Are size and mitochondrial power of cells inter-determined?

Mitochondria are the central hub of ATP production in most eukaryotic cells. Cellular power (energy per unit time), which is primarily generated in these organelles, is crucial to our understanding of cell function in health and disease. We investigated the relation between a mitochondrion's power (metabolic rate) and host cell size by combining metabolic theory with the analysis of two recent databases, one covering 109 protists and the other 63 species including protists, metazoans, microalgae, and vascular plants. We uncovered an interesting statistical regularity: in well-fed protists, relatively elevated values of mitochondrion power cluster around the smallest cell sizes and the medium-large cell sizes. In contrast, in starved protists and metazoans, the relation between mitochondrion power and cell size is inconclusive, and in microalgae and plants, mitochondrion power seems to increase from smaller cells to larger ones (where this investigation includes plant cells of volume up to ca. 2.18 × 105 µm3). Using these results, estimates are provided of the number of active ATP synthase molecules and basal uncouplers.

A fast approximate extension of the interacting quantum atoms energy decomposition to excited states.

An approach is developed for the fast calculation of the interacting quantum atoms energy decomposition (IQA) from the information contained in the first order reduced density matrix only. The proposed methodology utilizes an approximate exchange-correlation density from Density Matrix Functional Theory without the need to evaluate the correlation-exchange contribution directly. Instead, weight factors are estimated to decompose the exact Vxc into atomic and pairwise contributions. In this way, the sum of the IQA contributions recovers the energy obtained from the electronic structure calculation. This method can, hence, be applied to obtain atomic contributions in excited states on the same footing as in their ground states using any method that delivers the reduced first-order density matrix. In this way, one can locate chromophores from first principles quantum chemical calculations. Test calculations on the ground and excited states of a set of small molecules indicate that the scaled atomic contributions reproduce vertical electronic transition energies calculated exactly. This approach may be useful to extend the applicability of the IQA approach in the study of large photochemical systems especially when the calculations of the second order reduced density matrices is prohibitive or not possible.

Bonding and metastability for Group 12 dications.

Electronic structure and bonding properties of the Group 12 dications M2 2+ (M = Zn, Cd, Hg) are investigated and electron density-derived quantities are used to characterize the metastability of these species. Of particular interest are the complementary descriptions afforded by the Laplacian of the electron density ∇2 ρ(r) and the one-electron Bohm quantum potential (Q = ∇ 2 ρ r / 2 ρ r ) along the bond path. Further, properties derived from the pair density including the localization-delocalization matrices (LDMs) and the interacting quantum atoms (IQA) energies are analyzed within the framework of the quantum theory of atoms in molecules (QTAIM). From the crossing points of the singlet (ground) and triplet (excited) potential energy curves, the barriers for dissociation (BFD) are estimated to be 25.2 kcal/mol (1.09 eV) for Zn2 2+ , 22.8 kcal/mol (0.99 eV) for Cd2 2+ , and 26.4 kcal/mol (1.14 eV) for Hg2 2+ . For comparison and benchmarking purposes, the case of N2 2+ is considered as a texbook example of metastability. At the equilibrium geometries, LDMs, which are used here as an electronic fingerprinting tool, discriminate and group together Group 12 M2 2+ from its isoelectronic Group 11 M2 . While "classical" bonding indices are inconclusive in establishing regions of metastability in the bonding, it is shown that the one-electron Bohm quantum potential is promising in this regard.

On the power per mitochondrion and the number of associated active ATP synthases.

Recent experiments and thermodynamic arguments suggest that mitochondrial temperatures are higher than those of the cytoplasm. A "hot mitochondrion" calls for a closer examination of the energy balance that endows it with these claimed elevated temperatures. As a first step in this effort, we present here a semi-quantitative bookkeeping whereby, in one stroke, a formula is proposed that yields the rate of heat production in a typical mitochondrion and a formula for estimating the number of "active" ATP synthase molecules per mitochondrion. The number of active ATP synthase molecules is the equivalent number of ATP synthases operating at 100% capacity to maintain the rate of mitochondrial heat generation. Scaling laws are shown to determine the number of active ATP synthase molecules in a mitochondrion and mitochondrial rate of heat production, whereby both appear to scale with cell volume. Four heterotrophic protozoan cell types are considered in this study. The studied cells, selected to cover a wide range of sizes (volumes) fromca.100µm3to 1 millionµm3, are estimated to exhibit a power per mitochondrion ranging fromca.1 pW to 0.03 pW. In these cells, the corresponding number of active ATP synthases per mitochondrion ranges from 5000 to just about a hundred. The absolute total number of ATP synthase molecules per mitochondrion, regardless of their activity status, can be up to two orders of magnitudes higher.

