Genome-Scale Reconstruction of Microbial Dynamic Phenotype: Successes and Challenges
Abstract
:1. Introduction
Everything should be made as simple as possible... but not simpler.Albert Einstein
2. Simple and Complex Growth: The Basic Principles
- The microbial specific growth rate (SGR) depends on environmental conditions and the macromolecular cell composition (MMCC). MMCC variation is the result of self-regulation, including differential gene expression in response to a changeable environment.
- Variable MMCC is the main reason for the higher complexity of microbial growth kinetics vs. chemical and enzymatic reactions.
- A nutrient supply is the primary environmental factor controlling microbial behavior; the effects of other modifying factors (T, pH, osmolarity, etc.) can be understood only in combination with the nutritional factor.
- MMCC dependence on SGR is a common misconception; both complex variables depend on the environmental conditions.
- A growth is called simple (syn: balanced and steady state) if it proceeds exponentially under steady environmental conditions with constant SGR and MMCC. Otherwise, the cell dynamics are complex.
2.1. MMCC and Growth Kinetics
2.2. Limited Applicability of Enzyme Kinetics to Microbial Growth
2.3. Growth Conditions, the Hierarchy of Factors
2.4. SGR and MMCC, the Chicken and the Egg Dilemma
- SGR → rRNA—the SGR is the causative factor for the variable rRNA content.
- rRNA → SGR—reverse causation.
- s → rRNA and s → SGR—both variables are affected by substrate concentration, s.
- —options 2 and 3 are combined.
2.5. Drawing the Line between Simple and Complex Biodynamics
3. Typical Examples of Simple and Complex Biodynamics
3.1. Batch Culture
3.2. Continuous Culture
4. Pre-Genomic Models of Microbial Growth
4.1. From Malthusian Exponent to the Cybernetic Models
ODE | Equation | Comments |
---|---|---|
(4) | Exponential growth [68]. SGR is constant | |
(5) | Logistic equation [69]. Growth is restricted by the negative biotic interactions; K is the upper x limit | |
(6) | Monod chemostat model [70] with a maintenance term [14]. SGR is a hyperbolic function of s and is negative below threshold s*. The yield Y varies because of the maintenance | |
(7) | Monod-Ierusalimsky model [22] accounting self-inhibition by the product, p; x and s are defined by (6) | |
(8) | Droop model [22,71]. The ‘cell quota’ σ is the content of deficient nutrient element in cells. The model was specially designed for microbial growth limited by the conserved nutrient substrates | |
(9) | Structured models with multiple internal variables Ci [72]. Model includes two types of processes: (i) exchange reactions between cells and surrounding milieu (nutrients uptake, products release, see Equations (3)–(5)) and (ii) the MMCC changes | |
(10) | Cybernetic models [73] describing the diauxic growth of bacteria on the mixture of glucose and lactose taken up by transporters e1 and e2 respectively. The cybernetic variables regulate transcription (u) and uptake rates (v), e.g., | |
(11) | Synthetic Chemostat Model [74]. The r-variable integrates the MMCC variation and tunes the kinetic terms earlier assumed to be constants (m, Q, a, and Ks). The ODE dr/dt explains the observed biological inertia. See the Section 4.3 for other details |
4.2. Synthetic Chemostat Model (SCM)
4.3. Strength and Limitations of SCM
5. Genome-Scale Models
5.1. GEMs Cover Only the Part of the Genome
5.2. Flux Balance Analysis (FBA)
5.3. The Dynamic FBA (dFBA)
5.4. The Modification of dFBA:rFBA and iFBA
5.5. ME-Models
- The metabolic network was treated similarly to FBA using constraints and objective functions. The maximizing growth rate was combined with minimizing biosynthetic costs of macromolecules. Substrate concentration was never shown as an independent variable; nutrient deficiency was accounted for by using the substrate availability bounds.
