The function of biomolecules such as proteins depends on their ability to interconvert between a wide range of structures or conformations. Researchers have endeavored for decades to develop computational methods to predict the distribution of conformations, which is far harder to determine experimentally than a static folded structure. We present ConforMix, an inference-time algorithm that enhances sampling of conformational distributions using a combination of classifier guidance, filtering, and free energy estimation. Our approach upgrades diffusion models---whether trained for static structure prediction or conformational generation---to enable more efficient discovery of conformational variability without requiring prior knowledge of major degrees of freedom. ConforMix is orthogonal to improvements in model pretraining and would benefit even a hypothetical model that perfectly reproduced the Boltzmann distribution. Remarkably, when applied to a diffusion model trained for static structure prediction, ConforMix captures structural changes including domain motion, cryptic pocket flexibility, and transporter cycling, while avoiding unphysical states. Case studies of biologically critical proteins demonstrate the scalability, accuracy, and utility of this method.

Generative models, especially diffusion models (DMs), have achieved promising results for generating feature-rich geometries and advancing foundational science problems such as molecule design. Inspired by the recent huge success of Stable (latent) Diffusion models, we propose a novel and principled method for 3D molecule generation named Geometric Latent Diffusion Models (GeoLDM). GeoLDM is the first latent DM model for the molecular geometry domain, composed of autoencoders encoding structures into continuous latent codes and DMs operating in the latent space. Our key innovation is that for modeling the 3D molecular geometries, we capture its critical roto-translational equivariance constraints by building a point-structured latent space with both invariant scalars and equivariant tensors. Extensive experiments demonstrate that GeoLDM can consistently achieve better performance on multiple molecule generation benchmarks, with up to 7% improvement for the valid percentage of large biomolecules. Results also demonstrate GeoLDM's higher capacity for controllable generation thanks to the latent modeling. Code is provided at https://github.com/MinkaiXu/GeoLDM.

Anton 3 is the newest member in a family of supercomputers specially designed for atomic-level simulation of molecules relevant to biology (e.g., DNA, proteins, and drug molecules). Anton 3 achieves order-of-magnitude improvements in time-to-solution over its predecessor, Anton 2 (the current state of the art), and is over 100-fold faster than any other currently available supercomputer, thereby enabling broad new avenues of research on critical questions in biology and drug discovery. This speedup means that a 512-node Anton 3 simulates a million atoms at over 100 microseconds per day. Furthermore, Anton 3 attains this performance while consuming an order of magnitude less energy per simulated microsecond than any other machine. Like its predecessors, Anton 3 was designed from the ground up around a new custom chip to best exploit the capabilities offered by new technologies. We present here the main architectural and algorithmic developments that were necessary to achieve such significant advances.

Despite an explosion in the number of experimentally determined, atomically detailed structures of biomolecules, many critical tasks in structural biology remain data-limited. Whether performance in such tasks can be improved by using large repositories of tangentially related structural data remains an open question. To address this question, we focused on a central problem in biology: predicting how proteins interact with one another—that is, which surfaces of one protein bind to those of another protein. We built a training dataset, the Database of Interacting Protein Structures (DIPS), that contains biases but is two orders of magnitude larger than those used previously. We found that these biases significantly degrade the performance of existing methods on gold-standard data. Hypothesizing that assumptions baked into the hand-crafted features on which these methods depend were the source of the problem, we developed the first end-to-end learning model for protein interface prediction, the Siamese Atomic Surfacelet Network (SASNet). Using only spatial coordinates and identities of atoms, SASNet outperforms state-of-the-art methods trained on gold-standard structural data, even when trained on only 3% of our new dataset. Code and data available at https://github.com/drorlab/DIPS.