Drug design by machine-trained elastic networks: predicting Ser/Thr-protein kinase inhibitors' activities.

An elastic network model (ENM) represents a molecule as a matrix of pairwise atomic interactions. Rich in coded information, ENMs are hereby proposed as a novel tool for the prediction of the activity of series of molecules, with widely different chemical structures, but a common biological activity. The new approach is developed and tested using a set of 183 inhibitors of serine/threonine-protein kinase enzyme (Plk3) which is an enzyme implicated in the regulation of cell cycle and tumorigenesis. The elastic network (EN) predictive model is found to exhibit high accuracy and speed compared to descriptor-based machine-trained modeling. EN modeling appears to be a highly promising new tool for the high demands of industrial applications such as drug and material design.

Heat Shock Proteins in the "Hot" Mitochondrion: Identity and Putative Roles.

The mitochondrion is known as the "powerhouse" of eukaryotic cells since it is the main site of adenosine 5'-triphosphate (ATP) production. Using a temperature-sensitive fluorescent probe, it has recently been suggested that the stray free energy, not captured into ATP, is potentially sufficient to sustain mitochondrial temperatures higher than the cellular environment, possibly reaching up to 50 °C. By 50 °C, some DNA and mitochondrial proteins may reach their melting temperatures; how then do these biomolecules maintain their structure and function? Further, the production of reactive oxygen species (ROS) accelerates with temperature, implying higher oxidative stresses in the mitochondrion than generally appreciated. Herein, it is proposed that mitochondrial heat shock proteins (particularly Hsp70), in addition to their roles in protein transport and folding, protect mitochondrial proteins and DNA from thermal and ROS damage. Other thermoprotectant mechanisms are also discussed.

Manipulation of Diatomic Molecules with Oriented External Electric Fields: Linear Correlations in Atomic Properties Lead to Nonlinear Molecular Responses.

Oriented external electric fields (OEEFs) have been shown to have great potential in being able to provide unprecedented control of chemical reactions, catalysis, and selectivity with applications ranging from H2 storage to molecular machines. We report a theoretical study of the atomic origins of molecular changes because of OEEFs since understanding the characteristics of OEEF-induced couplings between atomic and molecular properties is an important step toward comprehensive understanding of the effects of strong external fields on the molecular structure, stability, and reactivity. We focus on the atomic and molecular (bond) properties of a set of homo- (H2, N2, O2, F2, and Cl2) and heterodiatomic (HF, HCl, CO, and NO) molecules under intense external electric fields in the context of quantum theory of atoms in molecules (QTAIM). It is shown that the atomic properties (atomic charges, energies, and localization indices) correlate linearly with the field strengths, but molecular properties (bond length, electron density at the bond critical point, and electron delocalization index) exhibit nonlinear responses to the imposed fields. In particular, the changes in the electron density distribution alter the shapes and locations of the zero-flux surfaces, atomic volumes, atomic electron population, and localization/delocalization indices. The topography and topology of the molecular electrostatic potential undergo dramatic changes. External fields also perturb the covalent-polar-ionic characteristic of the studied chemical bonds, hallmarking the impact of electric fields on the stability and reactivity of chemical compounds. The findings are well-rationalized within the framework of the QTAIM and form a coherent conceptual understanding of these effects in prototypical diatomic molecules.

Quantum crystallography: A perspective.

