Fundamental limitations on efficiently forecasting certain epidemic measures in network models.

The ongoing COVID-19 pandemic underscores the importance of developing reliable forecasts that would allow decision makers to devise appropriate response strategies. Despite much recent research on the topic, epidemic forecasting remains poorly understood. Researchers have attributed the difficulty of forecasting contagion dynamics to a multitude of factors, including complex behavioral responses, uncertainty in data, the stochastic nature of the underlying process, and the high sensitivity of the disease parameters to changes in the environment. We offer a rigorous explanation of the difficulty of short-term forecasting on networked populations using ideas from computational complexity. Specifically, we show that several forecasting problems (e.g., the probability that at least a given number of people will get infected at a given time and the probability that the number of infections will reach a peak at a given time) are computationally intractable. For instance, efficient solvability of such problems would imply that the number of satisfying assignments of an arbitrary Boolean formula in conjunctive normal form can be computed efficiently, violating a widely believed hypothesis in computational complexity. This intractability result holds even under the ideal situation, where all the disease parameters are known and are assumed to be insensitive to changes in the environment. From a computational complexity viewpoint, our results, which show that contagion dynamics become unpredictable for both macroscopic and individual properties, bring out some fundamental difficulties of predicting disease parameters. On the positive side, we develop efficient algorithms or approximation algorithms for restricted versions of forecasting problems.

Acoustic Mist Ionization Platform for Direct and Contactless Ultrahigh-Throughput Mass Spectrometry Analysis of Liquid Samples.

Mass spectrometry (MS) has many advantages as a quantitative detection technology for applications within drug discovery. However, current methods of liquid sample introduction to a detector are slow and limit the use of mass spectrometry for kinetic and high-throughput applications. We present the development of an acoustic mist ionization (AMI) interface capable of contactless nanoliter-scale "infusion" of up to three individual samples per second into the mass detector. Installing simple plate handling automation allowed us to reach a throughput of 100 000 samples per day on a single mass spectrometer. We applied AMI-MS to identify inhibitors of a human histone deacetylase from AstraZeneca's collection of 2 million small molecules and measured their half-maximal inhibitory concentration. The speed, sensitivity, simplicity, robustness, and consumption of nanoliter volumes of sample suggest that this technology will have a major impact across many areas of basic and applied research.

Acoustic Injectors for Drop-On-Demand Serial Femtosecond Crystallography.

X-ray free-electron lasers (XFELs) provide very intense X-ray pulses suitable for macromolecular crystallography. Each X-ray pulse typically lasts for tens of femtoseconds and the interval between pulses is many orders of magnitude longer. Here we describe two novel acoustic injection systems that use focused sound waves to eject picoliter to nanoliter crystal-containing droplets out of microplates and into the X-ray pulse from which diffraction data are collected. The on-demand droplet delivery is synchronized to the XFEL pulse scheme, resulting in X-ray pulses intersecting up to 88% of the droplets. We tested several types of samples in a range of crystallization conditions, wherein the overall crystal hit ratio (e.g., fraction of images with observable diffraction patterns) is a function of the microcrystal slurry concentration. We report crystal structures from lysozyme, thermolysin, and stachydrine demethylase (Stc2). Additional samples were screened to demonstrate that these methods can be applied to rare samples.

Moving Liquids with Sound: The Physics of Acoustic Droplet Ejection for Robust Laboratory Automation in Life Sciences.

Liquid handling instruments for life science applications based on droplet formation with focused acoustic energy or acoustic droplet ejection (ADE) were introduced commercially more than a decade ago. While the idea of "moving liquids with sound" was known in the 20th century, the development of precise methods for acoustic dispensing to aliquot life science materials in the laboratory began in earnest in the 21st century with the adaptation of the controlled "drop on demand" acoustic transfer of droplets from high-density microplates for high-throughput screening (HTS) applications. Robust ADE implementations for life science applications achieve excellent accuracy and precision by using acoustics first to sense the liquid characteristics relevant for its transfer, and then to actuate transfer of the liquid with customized application of sound energy to the given well and well fluid in the microplate. This article provides an overview of the physics behind ADE and its central role in both acoustical and rheological aspects of robust implementation of ADE in the life science laboratory and its broad range of ejectable materials.

Acoustic Methods to Monitor Protein Crystallization and to Detect Protein Crystals in Suspensions of Agarose and Lipidic Cubic Phase.

