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Fueled by breakthrough technology developments, the biological, biomedical, and behavioral sciences are now collecting more data than ever before. There is a critical need for time- and cost-efficient strategies to analyze and interpret these data to advance human health. The recent rise of machine learning as a powerful technique to integrate multimodality, multifidelity data, and reveal correlations between intertwined phenomena presents a special opportunity in this regard. However, machine learning alone ignores the fundamental laws of physics and can result in ill-posed problems or non-physical solutions. Multiscale modeling is a successful strategy to integrate multiscale, multiphysics data and uncover mechanisms that explain the emergence of function. However, multiscale modeling alone often fails to efficiently combine large datasets from different sources and different levels of resolution. Here we demonstrate that machine learning and multiscale modeling can naturally complement each other to create robust predictive models that integrate the underlying physics to manage ill-posed problems and explore massive design spaces. We review the current literature, highlight applications and opportunities, address open questions, and discuss potential challenges and limitations in four overarching topical areas: ordinary differential equations, partial differential equations, data-driven approaches, and theory-driven approaches. Towards these goals, we leverage expertise in applied mathematics, computer science, computational biology, biophysics, biomechanics, engineering mechanics, experimentation, and medicine. Our multidisciplinary perspective suggests that integrating machine learning and multiscale modeling can provide new insights into disease mechanisms, help identify new targets and treatment strategies, and inform decision making for the benefit of human health.

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The question of how enzymes greatly enhance the rate of reactions has been discussed for years but remains a vigorously debated issue. Rapid progress has been made on the mechanism of individual enzymes by a combination of kinetic, chemical, and structural approaches. The push and pull of electrons and the resulting bond changes are well understood for many enzymes. However, the larger question of general features that enzymes use to produce rate accelerations of 10 8 -10 15 has remained a contentious issue. We believe that such rate accelerations can be readily explained by reasonable physical principles (1). Though much of this understanding stems from research done in the 1970s and 1980s, these insights are often underappreciated or even completely neglected when examining enzymic rate accelerations. Perhaps this is because of our intense focus on enzymes themselves and relative neglect of the reference solution reactions to which they are compared, consequentially, resulting in a mechanistic tunnel vision. Transition State Theory and Thermodynamic CyclesDrawing on an earlier analysis (1) and work cited herein, we wish to examine a popular model for comparing the rates of catalyzed and uncatalyzed reactions, that is, the thermodynamic cycle as set up in Scheme 1, which compares a transformation of a reactant (S) in solution through its transition state (S ‡ ) with the same reaction catalyzed by an enzyme (E) from its ground state (ES) to its transition state (ES ‡ ).The solution reaction is characterized by the reaction rate k non , and the enzyme-catalyzed reaction is characterized by the Michaelis-Menten constants k cat and K m . An apparent equilibrium constant for the dissociation of the transition state of the reactant from the enzyme can be obtained using transition state theory (2),Ϫ1 . The value of K TS is generally significantly smaller than the dissociation constant for the substrate from the enzyme, K S , leading to a large and favorable free energy of binding for the enzyme and S ‡ (3-5). As a result of the small value of K TS , analogs of the reactant in its transition state geometry (transition state analog (TSA) 1 )have been sought as enzyme inhibitors. In addition, TSAs and the scenario of Scheme 1 have been used as the foundation for the design of catalysts from antibodies, in which immunization against a TSA is used to elicit the formation of antibodies that strongly bind the TSA. The thermodynamic cycle set up in Scheme 1 is useful as a model for understanding many aspects of rate accelerations. However, as in all models of complex phenomena, its limitations must also be kept in mind. Can We Do Better?Without conjecture, all we can say from the analysis of the thermodynamic cycle is that, if the virtual binding of the reactant in its transition state geometry were physically able to occur, the process would be very favorable in terms of free energy. The difference in the apparent free energy of binding of S ‡ to the enzyme relative to S may result from two scenarios. In the first scenario, ...

We have analysed enzyme catalysis through a re-examination of the reaction coordinate. The ground state of the enzyme-substrate complex is shown to be related to the transition state through the mean force acting along the reaction path; as such, catalytic strategies cannot be resolved into ground state destabilization versus transition state stabilization. We compare the role of active-site residues in the chemical step with the analogous role played by solvent molecules in the environment of the noncatalysed reaction. We conclude that enzyme catalysis is significantly enhanced by the ability of the enzyme to preorganize the reaction environment. This complementation of the enzyme to the substrate's transition state geometry acts to eliminate the slow components of solvent reorganization required for reactions in aqueous solution. Dramatically strong binding of the transition state geometry is not required.

Microorganisms in nature form diverse communities that dynamically change in structure and function in response to environmental variations. As a complex adaptive system, microbial communities show higher-order properties that are not present in individual microbes, but arise from their interactions. Predictive mathematical models not only help to understand the underlying principles of the dynamics and emergent properties of natural and synthetic microbial communities, but also provide key knowledge required for engineering them. In this article, we provide an overview of mathematical tools that include not only current mainstream approaches, but also less traditional approaches that, in our opinion, can be potentially useful. We discuss a broad range of methods ranging from low-resolution supra-organismal to high-resolution individual-based modeling. Particularly, we highlight the integrative approaches that synergistically combine disparate methods. In conclusion, we provide our outlook for the key aspects that should be further developed to move microbial community modeling towards greater predictive power.

Hardness of { lOT0) ZnO Surfaces Immersed in an Electrolyte," J . Appl. Phys., 49 121 614 ~1 7 (1978). "'J. S . Ahearn, J. I. Mills, and A . R. C. Westwood. "Effect of Electrolyte pH and Bias Voltage o n the Hardness of the (0001) ZnO Surface," J . Appl. Phys., 49 [I] Y6-102 (1978). 'IJ. S. Ahearn. J.

SUMMARY Transcriptional and translational feedback loops in fungi and animals drive circadian rhythms in transcript levels that provide output from the clock, but post-transcriptional mechanisms also contribute. To determine the extent and underlying source of this regulation, we applied newly developed analytical tools to a long-duration, deeply sampled, circadian proteomics time course comprising half of the proteome. We found a quarter of expressed proteins are clock regulated, but >40% of these do not arise from clock-regulated transcripts, and our analysis predicts that these protein rhythms arise from oscillations in translational rates. Our data highlighted the impact of the clock on metabolic regulation, with central carbon metabolism reflecting both transcriptional and post-transcriptional control and opposing metabolic pathways showing peak activities at different times of day. The transcription factor CSP-1 plays a role in this metabolic regulation, contributing to the rhythmicity and phase of clock-regulated proteins.