Learning heterogeneous reaction kinetics from X-ray videos pixel by pixel.

Reaction rates at spatially heterogeneous, unstable interfaces are notoriously difficult to quantify, yet are essential in engineering many chemical systems, such as batteries1 and electrocatalysts2. Experimental characterizations of such materials by operando microscopy produce rich image datasets3-6, but data-driven methods to learn physics from these images are still lacking because of the complex coupling of reaction kinetics, surface chemistry and phase separation7. Here we show that heterogeneous reaction kinetics can be learned from in situ scanning transmission X-ray microscopy (STXM) images of carbon-coated lithium iron phosphate (LFP) nanoparticles. Combining a large dataset of STXM images with a thermodynamically consistent electrochemical phase-field model, partial differential equation (PDE)-constrained optimization and uncertainty quantification, we extract the free-energy landscape and reaction kinetics and verify their consistency with theoretical models. We also simultaneously learn the spatial heterogeneity of the reaction rate, which closely matches the carbon-coating thickness profiles obtained through Auger electron microscopy (AEM). Across 180,000 image pixels, the mean discrepancy with the learned model is remarkably small (<7%) and comparable with experimental noise. Our results open the possibility of learning nonequilibrium material properties beyond the reach of traditional experimental methods and offer a new non-destructive technique for characterizing and optimizing heterogeneous reactive surfaces.

Closed-loop optimization of fast-charging protocols for batteries with machine learning.

Simultaneously optimizing many design parameters in time-consuming experiments causes bottlenecks in a broad range of scientific and engineering disciplines1,2. One such example is process and control optimization for lithium-ion batteries during materials selection, cell manufacturing and operation. A typical objective is to maximize battery lifetime; however, conducting even a single experiment to evaluate lifetime can take months to years3-5. Furthermore, both large parameter spaces and high sampling variability3,6,7 necessitate a large number of experiments. Hence, the key challenge is to reduce both the number and the duration of the experiments required. Here we develop and demonstrate a machine learning methodology  to efficiently optimize a parameter space specifying the current and voltage profiles of six-step, ten-minute fast-charging protocols for maximizing battery cycle life, which can alleviate range anxiety for electric-vehicle users8,9. We combine two key elements to reduce the optimization cost: an early-prediction model5, which reduces the time per experiment by predicting the final cycle life using data from the first few cycles, and a Bayesian optimization algorithm10,11, which reduces the number of experiments by balancing exploration and exploitation to efficiently probe the parameter space of charging protocols. Using this methodology, we rapidly identify high-cycle-life charging protocols among 224 candidates in 16 days (compared with over 500 days using exhaustive search without early prediction), and subsequently validate the accuracy and efficiency of our optimization approach. Our closed-loop methodology automatically incorporates feedback from past experiments to inform future decisions and can be generalized to other applications in battery design and, more broadly, other scientific domains that involve time-intensive experiments and multi-dimensional design spaces.

Analysis of Poly(ethylene terephthalate) degradation kinetics of evolved IsPETase variants using a surface crowding model.

Poly(ethylene terephthalate) (PET) is a major plastic polymer utilized in the single-use and textile industries. The discovery of PET-degrading enzymes (PETases) has led to an increased interest in the biological recycling of PET in addition to mechanical recycling. IsPETase from Ideonella sakaiensis is a candidate catalyst, but little is understood about its structure-function relationships with regards to PET degradation. To understand the effects of mutations on IsPETase productivity, we develop a directed evolution assay to identify mutations beneficial to PET film degradation at 30 °C. IsPETase also displays enzyme concentration-dependent inhibition effects, and surface crowding has been proposed as a causal phenomenon. Based on total internal reflectance fluorescence microscopy and adsorption experiments, IsPETase is likely experiencing crowded conditions on PET films. Molecular dynamics simulations of IsPETase variants reveal a decrease in active site flexibility in free enzymes and reduced probability of productive active site formation in substrate-bound enzymes under crowding. Hence, we develop a surface crowding model to analyze the biochemical effects of three hit mutations (T116P, S238N, S290P) that enhanced ambient temperature activity and/or thermostability. We find that T116P decreases susceptibility to crowding, resulting in higher PET degradation product accumulation despite no change in intrinsic catalytic rate. In conclusion, we show that a macromolecular crowding-based biochemical model can be used to analyze the effects of mutations on properties of PETases and that crowding behavior is a major property to be targeted for enzyme engineering for improved PET degradation.