- The mostly unknown kcat values for translational and transcriptional enzymes were set up as a gross average 65 s−1. Considerable improvement in the simulation was achieved by combining the ME model with proteomic data as the model’s input [125]. It allowed an estimation of the individual turnover rates keff for E. coli. The range of keff varied within eight orders of magnitude, and surprisingly, it was not significantly impacted by variations of the cultivation conditions (four different C-sources).
- It can be shown (Appendix B.2.5) that the rate constant keff is dependent on the concentration of the respective intracellular substrate, M, e.g., in the form of the Michaelis–Menten equation: keff = kcatM/(Km + M). For unlimited growth, M Km, and keff = kcat, while at the nutrient limitation, keff < kcat. However, in vitro kinetic data for the isolated E. coli enzymes remain incomplete and most probably not adequately characterize the in vivo metabolic processes (Appendix B.3.5). Instead of using published data, the authors applied a convoluted two-steps binary search procedure involving an auxiliary ‘dummy protein’ computing (first step) followed by the second binary search to find the minimal ratio keff/kcat as a condition making dummy protein formation to be zero.
- The rates of transcription and translation have been assumed to follow the empirical hyperbolic function of SGR, e.g., the translation rate .
- The biomass reaction, Equation (13), was completely removed, because most of the components (amino acids, nucleotides, etc.) were already accounted for in the proteins and RNA biosynthesis reactions. Instead, the reduced pseudo-reaction was used for the remaining cell constituents: glycogen; DNA; lipids; peptidoglycans; and several cofactors (NAD, coenzyme A, etc.). The expressed but not incorporated into the model proteins were called the unmodeled protein biomass. Most likely, these proteins are responsible for stress resistance (U cluster in SCM). This fraction has been also added to the modified biomass reaction to comply with the growth–mass balance but excluded from discussion of their biological role.
- The only sink for macromolecules was assumed to be their dilution caused by growth, so any metabolic rate vi and translation rates of the respective enzymes were set up as follows:
6. Whole-Cell Genome-Scale Simulations (WC Models)
6.1. Mycoplasma genitalium
6.2. Escherichia coli K-12
6.3. Saccharomyces cerevisiae BY4741
6.4. Limitations of the WC Models
6.5. Cell Cycle as a Part of Growth Kinetics
7. Conclusions: Strengths, Weaknesses, and Prospects of Specific GEMs
- (1)
- to account for the effects of environmental factors on cell dynamics, especially related to the nutrient supply (limiting substrate, its concentrations, and regime of delivery).
- (2)
- to simulate the adaptive MMCC changes as conditional gene/protein expressions in response to a changeable environment.
- (3)
- to predict the SGR as a complex function of the MMCC status and environmental conditions rather than a fixed input parameter.
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix A.1. Common Abbreviations
GEM | Genome-scale models |
ODE | Ordinary differential equation |
PDE | Partial differential equation |
MMCC | Macro-Molecular Cell Composition |
FBA | Flux Balance Analysis |
COBRA | COnstraint-Based Reconstruction and Analysis |
LP | linear programming |
NLP | non-linear programming |
dFBA | Dynamic Flux Balance Analysis |
SOA | static optimization approaches for solving dFBA |
DOA | dynamic optimization alternative |
rFBA | Regulated Flux Balance Analysis |
ME-models | GEM simulating metabolism and gene expression |
WC models | whole cell GEM |
VBNC | Viable but nonculturable cells |
NZG | near-zero growth under chronic starvation |
SCM | Synthetic Chemostat Model |
SOD | superoxide dismutase |
TF | transcription factor |
PHB | polyhydroxybutyrate, cellular C-storage |
ROS | reactive oxygen species |
WT | wild type distinct from mutants |
t | time |
V | the volume of cell culture, kept constant in chemostat |
F | the medium feeding rate |
D = F/V | chemostat dilution rate |
x | cell mass concentration |
s | limiting nutrient substrate concentration |
