Exploring experimental fitness landscapes for chemical synthesis and property optimization.

Optimization is a central goal in the chemical sciences, encompassing diverse objectives including synthesis yield, catalytic activity of a material, and binding efficiency of a molecule to a target protein. Considering the enormous size of chemical space and the expected large numbers of experiments necessary to search through it in any particular application, optimization in chemistry is surprisingly efficient. This good fortune has recently been explained by analysis of the fitness landscape, i.e., the functional relationship between a target objective J (e.g., percent yield, catalytic activity) and a suitable set of variables (e.g., resources such as reactant concentrations and processing conditions). Mathematical analysis has demonstrated that, upon satisfaction of reasonable physical assumptions, the fitness landscape contains no local sub-optimal "traps" that preclude identification of the globally best value of J, in a development called the "OptiChem" theorem. One of the key assumptions behind the theorem is that sufficient resources are available to achieve the posed optimization goal. This work assesses the validity of this assumption underlying the OptiChem theorem through examination of experimental data from the recent literature. In order to explore fitness landscapes in high dimensions where the landscape cannot be visualized, a high dimensional model representation (HDMR) of experimental data is used to construct a model landscape amenable to topology assessment via gradient algorithm search. This method is shown to correctly capture the trap-free topology of a four-dimensional landscape where the objective is to optimize the composition of a solid state material (subject to an elemental mole-fraction constraint) for catalytic activity towards the oxygen evolution reaction. Analysis of a six-dimensional landscape for the objective of maximizing the photoluminescence of rare-earth solid state materials subject to two elemental mole-fraction constraints and a fixed set of processing conditions reveals the presence of one landscape trap, which likely arises from the significantly constrained elemental composition of the materials and/or the fixed processing conditions.

Ultrasensitive regulation of anapleurosis via allosteric activation of PEP carboxylase.

Anapleurosis is the filling of the tricarboxylic acid cycle with four-carbon units. The common substrate for both anapleurosis and glucose phosphorylation in bacteria is the terminal glycolytic metabolite phosphoenolpyruvate (PEP). Here we show that Escherichia coli quickly and almost completely turns off PEP consumption upon glucose removal. The resulting buildup of PEP is used to quickly import glucose if it becomes available again. The switch-like termination of anapleurosis results from depletion of fructose-1,6-bisphosphate (FBP), an ultrasensitive allosteric activator of PEP carboxylase. E. coli expressing an FBP-insensitive point mutant of PEP carboxylase grow normally when glucose is steadily available. However, they fail to build up PEP upon glucose removal, grow poorly when glucose availability oscillates and suffer from futile cycling at the PEP node on gluconeogenic substrates. Thus, bacterial central carbon metabolism is intrinsically programmed with ultrasensitive allosteric regulation to enable rapid adaptation to changing environmental conditions.

Quiescent fibroblasts exhibit high metabolic activity.

Many cells in mammals exist in the state of quiescence, which is characterized by reversible exit from the cell cycle. Quiescent cells are widely reported to exhibit reduced size, nucleotide synthesis, and metabolic activity. Much lower glycolytic rates have been reported in quiescent compared with proliferating lymphocytes. In contrast, we show here that primary human fibroblasts continue to exhibit high metabolic rates when induced into quiescence via contact inhibition. By monitoring isotope labeling through metabolic pathways and quantitatively identifying fluxes from the data, we show that contact-inhibited fibroblasts utilize glucose in all branches of central carbon metabolism at rates similar to those of proliferating cells, with greater overflow flux from the pentose phosphate pathway back to glycolysis. Inhibition of the pentose phosphate pathway resulted in apoptosis preferentially in quiescent fibroblasts. By feeding the cells labeled glutamine, we also detected a "backwards" flux in the tricarboxylic acid cycle from α-ketoglutarate to citrate that was enhanced in contact-inhibited fibroblasts; this flux likely contributes to shuttling of NADPH from the mitochondrion to cytosol for redox defense or fatty acid synthesis. The high metabolic activity of the fibroblasts was directed in part toward breakdown and resynthesis of protein and lipid, and in part toward excretion of extracellular matrix proteins. Thus, reduced metabolic activity is not a hallmark of the quiescent state. Quiescent fibroblasts, relieved of the biosynthetic requirements associated with generating progeny, direct their metabolic activity to preservation of self integrity and alternative functions beneficial to the organism as a whole.

