Assessment of mutation probabilities of KRAS G12 missense mutants and their long-timescale dynamics by atomistic molecular simulations and Markov state modeling.

A mutated KRAS protein is frequently observed in human cancers. Traditionally, the oncogenic properties of KRAS missense mutants at position 12 (G12X) have been considered as equal. Here, by assessing the probabilities of occurrence of all KRAS G12X mutations and KRAS dynamics we show that this assumption does not hold true. Instead, our findings revealed an outstanding mutational bias. We conducted a thorough mutational analysis of KRAS G12X mutations and assessed to what extent the observed mutation frequencies follow a random distribution. Unique tissue-specific frequencies are displayed with specific mutations, especially with G12R, which cannot be explained by random probabilities. To clarify the underlying causes for the nonrandom probabilities, we conducted extensive atomistic molecular dynamics simulations (170 µs) to study the differences of G12X mutations on a molecular level. The simulations revealed an allosteric hydrophobic signaling network in KRAS, and that protein dynamics is altered among the G12X mutants and as such differs from the wild-type and is mutation-specific. The shift in long-timescale conformational dynamics was confirmed with Markov state modeling. A G12X mutation was found to modify KRAS dynamics in an allosteric way, which is especially manifested in the switch regions that are responsible for the effector protein binding. The findings provide a basis to understand better the oncogenic properties of KRAS G12X mutants and the consequences of the observed nonrandom frequencies of specific G12X mutations.

Theoretical analysis of microtubule dynamics at all times.

Microtubules are biopolymers consisting of tubulin dimer subunits. As a major component of cytoskeleton they are essential for supporting most important cellular processes such as cell division, signaling, intracellular transport and cell locomotion. The hydrolysis of guanosine triphosphate (GTP) molecules attached to each tubulin subunit supports the nonequilibrium nature of microtubule dynamics. One of the most spectacular properties of microtubules is their dynamic instability when their growth from continuous attachment of tubulin dimers stochastically alternates with periods of shrinking. Despite the critical importance of this process to all cellular activities, its mechanism remains not fully understood. We investigated theoretically microtubule dynamics at all times by analyzing explicitly temporal evolution of various length clusters of unhydrolyzed subunits. It is found that the dynamic behavior of microtubules depends strongly on initial conditions. Our theoretical findings provide a microscopic explanation for recent experiments which found that the frequency of catastrophes increases with the lifetime of microtubules. It is argued that most growing microtubule configurations cannot transit in one step into a shrinking state, leading to a complex overall temporal behavior. Theoretical calculations combined with Monte Carlo computer simulations are also directly compared with experimental observations, and good agreement is found.

Theoretical analysis of microtubules dynamics using a physical-chemical description of hydrolysis.

Microtubules are cytoskeleton multifilament proteins that support many fundamental biological processes such as cell division, cellular transport, and motility. They can be viewed as dynamic polymers that function in nonequilibrium conditions stimulated by hydrolysis of GTP (guanosine triphosphate) molecules bound to their monomers. We present a theoretical description of microtubule dynamics based on discrete-state stochastic models that explicitly takes into account all relevant biochemical transitions. In contrast to previous theoretical analysis, a more realistic physical-chemical description of GTP hydrolysis is presented, in which the hydrolysis rate at a given monomer depends on the chemical composition of the neighboring monomers. This dependence naturally leads to a cooperativity in the hydrolysis. It is found that this cooperativity significantly influences all dynamic properties of microtubules. It is suggested that the dynamic instability in cytoskeleton proteins might be observed only for weak cooperativity, while the strong cooperativity in hydrolysis suppresses the dynamic instability. The presented microscopic analysis is compared with existing phenomenological descriptions of hydrolysis processes. Our analytical calculations, supported by computer Monte Carlo simulations, are also compared with available experimental observations.

Microtubule dynamic instability: a new model with coupled GTP hydrolysis and multistep catastrophe.

A key question in understanding microtubule dynamics is how GTP hydrolysis leads to catastrophe, the switch from slow growth to rapid shrinkage. We first provide a review of the experimental and modeling literature, and then present a new model of microtubule dynamics. We demonstrate that vectorial, random, and coupled hydrolysis mechanisms are not consistent with the dependence of catastrophe on tubulin concentration and show that, although single-protofilament models can explain many features of dynamics, they do not describe catastrophe as a multistep process. Finally, we present a new combined (coupled plus random hydrolysis) multiple-protofilament model that is a simple, analytically solvable generalization of a single-protofilament model. This model accounts for the observed lifetimes of growing microtubules, the delay to catastrophe following dilution and describes catastrophe as a multistep process.

Understanding phase behavior of plant cell cortex microtubule organization.