Molecular dynamics (MD) simulations have become a powerful and popular method for the study of protein allostery, the widespread phenomenon in which a stimulus at one site on a protein influences the properties of another site on the protein. By capturing the motions of a protein's constituent atoms, simulations can enable the discovery of allosteric binding sites and the determination of the mechanistic basis for allostery. These results can provide a foundation for applications including rational drug design and protein engineering. Here, we provide an introduction to the investigation of protein allostery using molecular dynamics simulation. We emphasize the importance of designing simulations that include appropriate perturbations to the molecular system, such as the addition or removal of ligands or the application of mechanical force. We also demonstrate how the bidirectional nature of allostery-the fact that the two sites involved influence one another in a symmetrical manner-can facilitate such investigations. Through a series of case studies, we illustrate how these concepts have been used to reveal the structural basis for allostery in several proteins and protein complexes of biological and pharmaceutical interest.

Anton 2 is a second-generation special-purpose supercomputer for molecular dynamics simulations that achieves significant gains in performance, programmability, and capacity compared to its predecessor, Anton 1. The architecture of Anton 2 is tailored for fine-grained event-driven operation, which improves performance by increasing the overlap of computation with communication, and also allows a wider range of algorithms to run efficiently, enabling many new software-based optimizations. A 512-node Anton 2 machine, currently in operation, is up to ten times faster than Anton 1 with the same number of nodes, greatly expanding the reach of all-atom bio molecular simulations. Anton 2 is the first platform to achieve simulation rates of multiple microseconds of physical time per day for systems with millions of atoms. Demonstrating strong scaling, the machine simulates a standard 23,558-atom benchmark system at a rate of 85 μs/day -- 180 times faster than any commodity hardware platform or general-purpose supercomputer.

Exploiting parallelism to accelerate a computation typically involves dividing it into many small tasks that can be assigned to different processing elements. An efficient execution schedule for these tasks can be difficult or impossible to determine in advance, however, if there is uncertainty as to when each task's input data will be available. Ideally, each task would run in direct response to the arrival of its input data, thus allowing the computation to proceed in a fine-grained event-driven manner. Realizing this ideal is difficult in practice, and typically requires sacrificing flexibility for performance.

Special-purpose computing hardware can provide significantly better performance and power efficiency for certain applications than general-purpose processors. Even within a single application area, however, a special-purpose machine can be far more valuable if it is capable of efficiently supporting a number of different computational methods that, taken together, expand the machine's functionality and range of applicability. We have previously described a massively parallel special-purpose supercomputer, called Anton, and have shown that it executes traditional molecular dynamics simulations orders of magnitude faster than the previous state of the art. Here, we describe how we extended Anton's software to support a more diverse set of methods, allowing scientists to simulate a broader class of biological phenomena at extremely high speeds. Key elements of our approach, which exploits Anton's tightly integrated hardwired pipelines and programmable cores, are applicable to the hardware and software design of various other specialized or heterogeneous parallel computing platforms.

We describe a high-performance digit-recurrence algorithm for computing exactly rounded reciprocals, square roots, and reciprocal square roots in hardware at a rate of three result bits - one radix-8 digit - per recurrence iteration. To achieve a single-cycle recurrence at a short cycle time, we adapted the digit-by-rounding algorithm, which is normally applied at much higher radices, for efficient operation at radix 8. Using this approach avoids in the recurrence step the lookup table required by SRT - the usual algorithm used for hardware digit recurrences. The increasing access latency of this table, the size of which grows super linearly in the radix, limits high-frequency SRT implementations to radix 4 or lower. We also developed a series of novel optimizations focused on further reducing the critical path through the recurrence. We propose, for example, decreasing data path widths to a point where erroneous results sometimes occur and then correcting these errors off the critical path. We present a specific implementation that computes any of these functions to 31 bits of precision in 13 cycles. Our implementation achieves a cycle time only 11% longer than the best reported SRT design for the same functions, yet delivers results in five fewer cycles. Finally, we show that even at lower radices, a digit-by-rounding design is likely to have a shorter critical path than one using SRT at the same radix.