Inhibition of glucose transport synergizes with chemical or genetic disruption of mitochondrial metabolism and suppresses TCA cycle-deficient tumors.

Efforts to target glucose metabolism in cancer have been limited by the poor potency and specificity of existing anti-glycolytic agents and a poor understanding of the glucose dependence of cancer subtypes in vivo. Here, we present an extensively characterized series of potent, orally bioavailable inhibitors of the class I glucose transporters (GLUTs). The representative compound KL-11743 specifically blocks glucose metabolism, triggering an acute collapse in NADH pools and a striking accumulation of aspartate, indicating a dramatic shift toward oxidative phosphorylation in the mitochondria. Disrupting mitochondrial metabolism via chemical inhibition of electron transport, deletion of the malate-aspartate shuttle component GOT1, or endogenous mutations in tricarboxylic acid cycle enzymes, causes synthetic lethality with KL-11743. Patient-derived xenograft models of succinate dehydrogenase A (SDHA)-deficient cancers are specifically sensitive to KL-11743, providing direct evidence that TCA cycle-mutant tumors are vulnerable to GLUT inhibitors in vivo.

Metabolome remodeling during the acidogenic-solventogenic transition in Clostridium acetobutylicum.

The fermentation carried out by the biofuel producer Clostridium acetobutylicum is characterized by two distinct phases. Acidogenesis occurs during exponential growth and involves the rapid production of acids (acetate and butyrate). Solventogenesis initiates as cell growth slows down and involves the production of solvents (butanol, acetone, and ethanol). Using metabolomics, isotope tracers, and quantitative flux modeling, we have mapped the metabolic changes associated with the acidogenic-solventogenic transition. We observed a remarkably ordered series of metabolite concentration changes, involving almost all of the 114 measured metabolites, as the fermentation progresses from acidogenesis to solventogenesis. The intracellular levels of highly abundant amino acids and upper glycolytic intermediates decrease sharply during this transition. NAD(P)H and nucleotide triphosphates levels also decrease during solventogenesis, while low-energy nucleotides accumulate. These changes in metabolite concentrations are accompanied by large changes in intracellular metabolic fluxes. During solventogenesis, carbon flux into amino acids, as well as flux from pyruvate (the last metabolite in glycolysis) into oxaloacetate, decreases by more than 10-fold. This redirects carbon into acetyl coenzyme A, which cascades into solventogenesis. In addition, the electron-consuming reductive tricarboxylic acid (TCA) cycle is shutdown, while the electron-producing oxidative (clockwise) right side of the TCA cycle remains active. Thus, the solventogenic transition involves global remodeling of metabolism to redirect resources (carbon and reducing power) from biomass production into solvent production.

Why is chemical synthesis and property optimization easier than expected?

Identifying optimal conditions for chemical and material synthesis as well as optimizing the properties of the products is often much easier than simple reasoning would predict. The potential search space is infinite in principle and enormous in practice, yet optimal molecules, materials, and synthesis conditions for many objectives can often be found by performing a reasonable number of distinct experiments. Considering the goal of chemical synthesis or property identification as optimal control problems provides insight into this good fortune. Both of these goals may be described by a fitness function J that depends on a suitable set of variables (e.g., reactant concentrations, components of a material, processing conditions, etc.). The relationship between J and the variables specifies the fitness landscape for the target objective. Upon making simple physical assumptions, this work demonstrates that the fitness landscape for chemical optimization contains no local sub-optimal maxima that may hinder attainment of the absolute best value of J. This feature provides a basis to explain the many reported efficient optimizations of synthesis conditions and molecular or material properties. We refer to this development as OptiChem theory. The predicted characteristics of chemical fitness landscapes are assessed through a broad examination of the recent literature, which shows ample evidence of trap-free landscapes for many objectives. The fundamental and practical implications of OptiChem theory for chemistry are discussed.

