Modelling the impact of nucleolin expression level on the activity of F3 peptide-targeted pH-sensitive pegylated liposomes containing doxorubicin.

Strategies targeting nucleolin have enabled a significant improvement in intracellular bioavailability of their encapsulated payloads. In this respect, assessment of the impact of target cell heterogeneity and nucleolin homology across species (structurally and functionally) is of major importance. This work also aimed at mathematically modelling the nucleolin expression levels at the cell membrane, binding and internalization of pH-sensitive pegylated liposomes encapsulating doxorubicin and functionalized with the nucleolin-binding F3 peptide (PEGASEMP), and resulting cytotoxicity against cancer cells from mouse, rat, canine, and human origin. Herein, it was shown that nucleolin expression levels were not a limitation on the continuous internalization of F3 peptide-targeted liposomes, despite the saturable nature of the binding mechanism. Modeling enabled the prediction of nucleolin-mediated total doxorubicin exposure provided by the experimental settings of the assessment of PEGASEMP's impact on cell death. The former increased proportionally with nucleolin-binding sites, a measure relevant for patient stratification. This pattern of variation was observed for the resulting cell death in nonsaturating conditions, depending on the cancer cell sensitivity to doxorubicin. This approach differs from standard determination of cytotoxic concentrations, which normally report values of incubation doses rather than the actual intracellular bioactive drug exposure. Importantly, in the context of development of nucleolin-based targeted drug delivery, the structural nucleolin homology (higher than 84%) and functional similarity across species presented herein, emphasized the potential to use toxicological data and other metrics from lower species to infer the dose for a first-in-human trial.

Entropy of Two-Molecule Correlated Translational-Rotational Motions Using the kth Nearest Neighbor Method.

The entropy associated with rotations, translations, and their coupled motions provides an important contribution to the free energy of many physicochemical processes such as association and solvation. The kth nearest neighbor method, which offers a convenient way to estimate the entropy in high-dimensional spaces, has been previously applied for translational-rotational entropy estimation. Here, we explore the possibility of extending the kth nearest neighbor method to the computation of the entropy of correlated translation-rotations of two molecules, i.e., in the product space of two translation-rotations, both referred to the same independent reference system, which is relevant for all cases in which the correlated translational-rotational motion of more than two molecules is involved. Numerical tests show that, albeit the relatively high dimensionality (12) of the space, the kth nearest neighbor approach provides an accurate estimate for the entropy of two correlated translational-rotational motions, even when computed from a limited number of samples.

Machine Learning Identifies Chemical Characteristics That Promote Enzyme Catalysis.

Despite tremendous progress in understanding and engineering enzymes, knowledge of how enzyme structures and their dynamics induce observed catalytic properties is incomplete, and capabilities to engineer enzymes fall far short of industrial needs. Here, we investigate the structural and dynamic drivers of enzyme catalysis for the rate-limiting step of the industrially important enzyme ketol-acid reductoisomerase (KARI) and identify a region of the conformational space of the bound enzyme-substrate complex that, when populated, leads to large increases in reactivity. We apply computational statistical mechanical methods that implement transition interface sampling to simulate the kinetics of the reaction and combine this with machine learning techniques from artificial intelligence to select features relevant to reactivity and to build predictive models for reactive trajectories. We find that conformational descriptors alone, without the need for dynamic ones, are sufficient to predict reactivity with greater than 85% accuracy (90% AUC). Key descriptors distinguishing reactive from almost-reactive trajectories quantify substrate conformation, substrate bond polarization, and metal coordination geometry and suggest their role in promoting substrate reactivity. Moreover, trajectories constrained to visit a region of the reactant well, separated from the rest by a simple hyperplane defined by ten conformational parameters, show increases in computed reactivity by many orders of magnitude. This study provides evidence for the existence of reactivity promoting regions within the conformational space of the enzyme-substrate complex and develops methodology for identifying and validating these particularly reactive regions of phase space. We suggest that identification of reactivity promoting regions and re-engineering enzymes to preferentially populate them may lead to significant rate enhancements.

Rational design of thiolase substrate specificity for metabolic engineering applications.