Mechanistic modeling of in vitro transcription incorporating effects of magnesium pyrophosphate crystallization.

The in vitro transcription (IVT) reaction used in the production of messenger RNA vaccines and therapies remains poorly quantitatively understood. Mechanistic modeling of IVT could inform reaction design, scale-up, and control. In this work, we develop a mechanistic model of IVT to include nucleation and growth of magnesium pyrophosphate crystals and subsequent agglomeration of crystals and DNA. To help generalize this model to different constructs, a novel quantitative description is included for the rate of transcription as a function of target sequence length, DNA concentration, and T7 RNA polymerase concentration. The model explains previously unexplained trends in IVT data and quantitatively predicts the effect of adding the pyrophosphatase enzyme to the reaction system. The model is validated on additional literature data showing an ability to predict transcription rates as a function of RNA sequence length.

Mechanistic modeling of viral particle production.

Viral systems such as wild-type viruses, viral vectors, and virus-like particles are essential components of modern biotechnology and medicine. Despite their importance, the commercial-scale production of viral systems remains highly inefficient for multiple reasons. Computational strategies are a promising avenue for improving process development, optimization, and control, but require a mathematical description of the system. This article reviews mechanistic modeling strategies for the production of viral particles, both at the cellular and bioreactor scales. In many cases, techniques and models from adjacent fields such as epidemiology and wild-type viral infection kinetics can be adapted to construct a suitable process model. These process models can then be employed for various purposes such as in-silico testing of novel process operating strategies and/or advanced process control.

Water electrolysis: from textbook knowledge to the latest scientific strategies and industrial developments.

Replacing fossil fuels with energy sources and carriers that are sustainable, environmentally benign, and affordable is amongst the most pressing challenges for future socio-economic development. To that goal, hydrogen is presumed to be the most promising energy carrier. Electrocatalytic water splitting, if driven by green electricity, would provide hydrogen with minimal CO2 footprint. The viability of water electrolysis still hinges on the availability of durable earth-abundant electrocatalyst materials and the overall process efficiency. This review spans from the fundamentals of electrocatalytically initiated water splitting to the very latest scientific findings from university and institutional research, also covering specifications and special features of the current industrial processes and those processes currently being tested in large-scale applications. Recently developed strategies are described for the optimisation and discovery of active and durable materials for electrodes that ever-increasingly harness first-principles calculations and machine learning. In addition, a technoeconomic analysis of water electrolysis is included that allows an assessment of the extent to which a large-scale implementation of water splitting can help to combat climate change. This review article is intended to cross-pollinate and strengthen efforts from fundamental understanding to technical implementation and to improve the 'junctions' between the field's physical chemists, materials scientists and engineers, as well as stimulate much-needed exchange among these groups on challenges encountered in the different domains.

Weighing the DNA Content of Adeno-Associated Virus Vectors with Zeptogram Precision Using Nanomechanical Resonators.

Quantifying the composition of viral vectors used in vaccine development and gene therapy is critical for assessing their functionality. Adeno-associated virus (AAV) vectors, which are the most widely used viral vectors for in vivo gene therapy, are typically characterized using PCR, ELISA, and analytical ultracentrifugation which require laborious protocols or hours of turnaround time. Emerging methods such as charge-detection mass spectroscopy, static light scattering, and mass photometry offer turnaround times of minutes for measuring AAV mass using optical or charge properties of AAV. Here, we demonstrate an orthogonal method where suspended nanomechanical resonators (SNR) are used to directly measure both AAV mass and aggregation from a few microliters of sample within minutes. We achieve a precision near 10 zeptograms which corresponds to 1% of the genome holding capacity of the AAV capsid. Our results show the potential of our method for providing real-time quality control of viral vectors during biomanufacturing.

Fictitious phase separation in Li layered oxides driven by electro-autocatalysis.