Systems-level metabolic flux profiling elucidates a complete, bifurcated tricarboxylic acid cycle in Clostridium acetobutylicum.

Obligatory anaerobic bacteria are major contributors to the overall metabolism of soil and the human gut. The metabolic pathways of these bacteria remain, however, poorly understood. Using isotope tracers, mass spectrometry, and quantitative flux modeling, here we directly map the metabolic pathways of Clostridium acetobutylicum, a soil bacterium whose major fermentation products include the biofuels butanol and hydrogen. While genome annotation suggests the absence of most tricarboxylic acid (TCA) cycle enzymes, our results demonstrate that this bacterium has a complete, albeit bifurcated, TCA cycle; oxaloacetate flows to succinate both through citrate/alpha-ketoglutarate and via malate/fumarate. Our investigations also yielded insights into the pathways utilized for glucose catabolism and amino acid biosynthesis and revealed that the organism's one-carbon metabolism is distinct from that of model microbes, involving reversible pyruvate decarboxylation and the use of pyruvate as the one-carbon donor for biosynthetic reactions. This study represents the first in vivo characterization of the TCA cycle and central metabolism of C. acetobutylicum. Our results establish a role for the full TCA cycle in an obligatory anaerobic organism and demonstrate the importance of complementing genome annotation with isotope tracer studies for determining the metabolic pathways of diverse microbes.

Metabolomics-driven quantitative analysis of ammonia assimilation in E. coli.

Despite extensive study of individual enzymes and their organization into pathways, the means by which enzyme networks control metabolite concentrations and fluxes in cells remains incompletely understood. Here, we examine the integrated regulation of central nitrogen metabolism in Escherichia coli through metabolomics and ordinary-differential-equation-based modeling. Metabolome changes triggered by modulating extracellular ammonium centered around two key intermediates in nitrogen assimilation, alpha-ketoglutarate and glutamine. Many other compounds retained concentration homeostasis, indicating isolation of concentration changes within a subset of the metabolome closely linked to the nutrient perturbation. In contrast to the view that saturated enzymes are insensitive to substrate concentration, competition for the active sites of saturated enzymes was found to be a key determinant of enzyme fluxes. Combined with covalent modification reactions controlling glutamine synthetase activity, such active-site competition was sufficient to explain and predict the complex dynamic response patterns of central nitrogen metabolites.

Discovery and Optimization of Glucose Uptake Inhibitors.

Aerobic glycolysis, originally identified by Warburg as a hallmark of cancer, has recently been implicated in immune cell activation and growth. Glucose, the starting material for glycolysis, is transported through the cellular membrane by a family of glucose transporters (GLUTs). Therefore, targeting glucose transporters to regulate aerobic glycolysis is an attractive approach to identify potential therapeutic agents for cancers and autoimmune diseases. Herein, we describe the discovery and optimization of a class of potent, orally bioavailable inhibitors of glucose transporters, targeting both GLUT1 and GLUT3.

Biclustering via optimal re-ordering of data matrices in systems biology: rigorous methods and comparative studies.