Improvements needed for automated crystallography include crystal detection and crystal harvesting. A technique that uses acoustic droplet ejection to harvest crystals was previously reported. Here a method is described for using the same acoustic instrument to detect protein crystals and to monitor crystal growth. Acoustic pulses were used to monitor the progress of crystallization trials and to detect the presence and location of protein crystals. Crystals were detected, and crystallization was monitored in aqueous solutions and in lipidic cubic phase. Using a commercially available acoustic instrument, crystals measuring ~150 µm or larger were readily detected. Simple laboratory techniques were used to increase the sensitivity to 50 µm by suspending the crystals away from the plastic surface of the crystallization plate. This increased the sensitivity by separating the strong signal generated by the plate bottom that can mask the signal from small protein crystals. It is possible to further boost the acoustic reflection from small crystals by reducing the wavelength of the incident sound pulse, but our current instrumentation does not allow this option. In the future, commercially available sound-emitting transducers with a characteristic frequency near 300 MHz should detect and monitor the growth of individual 3 µm crystals.

Technologies That Enable Accurate and Precise Nano- to Milliliter-Scale Liquid Dispensing of Aqueous Reagents Using Acoustic Droplet Ejection.

Acoustic liquid handling uses high-frequency acoustic signals that are focused on the surface of a fluid to eject droplets with high accuracy and precision for various life science applications. Here we present a multiwell source plate, the Echo Qualified Reservoir (ER), which can acoustically transfer over 2.5 mL of fluid per well in 25-nL increments using an Echo 525 liquid handler. We demonstrate two Labcyte technologies-Dynamic Fluid Analysis (DFA) methods and a high-voltage (HV) grid-that are required to maintain accurate and precise fluid transfers from the ER at this volume scale. DFA methods were employed to dynamically assess the energy requirements of the fluid and adjust the acoustic ejection parameters to maintain a constant velocity droplet. Furthermore, we demonstrate that the HV grid enhances droplet velocity and coalescence at the destination plate. These technologies enabled 5-µL per destination well transfers to a 384-well plate, with accuracy and precision values better than 4%. Last, we used the ER and Echo 525 liquid handler to perform a quantitative polymerase chain reaction (qPCR) assay to demonstrate an application that benefits from the flexibility and larger volume capabilities of the ER.

Acoustic methods for high-throughput protein crystal mounting at next-generation macromolecular crystallographic beamlines.

To take full advantage of advanced data collection techniques and high beam flux at next-generation macromolecular crystallography beamlines, rapid and reliable methods will be needed to mount and align many samples per second. One approach is to use an acoustic ejector to eject crystal-containing droplets onto a solid X-ray transparent surface, which can then be positioned and rotated for data collection. Proof-of-concept experiments were conducted at the National Synchrotron Light Source on thermolysin crystals acoustically ejected onto a polyimide `conveyor belt'. Small wedges of data were collected on each crystal, and a complete dataset was assembled from a well diffracting subset of these crystals. Future developments and implementation will focus on achieving ejection and translation of single droplets at a rate of over one hundred per second.

Acoustically mounted microcrystals yield high-resolution X-ray structures.

We demonstrate a general strategy for determining structures from showers of microcrystals. It uses acoustic droplet ejection to transfer 2.5 nL droplets from the surface of microcrystal slurries, through the air, onto mounting micromesh pins. Individual microcrystals are located by raster-scanning a several-micrometer X-ray beam across the cryocooled micromeshes. X-ray diffraction data sets merged from several micrometer-sized crystals are used to determine 1.8 Ǻ resolution crystal structures.

Acoustic auditing as a real-time, non-invasive quality control process for both source and assay plates.

Acoustic auditing is a non-destructive, non-invasive technique to monitor the composition and volume of fluids in open or sealed microplates and storage tubes. When acoustic energy encounters an interface between two materials, some of the energy passes through the interface, while the remainder is reflected. Acoustic energy applied to the bottom of a multi-well plate or a storage tube is reflected by the fluid contents of the microplate or tube. The amplitude of these reflections or echoes correlates directly with properties of the fluid, including the speed of sound and the concentration of water in the fluid. Once the speed of sound in the solution is known from the analysis of these echoes, it is easy to determine the depth of liquid and, thereby, the volume by monitoring how long it takes for sound energy to reflect off the fluid meniscus. This technique is rapid (>100,000 samples per day), precise (<1% coefficient of variation for hydration measurements, <4% coefficient of variation for volume measurements), and robust. It does not require uncapping tubes or unsealing or unlidding microplates. The sound energy is extremely gentle and has no deleterious impact upon the fluid or compounds dissolved in it.