Digit-by-rounding algorithms enable efficient hardware implementations of algebraic functions such as the reciprocal, square root, or reciprocal square root, but certifying the correctness of such algorithms is a nontrivial endeavor. Traditionally, sufficient conditions for correctness are derived as closed-form formulae relating key design parameters. These sufficient conditions, however, often prove stricter than necessary, excluding correct and efficient designs. In this paper, we present a rigorous, computer-aided method for correctness certification that better approximates the necessary conditions, lowering the risk of rejecting correct designs. We also present two specific applications of this method. First, when applied to a conventional digit-by-rounding reciprocal square root design, our method enabled a fourfold reduction in lookup table size relative to the minimum dictated by a standard sufficient condition. Second, our method certified the correctness of a novel reciprocal square root design that we developed to parallelize two computational steps whose sequential execution lies on the critical path of conventional designs. The difficulty in deriving closed-form sufficient conditions to ascertain this design's correctness provided the original motivation for development of the new certification method.

Most pseudorandom number generators (PRNGs) scale poorly to massively parallel high-performance computation because they are designed as sequentially dependent state transformations. We demonstrate that independent, keyed transformations of counters produce a large alternative class of PRNGs with excellent statistical properties (long period, no discernable structure or correlation). These counter-based PRNGs are ideally suited to modern multi-core CPUs, GPUs, clusters, and special-purpose hardware because they vectorize and parallelize well, and require little or no memory for state. We introduce several counter-based PRNGs: some based on cryptographic standards (AES, Threefish) and some completely new (Philox). All our PRNGs pass rigorous statistical tests (including TestU01's BigCrush) and produce at least 264 unique parallel streams of random numbers, each with period 2128 or more. In addition to essentially unlimited parallel scalability, our PRNGs offer excellent single-chip performance: Philox is faster than the CURAND library on a single NVIDIA GPU.

Strong scaling of scientific applications on parallel architectures is increasingly limited by communication latency. This paper describes the techniques used to mitigate latency in Anton, a massively parallel special-purpose machine that accelerates molecular dynamics (MD) simulations by orders of magnitude compared with the previous state of the art. Achieving this speedup required a combination of hardware mechanisms and software constructs to reduce network latency, sender and receiver overhead, and synchronization costs. Key elements of Anton's approach, in addition to tightly integrated communication hardware, include formulating data transfer in terms of counted remote writes, leveraging fine-grained communication, and establishing fixed, optimized communication patterns. Anton delivers software-to-software inter-node latency significantly lower than any other large-scale parallel machine, and the total critical-path communication time for an Anton MD simulation is less than 4% that of the next fastest MD platform.

Anton is a recently completed special-purpose supercomputer designed for molecular dynamics (MD) simulations of biomolecular systems. The machine's specialized hardware dramatically increases the speed of MD calculations, making possible for the first time the simulation of biological molecules at an atomic level of detail for periods on the order of a millisecond---about two orders of magnitude beyond the previous state of the art. Anton is now running simulations on a timescale at which many critically important, but poorly understood phenomena are known to occur, allowing the observation of aspects of protein dynamics that were previously inaccessible to both computational and experimental study. Here, we report Anton's performance when executing actual MD simulations whose accuracy has been validated against both existing MD software and experimental observations. We also discuss the manner in which novel algorithms have been coordinated with Anton's co-designed, application-specific hardware to achieve these results.

Anton is a recently completed special-purpose supercomputer designed for molecular dynamics (MD) simulations of biomolecular systems. The machine's specialized hardware dramatically increases the speed of MD calculations, making possible for the first time the simulation of biological molecules at an atomic level of detail for periods on the order of a millisecond---about two orders of magnitude beyond the previous state of the art. Anton is now running simulations on a timescale at which many critically important, but poorly understood phenomena are known to occur, allowing the observation of aspects of protein dynamics that were previously inaccessible to both computational and experimental study. Here, we report Anton's performance when executing actual MD simulations whose accuracy has been validated against both existing MD software and experimental observations. We also discuss the manner in which novel algorithms have been coordinated with Anton's co-designed, application-specific hardware to achieve these results.