Extraction of the complete quantum mechanics from X-ray scattering data is the ultimate goal of quantum crystallography. This article delivers a perspective for that possibility. It is desirable to have a method for the conversion of X-ray diffraction data into an electron density that reflects the antisymmetry of an N-electron wave function. A formalism for this was developed early on for the determination of a constrained idempotent one-body density matrix. The formalism ensures pure-state N-representability in the single determinant sense. Applications to crystals show that quantum mechanical density matrices of large molecules can be extracted from X-ray scattering data by implementing a fragmentation method termed the kernel energy method (KEM). It is shown how KEM can be used within the context of quantum crystallography to derive quantum mechanical properties of biological molecules (with low data-to-parameters ratio). © 2017 Wiley Periodicals, Inc.

An Electron Density Source-Function Study of DNA Base Pairs in Their Neutral and Ionized Ground States†.

The source function (SF) decomposes the electron density at any point into contributions from all other points in the molecule, complex, or crystal. The SF "illuminates" those regions in a molecule that most contribute to the electron density at a point of reference. When this point of reference is the bond critical point (BCP), a commonly used surrogate of chemical bonding, then the SF analysis at an atomic resolution within the framework of Bader's Quantum Theory of Atoms in Molecules returns the contribution of each atom in the system to the electron density at that BCP. The SF is used to locate the important regions that control the hydrogen bonds in both Watson-Crick (WC) DNA dimers (adenine:thymine (AT) and guanine:cytosine (GC)) which are studied in their neutral and their singly ionized (radical cationic and anionic) ground states. The atomic contributions to the electron density at the BCPs of the hydrogen bonds in the two dimers are found to be delocalized to various extents. Surprisingly, gaining or loosing an electron has similar net effects on some hydrogen bonds concealing subtle compensations traced to atomic sources contributions. Coarser levels of resolutions (groups, rings, and/or monomers-in-dimers) reveal that distant groups and rings often have non-negligible effects especially on the weaker hydrogen bonds such as the third weak CH⋅⋅⋅O hydrogen bond in AT. Interestingly, neither the purine nor the pyrimidine in the neutral or ionized forms dominate any given hydrogen bond despite that the former has more atoms that can act as source or sink for the density at its BCP. © 2018 Wiley Periodicals, Inc.

Quantum Crystallography: Current Developments and Future Perspectives.

Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.

Adenine-thymine tautomerization under the influence of strong homogeneous electric fields.

The effect of strong electric fields on the tautomerization of the adenine-thymine (AT) base pair in DNA is explored using density functional theory. It was found that the AT base pair is not likely to undergo a double proton transfer reaction even in the presence of electric fields ranging from 5.14 × 108 to 5.14 × 109 V m-1. This conclusion holds true in Gibbs energies computed at 25 °C or 37 °C. Energy correction terms to the electronic energy, such as total internal energy, Gibbs energy, zero-point energy, enthalpy and entropy corrections, were investigated in detail to pinpoint the major contributors to the low probability of the AT tautomerization. It was found that the entropy corrections are the least significant, while zero-point energy and Gibbs energy corrections can be large enough to thermodynamically inhibit the DPT in AT.

On the Unusual Synclinal Conformations of Hexafluorobutadiene and Structurally Similar Molecules.

An explanation is presented for the unusual conformations of some molecules that contain the C═C-C═C core, namely, butadienes, biphenyls, and styrenes. Small substituents often induce a synclinal conformation, which brings the substituents into close proximity, and sometimes, there is no anticlinal minimum at all. This would not be predicted from steric repulsion arguments nor would it be expected that atoms that are nonbonded in a Lewis structure would approach closer than the sum of their van der Waals radii. Atomic energies calculated according to the quantum theory of atoms in molecules (QTAIM) do not show a consistent pattern for these structurally similar molecules, nor are intersubstituent bond paths consistently found, nor favorable diatomic interaction energies calculated using the interacting quantum atoms (IQA) scheme. Instead, the synclinal conformations are found to be driven by the attraction energy of the electron distribution of the carbon atoms and the nuclei of the molecule.

Notes on The Energy Equivalence of Information.