Metabolic engineering efforts require enzymes that are both highly active and specific toward the synthesis of a desired output product to be commercially feasible. The 3-hydroxyacid (3HA) pathway, also known as the reverse ß-oxidation or coenzyme-A-dependent chain-elongation pathway, can allow for the synthesis of dozens of useful compounds of various chain lengths and functionalities. However, this pathway suffers from byproduct formation, which lowers the yields of the desired longer chain products, as well as increases downstream separation costs. The thiolase enzyme catalyzes the first reaction in this pathway, and its substrate specificity at each of its two catalytic steps sets the chain length and composition of the chemical scaffold upon which the other downstream enzymes act. However, there have been few attempts reported in the literature to rationally engineer thiolase substrate specificity. In this study, we present a model-guided, rational design study of ordered substrate binding applied to two biosynthetic thiolases, with the goal of increasing the ratio of C6/C4 products formed by the 3HA pathway, 3-hydroxy-hexanoic acid and 3-hydroxybutyric acid. We identify thiolase mutants that result in nearly 10-fold increases in C6/C4 selectivity. Our findings can extend to other pathways that employ the thiolase for chain elongation, as well as expand our knowledge of sequence-structure-function relationship for this important class of enzymes.

Intramolecular Hydrogen Bonding Restricts Gd-Aqua-Ligand Dynamics.

Aqua ligands can undergo rapid internal rotation about the M-O bond. For magnetic resonance contrast agents, this rotation results in diminished relaxivity. Herein, we show that an intramolecular hydrogen bond to the aqua ligand can reduce this internal rotation and increase relaxivity. Molecular modeling was used to design a series of four Gd complexes capable of forming an intramolecular H-bond to the coordinated water ligand, and these complexes had anomalously high relaxivities compared to similar complexes lacking a H-bond acceptor. Molecular dynamics simulations supported the formation of a stable intramolecular H-bond, while alternative hypotheses that could explain the higher relaxivity were systematically ruled out. Intramolecular H-bonding represents a useful strategy to limit internal water rotational motion and increase relaxivity of Gd complexes.

Strong Enrichment of Aromatic Residues in Binding Sites from a Charge-neutralized Hyperthermostable Sso7d Scaffold Library.

The Sso7d protein from the hyperthermophilic archaeon Sulfolobus solfataricus is an attractive binding scaffold because of its small size (7 kDa), high thermal stability (Tm of 98 °C), and absence of cysteines and glycosylation sites. However, as a DNA-binding protein, Sso7d is highly positively charged, introducing a strong specificity constraint for binding epitopes and leading to nonspecific interaction with mammalian cell membranes. In the present study, we report charge-neutralized variants of Sso7d that maintain high thermal stability. Yeast-displayed libraries that were based on this reduced charge Sso7d (rcSso7d) scaffold yielded binders with low nanomolar affinities against mouse serum albumin and several epitopes on human epidermal growth factor receptor. Importantly, starting from a charge-neutralized scaffold facilitated evolutionary adaptation of binders to differentially charged epitopes on mouse serum albumin and human epidermal growth factor receptor, respectively. Interestingly, the distribution of amino acids in the small and rigid binding surface of enriched rcSso7d-based binders is very different from that generally found in more flexible antibody complementarity-determining region loops but resembles the composition of antibody-binding energetic hot spots. Particularly striking was a strong enrichment of the aromatic residues Trp, Tyr, and Phe in rcSso7d-based binders. This suggests that the rigidity and small size of this scaffold determines the unusual amino acid composition of its binding sites, mimicking the energetic core of antibody paratopes. Despite the high frequency of aromatic residues, these rcSso7d-based binders are highly expressed, thermostable, and monomeric, suggesting that the hyperstability of the starting scaffold and the rigidness of the binding surface confer a high tolerance to mutation.

A Fungal-Selective Cytochrome bc1 Inhibitor Impairs Virulence and Prevents the Evolution of Drug Resistance.

To cause disease, a microbial pathogen must adapt to the challenges of its host environment. The leading fungal pathogen Candida albicans colonizes nutrient-poor bodily niches, withstands attack from the immune system, and tolerates treatment with azole antifungals, often evolving resistance. To discover agents that block these adaptive strategies, we screened 300,000 compounds for inhibition of azole tolerance in a drug-resistant Candida isolate. We identified a novel indazole derivative that converts azoles from fungistatic to fungicidal drugs by selective inhibition of mitochondrial cytochrome bc1. We synthesized 103 analogs to optimize potency (half maximal inhibitory concentration 0.4 ?M) and fungal selectivity (28-fold over human). In addition to reducing azole resistance, targeting cytochrome bc1 prevents C. albicans from adapting to the nutrient-deprived macrophage phagosome and greatly curtails its virulence in mice. Inhibiting mitochondrial respiration and restricting metabolic flexibility with this synthetically tractable chemotype provides an attractive therapeutic strategy to limit both fungal virulence and drug resistance.

