MCell4 with BioNetGen: A Monte Carlo simulator of rule-based reaction-diffusion systems with Python interface.

Biochemical signaling pathways in living cells are often highly organized into spatially segregated volumes, membranes, scaffolds, subcellular compartments, and organelles comprising small numbers of interacting molecules. At this level of granularity stochastic behavior dominates, well-mixed continuum approximations based on concentrations break down and a particle-based approach is more accurate and more efficient. We describe and validate a new version of the open-source MCell simulation program (MCell4), which supports generalized 3D Monte Carlo modeling of diffusion and chemical reaction of discrete molecules and macromolecular complexes in solution, on surfaces representing membranes, and combinations thereof. The main improvements in MCell4 compared to the previous versions, MCell3 and MCell3-R, include a Python interface and native BioNetGen reaction language (BNGL) support. MCell4's Python interface opens up completely new possibilities for interfacing with external simulators to allow creation of sophisticated event-driven multiscale/multiphysics simulations. The native BNGL support, implemented through a new open-source library libBNG (also introduced in this paper), provides the capability to run a given BNGL model spatially resolved in MCell4 and, with appropriate simplifying assumptions, also in the BioNetGen simulation environment, greatly accelerating and simplifying model validation and comparison.

A spatial model of autophosphorylation of CaMKII in a glutamatergic spine suggests a network-driven kinetic mechanism for bistable changes in synaptic strength.

Activation of N-methyl-D-aspartate-type glutamate receptors (NMDARs) at synapses in the CNS triggers changes in synaptic strength that underlie memory formation in response to strong synaptic stimuli. The primary target of Ca2+ flowing through NMDARs is Ca2+/calmodulin-dependent protein kinase II (CaMKII) which forms dodecameric holoenzymes that are highly concentrated at the postsynaptic site. Activation of CaMKII is necessary to trigger long-term potentiation of synaptic strength (LTP), and is prolonged by autophosphorylation of subunits within the holoenzyme. Here we use MCell4, an agent-based, stochastic, modeling platform to model CaMKII holoenzymes placed within a realistic spine geometry. We show how two mechanisms of regulation of CaMKII, 'Ca2+-calmodulin-trapping (CaM-trapping)' and dephosphorylation by protein phosphatase-1 (PP1) shape the autophosphorylation response during a repeated high-frequency stimulus. Our simulation results suggest that autophosphorylation of CaMKII does not constitute a bistable switch. Instead, prolonged but temporary, autophosphorylation of CaMKII may contribute to a biochemical-network-based 'kinetic proof-reading" mechanism that controls induction of synaptic plasticity.

Interactions between calmodulin and neurogranin govern the dynamics of CaMKII as a leaky integrator.

Calmodulin-dependent kinase II (CaMKII) has long been known to play an important role in learning and memory as well as long term potentiation (LTP). More recently it has been suggested that it might be involved in the time averaging of synaptic signals, which can then lead to the high precision of information stored at a single synapse. However, the role of the scaffolding molecule, neurogranin (Ng), in governing the dynamics of CaMKII is not yet fully understood. In this work, we adopt a rule-based modeling approach through the Monte Carlo method to study the effect of Ca2+ signals on the dynamics of CaMKII phosphorylation in the postsynaptic density (PSD). Calcium surges are observed in synaptic spines during an EPSP and back-propagating action potential due to the opening of NMDA receptors and voltage dependent calcium channels. Using agent-based models, we computationally investigate the dynamics of phosphorylation of CaMKII monomers and dodecameric holoenzymes. The scaffolding molecule, Ng, when present in significant concentration, limits the availability of free calmodulin (CaM), the protein which activates CaMKII in the presence of calcium. We show that Ng plays an important modulatory role in CaMKII phosphorylation following a surge of high calcium concentration. We find a non-intuitive dependence of this effect on CaM concentration that results from the different affinities of CaM for CaMKII depending on the number of calcium ions bound to the former. It has been shown previously that in the absence of phosphatase, CaMKII monomers integrate over Ca2+ signals of certain frequencies through autophosphorylation (Pepke et al, Plos Comp. Bio., 2010). We also study the effect of multiple calcium spikes on CaMKII holoenzyme autophosphorylation, and show that in the presence of phosphatase, CaMKII behaves as a leaky integrator of calcium signals, a result that has been recently observed in vivo. Our models predict that the parameters of this leaky integrator are finely tuned through the interactions of Ng, CaM, CaMKII, and PP1, providing a mechanism to precisely control the sensitivity of synapses to calcium signals. Author Summary not valid for PLOS ONE submissions.

Functional Dissection of a Viral DNA Packaging Machine's Walker B Motif.