Anton, a massively parallel special-purpose machine for molecular dynamics simulations, performs a 32x32x32 FFT in 3.7 microseconds and a 64x64x64 FFT in 13.3 microseconds on a configuration with 512 nodes---an order of magnitude faster than all other FFT implementations of which we are aware. Achieving this FFT performance requires a coordinated combination of computation and communication techniques that leverage Anton's underlying hardware mechanisms. Most significantly, Anton's communication subsystem provides over 300 gigabits per second of bandwidth per node, message latency in the hundreds of nanoseconds, and support for word-level writes and single-ended communication. In addition, Anton's general-purpose computation system incorporates primitives that support the efficient parallelization of small 1D FFTs. Although Anton was designed specifically for molecular dynamics simulations, a number of the hardware primitives and software implementation techniques described in this paper may also be applicable to the acceleration of FFTs on general-purpose high-performance machines.

Design verification of complex digital circuits typically starts only after the register-transfer level (RTL) description is complete. This frequently makes verification more difficult than necessary because logic that is intrinsically hard to verify, such as memories, counters and deep first-in, first-out (FIFO) structures, becomes immutable in the design. This paper proposes a new approach that exploits formal verification of conditional coverage points with the goal of early identification of hard-to-verify logic. We use the difficulty of formal verification problems as an early estimator of the verification complexity of a design. While traditional verification methods consider conditional coverage only in the design verification phase, we describe an approach that uses conditional coverage at a much earlier stage---the design phase, during which changes to the RTL code are still possible. The method is illustrated using real examples from the verification of an ASIC designed for a specialized supercomputer.

An effective special-purpose supercomputer for molecular dynamics (MD) requires much more than high-performance acceleration of computational kernels: such accelerators must be balanced with general-purpose computation and communication resources. Achieving this balance was a significant challenge in the design of Anton, a parallel machine that will accelerate MD simulations by several orders of magnitude. Anton executes its most computationally demanding calculations on a highly specialized, enormously parallel, but largely non-programmable high-throughput interaction subsystem (HTIS). Other elements of the simulation have a less uniform algorithmic structure, and may also change in response to future advances in physical models and simulation techniques. Such calculations are executed on Antonpsilas flexible subsystem, which combines programmability with the computational power required to avoid ldquoAmdahlpsilas Lawrdquo bottlenecks arising from the extremely high throughput of the HTIS. Antonpsilas flexible subsystem is a heterogeneous multiprocessor with 12 cores, each organized around a 128-bit data path. This subsystem includes hardware support for synchronization, data transfer and certain types of particle interactions, along with specialized instructions for geometric operations. All aspects of the flexible subsystem were designed specifically to accelerate MD simulations, and although it relies primarily on what may be regarded as ldquogeneral-purposerdquo processors, even this subsystem contains more application-specific features than many recently proposed ldquospecializedrdquo architectures.

Anton is a massively parallel special-purpose supercomputer designed to accelerate molecular dynamics (MD) simulations by several orders of magnitude, making possible for the first time the atomic-level simulation of many biologically important phenomena that take place over microsecond to millisecond time scales. The majority of the computation required for MD simulations involves the calculation of pairwise interactions between particles and/or gridpoints separated by no more than some specified cutoff radius. In Anton, such range-limited interactions are handled by a high-throughput interaction subsystem (HTIS). The HTIS on each of Antonpsilas 512 ASICs includes 32 computational pipelines running at 800 MHz, each producing a result on every cycle that would require approximately 50 arithmetic operations to compute on a general-purpose processor. In order to feed these pipelines and collect their results at a speed sufficient to take advantage of this computational power, Anton uses two novel techniques to limit inter- and intra-chip communication. The first is a recently developed parallelization algorithm for the range-limited N-body problem that offers major advantages in both asymptotic and absolute terms by comparison with traditional methods. The second is an architectural feature that processes pairs of points chosen from two point sets in time proportional to the product of the sizes of those sets, but with input and output volume proportional only to their sum. Together, these features allow Anton to perform pairwise interactions with very high throughput and unusually low latency, enabling MD simulations on time scales inaccessible to other general- and special-purpose parallel systems.