Exploiting Temporal Collateral Sensitivity in Tumor Clonal Evolution.

The prevailing approach to addressing secondary drug resistance in cancer focuses on treating the resistance mechanisms at relapse. However, the dynamic nature of clonal evolution, along with potential fitness costs and cost compensations, may present exploitable vulnerabilities-a notion that we term "temporal collateral sensitivity." Using a combined pharmacological screen and drug resistance selection approach in a murine model of Ph(+) acute lymphoblastic leukemia, we indeed find that temporal and/or persistent collateral sensitivity to non-classical BCR-ABL1 drugs arises in emergent tumor subpopulations during the evolution of resistance toward initial treatment with BCR-ABL1-targeted inhibitors. We determined the sensitization mechanism via genotypic, phenotypic, signaling, and binding measurements in combination with computational models and demonstrated significant overall survival extension in mice. Additional stochastic mathematical models and small-molecule screens extended our insights, indicating the value of focusing on evolutionary trajectories and pharmacological profiles to identify new strategies to treat dynamic tumor vulnerabilities.

Efficient Bayesian estimates for discrimination among topologically different systems biology models.

A major effort in systems biology is the development of mathematical models that describe complex biological systems at multiple scales and levels of abstraction. Determining the topology-the set of interactions-of a biological system from observations of the system's behavior is an important and difficult problem. Here we present and demonstrate new methodology for efficiently computing the probability distribution over a set of topologies based on consistency with existing measurements. Key features of the new approach include derivation in a Bayesian framework, incorporation of prior probability distributions of topologies and parameters, and use of an analytically integrable linearization based on the Fisher information matrix that is responsible for large gains in efficiency. The new method was demonstrated on a collection of four biological topologies representing a kinase and phosphatase that operate in opposition to each other with either processive or distributive kinetics, giving 8-12 parameters for each topology. The linearization produced an approximate result very rapidly (CPU minutes) that was highly accurate on its own, as compared to a Monte Carlo method guaranteed to converge to the correct answer but at greater cost (CPU weeks). The Monte Carlo method developed and applied here used the linearization method as a starting point and importance sampling to approach the Bayesian answer in acceptable time. Other inexpensive methods to estimate probabilities produced poor approximations for this system, with likelihood estimation showing its well-known bias toward topologies with more parameters and the Akaike and Schwarz Information Criteria showing a strong bias toward topologies with fewer parameters. These results suggest that this linear approximation may be an effective compromise, providing an answer whose accuracy is near the true Bayesian answer, but at a cost near the common heuristics.

Molecular mechanisms and design principles for promiscuous inhibitors to avoid drug resistance: lessons learned from HIV-1 protease inhibition.

Molecular recognition is central to biology and ranges from highly selective to broadly promiscuous. The ability to modulate specificity at will is particularly important for drug development, and discovery of mechanisms contributing to binding specificity is crucial for our basic understanding of biology and for applications in health care. In this study, we used computational molecular design to create a large dataset of diverse small molecules with a range of binding specificities. We then performed structural, energetic, and statistical analysis on the dataset to study molecular mechanisms of achieving specificity goals. The work was done in the context of HIV-1 protease inhibition and the molecular designs targeted a panel of wild-type and drug-resistant mutant HIV-1 protease structures. The analysis focused on mechanisms for promiscuous binding to bind robustly even to resistance mutants. Broadly binding inhibitors tended to be smaller in size, more flexible in chemical structure, and more hydrophobic in nature compared to highly selective ones. Furthermore, structural and energetic analyses illustrated mechanisms by which flexible inhibitors achieved binding; we found ligand conformational adaptation near mutation sites and structural plasticity in targets through torsional flips of asymmetric functional groups to form alternative, compensatory packing interactions or hydrogen bonds. As no inhibitor bound to all variants, we designed small cocktails of inhibitors to do so and discovered that they often jointly covered the target set through mechanistic complementarity. Furthermore, using structural plasticity observed in experiments, and potentially in simulations, is suggested to be a viable means of designing adaptive inhibitors that are promiscuous binders.

