A mathematical theory of size distributions in tissue culture

A model for growth of a tissue culture consisting of cell clumps is given. A set of equations for following the size distribution of clumps is used to determine total biomass accumulation. Existence and uniqueness of a solution to the equations is proved, and estimates of the biomass growth is given in a number of situations.     

The effects of 7-dehydrocholesterol on the structural properties of membranes

Smith-Lemli-Opitz syndrome, a congenital and developmental malformation disease, is typified by abnormal accumulation of 7-dehydrocholesterol (7DHC), the immediate precursor of cholesterol (CHOL), and depletion thereof. Knowledge of the effect of 7DHC on the biological membrane is, however, still fragmentary. In this study, large-scale atomistic molecular dynamics simulations, employing two distinct force fields, have been conducted to elucidate differences in the structural properties of a hydrated dimyristoylphosphatidylcholine bilayer due to CHOL and 7DHC. The present series of results indicate that CHOL and 7DHC possess virtually the same ability to condense and order membranes. Furthermore, the condensing and ordering effects are shown to be strengthened at increasing sterol concentrations.     

Diffusion of glycerol through Escherichia coli aquaglyceroporin GlpF

The glycerol uptake facilitator, GlpF, a major intrinsic protein found in Escherichia coli, selectively conducts water and glycerol across the inner membrane. The free energy landscape characterizing the assisted transport of glycerol by this homotetrameric aquaglyceroporin has been explored by means of equilibrium molecular dynamics over a timescale spanning 0.12 μs. To overcome the free energy barriers of the conduction pathway, an adaptive biasing force is applied to the glycerol molecule confined in each of the four channels. The results illuminate the critical role played by intramolecular relaxation on the diffusion properties of the permeant. These free energy calculations reveal that glycerol tumbles and isomerizes on a timescale comparable to that spanned by its adaptive-biasing-force-assisted conduction in GlpF. As a result, reorientation and conformational equilibrium of glycerol in GlpF constitute a bottleneck in the molecular simulations of the permeation event. A profile characterizing the position-dependent diffusion of the permeant has been determined, allowing reaction rate theory to be applied for investigating conduction kinetics based on the measured free energy landscape.     

Molecular dynamics investigation of an oriented cyclic peptide nanotube in DMPC bilayers

Nanotubes resulting from the self-assembly of cyclic peptides formed by eight alpha-amino acids and inserted into lipid bilayers have been shown to function as synthetic, integral transmembrane channels. A nanotube consisting of eight cyclo[(L-Trp-D-Leu)(3)-L-Gln-D-Leu] subunits, organized in an antiparallel, beta-sheetlike channel embedded in a hydrated dimyristoylphosphatidylcholine bilayer was investigated in an 8-ns molecular dynamics trajectory. This large-scale statistical simulation brings to light not only the atomic-level structural features of the synthetic channel, but also its dynamical properties. Overall, the nanotube conserves its hollow tubular structure. The calculation reproduces the tilt of the channel with respect to the normal of the bilayer, in reasonable agreement with experiment. The results show a dislocation of the nanotube indicative of a possible disassembly process that may influence the channel conduction. The dynamics of the water in the hollow tubular structure has been characterized, and the conductance of the channel has been estimated. Transport properties of the peptide nanotube are discussed in comparison with other transporters.     

Membrane Peptides and their Role in Protobiological Evolution

How simple membrane peptides performed such essential protocellular functions as transport of ions and organic matter across membranes separatingthe interior of the cell from the environment, capture and utilization ofenergy, and transduction of environmental signals, is a key question inprotobiological evolution.On the basis of detailed, molecular-level computer simulations we explainhow these peptides fold at water-membrane interfaces, insert intomembranes, self-assemble into higher-order structures and acquire functions.We have investigated the interfacial behavior and folding of several peptides builtof leucine and glutamine residues and have demonstrated that many of them tendto adopt ordered structures. Further, we have studied the insertion of an -helical peptide containing leucine (L) and serine (S) of the form (LSLLLSL)₃ into a model membrane. The transmembranestate is metastable, and approximately 15 kcal mol^-1 is required to insert the peptide into the membrane.Investigations of dimers formed by (LSLLLSL)₃ and glycophorin A demonstratehow the favorable free energy of helix association can offset the unfavorable free energy of insertion, leading to self-assembly of peptidehelices in the membrane. An example of a self-assembled structure is thetetrameric transmembrane pore of the influenza virus M2 protein, which isan efficient and selective voltage-gated proton channel. Our simulations explain the gating mechanism and provide guidelines how to re-engineer thechannel to act as a simple proton pump. In general, emergence of integralmembrane proteins appears to be quite feasible and may be easierto envision than the emergence of water-soluble proteins.     