Many viruses employ ATP-powered motors for genome packaging. We combined genetic, biochemical, and single-molecule techniques to confirm the predicted Walker-B ATP-binding motif in the phage λ motor and to investigate the roles of the conserved residues. Most changes of the conserved hydrophobic residues resulted in >107-fold decrease in phage yield, but we identified nine mutants with partial activity. Several were cold-sensitive, suggesting that mobility of the residues is important. Single-molecule measurements showed that the partially active A175L exhibits a small reduction in motor velocity and increase in slipping, consistent with a slowed ATP binding transition, whereas G176S exhibits decreased slipping, consistent with an accelerated transition. All changes to the conserved D178, predicted to coordinate Mg2+•ATP, were lethal except conservative change D178E. Biochemical interrogation of the inactive D178N protein found no folding or assembly defects and near-normal endonuclease activity, but a ∼200-fold reduction in steady-state ATPase activity, a lag in the single-turnover ATPase time course, and no DNA packaging, consistent with a critical role in ATP-coupled DNA translocation. Molecular dynamics simulations of related enzymes suggest that the aspartate plays an important role in enhancing the catalytic activity of the motor by bridging the Walker motifs and precisely contributing its charged group to help polarize the bound nucleotide. Supporting this prediction, single-molecule measurements revealed that change D178E reduces motor velocity without increasing slipping, consistent with a slowed hydrolysis step. Our studies thus illuminate the mechanistic roles of Walker-B residues in ATP binding, hydrolysis, and DNA translocation by this powerful motor.

Evidence that a catalytic glutamate and an 'Arginine Toggle' act in concert to mediate ATP hydrolysis and mechanochemical coupling in a viral DNA packaging motor.

ASCE ATPases include ring-translocases such as cellular helicases and viral DNA packaging motors (terminases). These motors have conserved Walker A and B motifs that bind Mg2+-ATP and a catalytic carboxylate that activates water for hydrolysis. Here we demonstrate that Glu179 serves as the catalytic carboxylate in bacteriophage λ terminase and probe its mechanistic role. All changes of Glu179 are lethal: non-conservative changes abrogate ATP hydrolysis and DNA translocation, while the conservative E179D change attenuates ATP hydrolysis and alters single molecule translocation dynamics, consistent with a slowed chemical hydrolysis step. Molecular dynamics simulations of several homologous terminases suggest a novel mechanism, supported by experiments, wherein the conserved Walker A arginine 'toggles' between interacting with a glutamate residue in the 'lid' subdomain and the catalytic glutamate upon ATP binding; this switch helps mediate a transition from an 'open' state to a 'closed' state that tightly binds nucleotide and DNA, and also positions the catalytic glutamate next to the γ-phosphate to align the hydrolysis transition state. Concomitant reorientation of the lid subdomain may mediate mechanochemical coupling of ATP hydrolysis and DNA translocation. Given the strong conservation of these structural elements in terminase enzymes, this mechanism may be universal for viral packaging motors.

Nucleotide-dependent DNA gripping and an end-clamp mechanism regulate the bacteriophage T4 viral packaging motor.

ATP-powered viral packaging motors are among the most powerful biomotors known. Motor subunits arranged in a ring repeatedly grip and translocate the DNA to package viral genomes into capsids. Here, we use single DNA manipulation and rapid solution exchange to quantify how nucleotide binding regulates interactions between the bacteriophage T4 motor and DNA substrate. With no nucleotides, there is virtually no gripping and rapid slipping occurs with only minimal friction resisting. In contrast, binding of an ATP analog engages nearly continuous gripping. Occasional slips occur due to dissociation of the analog from a gripping motor subunit, or force-induced rupture of grip, but multiple other analog-bound subunits exert high friction that limits slipping. ADP induces comparably infrequent gripping and variable friction. Independent of nucleotides, slipping arrests when the end of the DNA is about to exit the capsid. This end-clamp mechanism increases the efficiency of packaging by making it essentially irreversible.

Walker-A Motif Acts to Coordinate ATP Hydrolysis with Motor Output in Viral DNA Packaging.

During the assembly of many viruses, a powerful ATP-driven motor translocates DNA into a preformed procapsid. A Walker-A "P-loop" motif is proposed to coordinate ATP binding and hydrolysis with DNA translocation. We use genetic, biochemical, and biophysical techniques to survey the roles of P-loop residues in bacteriophage lambda motor function. We identify 55 point mutations that reduce virus yield to below detectable levels in a highly sensitive genetic complementation assay and 33 that cause varying reductions in yield. Most changes in the predicted conserved residues K76, R79, G81, and S83 produce no detectable yield. Biochemical analyses show that R79A and S83A mutant proteins fold, assemble, and display genome maturation activity similar to wild-type (WT) but exhibit little ATPase or DNA packaging activity. Kinetic DNA cleavage and ATPase measurements implicate R79 in motor ring assembly on DNA, supporting recent structural models that locate the P-loop at the interface between motor subunits. Single-molecule measurements detect no translocation for K76A and K76R, while G81A and S83A exhibit strong impairments, consistent with their predicted roles in ATP binding. We identify eight residue changes spanning A78-K84 that yield impaired translocation phenotypes and show that Walker-A residues play important roles in determining motor velocity, pausing, and processivity. The efficiency of initiation of packaging correlates strongly with motor velocity. Frequent pausing and slipping caused by changes A78V and R79K suggest that these residues are important for ATP alignment and coupling of ATP binding to DNA gripping. Our findings support recent structural models implicating the P-loop arginine in ATP hydrolysis and mechanochemical coupling.