Layered oxides widely used as lithium-ion battery electrodes are designed to be cycled under conditions that avoid phase transitions. Although the desired single-phase composition ranges are well established near equilibrium, operando diffraction studies on many-particle porous electrodes have suggested phase separation during delithiation. Notably, the separation is not always observed, and never during lithiation. These anomalies have been attributed to irreversible processes during the first delithiation or reversible concentration-dependent diffusion. However, these explanations are not consistent with all experimental observations such as rate and path dependencies and particle-by-particle lithium concentration changes. Here, we show that the apparent phase separation is a dynamical artefact occurring in a many-particle system driven by autocatalytic electrochemical reactions, that is, an interfacial exchange current that increases with the extent of delithiation. We experimentally validate this population-dynamics model using the single-phase material Lix(Ni1/3Mn1/3Co1/3)O2 (0.5 < x < 1) and demonstrate generality with other transition-metal compositions. Operando diffraction and nanoscale oxidation-state mapping unambiguously prove that this fictitious phase separation is a repeatable non-equilibrium effect. We quantitatively confirm the theory with multiple-datastream-driven model extraction. More generally, our study experimentally demonstrates the control of ensemble stability by electro-autocatalysis, highlighting the importance of population dynamics in battery electrodes (even non-phase-separating ones).

Crystallization of a nonreplicating rotavirus vaccine candidate.

Nonreplicating rotavirus vaccine (NRRV) candidates are being developed with the aim of serving the needs of developing countries. A significant proportion of the cost of manufacturing such vaccines is the purification in multiple chromatography steps. Crystallization has the potential to reduce purification costs and provide new product storage modality, improved operational flexibility, and reduced facility footprints. This communication describes a systematic approach for the design of the crystallization of an NRRV candidate, VP8 subunit proteins fused to the P2 epitope of tetanus toxin, using first-principles models and preliminary experimental data. The first-principles models are applied to literature data to obtain feasible crystallization conditions and lower bounds for nucleation and growth rates. Crystallization is then performed in a hanging-drop vapor diffusion system, resulting in the nucleation and growth of NRRV crystals. The crystals obtained in a scaled-up evaporative crystallization contain proteins truncated in the P2 region, but have no significant differences with the original samples in terms of antibody binding and overall conformational stability. These results demonstrate the promise of evaporative crystallization of the NRRV.

Model-based control for column-based continuous viral inactivation of biopharmaceuticals.

Batch low-pH hold is a common processing step to inactivate enveloped viruses for biologics derived from mammalian sources. Increased interest in the transition of biopharmaceutical manufacturing from batch to continuous operation resulted in numerous attempts to adapt batch low-pH hold to continuous processing. However, control challenges with operating this system have not been directly addressed. This article describes a low-cost, column-based continuous viral inactivation system constructed with off-the-shelf components. Model-based, reaction-invariant pH controller is implemented to account for the nonlinearities with Bayesian estimation addressing variations in the operation. The residence time distribution is modeled as a plug flow reactor with axial dispersion in series with a continuously stirred tank reactor, and is periodically estimated during operation through inverse tracer experiments. The estimated residence time distribution quantifies the minimum residence time, which is used to adjust feed flow rates. Controller validation experiments demonstrate that pH and minimum residence time setpoint tracking and disturbance rejection are achieved with fast and accurate response and no instability. Viral inactivation testing demonstrates tight control of logarithmic reduction values over extended operation. This study provides tools for the design and operation of continuous viral inactivation systems in service of increasing productivity, improving product quality, and enhancing patient safety.

Modeling of copy number variability in Pichia pastoris.

Development of continuous biopharmaceutical manufacturing processes is an area of active research. This study considers the long-term transgene copy number stability of Pichia pastoris in continuous bioreactors. We propose a model of copy number loss that quantifies population heterogeneity. An analytical solution is derived and compared with existing experimental data. The model is then used to provide guidance for stable operating timescales. The model is extended to consider copy number dependent growth such as in the case of Zeocin supplementation. The model is also extended to analyze a continuous seeding strategy. This study is a critical step towards understanding the impact of continuous processing on the stability of Pichia pastoris and the resultant products.

Macroscopic modeling of bioreactors for recombinant protein producing Pichia pastoris in defined medium.