BACKGROUND: The analysis of large-scale data sets via clustering techniques is utilized in a number of applications. Biclustering in particular has emerged as an important problem in the analysis of gene expression data since genes may only jointly respond over a subset of conditions. Biclustering algorithms also have important applications in sample classification where, for instance, tissue samples can be classified as cancerous or normal. Many of the methods for biclustering, and clustering algorithms in general, utilize simplified models or heuristic strategies for identifying the "best" grouping of elements according to some metric and cluster definition and thus result in suboptimal clusters. RESULTS: In this article, we present a rigorous approach to biclustering, OREO, which is based on the Optimal RE-Ordering of the rows and columns of a data matrix so as to globally minimize the dissimilarity metric. The physical permutations of the rows and columns of the data matrix can be modeled as either a network flow problem or a traveling salesman problem. Cluster boundaries in one dimension are used to partition and re-order the other dimensions of the corresponding submatrices to generate biclusters. The performance of OREO is tested on (a) metabolite concentration data, (b) an image reconstruction matrix, (c) synthetic data with implanted biclusters, and gene expression data for (d) colon cancer data, (e) breast cancer data, as well as (f) yeast segregant data to validate the ability of the proposed method and compare it to existing biclustering and clustering methods. CONCLUSION: We demonstrate that this rigorous global optimization method for biclustering produces clusters with more insightful groupings of similar entities, such as genes or metabolites sharing common functions, than other clustering and biclustering algorithms and can reconstruct underlying fundamental patterns in the data for several distinct sets of data matrices arising in important biological applications.

Dissecting enzyme regulation by multiple allosteric effectors: nucleotide regulation of aspartate transcarbamoylase.

The enzyme aspartate transcarbamoylase (ATCase, EC 2.1.3.2 of Escherichia coli), which catalyzes the committed step of pyrimidine biosynthesis, is allosterically regulated by all four ribonucleoside triphosphates (NTPs) in a nonlinear manner. Here, we dissect this regulation using the recently developed approach of random sampling-high-dimensional model representation (RS-HDMR). ATCase activity was measured in vitro at 300 random NTP concentration combinations, each involving (consistent with in vivo conditions) all four NTPs being present. These data were then used to derive a RS-HDMR model of ATCase activity over the full four-dimensional NTP space. The model accounted for 90% of the variance in the experimental data. Its main elements were positive ATCase regulation by ATP and negative by CTP, with the negative effects of CTP dominating the positive ones of ATP when both regulators were abundant (i.e., a negative cooperative effect of ATP x CTP). Strong sensitivity to both ATP and CTP concentrations occurred in their physiological concentration ranges. UTP had only a slight effect, and GTP had almost none. These findings support a predominant role of CTP and ATP in ATCase regulation. The general approach provides a new paradigm for dissecting multifactorial regulation of biological molecules and processes.

Diverse metabolic model parameters generate similar methionine cycle dynamics.

Parameter estimation constitutes a major challenge in dynamic modeling of metabolic networks. Here we examine, via computational simulations, the influence of system nonlinearity and the nature of available data on the distribution and predictive capability of identified model parameters. Simulated methionine cycle metabolite concentration data (both with and without corresponding flux data) was inverted to identify model parameters consistent with it. Thousands of diverse parameter families were found to be consistent with the data to within moderate error, with most of the parameter values spanning over 1000-fold ranges irrespective of whether flux data was included. Due to strong correlations within the extracted parameter families, model predictions were generally reliable despite the broad ranges found for individual parameters. Inclusion of flux data, by strengthening these correlations, resulted in substantially more reliable flux predictions. These findings suggest that, despite the difficulty of extracting biochemically accurate model parameters from system level data, such data may nevertheless prove adequate for driving the development of predictive dynamic metabolic models.

Descriptor-free molecular discovery in large libraries by adaptive substituent reordering.

Molecular discovery often involves identification of the best functional groups (substituents) on a scaffold. When multiple substitution sites are present, the number of possible substituent combinations can be very large. This article introduces a strategy for efficiently optimizing the substituent combinations by iterative rounds of compound sampling, substituent reordering to produce the most regular property landscape, and property estimation over the landscape. Application of this approach to a large pharmaceutical compound library demonstrates its ability to find active compounds with a threefold reduction in synthetic and assaying effort, even without knowing the molecular identity of any compound.

Toward closed-loop optimization of deep brain stimulation for Parkinson's disease: concepts and lessons from a computational model.