sr | input substrate concentration in chemostat culture |
p | product concentration |
M | concentration of intracellular metabolites |
σ | mass of element (N, P, S, etc.) per g of total cell mass |
σ0 and σm | resp. low and upper limits of σ-variation |
μ = (1/x)·dx/dt | specific growth rate (SGR) |
μm | the maximum SGR, μ→ μm as s→ ∞ |
Y = −dx/ds | cell yield per unit of consumed substrate |
qs = (1/x)·ds/dt | specific substrate uptake rate (SUR) |
m | maintenance term, the catabolic rate qs→m, as μ→0 |
Qs | maximum SUR |
qp = (1/x)·dp/dt | specific product formation rate (SPR) |
Qp | maximum SPR |
Ks | saturation constant, at s = Ks, qs = 0.5 Qs or μ = 0.5 μm |
Kp | product inhibition constant, at p = Kp, qs = 0.5 Qs |
Kr | saturation constant for r-variable |
r | SCM variable [0,1] reporting the status of MMCC |
Appendix A.2. Glossary
Affinity to substrate | Auto-selection, selection sweep |
Substrate binding strength of transmembrane transporters characterized by the parameter Ks. The lower Ks the higher affinity | A process observed in long-term continuous culture, a displacement of the parental population by a spontaneous mutant having higher SGR |
Balanced growth | Steady-state continuous growth |
A proportional increase in the content of all cell constituents (constancy of MMCC) observed in a steady state chemostat or exponential phase of batch culture. | A situation in which all state variables (cell mass, nutrients, and products concentration, MMCC) remain constant as the opposite processes (input–output and growth–washout) match each other |
Quasi-steady state growth | Transient processes |
Only fast variables are stabilized, other not | A movement from one steady state to another |
Catabolic nutrient substrates | Conserved or anabolic nutrient substrates |
Sources of energy; undergo irreversible oxidation to form nonutilizable waste products (H2O and CO2) coupled to ATP generation | Sources of biogenic elements (N, P, K, Fe, etc.) that are consumed reversibly (can leak out and re-consumed) and incorporated into cellular constituents |
Kinetics | Metabolic stoichiometry |
Scientific discipline studying the development of biological or physicochemical processes over time; combines experiments with mechanistic mathematical models. | A quantitative relationship between reactants and products in bioprocesses complying with the mass- and energy conservation conditions |
Maintenance energy | Primary and secondary metabolism |
Some fraction of available energy used for other than growth functions: osmoregulation; motility; and turnover of macromolecules (proteins, nucleic acids, and cell wall) | The primary metabolism produces new cell mass (growth) while the secondary metabolism supports enhanced stress resistance and other functions |
Starvation | Chronic starvation |
Self-degradation of cells (net SGR ≤ 0) caused by a complete absence of one or more essential nutrients | Deep substrate limitation in continuous culture causing a significant decrease of growth rate, SGR μm |
Growth limitation and inhibition | Single or multiple substrate limitation |
Growth condition decreasing SGR (<μm) by low nutrients concentration (substrate limitation) or by toxic compounds (growth inhibition) | Respectively, one or several nutrients concurrently affect growth, including SGR, SUR, yield, and MMCC |
Appendix B. Derivation and Explanation of Biokinetic Equations
Appendix B.1. Structured Models, the Internal and External State Variables
Appendix B.2. The Effects of Substrate Concentration
Appendix B.2.1. Steady-State Concentrations of Metabolic Intermediates
Kinetic Order | Rate vs. Substrate Concentration | Reaction Progress over Time | |||
Zero-order | Rate, mmol per min | Residual substrate, linear scale | Residual substrate, log scale | ||
First-order | |||||
Second order | |||||
Michaelis-Menten equation | |||||
Hill-Langmuir equation | |||||
Substrate concentration, mM | Time, min |
Appendix B.2.2. Kinetic Order of Metabolic Reactions
Appendix B.2.3. In Vivo Concentration of Metabolic Intermediates
Cluster | Pool Size Range | Contribution to Metabolome | Representatives, Values in Brackets Are Concentrations (mM) for the Most Abundant Compounds | |
---|---|---|---|---|