The methylotrophic yeast Pichia pastoris is widely used as a microbial host for recombinant protein production. Bioreactor models for P. pastoris can inform understanding of cellular metabolism and can be used to optimize bioreactor operation. This article constructs an extensive macroscopic bioreactor model for P. pastoris which describes substrates, biomass, total protein, other medium components, and off-gas components. Species and elemental balances are introduced to describe uptake and evolution rates for medium components and off-gas components. Additionally, a pH model is constructed using an overall charge balance, acid/base equilibria, and activity coefficients to describe production of recombinant protein and precipitation of medium components. The extent of run-to-run variability is modeled by distributions of a subset of the model parameters, which are estimated using the maximum likelihood method. Model prediction from the extensive macroscopic bioreactor model well describes experimental data with different operating conditions. The probability distributions of the model predictions quantified from the parameter distribution are quantifiably consistent with the run-to-run variability observed in the experimental data. The uncertainty description in this macroscopic bioreactor model identifies the model parameters that have large variability and provides guidance as to which aspects of cellular metabolism should be the focus of additional experimental studies. The model for medium components with pH and precipitation can be used for improving chemically defined medium by minimizing the amount of components needed while meeting cellular requirements.

Learning the Physics of Pattern Formation from Images.

Using a framework of partial differential equation-constrained optimization, we demonstrate that multiple constitutive relations can be extracted simultaneously from a small set of images of pattern formation. Examples include state-dependent properties in phase-field models, such as the diffusivity, kinetic prefactor, free energy, and direct correlation function, given only the general form of the Cahn-Hilliard equation, Allen-Cahn equation, or dynamical density functional theory (phase-field crystal model). Constraints can be added based on physical arguments to accelerate convergence and avoid spurious results. Reconstruction of the free energy functional, which contains nonlinear dependence on the state variable and differential or convolutional operators, opens the possibility of learning nonequilibrium thermodynamics from only a few snapshots of the dynamics.

A method for learning a sparse classifier in the presence of missing data for high-dimensional biological datasets.

MOTIVATION: This work addresses two common issues in building classification models for biological or medical studies: learning a sparse model, where only a subset of a large number of possible predictors is used, and training in the presence of missing data. This work focuses on supervised generative binary classification models, specifically linear discriminant analysis (LDA). The parameters are determined using an expectation maximization algorithm to both address missing data and introduce priors to promote sparsity. The proposed algorithm, expectation-maximization sparse discriminant analysis (EM-SDA), produces a sparse LDA model for datasets with and without missing data. RESULTS: EM-SDA is tested via simulations and case studies. In the simulations, EM-SDA is compared with nearest shrunken centroids (NSCs) and sparse discriminant analysis (SDA) with k-nearest neighbors for imputation for varying mechanism and amount of missing data. In three case studies using published biomedical data, the results are compared with NSC and SDA models with four different types of imputation, all of which are common approaches in the field. EM-SDA is more accurate and sparse than competing methods both with and without missing data in most of the experiments. Furthermore, the EM-SDA results are mostly consistent between the missing and full cases. Biological relevance of the resulting models, as quantified via a literature search, is also presented. AVAILABILITY AND IMPLEMENTATION: A Matlab implementation published under GNU GPL v.3 license is available at http://web.mit.edu/braatzgroup/links.html . CONTACT: braatz@mit.edu. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

A systematic approach for finding the objective function and active constraints for dynamic flux balance analysis.

Dynamic flux balance analysis (DFBA) has become an instrumental modeling tool for describing the dynamic behavior of bioprocesses. DFBA involves the maximization of a biologically meaningful objective subject to kinetic constraints on the rate of consumption/production of metabolites. In this paper, we propose a systematic data-based approach for finding both the biological objective function and a minimum set of active constraints necessary for matching the model predictions to the experimental data. The proposed algorithm accounts for the errors in the experiments and eliminates the need for ad hoc choices of objective function and constraints as done in previous studies. The method is illustrated for two cases: (1) for in silico (simulated) data generated by a mathematical model for Escherichia coli and (2) for actual experimental data collected from the batch fermentation of Bordetella Pertussis (whooping cough).

Opportunities and challenges of real-time release testing in biopharmaceutical manufacturing.