Deep brain stimulation (DBS) of the subthalamic nucleus with periodic, high-frequency pulse trains is an increasingly standard therapy for advanced Parkinson's disease. Here, we propose that a closed-loop global optimization algorithm may identify novel DBS waveforms that could be more effective than their high-frequency counterparts. We use results from a computational model of the Parkinsonian basal ganglia to illustrate general issues relevant to eventual clinical or experimental tests of such an algorithm. Specifically, while the relationship between DBS characteristics and performance is highly complex, global search methods appear able to identify novel and effective waveforms with convergence rates that are acceptably fast to merit further investigation in laboratory or clinical settings.

Maximal use of minimal libraries through the adaptive substituent reordering algorithm.

This paper describes an adaptive algorithm for interpolation over a library of molecules subjected to synthesis and property assaying. Starting with a coarse sampling of the library compounds, the algorithm finds the optimal substituent orderings on all of the functionalized scaffold sites to allow for accurate property interpolation over all remaining compounds in the full library space. A previous paper introduced the concept of substituent reordering and a smoothness-based criterion to search for optimal orderings (Shenvi, N.; Geremia, J. M.; Rabitz, H. J. Phys. Chem. A 2003, 107, 2066). Here, we propose a data-driven root-mean-squared (RMS) criteria and a combined RMS/smoothness criteria as alternative methods for the discovery of optimal substituent orderings. Error propagation from the property measurements of the sampled compounds is determined to provide confidence intervals on the interpolated molecular property values, and a substituent rescaling technique is introduced to manage poorly designed/sampled libraries. Finally, various factors are explored that can influence the applicability and interpolation quality of the algorithm. An adaptive methodology is proposed to iteratively and efficiently use laboratory experiments to optimize these algorithmic factors, so that the accuracy of property predictions is maximized. The enhanced algorithm is tested on copolymer and transition metal complex libraries, and the results demonstrate the capability of the algorithm to accurately interpolate various properties of both molecular libraries.

Closed-loop learning control of bio-networks.

A general goal of systems biology is to acquire a detailed quantitative understanding of the life-sustaining interactions between genes and proteins. There arises an interesting question of whether these network dynamics can be controlled externally. In the open-loop approach to experimental biology, a control design would be chosen based on a desired target response and modeling with all the available knowledge about the system. If the system is not completely understood or disturbances occur, then unexpected deviations from the desired response can arise. A means to circumvent this difficulty is to optimize the controls in a closed-loop operation by modifying successive input controls based on the performance of previous controls. This paper presents a simulation of closed-loop learning control applied to biological systems in order to generate a desired response. The most powerful advantage of this technique is that the controls are deduced based on experimental results and the process can operate without a model for the underlying biochemical network. This feature eliminates the problem of faulty predictions as well as the need for a detailed understanding of the underlying molecular pathways, suggesting that biological systems can be controlled even before the post-systems biology era.

Identifying biological network structure, predicting network behavior, and classifying network state with High Dimensional Model Representation (HDMR).

This work presents an adapted Random Sampling - High Dimensional Model Representation (RS-HDMR) algorithm for synergistically addressing three key problems in network biology: (1) identifying the structure of biological networks from multivariate data, (2) predicting network response under previously unsampled conditions, and (3) inferring experimental perturbations based on the observed network state. RS-HDMR is a multivariate regression method that decomposes network interactions into a hierarchy of non-linear component functions. Sensitivity analysis based on these functions provides a clear physical and statistical interpretation of the underlying network structure. The advantages of RS-HDMR include efficient extraction of nonlinear and cooperative network relationships without resorting to discretization, prediction of network behavior without mechanistic modeling, robustness to data noise, and favorable scalability of the sampling requirement with respect to network size. As a proof-of-principle study, RS-HDMR was applied to experimental data measuring the single-cell response of a protein-protein signaling network to various experimental perturbations. A comparison to network structure identified in the literature and through other inference methods, including Bayesian and mutual-information based algorithms, suggests that RS-HDMR can successfully reveal a network structure with a low false positive rate while still capturing non-linear and cooperative interactions. RS-HDMR identified several higher-order network interactions that correspond to known feedback regulations among multiple network species and that were unidentified by other network inference methods. Furthermore, RS-HDMR has a better ability to predict network response under unsampled conditions in this application than the best statistical inference algorithm presented in the recent DREAM3 signaling-prediction competition. RS-HDMR can discern and predict differences in network state that arise from sources ranging from intrinsic cell-cell variability to altered experimental conditions, such as when drug perturbations are introduced. This ability ultimately allows RS-HDMR to accurately classify the experimental conditions of a given sample based on its observed network state.

