Does nonequilibrium thermodynamics govern metabolic network expression in microbial communities

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Does non-equilibrium thermodynamics govern
metabolic network expression in microbial
communities?
Joe Vallino
MBI Workshop May 2006
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Why Thermodynamics?

• Save conservation of mass (and sometimes energy),
  we have no fundamental laws that pertain to
  living systems.
• Instead, reductionist-mechanistic approaches are
  used.

?
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Kinetics Example
Growth kinetics are dependent on the organisms
present, which in turn are dependent on
environmental resource availability.
Eutrophic
Mesotrophic
Oligotrophic
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Overview

• Revisit application of thermodynamics, and other
  goal-based functions, to the study of ecosystems.
• Examine usefulness of the species concept
• Development of a metabolically-based,
  thermodynamically constrained, ecosystem network
  model.
• Application of microbial microcosms as model
  systems

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Focus

• Understanding and prediction of ecosystem
  biogeochemistry in particular,
  microbial biogeochemistry
• Carbon fixation
• Denitrification
• Methanogenesis
• Sulfate reduction
• Metal redox reactions
• Etc.

• Build around fundamental principles
• Focus on ecosystem metabolic networks, not
  organisms, species, populations or guilds

(Paerl and Pinckney, 1996)
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Goal-Based Ecosystem Descriptors
Several theories have been postulate to describe
ecosystem dynamics, a few of these include

• Maximize Power (Lotka 1922) energy throughput.
• Maximize Storage, Exergy (Jorgensen Mejer
  1979) usable energy.
• Maximize Empower, Emergy (Odum 1988) energy
  quality.
• Maximize Ascendency (Ulanowicz 1986)
  through-flow times information.
• Maximize Entropy (PrigogineStengers 1984).
• Maximize Dissipation (SchneiderKay 1990)
  Degrade energy gradients.
• Maximize Cycling (Morowitz 1968) flows.
• Maximize Residence Time (CheslakLamarra 1981) of
  energy.
• Minimize Specific Dissipation (Onsager 1931,
  Prigogine 1947).
• Minimize Empower/Exergy Ratio (BastianoniMarchett
  ini 1997).

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Why are these theories not used?

• Confusion Which one is right Exergy?, Emergy?,
  Maximum power?
• Uncertain theoretical bases. Mostly intuition
  based on observations and generalizations.
• Very little experimental support, and often only
  with large systems.
• Not applied at the right scale. (They dont apply
  to species)
• Not mathematical framework for implementation.

However, the theories are more similar than
different. Fath et al. (2001), Jorgensen et al.
(2000). Maybe there is just one.
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Maximum Entropy Production (MEP)
Global heat transport (Paltridge 1975), Mars and
Titan (Lorenz et al. 2001). See review Ozawa et
al. (2003).
Global biogeochemistry (wrt. GPP) Kleidon
(2004), Climate Change. Ecosystems and evolution
Swenson (1989)
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MEP Theoretical Basis

• Dewar (2003) used Jaynes information theory and
  statistical mechanics to show that the MEP state
  is the most probable state for non-equilibrium
  systems at steady-state.
• Basically, the macrostate with the greatest
  number of microstates is the most probable state.
  (Same basic idea Boltzmann used to explain
  entropy in equilibrium thermodynamics).
• The principle only applies to systems with
  sufficient degrees of freedom.
• Systems do not have to be at MEP, they are just
  more likely to be found there.

Dewar, R., 2003. Journal of Physics A 36 631-641.
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Implications of MEP

• MEP principle provides a firm theoretical
  footing.
• Applies to abiological as well as biological
  systems. For instance, preferred MEP route for
  CH4 O2 is combustion.
• Systems that degrade available energy faster will
  be selected for. (Similar to Schneider and
  Kays hypothesis.)
• MEP principle states that there should be
  multiple microstate configurations that give rise
  to the same macrostate (e.g., entropy production
  rate).
• If we view a microstate as one food web
  configuration, then MEP implies there should be
  many food web configurations that produce the
  same macrostate (e.g., biogeochemistry).

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Chemical Potential Exploitation
H2S oxidation by NO3-
CH4 oxidation by SO42-
Anammox NH4 NO2- N2 2H2O
Boetius et al. 2000
Schulz et al. 1999 Thiomargarita namibiensis
Strous et al. 1999 Planctomycete
ADD CH4 oxidation by NO3 (raghoebarsing2006)
1 mm
Observations consistent with systems maximizing
energy degradationand MEP
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Example of MEP and Food Webs
n(t) Nitrogen p(t) Methane partial
pressure c(t) Dissolved methane m(t) Methanotrop
hs g(t) Grazers
Energy-Potential stat (?)
CH4, O2, CO2, H2O
CH4, O2
Standard Model
p(t)
?m
?g
Note, microcosm starts with fixed nutrient
resources (N limited). Only energy is constantly
supplied.
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Conventional Compartment Model
Of course, kinetic growth parameters poorly known
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Methanotroph Growth, No grazers
?m
Or entropy production
With out grazes, growth is limited by mortality
of methanotrophs. Biomass is high and DIN is low.
Time (d)
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Methanotroph Growth, With grazers
Presence of grazers increases methane
consumption, or entropy production. Note, total
biomass in less.
Just one parameter set
Time (d)
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MEP methanotroph grazer ratio
MEP state
(d-1)
Grazers serve to turnover biomass and recycle
nutrients
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Basic Cycling Premise
Faster cycling leads to resilience to
perturbations
Energy
P
Primary producers
Self organizes towards MEP
R
Resources
C
Heat (Entropy)
Consumers
But with many possible system configurations
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Top-down or bottom-up?