Maxwell's demon makes observations and thereby collects information. As Brillouin points out such information is the negative of entropy (negentropy) and is the equivalent of a cost in energy. The energy cost of information can be quantified in the relationship E = kT ln 2, where k is the Boltzmann constant, T is the absolute temperature, and the factor ln 2 arises from the existence of two possibilities for a "yes/no" circumstance, as, for example, in the passage of a proton through a barrier controlled by a Maxwell's demon. This paper considers further conclusions that follow from the quantification of the energy cost of information. First, consideration of the minimum uncertainty in the measurement of energy cost of information leads to an expression for the uncertainty in the corresponding time of the measurement, which depends inversely upon temperature at which the measurements occur. Second, because of the universal connection between energy and mass, an almost imperceptible mass accompanies the accumulation of information. And third, to account for the total free energy change that describes the action of adenosine triphosphate (ATP) synthase, an additional term is suggested to be appended to the Mitchell chemiosmotic equation, which describes this process. The additional term accounts for the energy cost of sorting away from background ions those protons allowed to enter the ATP synthase.

The barrier to the methyl rotation in Cis-2-butene and its isomerization energy to Trans-2-butene, revisited.

We respond to the two questions posed by Weinhold, Schleyer, and McKee (WSM) in their study of cis-2-butene (Weinhold et al., J Comput Chem 2014, 35, 1499), in which they solicit explanations for the relative conformational energies of this molecule in terms of the Quantum Theory of Atoms in Molecules (QTAIM). WSM requested answers to the questions: (1) why is cis-2-butene less stable than trans-2-butene despite the presence of a hydrogen-hydrogen (H⋯H) bond path in the former but not in the latter if the H⋯H bond path is stabilizing? (2) Why is the potential well of the conformational global minimum of cis-2-butene only 0.8 kcal/mol deep when the H⋯H bonding is stabilizing by 5 kcal/mol? Both questions raised by WSM are answered by considering the changes in the energies of all atoms as a function of the rotation of one of the two methyl groups from the minimum-energy structure, which exhibits the H⋯H bond path, to the transition state, which is devoid of this bond path. It is found that the stability gained by the H⋯H bonding interaction is cancelled by the destabilization of one of the ethylenic carbon atoms which, alone, destabilizes the system by as much as 5 kcal/mol in the global minimum conformation. Further, it is found that the 1.1 kcal/mol stability of trans-2-butene with respect to the cis-isomer is driven by the considerable destabilization of the ethylenic carbons by 11 kcal/mol, while the changes in the atomic energies of the other corresponding atoms in the two isomers account for the observed different stabilities. The error introduced into QTAIM atomic energies by neglecting the virials of the forces on the nuclei for partially optimized structures is discussed.

Nonnuclear Attractors in Heteronuclear Diatomic Systems.

Nonnuclear attractors (NNAs) are observed in the electron density of a variety of systems, but the factors governing their appearance and their contribution to the system's properties remain a mystery. The NNA occurring in homo- and heteronuclear diatomics of main group elements with atomic numbers up to Z = 38 is investigated computationally (at the UCCSD/cc-pVQZ level of theory) by varying internuclear separations. This was done to determine the NNA occurrence window along with the evolution of the respective pseudoatomic basin properties. Two distinct categories of NNAs were detected in the data analyzed by means of catastrophe theory. Type "a" implies electronic charge transfer between atoms mediated by a pseudoatom. Type "b" shows an initial relocation of some electronic charge to a pseudoatom, which posteriorly returns to the same atom that donated this charge in the first place. A small difference of polarizability between the atoms that compose these heteronuclear diatomics seems to favor NNA formation. We also show that the NNA arising tends to result in some perceptible effects on molecular dipole and/or quadrupole moment curves against internuclear distance. Finally, successive cationic ionization results in the fast disappearance of the NNA in Li2 indicating that its formation is mainly governed by the field generated by the quantum mechanical electronic density and only depends parametrically on the bare nuclear field/potential at a given molecular geometry.

Spontaneous Reduction of a Hydroborane To Generate a B-B Single Bond by the Use of a Lewis Pair.

The ansa-aminohydroborane 1-NMe2 -2-(BH2 )C6 H4 crystallizes in an unprecedented type of dimer containing a B-H bond activated by one FLP moiety. Upon mild heating and without the use of any catalyst, this molecule liberates one equivalent of hydrogen to generate a diborane molecule. The synthesis and structural characterization of these new compounds, as well as the kinetic monitoring of the reaction and the DFT investigation of its mechanism, are reported.

Energy Equivalence of Information in the Mitochondrion and the Thermodynamic Efficiency of ATP Synthase.

