentice Hall, Upper Saddle River, NJ.
Margalef, R. 1968. Perspectives in Ecological Theory, University of Chicago Press, Chicago.
Morowitz, H. J. 1968. Energy Flow in Biology: Biological Organization As a Problem in Thermal Physics. Academic Press, New York.
Nielsen, S. N. 1995. Optimization of exergy in a structural dynamic model. Ecol. Model. 77: 111–122.
Nielsen, S. N., and R. E. Ulanowicz. 2000. On the consistency between thermodynamical and network approaches to ecosystems. Ecol. Model. 132: 23–31.
Odum, H. T. 1971. Environment, Power and Society. John Wiley, New York.
Odum, H. T. 1983. Systems Ecology. John Wiley, Toronto.
Odum, H. T., and R. C. Pinkerton. 1955. Time’s speed regulator: the optimum efficiency for maximum power output in physical and biological systems. Am. Sci. 43: 321–343.
Onsager, L. 1931. Reciprocal relations in irreversible processes. Phys. Rev. 37: 405–426.[ISI]
Prigogine, I. 1955. Introduction to Thermodynamics of Irreversible Processes, John Wiley, New York.
Prigogine, I. 1978. Time, structure, and fluctuations. Science 201: 777–785.[Abstract/Free Full Text]
Prigogine, I., and G. Nicolis. 1971. Biological order, structure and instabilities. Q. Rev. Biophys. 4: 107–148.[Medline]
Schlesinger, W. H. 1997. Biogeochemistry: An Analysis of Global Change, 2nd ed. Academic Press, San Diego, CA.
Schneider, E. D. 1988. Thermodynamics, ecological succession, and natural selection: a common thread. Pp. 107–138 in Entropy, Information, and Evolution: New Perspectives on Physical and Biological Evolution, B. H. Weber, D. J. Depew, and J. D. Smith, eds. MIT Press, Cambridge, MA.
Schneider, E. D., and J. J. Kay. 1994. Complexity and thermodynamics: towards a new ecology. Futures 26: 626–647.
Schrödinger, E. 1944. What Is Life? Cambridge University Press, Cambridge, UK.
Schulz, H. N., T. Brinkhoff, T. G. H. M. M. Ferdelman, A. Teske, and B. B. Jørgensen. 1999. Dense populations of a giant sulfur bacterium in Namibian shelf sediments. Science 284: 493–495.[Abstract/Free Full Text]
Toussaint, O., and E. D. Schneider. 1998. The thermodynamics and evolution of complexity in biological systems. Comp. Biochem. Physiol. A 120: 3–9.
Ulanowicz, R. E. 1986. Growth and Development: Ecosystems Phenomenology. Springer-Verlag, New York.
Ulanowicz, R. E. 1997. Ecology, the Ascendent Perspective. Columbia University Press, New York.
Vallino, J. J. 2000. Improving marine ecosystem models: use of data assimilation and mesocosm experiments. J. Mar. Res. 58: 117–164.
Vallino, J. J., C. S. Hopkinson, and J. E. Hobbie. 1996. Modeling bacterial utilization of dissolved organic matter: optimization replaces Monod growth kinetics. Limnol. Oceanogr. 41: 1591–1609.
Wiley, E. O. 1988. Entropy and evolution. Pp. 173–188 in Entropy, Information, and Evolution: New Perspectives on Physical and Biological Evolution, B. H. Weber, D. J. Depew, and J. D. Smith, eds. MIT Press, Cambridge, MA.
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Abstract
Nonequilibrium Thermodynamics
