Markov field models of molecular kinetics

Computer simulations such as molecular dynamics (MD) provide a possible means to understand protein dynamics and mechanisms on an atomistic scale. The resulting simulation data can be analyzed with Markov state models (MSMs), yielding a quantitative kinetic model that, e.g., encodes state populations and transition rates. However, the larger an investigated system, the more data is required to estimate a valid kinetic model. In this work, we show that this scaling problem can be escaped when decomposing a system into smaller ones, leveraging weak couplings between local domains. Our approach, termed independent Markov decomposition (IMD), is a first-order approximation neglecting couplings, i.e., it represents a decomposition of the underlying global dynamics into a set of independent local ones. We demonstrate that for truly independent systems, IMD can reduce the sampling by three orders of magnitude. IMD is applied to two biomolecular systems. First, synaptotagmin-1 is analyzed, a rapid calcium switch from the neurotransmitter release machinery. Within its C2A domain, local conformational switches are identified and modeled with independent MSMs, shedding light on the mechanism of its calcium-mediated activation. Second, the catalytic site of the serine protease TMPRSS2 is analyzed with a local drug-binding model. Equilibrium populations of different drug-binding modes are derived for three inhibitors, mirroring experimentally determined drug efficiencies. IMD is subsequently extended to an end-to-end deep learning framework called iVAMPnets, which learns a domain decomposition from simulation data and simultaneously models the kinetics in the local domains. We finally classify IMD and iVAMPnets as Markov field models (MFM), which we define as a class of models that describe dynamics by decomposing systems into local domains. Overall, this thesis introduces a local approach to Markov modeling that enables to quantitatively assess the kinetics of large macromolecular complexes, opening up possibilities to tackle current and future computational molecular biology questions

Deep learning to decompose macromolecules into independent Markovian domains

The increasing interest in modeling the dynamics of ever larger proteins has revealed a fundamental problem with models that describe the molecular system as being in a global configuration state. This notion limits our ability to gather sufficient statistics of state probabilities or state-to-state transitions because for large molecular systems the number of metastable states grows exponentially with size. In this manuscript, we approach this challenge by introducing a method that combines our recent progress on independent Markov decomposition (IMD) with VAMPnets, a deep learning approach to Markov modeling. We establish a training objective that quantifies how well a given decomposition of the molecular system into independent subdomains with Markovian dynamics approximates the overall dynamics. By constructing an end-to-end learning framework, the decomposition into such subdomains and their individual Markov state models are simultaneously learned, providing a data-efficient and easily interpretable summary of the complex system dynamics. While learning the dynamical coupling between Markovian subdomains is still an open issue, the present results are a significant step towards learning Ising models of large molecular complexes from simulation data

Noncommutative knot theory

The classical abelian invariants of a knot are the Alexander module, which is the first homology group of the the unique infinite cyclic covering space of S^3-K, considered as a module over the (commutative) Laurent polynomial ring, and the Blanchfield linking pairing defined on this module. From the perspective of the knot group, G, these invariants reflect the structure of G^(1)/G^(2) as a module over G/G^(1) (here G^(n) is the n-th term of the derived series of G). Hence any phenomenon associated to G^(2) is invisible to abelian invariants. This paper begins the systematic study of invariants associated to solvable covering spaces of knot exteriors, in particular the study of what we call the n-th higher-order Alexander module, G^(n+1)/G^(n+2), considered as a Z[G/G^(n+1)$-module. We show that these modules share almost all of the properties of the classical Alexander module. They are torsion modules with higher-order Alexander polynomials whose degrees give lower bounds for the knot genus. The modules have presentation matrices derived either from a group presentation or from a Seifert surface. They admit higher-order linking forms exhibiting self-duality. There are applications to estimating knot genus and to detecting fibered, prime and alternating knots. There are also surprising applications to detecting symplectic structures on 4-manifolds. These modules are similar to but different from those considered by the author, Kent Orr and Peter Teichner and are special cases of the modules considered subsequently by Shelly Harvey for arbitrary 3-manifolds.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-19.abs.htm

toward modeling kinetics of biomolecular complexes

In order to advance the mission of in silico cell biology, modeling the interactions of large and complex biological systems becomes increasingly relevant. The combination of molecular dynamics (MD) and Markov state models (MSMs) have enabled the construction of simplified models of molecular kinetics on long timescales. Despite its success, this approach is inherently limited by the size of the molecular system. With increasing size of macromolecular complexes, the number of independent or weakly coupled subsystems increases, and the number of global system states increase exponentially, making the sampling of all distinct global states unfeasible. In this work, we present a technique called Independent Markov Decomposition (IMD) that leverages weak coupling between subsystems in order to compute a global kinetic model without requiring to sample all combinatorial states of subsystems. We give a theoretical basis for IMD and propose an approach for finding and validating such a decomposition. Using empirical few-state MSMs of ion channel models that are well established in electrophysiology, we demonstrate that IMD can reproduce experimental conductance measurements with a major reduction in sampling compared with a standard MSM approach. We further show how to find the optimal partition of all-atom protein simulations into weakly coupled subunits

Camostat mesylate inhibits SARS-CoV-2 activation by TMPRSS2-related proteases and its metabolite GBPA exerts antiviral activity