Multilevel modeling and value of information in clinical trial decision support.

BACKGROUND: Clinical trials are the main method for evaluating safety and efficacy of medical interventions and have produced many advances in improving human health. The Women's Health Initiative overturned a half-century of harmful practice in hormone therapy, the National Lung Screening Trial identified the first successful lung cancer screening tool and the Prostate, Lung, Colorectal and Ovarian Cancer Screening Trial overturned decades-long assumptions. While some trials identify unforeseen safety issues or harms, many fail to demonstrate efficacy. Large trials require substantial resources; to ensure reliable outcomes, we must seek ways to improve the predictive information used as the basis of trials. RESULTS: Here we demonstrate a modeling framework for linking knowledge of underlying biological mechanism to evaluate the expectation of trial outcomes. Key features include the ability to propagate uncertainty in biological mechanism to uncertainty in trial outcome and mechanisms for identifying knowledge gaps most responsible for unexpected outcomes. The framework was used to model the effect of selenium supplementation for prostate cancer prevention and parallels the Selenium and Vitamin E Cancer Prevention Trial that showed no efficacy despite suggestive data from secondary endpoints in the Nutritional Prevention of Cancer trial and found increased incidence of high-grade prostate cancer in certain subgroups. CONCLUSION: Using machine learning methods, we identified the parameters of the model that are most predictive of trial outcome and found that the top four are directly related to the rates of reactions producing methylselenol and transporting extracellular selenium into the cell as selenide. This modeling process demonstrates how the approach can be used in advance of a large clinical trial to identify the best targets for conducting further research to reduce the uncertainty in the trial outcome.

Efficient Computation of Small-Molecule Configurational Binding Entropy and Free Energy Changes by Ensemble Enumeration.

Here we present a novel, end-point method using the dead-end-elimination and A* algorithms to efficiently and accurately calculate the change in free energy, enthalpy, and configurational entropy of binding for ligand-receptor association reactions. We apply the new approach to the binding of a series of human immunodeficiency virus (HIV-1) protease inhibitors to examine the effect ensemble reranking has on relative accuracy as well as to evaluate the role of the absolute and relative ligand configurational entropy losses upon binding in affinity differences for structurally related inhibitors. Our results suggest that most thermodynamic parameters can be estimated using only a small fraction of the full configurational space, and we see significant improvement in relative accuracy when using an ensemble versus single-conformer approach to ligand ranking. We also find that using approximate metrics based on the single-conformation enthalpy differences between the global minimum energy configuration in the bound as well as unbound states also correlates well with experiment. Using a novel, additive entropy expansion based on conditional mutual information, we also analyze the source of ligand configurational entropy loss upon binding in terms of both uncoupled per degree of freedom losses as well as changes in coupling between inhibitor degrees of freedom. We estimate entropic free energy losses of approximately +24 kcal/mol, 12 kcal/mol of which stems from loss of translational and rotational entropy. Coupling effects contribute only a small fraction to the overall entropy change (1-2 kcal/mol) but suggest differences in how inhibitor dihedral angles couple to each other in the bound versus unbound states. The importance of accounting for flexibility in drug optimization and design is also discussed.

Substrate envelope-designed potent HIV-1 protease inhibitors to avoid drug resistance.

The rapid evolution of HIV under selective drug pressure has led to multidrug resistant (MDR) strains that evade standard therapies. We designed highly potent HIV-1 protease inhibitors (PIs) using the substrate envelope model, which confines inhibitors within the consensus volume of natural substrates, providing inhibitors less susceptible to resistance because a mutation affecting such inhibitors will simultaneously affect viral substrate processing. The designed PIs share a common chemical scaffold but utilize various moieties that optimally fill the substrate envelope, as confirmed by crystal structures. The designed PIs retain robust binding to MDR protease variants and display exceptional antiviral potencies against different clades of HIV as well as a panel of 12 drug-resistant viral strains. The substrate envelope model proves to be a powerful strategy to develop potent and robust inhibitors that avoid drug resistance.

Testing the substrate-envelope hypothesis with designed pairs of compounds.