Half a century ago, Johnson and Knudsen resolved the puzzle of the apparent low efficiency of the kidney (∼ 0.5%) compared to most other bodily organs (∼ 40%) by taking into account the entropic cost of ion sorting, the principal function of this organ. Similarly, it is shown that the efficiency of energy transduction of the chemiosmotic proton-motive force by ATP synthase is closer to 90% instead of the oft-quoted textbook value of only 60% when information theoretic considerations are applied to the mitochondrion. This high efficiency is consistent with the mechanical energy transduction of ATP synthase known to be close to the 100% thermodynamic limit. It would have been wasteful for evolution to maximize the mechanical energy transduction to 100% while wasting 40% of the chemiosmotic free energy in the conversion of the proton-motive force into mechanical work before being captured as chemical energy in adenosine 5'-triphosphate.

Modeling biophysical and biological properties from the characteristics of the molecular electron density, electron localization and delocalization matrices, and the electrostatic potential.

The electron density and the electrostatic potential are fundamentally related to the molecular hamiltonian, and hence are the ultimate source of all properties in the ground- and excited-states. The advantages of using molecular descriptors derived from these fundamental scalar fields, both accessible from theory and from experiment, in the formulation of quantitative structure-to-activity and structure-to-property relationships, collectively abbreviated as QSAR, are discussed. A few such descriptors encode for a wide variety of properties including, for example, electronic transition energies, pK(a)'s, rates of ester hydrolysis, NMR chemical shifts, DNA dimers binding energies, π-stacking energies, toxicological indices, cytotoxicities, hepatotoxicities, carcinogenicities, partial molar volumes, partition coefficients (log P), hydrogen bond donor capacities, enzyme-substrate complementarities, bioisosterism, and regularities in the genetic code. Electronic fingerprinting from the topological analysis of the electron density is shown to be comparable and possibly superior to Hammett constants and can be used in conjunction with traditional bulk and liposolubility descriptors to accurately predict biological activities. A new class of descriptors obtained from the quantum theory of atoms in molecules' (QTAIM) localization and delocalization indices and bond properties, cast in matrix format, is shown to quantify transferability and molecular similarity meaningfully. Properties such as "interacting quantum atoms (IQA)" energies which are expressible into an interaction matrix of two body terms (and diagonal one body "self" terms, as IQA energies) can be used in the same manner. The proposed QSAR-type studies based on similarity distances derived from such matrix representatives of molecular structure necessitate extensive investigation before their utility is unequivocally established.

The localization-delocalization matrix and the electron-density-weighted connectivity matrix of a finite graphene nanoribbon reconstructed from kernel fragments.

Bader's quantum theory of atoms in molecules (QTAIM) and chemical graph theory, merged in the localization-delocalization matrices (LDMs) and the electron-density-weighted connectivity matrices (EDWCM), are shown to benefit in computational speed from the kernel energy method (KEM). The LDM and EDWCM quantum chemical graph matrices of a 66-atom C46H20 hydrogen-terminated armchair graphene nanoribbon, in 14 (2×7) rings of C2v symmetry, are accurately reconstructed from kernel fragments. (This includes the full sets of electron densities at 84 bond critical points and 19 ring critical points, and the full sets of 66 localization and 4290 delocalization indices (LIs and DIs).) The average absolute deviations between KEM and directly calculated atomic electron populations, obtained from the sum of the LIs and half of the DIs of an atom, are 0.0012 ± 0.0018 e(-) (∼0.02 ± 0.03%) for carbon atoms and 0.0007 ± 0.0003 e(-) (∼0.01 ± 0.01%) for hydrogen atoms. The integration errors in the total electron population (296 electrons) are +0.0003 e(-) for the direct calculation (+0.0001%) and +0.0022 e(-) for KEM (+0.0007%). The accuracy of the KEM matrix elements is, thus, probably of the order of magnitude of the combined precision of the electronic structure calculation and the atomic integrations. KEM appears capable of delivering not only the total energies with chemical accuracy (which is well documented) but also local and nonlocal properties accurately, including the DIs between the fragments (crossing fragmentation lines). Matrices of the intact ribbon, the kernels, the KEM-reconstructed ribbon, and errors are available as Supporting Information .