David M. Rogers

Catalytic Role of the Substrate Defines Specificity of Therapeutic l-Asparaginase

Type II bacterial L-asparaginases (L-ASP) have played an important therapeutic role in cancer treatment for over four decades, yet their exact reaction mechanism remains elusive. L-ASP from Escherichia coli deamidates asparagine (Asn) and glutamine, with an ~10(4) higher specificity (kcat/Km) for asparagine despite only one methylene difference in length. Through a sensitive kinetic approach, we quantify competition among the substrates and interpret its clinical role. To understand specificity, we use molecular simulations to characterize enzyme interactions with substrates and a product (aspartate). We present evidence that the aspartate product in the crystal structure of L-ASP exists in an unusual α-COOH protonation state. Consequently, the set of enzyme-product interactions found in the crystal structure, which guided prior mechanistic interpretations, differs from those observed in dynamic simulations of the enzyme with the substrates. Finally, we probe the initial nucleophilic attack with ab initio simulations. The unusual protonation state reappears, suggesting that crystal structures (wild type and a T89V mutant) represent intermediate steps rather than initial binding. Also, a proton transfers spontaneously to Asn, advancing a new hypothesis that the substrates α-carboxyl serves as a proton acceptor and activates one of the catalytic threonines during L-ASPs nucleophilic attack on the amide carbon. That hypothesis explains for the first time why proximity of the substrate α-COO(-) group to the carboxamide is absolutely required for catalysis. The substrates catalytic role is likely the determining factor in enzyme specificity as it constrains the allowed distance between the backbone carboxyl and the amide carbon of any L-ASP substrate.

Extension of Kirkwood-Buff theory to the canonical ensemble

Kirkwood-Buff (KB) integrals are notoriously difficult to converge from a canonical simulation because they require estimating the grand-canonical radial distribution. The same essential difficulty is encountered when attempting to estimate the direct correlation function of Ornstein-Zernike theory by inverting the pair correlation functions. We present a new theory that applies to the entire, finite, simulation volume, so that no cutoff issues arise at all. The theory gives the direct correlation function for closed systems, while smoothness of the direct correlation function in reciprocal space allows calculating canonical KB integrals via a well-posed extrapolation to the origin. The present analysis method represents an improvement over previous work because it makes use of the entire simulation volume and its convergence can be accelerated using known properties of the direct correlation function. Using known interaction energy functions can make this extrapolation near perfect accuracy in the low-density case. Because finite size effects are stronger in the canonical than in the grand-canonical ensemble, we state ensemble correction formulas for the chemical potential and the KB coefficients. The new theory is illustrated with both analytical and simulation results on the 1D Ising model and a supercritical Lennard-Jones fluid. For the latter, the finite-size corrections are shown to be small.

Einstein-Podolsky-Rosen paradox implies a minimum achievable temperature

This work examines the thermodynamic consequences of the repeated partial projection model for coupling a quantum system to an arbitrary series of environments under feedback control. This paper provides observational definitions of heat and work that can be realized in current laboratory setups. In contrast to other definitions, it uses only properties of the environment and the measurement outcomes, avoiding references to the measurement of the central systems state in any basis. These definitions are consistent with the usual laws of thermodynamics at all temperatures, while never requiring complete projective measurement of the entire system. It is shown that the back action of measurement must be counted as work rather than heat to satisfy the second law. Comparisons are made to quantum jump (unravelling) and transition-probability based definitions, many of which appear as particular limits of the present model. These limits show that our total entropy production is a lower bound on traditional definitions of heat that trace out the measurement device. Examining the master equation approximation to the process at finite measurement rates, we show that most interactions with the environment make the system unable to reach absolute zero. We give an explicit formula for the minimum temperature achievable in repeatedly measured quantum systems. The phenomenon of minimum temperature offers an explanation of recent experiments aimed at testing fluctuation theorems in the quantum realm and places a fundamental purity limit on quantum computers.

Driving forces in MD simulations of transition and ‘Free’ flows

Abstract Simulations of porous gaseous flows are routinely used to investigate membrane permeation in catalytic adsorption and separation problems. Although basic continuum equations are supposed to breakdown in these nanoscale pores, many studies of force/flow relations assume flow to be linear in chemical potential or pressure differences. This work tests common assumptions using simulations of an atomistic, Lennard–Jones pore flow with distant, Langevin forcing at densities stretching through the transition and free flow regimes. Using NVE dynamics in very large boundary reservoirs, we find local equilibrium is established in the steady-state, but also identify two new finite-size effects. First, there is a steady flow of heat from the high-pressure reservoir backward to the thermostat region, and second, a significant proportion of the channel flow originates from the monolayer adsorbed to the flat outer wall. All walls are shown to obey a simple Langmuir adsorption isotherm at these low ( kPa) pressures, even in the presence of flow. Despite multi-layer formation on the inner pore walls as density increases, the current carried by atoms at the wall has the same proportion to current carried through the channel center under nearly all conditions tested (with constant pore diameter). Comparing our flow rates to Fickian and Knudsen linear relations shows that the difference in reservoir pressure is significantly more predictive than the difference in chemical potential for this size regime.