Acquired resistance to therapeutic agents is a significant barrier to the development of clinically effective treatments for diseases in which evolution occurs on clinical time scales, frequently arising from target mutations. We previously reported a general strategy to design effective inhibitors for rapidly mutating enzyme targets, which we demonstrated for HIV-1 protease inhibition [Altman et al. J. Am. Chem. Soc. 2008, 130, 6099-6113]. Specifically, we developed a computational inverse design procedure with the added constraint that designed inhibitors bind entirely inside the substrate envelope, a consensus volume occupied by natural substrates. The rationale for the substrate-envelope constraint is that it prevents designed inhibitors from making interactions beyond those required by substrates and thus limits the availability of mutations tolerated by substrates but not by designed inhibitors. The strategy resulted in subnanomolar inhibitors that bind robustly across a clinically derived panel of drug-resistant variants. To further test the substrate-envelope hypothesis, here we have designed, synthesized, and assayed derivatives of our original compounds that are larger and extend outside the substrate envelope. Our designs resulted in pairs of compounds that are very similar to one another, but one respects and one violates the substrate envelope. The envelope-respecting inhibitor demonstrates robust binding across a panel of drug-resistant protease variants, whereas the envelope-violating one binds tightly to wild type but loses affinity to at least one variant. This study provides strong support for the substrate-envelope hypothesis as a design strategy for inhibitors that reduce susceptibility to resistance mutations.

Modeling stem cell induction processes.

Technology for converting human cells to pluripotent stem cell using induction processes has the potential to revolutionize regenerative medicine. However, the production of these so called iPS cells is still quite inefficient and may be dominated by stochastic effects. In this work we build mass-action models of the core regulatory elements controlling stem cell induction and maintenance. The models include not only the network of transcription factors NANOG, OCT4, SOX2, but also important epigenetic regulatory features of DNA methylation and histone modification. We show that the network topology reported in the literature is consistent with the observed experimental behavior of bistability and inducibility. Based on simulations of stem cell generation protocols, and in particular focusing on changes in epigenetic cellular states, we show that cooperative and independent reaction mechanisms have experimentally identifiable differences in the dynamics of reprogramming, and we analyze such differences and their biological basis. It had been argued that stochastic and elite models of stem cell generation represent distinct fundamental mechanisms. Work presented here suggests an alternative possibility that they represent differences in the amount of information we have about the distribution of cellular states before and during reprogramming protocols. We show further that unpredictability and variation in reprogramming decreases as the cell progresses along the induction process, and that identifiable groups of cells with elite-seeming behavior can come about by a stochastic process. Finally we show how different mechanisms and kinetic properties impact the prospects of improving the efficiency of iPS cell generation protocols.

Combined model of intrinsic and extrinsic variability for computational network design with application to synthetic biology.

Biological systems are inherently variable, with their dynamics influenced by intrinsic and extrinsic sources. These systems are often only partially characterized, with large uncertainties about specific sources of extrinsic variability and biochemical properties. Moreover, it is not yet well understood how different sources of variability combine and affect biological systems in concert. To successfully design biomedical therapies or synthetic circuits with robust performance, it is crucial to account for uncertainty and effects of variability. Here we introduce an efficient modeling and simulation framework to study systems that are simultaneously subject to multiple sources of variability, and apply it to make design decisions on small genetic networks that play a role of basic design elements of synthetic circuits. Specifically, the framework was used to explore the effect of transcriptional and post-transcriptional autoregulation on fluctuations in protein expression in simple genetic networks. We found that autoregulation could either suppress or increase the output variability, depending on specific noise sources and network parameters. We showed that transcriptional autoregulation was more successful than post-transcriptional in suppressing variability across a wide range of intrinsic and extrinsic magnitudes and sources. We derived the following design principles to guide the design of circuits that best suppress variability: (i) high protein cooperativity and low miRNA cooperativity, (ii) imperfect complementarity between miRNA and mRNA was preferred to perfect complementarity, and (iii) correlated expression of mRNA and miRNA--for example, on the same transcript--was best for suppression of protein variability. Results further showed that correlations in kinetic parameters between cells affected the ability to suppress variability, and that variability in transient states did not necessarily follow the same principles as variability in the steady state. Our model and findings provide a general framework to guide design principles in synthetic biology.

Convergence in parameters and predictions using computational experimental design.