Systems-level metabolic flux profiling identifies fatty acid synthesis as a target for antiviral therapy.

Viruses rely on the metabolic network of their cellular hosts to provide energy and building blocks for viral replication. We developed a flux measurement approach based on liquid chromatography-tandem mass spectrometry to quantify changes in metabolic activity induced by human cytomegalovirus (HCMV). This approach reliably elucidated fluxes in cultured mammalian cells by monitoring metabolome labeling kinetics after feeding cells (13)C-labeled forms of glucose and glutamine. Infection with HCMV markedly upregulated flux through much of the central carbon metabolism, including glycolysis. Particularly notable increases occurred in flux through the tricarboxylic acid cycle and its efflux to the fatty acid biosynthesis pathway. Pharmacological inhibition of fatty acid biosynthesis suppressed the replication of both HCMV and influenza A, another enveloped virus. These results show that fatty acid synthesis is essential for the replication of two divergent enveloped viruses and that systems-level metabolic flux profiling can identify metabolic targets for antiviral therapy.

Optimal deep brain stimulation of the subthalamic nucleus--a computational study.

Deep brain stimulation (DBS) of the subthalamic nucleus, typically with periodic, high frequency pulse trains, has proven to be an effective treatment for the motor symptoms of Parkinson's disease (PD). Here, we use a biophysically-based model of spiking cells in the basal ganglia (Terman et al., Journal of Neuroscience, 22, 2963-2976, 2002; Rubin and Terman, Journal of Computational Neuroscience, 16, 211-235, 2004) to provide computational evidence that alternative temporal patterns of DBS inputs might be equally effective as the standard high-frequency waveforms, but require lower amplitudes. Within this model, DBS performance is assessed in two ways. First, we determine the extent to which DBS causes Gpi (globus pallidus pars interna) synaptic outputs, which are burstlike and synchronized in the unstimulated Parkinsonian state, to cease their pathological modulation of simulated thalamocortical cells. Second, we evaluate how DBS affects the GPi cells' auto- and cross-correlograms. In both cases, a nonlinear closed-loop learning algorithm identifies effective DBS inputs that are optimized to have minimal strength. The network dynamics that result differ from the regular, entrained firing which some previous studies have associated with conventional high-frequency DBS. This type of optimized solution is also found with heterogeneity in both the intrinsic network dynamics and the strength of DBS inputs received at various cells. Such alternative DBS inputs could potentially be identified, guided by the model-free learning algorithm, in experimental or eventual clinical settings.

A closed-loop identification protocol for nonlinear dynamical systems.

A previous work introduced an optimal identification (OI) technique for reliably extracting model parameters of biochemical reaction systems from tailored laboratory experiments. The notion of optimality enters through seeking an external control in the laboratory producing data that leads to minimum uncertainties in the identified parameter distributions. A number of algorithmic and operational improvements are introduced in this paper to OI, aiming to build a more practical and efficient closed-loop identification protocol/procedure (CLIP) for nonlinear dynamical systems. The improvements in CLIP include (a) inversion cost function modification to preferably search for the upper and lower boundaries of the parameter distributions consistent with the observed data, (b) dynamic search range updating of the unknown parameters to better exploit the information from the prior iterative experiments, (c) replacing the control genetic algorithm by the simplex method to enable better balance between operational cost and inversion quality, and (d) utilizing virtual sensitivity optimization techniques to further reduce the laboratory costs. The workings of CLIP utilizing these new algorithms are illustrated in indentifying a simulated tRNA proofreading model, and the results demonstrate enhanced performance of CLIP in terms of algorithmic reliability and efficiency.