Conformational Free-Energy Landscapes for a Peptide in Saline Environments

The conformations that proteins adopt in solution are a function of both their primary structure and surrounding aqueous environment. Recent experimental and computational work on small peptides, e.g., polyK, polyE, and polyR, have highlighted an interesting and unusual behavior in the presence of aqueous ions such as ClO₄⁻, Na⁺, and K⁺. Notwithstanding the aforementioned studies, as of this writing, the nature of the driving force induced by the presence of ions and its role on the conformational stability of peptides remains only partially understood. Molecular-dynamics simulations have been performed on the heptapeptide AEAAAEA in NaCl and KCl solutions at concentrations of 0.5, 1.0, and 2.0 M. Metadynamics in conjunction with a three-dimensional model reaction coordinate was used to sample the conformational space of the peptide. All simulations were run for 2 μs. Free-energy landscapes were computed over the model reaction coordinate for the peptide in each saline assay as well as in the absence of ions. Circular dichroism spectra were also calculated from each trajectory. In the presence of Na⁺ and K⁺ ions, no increase in helicity is observed with respect to the conformation in pure water.     

Impaired transport of nucleotides in a mitochondrial carrier explains severe human genetic diseases

The mitochondrial ADP/ATP carrier (AAC) is a prominent actor in the energetic regulation of the cell, importing ADP into the mitochondria and exporting ATP toward the cytoplasm. Severe genetic diseases have been ascribed to specific mutations in this membrane protein. How minute, well-localized modifications of the transporter impact the function of the mitochondria remains, however, largely unclear. Here, for the first time, the relationship between all documented pathological mutations of the AAC and its transport properties is established. Activity measurements combined synergistically with molecular-dynamics simulations demonstrate how all documented pathological mutations alter the binding affinity and the translocation kinetics of the nucleotides. Throwing a bridge between the pathologies and their molecular origins, these results reveal two distinct mechanisms responsible for AAC-related genetic disorders, wherein the mutations either modulate the association of the nucleotides to the carrier by modifying its electrostatic signature or reduce its conformational plasticity.     

Interaction of a peptide nanotube with a water-membrane interface

Inserting peptide nanotubes into lipid bilayers modulates the permeability properties of the cell wall, thus conferring potential bacteriocidal capability. Interaction of a peptide nanotube formed by eight cyclo[RRKWLWLW] subunits with the surface of a hydrated dimyristoylphosphatidylcholine bilayer is investigated using molecular dynamics simulations. The present sequence of alternated D-L-alpha-amino acids has been shown to yield remarkable antibacterial in vitro activity, and the chosen topoisomer corresponds to the optimum amphipathy of the tubular structure, whereby non-polar and charged side chains are segregated by the aqueous interface. The cohesion of the nanotube is ensured by a scaffold of intermolecular hydrogen bonds between adjacent cyclic peptides, supplemented by favorable like-charged contacts of arginine side chains. It is further reinforced by interactions of charged residues with the lipid head groups and of non-polar residues with the lipid acyl chains. The simulation reveals a partial breaking of the synthetic channel accompanying its early insertion into the lipid bilayer. The latter opens new questions about how peptide nanotubes permeate the membrane, in particular whether or not (i) self-assembly precedes partitioning and (ii) translocation occurs with the complete tubular structure.     

Recognition of methylated DNA through methyl-CpG binding domain proteins

DNA methylation is a key regulatory control route in epigenetics, involving gene silencing and chromosome inactivation. It has been recognized that methyl-CpG binding domain (MBD) proteins play an important role in interpreting the genetic information encoded by methylated DNA (mDNA). Although the function of MBD proteins has attracted considerable attention and is well characterized, the mechanism underlying mDNA recognition by MBD proteins is still poorly understood. In this article, we demonstrate that the methyl-CpG dinucleotides are recognized at the MBD-mDNA interface by two MBD arginines through an interplay of hydrogen bonding and cation-π interaction. Through molecular dynamics and quantum-chemistry calculations we investigate the methyl-cytosine recognition process and demonstrate that methylation enhances MBD-mDNA binding by increasing the hydrophobic interfacial area and by strengthening the interaction between mDNA and MBD proteins. Free-energy perturbation calculations also show that methylation yields favorable contribution to the binding free energy for MBD-mDNA complex.