Typically, biological models fitted to experimental data suffer from significant parameter uncertainty, which can lead to inaccurate or uncertain predictions. One school of thought holds that accurate estimation of the true parameters of a biological system is inherently problematic. Recent work, however, suggests that optimal experimental design techniques can select sets of experiments whose members probe complementary aspects of a biochemical network that together can account for its full behaviour. Here, we implemented an experimental design approach for selecting sets of experiments that constrain parameter uncertainty. We demonstrated with a model of the epidermal growth factor-nerve growth factor pathway that, after synthetically performing a handful of optimal experiments, the uncertainty in all 48 parameters converged below 10 per cent. Furthermore, the fitted parameters converged to their true values with a small error consistent with the residual uncertainty. When untested experimental conditions were simulated with the fitted models, the predicted species concentrations converged to their true values with errors that were consistent with the residual uncertainty. This paper suggests that accurate parameter estimation is achievable with complementary experiments specifically designed for the task, and that the resulting parametrized models are capable of accurate predictions.

Charge Optimization Theory for Induced-Fit Ligands.

The design of ligands with high affinity and specificity remains a fundamental challenge in understanding molecular recognition and developing therapeutic interventions. Charge optimization theory addresses this problem by determining ligand charge distributions that produce the most favorable electrostatic contribution to the binding free energy. The theory has been applied to the design of binding specificity as well. However, the formulations described only treat a rigid ligand-one that does not change conformation upon binding. Here, we extend the theory to treat induced-fit ligands for which the unbound ligand conformation may differ from the bound conformation. We develop a thermodynamic pathway analysis for binding contributions relevant to the theory, and we illustrate application of the theory using HIV-1 protease with our previously designed and validated subnanomolar inhibitor. Direct application of rigid charge optimization approaches to nonrigid cases leads to very favorable intramolecular electrostatic interactions that are physically unreasonable, and analysis shows the ligand charge distribution massively stabilizes the preconformed (bound) conformation over the unbound. After analyzing this case, we provide a treatment for the induced-fit ligand charge optimization problem that produces physically realistic results. The key factor is introducing the constraint that the free energy of the unbound ligand conformation be lower or equal to that of the preconformed ligand structure, which corresponds to the notion that the unbound structure is the ground unbound state. Results not only demonstrate the applicability of this methodology to discovering optimized charge distributions in an induced-fit model, but also provide some insights into the energetic consequences of ligand conformational change on binding. Specifically, the results show that, from an electrostatic perspective, induced-fit binding is not an adaptation designed to enhance binding affinity; at best, it can only achieve the same affinity as optimized rigid binding.

Design, synthesis, and biological and structural evaluations of novel HIV-1 protease inhibitors to combat drug resistance.

A series of new HIV-1 protease inhibitors (PIs) were designed using a general strategy that combines computational structure-based design with substrate-envelope constraints. The PIs incorporate various alcohol-derived P2 carbamates with acyclic and cyclic heteroatomic functionalities into the (R)-hydroxyethylamine isostere. Most of the new PIs show potent binding affinities against wild-type HIV-1 protease and three multidrug resistant (MDR) variants. In particular, inhibitors containing the 2,2-dichloroacetamide, pyrrolidinone, imidazolidinone, and oxazolidinone moieties at P2 are the most potent with K(i) values in the picomolar range. Several new PIs exhibit nanomolar antiviral potencies against patient-derived wild-type viruses from HIV-1 clades A, B, and C and two MDR variants. Crystal structure analyses of four potent inhibitors revealed that carbonyl groups of the new P2 moieties promote extensive hydrogen bond interactions with the invariant Asp29 residue of the protease. These structure-activity relationship findings can be utilized to design new PIs with enhanced enzyme inhibitory and antiviral potencies.

Exploring the gap between dynamic and constraint-based models of metabolism.

Systems biology provides new approaches for metabolic engineering through the development of models and methods for simulation and optimization of microbial metabolism. Here we explore the relationship between two modeling frameworks in common use namely, dynamic models with kinetic rate laws and constraint-based flux models. We compare and analyze dynamic and constraint-based formulations of the same model of the central carbon metabolism of Escherichia coli. Our results show that, if unconstrained, the space of steady states described by both formulations is the same. However, the imposition of parameter-range constraints can be mapped into kinetically feasible regions of the solution space for the dynamic formulation that is not readily transferable to the constraint-based formulation. Therefore, with partial kinetic parameter knowledge, dynamic models can be used to generate constraints that reduce the solution space below that identified by constraint-based models, eliminating infeasible solutions and increasing the accuracy of simulation and optimization methods.