Method for measuring the unbinding energy of strongly-bound membrane-associated proteins

We describe a new method to measure the activation energy for unbinding (enthalpy ΔH*u and free energy ΔG*u) of a strongly-bound membrane-associated protein from a lipid membrane. It is based on measuring the rate of release of a liposome-bound protein during centrifugation on a sucrose gradient as a function of time and temperature. The method is used to determine ΔH*u and ΔG*u for the soluble dengue virus envelope protein (sE) strongly bound to 80:20 POPC:POPG liposomes at pH5.5. ΔH*u is determined from the Arrhenius equation whereas ΔG*u is determined by fitting the data to a model based on mean first passage time for escape from a potential well. The binding free energy ΔGb of sE was also measured at the same pH for the initial, predominantly reversible, phase of binding to a 70:30 PC:PG lipid bilayer. The unbinding free energy (20±3kcal/mol, 20% PG) was found to be roughly three times the binding energy per monomer, (7.8±0.3kcal/mol for 30% PG, or est. 7.0kcal/mol for 20% PG). This is consistent with data showing that free sE is a monomer at pH5.5, but assembles into trimers after associating with membranes. This new method to determine unbinding energies should be useful to understand better the complex interactions of integral monotopic proteins and strongly-bound peripheral membrane proteins with lipid membranes.

Insertion of Dengue E into lipid bilayers studied by neutron reflectivity and molecular dynamics simulations

The envelope (E) protein of Dengue virus rearranges to a trimeric hairpin to mediate fusion of the viral and target membranes, which is essential for infectivity. Insertion of E into the target membrane serves to anchor E and possibly also to disrupt local order within the membrane. Both aspects are likely to be affected by the depth of insertion, orientation of the trimer with respect to the membrane normal, and the interactions that form between trimer and membrane. In the present work, we resolved the depth of insertion, the tilt angle, and the fundamental interactions for the soluble portion of Dengue E trimers (sE) associated with planar lipid bilayer membranes of various combinations of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-rac-glycerol (POPG), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE), and cholesterol (CHOL) by neutron reflectivity (NR) and by molecular dynamics (MD) simulations. The results show that the tip of E containing the fusion loop (FL) is located at the interface of the headgroups and acyl chains of the outer leaflet of the lipid bilayers, in good agreement with prior predictions. The results also indicate that E tilts with respect to the membrane normal upon insertion, promoted by either the anionic lipid POPG or CHOL. The simulations show that tilting of the protein correlates with hydrogen bond formation between lysines and arginines located on the sides of the trimer close to the tip (K246, K247, and R73) and nearby lipid headgroups. These hydrogen bonds provide a major contribution to the membrane anchoring and may help to destabilize the target membrane.

Efficient Primitives for Standard Tensor Linear Algebra

This paper presents the design and implementation of low-level library to compute general sums and products over multi-dimensional arrays (tensors). Using only 3 low-level functions, the API at once generalizes core BLAS1-3 as well as eliminates the need for most tensor transpositions. Despite their relatively low operation count, we show that these transposition steps can become performance limiting in typical use cases for BLAS on tensors. The execution of the present API achieves peak performance on the same order of magnitude as for vendor-optimized GEMM by utilizing a code generator to output CUDA source code for all computational kernels. The outline for these kernels is a multi-dimensional generalization of the MAGMA BLAS matrix multiplication on GPUs. Separate transpositions steps can be skipped because every kernel allows arbitrary multidimensional transpositions of the arguments. The library, including its methodology and programming techniques, are made available in SLACK. Future improvements to the library include a high-level interface to translate directly from a LATEX-like equation syntax to a data-parallel computation.

Overcoming the minimum image constraint using the closest point search

Finding the set of nearest images of a point in a simulation cell with periodic (torus) boundary conditions is of central importance for molecular dynamics algorithms. To compute all pairwise distances closer than a given cutoff in linear time requires region-based neighbor-listing algorithms. Available algorithms encounter increasing difficulties when the cutoff distance exceeds half the shortest cell length. This work provides details on two ways to directly and efficiently generate region-region interaction lists in n-dimensional space, free from the minimum image restriction. The solution is based on a refined version of existing algorithms solving the closest vector problem. A self-contained discussion of lattice reduction methods for efficient higher-dimensional searches is also provided. In the MD setting, these reduction criteria provide useful guidelines for lattice compaction.

Active Role of the Substrate During Catalysis by the Therapeutic Enzyme L-Asparaginase II

Bacterial type II L-Asparaginases (ASPII) have been used for over four decades to treat acute lymphoblastic leukemia, yet a full reaction mechanism remains unknown. ASPII enzymes catalyze the deamidation of both asparagine (Asn) and glutamine (Gln), which results in the formation of aspartate (Asp) and glutamate (Glu) respectively, and the by-product ammonia. Proposed ASPII mechanisms to date have yet to explain the absolute requirement of a substrate α-carboxyl group, and clearly identify the role of the catalytic threonines T12 and T89. Here, we study the reaction mechanism of asparagine degradation by ASPII through ab initio molecular dynamics (MD) simulations. We selected a reduced system from the substrate-bound enzyme obtained by classical MD, and explore different initial reaction pathways by driving the system in steered simulations. Our results show that direct nucleophilic attack by T12 produces a highly unstable substrate-enzyme intermediate, as the stabilization provided by the nearby protons (i.e., the “oxyanion hole”) is insufficient to sustain the high energy state. We find that the substrate-enzyme intermediate can be stabilized by first protonating the substrates amide oxygen through the K162-T89 proton bridge. Furthermore, the α-carboxyl of the substrate acts as a proton acceptor for the hydroxyl sidechain of T12 during nucleophilic attack. We conclude by showing that a complete deamidation mechanism may require a sequence of several nucleophilic attacks by both T12 and T89, with K162 playing a critical role as a proton buffer during the course of the reaction.