Background: Antivirals are needed to combat the COVID-19 pandemic, which is caused by SARS-CoV-2. The clinically-proven protease inhibitor Camostat mesylate inhibits SARS-CoV-2 infection by blocking the virus-activating host cell protease TMPRSS2. However, antiviral activity of Camostat mesylate metabolites and potential viral resistance have not been analyzed. Moreover, antiviral activity of Camostat mesylate in human lung tissue remains to be demonstrated. Methods: We used recombinant TMPRSS2, reporter particles bearing the spike protein of SARS-CoV-2 or authentic SARS-CoV-2 to assess inhibition of TMPRSS2 and viral entry, respectively, by Camostat mesylate and its metabolite GBPA. Findings: We show that several TMPRSS2-related proteases activate SARS-CoV-2 and that two, TMPRSS11D and TMPRSS13, are robustly expressed in the upper respiratory tract. However, entry mediated by these proteases was blocked by Camostat mesylate. The Camostat metabolite GBPA inhibited recombinant TMPRSS2 with reduced efficiency as compared to Camostat mesylate. In contrast, both inhibitors exhibited similar antiviral activity and this correlated with the rapid conversion of Camostat mesylate into GBPA in the presence of serum. Finally, Camostat mesylate and GBPA blocked SARS-CoV-2 spread in human lung tissue ex vivo and the related protease inhibitor Nafamostat mesylate exerted augmented antiviral activity. Interpretation: Our results suggest that SARS-CoV-2 can use TMPRSS2 and closely related proteases for spread in the upper respiratory tract and that spread in the human lung can be blocked by Camostat mesylate and its metabolite GBPA

Deeptime: a Python library for machine learning dynamical models from time series data

Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics. In the physical sciences, structures such as metastable and coherent sets, slow relaxation processes, collective variables, dominant transition pathways or manifolds and channels of probability flow can be of great importance for understanding and characterizing the kinetic, thermodynamic and mechanistic properties of the system. Deeptime is a general purpose Python library offering various tools to estimate dynamical models based on time-series data including conventional linear learning methods, such as Markov state models (MSMs), Hidden Markov Models and Koopman models, as well as kernel and deep learning approaches such as VAMPnets and deep MSMs. The library is largely compatible with scikit-learn, having a range of Estimator classes for these different models, but in contrast to scikit-learn also provides deep Model classes, e.g. in the case of an MSM, which provide a multitude of analysis methods to compute interesting thermodynamic, kinetic and dynamical quantities, such as free energies, relaxation times and transition paths. The library is designed for ease of use but also easily maintainable and extensible code. In this paper we introduce the main features and structure of the deeptime software. Deeptime can be found under https://deeptime-ml.github.io/

pre-clinical assessment of pharmacological and molecular properties

SARS-CoV-2, the cause of the COVID-19 pandemic, exploits host cell proteins for viral entry into human lung cells. One of them, the protease TMPRSS2, is required to activate the viral spike protein (S). Even though two inhibitors, camostat and nafamostat, are known to inhibit TMPRSS2 and block cell entry of SARS-CoV-2, finding further potent therapeutic options is still an important task. In this study, we report that a late-stage drug candidate, otamixaban, inhibits SARS-CoV-2 cell entry. We show that otamixaban suppresses TMPRSS2 activity and SARS-CoV-2 infection of a human lung cell line, although with lower potency than camostat or nafamostat. In contrast, otamixaban inhibits SARS-CoV-2 infection of precision cut lung slices with the same potency as camostat. Furthermore, we report that otamixaban's potency can be significantly enhanced by (sub-) nanomolar nafamostat or camostat supplementation. Dominant molecular TMPRSS2-otamixaban interactions are assessed by extensive 109 μs of atomistic molecular dynamics simulations. Our findings suggest that combinations of otamixaban with supplemental camostat or nafamostat are a promising option for the treatment of COVID-19

Predicting molecular vibronic spectra using time-domain analog quantum simulation

Spectroscopy is one of the most accurate probes of the molecular world. However, predicting molecular spectra accurately is computationally difficult because of the presence of entanglement between electronic and nuclear degrees of freedom. Although quantum computers promise to reduce this computational cost, existing quantum approaches rely on combining signals from individual eigenstates, an approach that is difficult to scale because the number of eigenstates grows exponentially with molecule size. Here, we introduce a method for scalable analog quantum simulation of molecular spectroscopy, by performing simulations in the time domain. Our approach can treat more complicated molecular models than previous ones, requires fewer approximations, and can be extended to open quantum systems with minimal overhead. We present a direct mapping of the underlying problem of time-domain simulation of molecular spectra to the degrees of freedom and control fields available in a trapped-ion quantum simulator. We experimentally demonstrate our algorithm on a trapped-ion device, exploiting both intrinsic electronic and motional degrees of freedom, showing excellent quantitative agreement for a single-mode vibronic photoelectron spectrum of SO$_2$.Comment: 13 pages, 8 figure

Bridging Alone: Religious Conservatism, Marital Homogamy, and Voluntary Association Membership

This study characterizes social insularity of religiously conservative American married couples by examining patterns of voluntary associationmembership. Constructing a dataset of 3938 marital dyads from the second wave of the National Survey of Families and Households, the author investigates whether conservative religious homogamy encourages membership in religious voluntary groups and discourages membership in secular voluntary groups. Results indicate that couples’ shared affiliation with conservative denominations, paired with beliefs in biblical authority and inerrancy, increases the likelihood of religious group membership for husbands and wives and reduces the likelihood of secular group membership for wives, but not for husbands. The social insularity of conservative religious groups appears to be reinforced by homogamy—particularly by wives who share faith with husbands