One of the major design verification challenges in the development of Anton, a massively parallel special-purpose machine for molecular dynamics, was to provide evidence that computations spanning more than a quadrillion clock cycles will produce valid scientific results. Our verification methodology addressed this problem by using a hierarchy of RTL, architectural, and numerical simulations. Block- and chip-level RTL models were verified by means of extensive co-simulation with a detailed C++ architectural simulator, ensuring that the RTL models could perform the same molecular dynamics computations as the architectural simulator. The output of the architectural simulator was compared to a parallelized numerical simulator that produces bitwise identical results to Anton, and is fast enough to verify the long-term numerical stability of computations on Anton. These explicit couplings between adjacent levels of the simulation hierarchy created a continuous verification chain from molecular dynamics to individual logic gates.

As parallel algorithms and architectures drive the longest molecular dynamics (MD) simulations towards the millisecond scale, traditional sequential post-simulation data analysis methods are becoming increasingly untenable. Inspired by the programming interface of Google's MapReduce, we have built a new parallel analysis framework called HiMach, which allows users to write trajectory analysis programs sequentially, and carries out the parallel execution of the programs automatically. We introduce (1) a new MD trajectory data analysis model that is amenable to parallel processing, (2) a new interface for defining trajectories to be analyzed, (3) a novel method to make use of an existing sequential analysis tool called VMD, and (4) an extension to the original MapReduce model to support multiple rounds of analysis. Performance evaluations on up to 512 cores demonstrate the efficiency and scalability of the HiMach framework on a Linux cluster.

The ability to perform long, accurate molecular dynamics (MD) simulations involving proteins and other biological macro-molecules could in principle provide answers to some of the most important currently outstanding questions in the fields of biology, chemistry and medicine. A wide range of biologically interesting phenomena, however, occur over time scales on the order of a millisecond--about three orders of magnitude beyond the duration of the longest current MD simulations.

Although molecular dynamics (MD) simulations of biomolecular systems often run for days to months, many events of great scientific interest and pharmaceutical relevance occur on long time scales that remain beyond reach. We present several new algorithms and implementation techniques that significantly accelerate parallel MD simulations compared with current state-of-the-art codes. These include a novel parallel decomposition method and message-passing techniques that reduce communication requirements, as well as novel communication primitives that further reduce communication time. We have also developed numerical techniques that maintain high accuracy while using single precision computation in order to exploit processor-level vector instructions. These methods are embodied in a newly developed MD code called Desmond that achieves unprecedented simulation throughput and parallel scalability on commodity clusters. Our results suggest that Desmond's parallel performance substantially surpasses that of any previously described code. For example, on a standard benchmark, Desmond's performance on a conventional Opteron cluster with 2K processors slightly exceeded the reported performance of IBM's Blue Gene/L machine with 32K processors running its Blue Matter MD code.

We present a new statistically optimal approach to estimate transcript levels and ratios from one or more gene array experiments. The Bayesian Estimation of Array Measurements (BEAM) technique uses a model of measurement noise and prior information to estimate biological expression levels. It provides a principled method to deal with negative expression level measurements, combine multiple measurements, and identify changes in expression level. BEAM is more flexible than existing techniques, because it does not assume a specific functional form for noise and prior models. Rather, it uses a more accurate noise model developed from experimental data, a process we illustrate here using Affymetrix yeast chips.

While computer vision systems often assume simple illumination models, real-world illumination is highly complex, consisting of reflected light from every direction as well as distributed and localized primary light sources. One can capture the illumination incident at a point in the real world from every direction photographically using a spherical illumination map. This paper illustrates, through analysis of photographically-acquired, high dynamic range illumination maps, that real-world illumination shares many of the statistical properties of natural images. In particular, the marginal and joint wavelet coefficient distributions, directional derivative distributions, and harmonic spectra of illumination maps resemble those documented in the natural image statistics literature. However, illumination maps differ from standard photographs in that illumination maps are statistically non-stationary and may contain localized light sources that dominate their power spectra. Our work provides a foundation for statistical models of real-world illumination that may facilitate robust estimation of shape, reflectance, and illumination from images.