Real-time release testing (RTRT) is defined as "the ability to evaluate and ensure the quality of in-process and/or final drug product based on process data, which typically includes a valid combination of measured material attributes and process controls" (ICH Q8[R2]). This article discusses sensors (process analytical technology, PAT) and control strategies that enable RTRT for the spectrum of critical quality attributes (CQAs) in biopharmaceutical manufacturing. Case studies from the small-molecule and biologic pharmaceutical industry are described to demonstrate how RTRT can be facilitated by integrated manufacturing and multivariable control strategies to ensure the quality of products. RTRT can enable increased assurance of product safety, efficacy, and quality-with improved productivity including faster release and potentially decreased costs-all of which improve the value to patients. To implement a complete RTRT solution, biologic drug manufacturers need to consider the special attributes of their industry, particularly sterility and the measurement of viral and microbial contamination. Continued advances in on-line and in-line sensor technologies are key for the biopharmaceutical manufacturing industry to achieve the potential of RTRT. Related article: http://onlinelibrary.wiley.com/doi/10.1002/bit.26378/full.

Optimal charging profiles for mechanically constrained lithium-ion batteries.

The cost and safety related issues of lithium-ion batteries require intelligent charging profiles that can efficiently utilize the battery. This paper illustrates the application of dynamic optimization in obtaining the optimal current profile for charging a lithium-ion battery using a single-particle model while incorporating intercalation-induced stress generation. In this paper, we focus on the problem of maximizing the charge stored in a given time while restricting the development of stresses inside the particle. Conventional charging profiles for lithium-ion batteries (e.g., constant current followed by constant voltage) were not derived by considering capacity fade mechanisms. These charging profiles are not only inefficient in terms of lifetime usage of the batteries but are also slower since they do not exploit the changing dynamics of the system. Dynamic optimization based approaches have been used to derive optimal charging and discharging profiles with different objective functions. The progress made in understanding the capacity fade mechanisms has paved the way for inclusion of that knowledge in deriving optimal controls. While past efforts included thermal constraints, this paper for the first time presents strategies for optimally charging batteries by guaranteeing minimal mechanical damage to the electrode particles during intercalation. In addition, an executable form of the code has been developed and provided. This code can be used to identify optimal charging profiles for any material and design parameters.

Modeling and analysis of drug-eluting stents with biodegradable PLGA coating: consequences on intravascular drug delivery.

Increasing interests have been raised toward the potential applications of biodegradable poly(lactic-co-glycolic acid) (PLGA) coatings for drug-eluting stents in order to improve the drug delivery and reduce adverse outcomes in stented arteries in patients. This article presents a mathematical model to describe the integrated processes of drug release in a stent with PLGA coating and subsequent drug delivery, distribution, and drug pharmacokinetics in the arterial wall. The integrated model takes into account the PLGA degradation and erosion, anisotropic drug diffusion in the arterial wall, and reversible drug binding. The model simulations first compare the drug delivery from a biodegradable PLGA coating with that from a biodurable coating, including the drug release profiles in the coating, average arterial drug levels, and arterial drug distribution. Using the model for the PLGA stent coating, the simulations further investigate drug internalization, interstitial fluid flow in the arterial wall, and stent embedment for their impact on drug delivery. Simulation results show that these three factors, while imposing little change in the drug release profiles, can greatly change the average drug concentrations in the arterial wall. In particular, each of the factors leads to significant and yet distinguished alterations in the arterial drug distribution that can potentially influence the treatment outcomes. The detailed integrated model provides insights into the design and evaluation of biodegradable PLGA-coated drug-eluting stents for improved intravascular drug delivery.

Analysis of Finite Difference Discretization Schemes for Diffusion in Spheres with Variable Diffusivity.

Two finite difference discretization schemes for approximating the spatial derivatives in the diffusion equation in spherical coordinates with variable diffusivity are presented and analyzed. The numerical solutions obtained by the discretization schemes are compared for five cases of the functional form for the variable diffusivity: (I) constant diffusivity, (II) temporally-dependent diffusivity, (III) spatially-dependent diffusivity, (IV) concentration-dependent diffusivity, and (V) implicitly-defined, temporally- and spatially-dependent diffusivity. Although the schemes have similar agreement to known analytical or semi-analytical solutions in the first four cases, in the fifth case for the variable diffusivity, one scheme produces a stable, physically reasonable solution, while the other diverges. We recommend the adoption of the more accurate and stable of these finite difference discretization schemes to numerically approximate the spatial derivatives of the diffusion equation in spherical coordinates for any functional form of variable diffusivity, especially cases where the diffusivity is a function of position.