• MEP removes the often debated top-down versus
  bottom-up assessments. Both are critical to
  attaining an MEP state.
• Studying food web structure and dynamics, such as
  trophic cascades and top-downbottom-up, are
  microstructure, transient analyses.
• If many food web configurations are possible,
  then we dont want to base our model on food webs
  and species.
• How else can we view ecosystems if not by species?

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Microbially-coupled Systems
Symbiosis and Endosymbiosis
Lichen FungiAlgae
Dinoflagellates in flatworm
Sulfur bacteria in Riftia
Mycorrhizae
Is emphasis on species boundaries helpful
here? Perhaps functional emphasis would be better
Caldwell et al. 1997 Biological systems develop
with multiple levels of organization and multiple
levels of proliferation.
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Biogeochemistry and Redox Reactions
Light Energy Input
CO2 NO3 H2O SO4
CH4 C6H12O6 NH4 O2 H2S
Low
High
Chemical Potential (oxidizing environ.)
It is the buildup and decay of chemical potential
that forms the basis of ecosystem
biogeochemistry.
? Base perspective solely on metabolic function,
not organisms.
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Ecosystem Metabolic Network
Mn4
Distributed Metabolism
NO2-
Fe2
Mn2
N2
NO3-
e-
CO2
e-
Fe3
NH3
O2
FePO4
NO N2O
Biological Structure
(CH2O)n
PO43-
SO42-
H2S
Propionate Butyrate Succinate Alcohols
CO2 H2
Acetate
S0
SO32-
S2O32-
CH4
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Modeling Overview

• Modeling Basis
• Distributed biological systems function as a
  multicellular organism.
• Metabolic function is universally distributed.
• Biogeochemistry is governed by maximum entropy
  production.

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Example Methanotroph Metabolic Network
Si Biological Structure
S4
NO3-
NH4
S5
S6
S1
CH4
CH2O
Si
S2
e-
O2
CO2
S3
Energy Coupling
H2O
ATP
ADP Pi
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Methanotroph Reactions
Reactions Rate Structure
CH4 H2O ? CH2O 4e- r1 S1 Methanotrophs CH2O
2H2O ? CO2 4e- r2 S2 Heterotrophs O2 4e- ?
H2O r3 S3 Respiration NO3- 8e- ? NH4
3H2O r4 S4 N uptake CH2O 0.158 NH4 0.05e- ?
S r5 S5 Structure Synthesis S ? CH2O 0.158 NH4
0.05e- r6 S6 Structure Degrade
Specific synthesis Specific
degradation
?ir5
?ir6
S1 S2 S3 S4
r5
S
CH2O
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Methanotroph Thermodynamics
CH4 H2O ? CH2O 4e- ?(2e- NAD H ?
NADH) ?(ATP H2O ? ADP Pi)
Note,
accounts for pH, temperature and ionic strength.
Reaction Rates
Thermodynamic Force
Kinetic Force
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Calculus of Variation (optimal control)
Subject to
st
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Example Output (feasible, non optimal)
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Biological Structure Rxn Rates
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Optimization Time Horizon?

• Instantaneous
• Final state over some time interval
• Integrated over some time interval

Or interval optimization
Objective
Time
t0
tf
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Methanotroph Community Experiment
Define mineral salts medium 700 ?M NO3- 70 ?M
PO43- pH 6.8, 20C 18 L total volume 4 identical
replicates Gas sparging 2.9 Methane in air 20
mL min-1 flow rate (MFCs). Computer controlled
sampling Inoculum 1 L from Cedar swamp (pH 4)
Sampling On Line O2, CO2, CH4, DO, pH, ORP Off
Line Microbial numbers ID Nutrients DOM and
POM Microbial DNA
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Methanotroph Microcosms 8 Jan 06 (Day 93)
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After 46 Days
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Microcosm On-Line Data
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Off-line Data
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Dissolved Organic C and TDN
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Experimental Objectives

• Reproducibility of the Macrostate (entropy
  production).
• Reinoculate from different environments, because
  M in MEP is information (metagenome) based.
• Examine species composition of different reactors
  to show multiple microstates.
• Measure nutrient recycling (?)
• Use molecular tools (qPCR) to measure metabolic
  allocations.
• Compare MEP-based metabolic ecosystem network
  model to observations.

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Summary

• Evidence for MEP is good, and now has strong
  theoretically footing (Dewar, 2003).
• MEP states that there should be a large number of
  modes that exhibit the same biogeochemistry.
• Applies at the energy dissipation level
  (macrostate) not at the species level. Must look
  at function, not species.
• Top-down and bottom-up are instantaneous
  dynamical assessments. In order to achieve MEP,
  both most come into balance at steady state.
• Microbial microcosms provide an ideal system to
  test hypotheses regarding MEP.

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Acknowledgements

• Funding
• NASA, Astrobiology
• NSF LTER
• Mellon Foundation

• Experimental
• Stefan Sievert, WHOI
• Emily Gains
• Hap Garritt