Mass % | Compounds Number | |||
1 | 10–100 mM | 59 | 4 | Glutamate (96), glutathione (17), FDP (15), ATP (10) |
2 | 0.1–10 mM | 40 | 57 | NTP, NDP, NAD+, FAD, 13 AA, glycolysis, TCA, and pentose pathway intermediates |
3 | 0.1–100 μM | <1 | 42 | 5 AA, dNTP, FMN, NADP, and other metabolites |
Appendix B.2.4. Substrate Saturation (SS) of Enzymes Catalyzing Polysubstrate Reactions
Ordered sequential reactions | (A14) | ||
Random sequential reactions | (A14′) | ||
Ping-pong reactions | (A14″) |
Appendix B.2.5. Simplified Kinetic Order of Metabolic Reactions
Appendix B.3. The Effect of Enzymatic Proteins Concentrations
Appendix B.3.1. The Simplest Case of Pure Enzyme
Appendix B.3.2. Conditional Expression of Proteins with Glucose Transporters as Example
Appendix B.3.3. Technical Details of Using the SCM
Appendix B.3.4. Extremely Low Proteins Concentration: Down to One Enzyme Molecule Per Cell
Appendix B.3.5. Extremely High Proteins Concentration: Macromolecular Crowding
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P-Components | U-Components |
---|---|
Related to the primary metabolism, required for intensive growth | Related to the secondary metabolism, improve stress resistance |
Upregulated under optimal growth conditions | Downregulated under optimal conditions |
Ribosomes (rRNA and r-proteins), enzymes involved in translation, and other key cellular processes | Protective pigments, C-storage (glycogen and PHB), antioxidants, high-affinity transporters, enzymes of drug resistance, and antibiotics formation |
Phenomena | Traditional Interpretation | SCM-Based Clarification |
---|---|---|
Lag-phase (τ) in batch culture | Metabolic adjustment (poorly predictable) | Lag-phase is predicted based on r-state of inoculum (r0); the higher r0 the shorter is τ. |
The stationary phase in batch culture limited by the C-source | The balance between true growth and cell death | There is no steady-state, dx/dt < 0, but starving cells differentiate into the active and dormant (VBNC) subpopulations. The cryptic growth is accompanied by upregulation of the U-components improving survival |
The death phase | Death rate exceeds growth | |
Batch growth limited by the anabolic (conserved) substrates | No explanations to the phenomenon of growth without uptake of deficient element from medium | The total amount of deficient element in the culture remains constant but σP progressively declines over time being shared between mother and daughter cells |
Shift-up and shift-down in chemostat culture (rise or drop of D) | The observed overshoots and undershoots are vaguely attributed to the biological inertia. Prediction is not available | The SCM reproduces inertia by allowing cells to reconfigure their MMCC (proteome profile, ribosomes number). Time delay is automatically generated by Equation (A24) since the pace of r change depends on SGR |
VBNC formation | A hypothetical ontogenetic stage in the natural life cycle of some bacteria | Ribosome-free cells produced under chronic starvation because of asymmetric distribution of rare ribosomes between mother and daughter cells |
Cells response to starvation, the impact of maintenance | Cells dye when the energy supply is below the m-level. The maintenance coefficient is constant | Cells survive under deep energy source limitation by adaptive reducing maintenance requirements. Growth becomes slow but never stops |
Inverse relationship between SGR and stress resistance | Reasons unknown, interpreted as a descriptive knowledge | Follows immediately from the P- and U-components definition and conservation condition P + U = 1 |
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Panikov, N.S. Genome-Scale Reconstruction of Microbial Dynamic Phenotype: Successes and Challenges. Microorganisms 2021, 9, 2352. https://doi.org/10.3390/microorganisms9112352
Panikov NS. Genome-Scale Reconstruction of Microbial Dynamic Phenotype: Successes and Challenges. Microorganisms. 2021; 9(11):2352. https://doi.org/10.3390/microorganisms9112352
Chicago/Turabian StylePanikov, Nicolai S. 2021. "Genome-Scale Reconstruction of Microbial Dynamic Phenotype: Successes and Challenges" Microorganisms 9, no. 11: 2352. https://doi.org/10.3390/microorganisms9112352