Plant microtubules are found to be strongly associated with the cell cortex and to experience polymerization/depolymerization processes that are responsible for the organization of microtubule cortical array. Here we propose a minimal model that incorporates the basic assembly dynamics and intermicrotubule interaction to understand the unexplored phase behavior of such a system. Through kinetic Monte Carlo simulations and theoretical calculations, we show that the self-organized patterns of plant cell cortical microtubules can be regulated by controlling single microtubule assembly dynamics. Biologically, this means that the structural reorganization can be regulated by microtubule-associated proteins via changing microtubule dynamic instability parameters, such as the microtubule plus-end growing rate, GTP-tubulin hydrolysis rate, etc. Such regulation is indirectly confirmed by various in vivo experiments. For the physical aspects, we not only construct the phase diagram that determines under what parameters ordered microtubule arrays form, but also predict that the essentially different ordered structures may appear through continuous and discontinuous transitions. The present study will play a central role in our understanding of the basic mechanism of plant cell noncentrosomal microtubule arrays.

Nonequilibrium self-assembly of a filament coupled to ATP/GTP hydrolysis.

We study the stochastic dynamics of growth and shrinkage of single actin filaments or microtubules taking into account insertion, removal, and ATP/GTP hydrolysis of subunits. The resulting phase diagram contains three different phases: two phases of unbounded growth: a rapidly growing phase and an intermediate phase, and one bounded growth phase. We analyze all these phases, with an emphasis on the bounded growth phase. We also discuss how hydrolysis affects force-velocity curves. The bounded growth phase shows features of dynamic instability, which we characterize in terms of the time needed for the ATP/GTP cap to disappear as well as the time needed for the filament to reach a length of zero (i.e., to collapse) for the first time. We obtain exact expressions for all these quantities, which we test using Monte Carlo simulations.

Compartment volume influences microtubule dynamic instability: a model study.

Microtubules (MTs) are cytoskeletal polymers that exhibit dynamic instability, the random alternation between growth and shrinkage. MT dynamic instability plays an essential role in cell development, division, and motility. To investigate dynamic instability, simulation models have been widely used. However, conditions under which the concentration of free tubulin fluctuates as a result of growing or shrinking MTs have not been studied before. Such conditions can arise, for example, in small compartments, such as neuronal growth cones. Here we investigate by means of computational modeling how concentration fluctuations caused by growing and shrinking MTs affect dynamic instability. We show that these fluctuations shorten MT growth and shrinkage times and change their distributions from exponential to non-exponential, gamma-like. Gamma-like distributions of MT growth and shrinkage times, which allow optimal stochastic searching by MTs, have been observed in various cell types and are believed to require structural changes in the MT during growth or shrinkage. Our results, however, show that these distributions can already arise as a result of fluctuations in the concentration of free tubulin due to growing and shrinking MTs. Such fluctuations are possible not only in small compartments but also when tubulin diffusion is slow or when many MTs (de)polymerize synchronously. Volume and all other factors that influence these fluctuations can affect MT dynamic instability and, consequently, the processes that depend on it, such as neuronal growth cone behavior and cell motility in general.

Near-critical behavior of aminoacyl-tRNA pools in E. coli at rate-limiting supply of amino acids.

The rates of consumption of different amino acids in protein synthesis are in general stoichiometrically coupled with coefficients determined by codon usage frequencies on translating ribosomes. We show that when the rates of synthesis of two or more amino acids are limiting for protein synthesis and exactly matching their coupled rates of consumption on translating ribosomes, the pools of aminoacyl-tRNAs in ternary complex with elongation factor Tu and GTP are hypersensitive to a variation in the rate of amino acid supply. This high sensitivity makes a macroscopic analysis inconclusive, because it is accompanied by almost free and anticorrelated diffusion in copy numbers of ternary complexes. This near-critical behavior is relevant for balanced growth of Escherichia coli cells in media that lack amino acids and for adaptation of E. coli cells after downshifts from amino-acid-containing to amino-acid-lacking growth media. The theoretical results are used to discuss transcriptional control of amino acid synthesis during multiple amino acid limitation, the recovery of E. coli cells after nutritional downshifts and to propose a robust mechanism for the regulation of RelA-dependent synthesis of the global effector molecule ppGpp.

Untangling ligand induced activation and desensitization of G-protein-coupled receptors.

Long-term treatment with a drug to a G-protein-coupled receptor (GPCR) often leads to receptor-mediated desensitization, limiting the therapeutic lifetime of the drug. To better understand how this therapeutic window might be controlled, we created a mechanistic Monte Carlo model of the early steps in GPCR signaling and desensitization. Using this model we found that the rates of G-protein activation and receptor phosphorylation can be partially decoupled by varying the drug-receptor dissociation rate constant, k(off), and the drug's efficacy, alpha. The maximum ratio of G-protein activation to receptor phosphorylation (GARP) was found for drugs with an intermediate k(off) value and small alpha-value. Changes to the cellular environment, such as changes in the diffusivity of membrane molecules and the G-protein inactivation rate constant, affected the GARP value of a drug but did not change the characteristic shape of the GARP curve. These model results are examined in light of experimental data for a number of GPCRs and are found to be in good agreement, lending support to the idea that the desensitization properties of a drug might be tailored to suit a specific application.