The enigma of microtubules and their self-organizing behavior in the cytoskeleton

Analysis of the strength of interfacial hydrogen bonds between tubulin dimers using quantum theory of atoms in molecules

Microtubules are key structural elements that, among numerous biological functions, maintain the cytoskeleton of the cell and have a major role in cell division, which makes them important cancer chemotherapy targets. Understanding the energy balance that brings tubulin dimers, the building blocks of microtubules, together to form a microtubule is especially important for revealing the mechanism of their dynamic instability. Several studies have been conducted to estimate various contributions to the free energy of microtubule formation. However, the hydrogen-bond contribution was not studied before as a separate component. In this work, we use concepts such as the quantum theory of atoms in molecules to estimate the per-residue strength of hydrogen bonds contributing to the overall stability that brings subunits together in pair of tubulin heterodimers, across both the longitudinal and lateral interfaces. Our study shows that hydrogen bonding plays a major role in the stability of tubulin systems. Several residues that are crucial to the binding of vinca alkaloids are shown to be strongly involved in longitudinal microtubule stabilization. This indicates a direct relation between the binding of these agents and the effect on the interfacial hydrogen-bonding network, and explains the mechanism of their action. Lateral contacts showed much higher stability than longitudinal ones (-462 ± 70 vs. -392 ± 59 kJ/mol), which suggests a dramatic lateral stabilization effect of the GTP cap in the β-subunit. The role of the M-loop in lateral stability in absence of taxol was shown to be minor. The B-lattice lateral hydrogen bonds are shown to be comparable in strength to the A-lattice ones (-462 ± 70 vs. -472 ± 46 kJ/mol). These findings establish the importance of hydrogen bonds to the stability of tubulin systems.

Microtubule stability studied by three-dimensional molecular theory of solvation

We study microtubular supramolecular architectures of tubulin dimers self-assembling into linear protofilaments, in turn forming a closed tube, which is an important component of the cytoskeleton. We identify the protofilament arrangements with the lowest free energy using molecular dynamics to optimize tubulin conformations. We then use the three-dimensional molecular theory of solvation to obtain the hydration structure of protofilaments built of optimized tubulins and the solvent-mediated effective potential between them. The latter theoretical method, based on first principles of statistical mechanics, is capable of predicting the structure and thermodynamics of solvation of supramolecular architectures. We obtained a set of profiles of the potential of mean force between protofilaments in a periodic two-dimensional sheet in aqueous solution. The profiles were calculated for a number of amino acid sequences, tubulin conformations, and spatial arrangements of protofilaments. The results indicate that the effective interaction between protofilaments in aqueous solution depends little on the isotypes studied; however, it strongly depends on the M loop conformation of beta-tubulin. Based on the analysis of the potential of mean force between adjacent protofilaments, we found the optimal arrangement of protofilaments, which is in good agreement with other studies. We also decomposed the potential of mean force into its energetic and entropic components, and found that both are considerable in the free-energy balance for the stabilized protofilament arrangements.

Information processing in brain microtubules

Models of the mind are based on the idea that neuron microtubules can perform computation. From this point of view, information processing is the fundamental issue for understanding the brain mechanisms that produce consciousness. The cytoskeleton polymers could store and process information through their dynamic coupling mediated by mechanical energy. We analyze the problem of information transfer and storage in brain microtubules, considering them as a communication channel. We discuss the implications of assuming that consciousness is generated by the subneuronal process.

Quantum models of the mind: are they compatible with environment decoherence?

Quantum models of the mind associate consciousness with coherent superposition of states in the brain. Some authors consider consciousness to be the result of a kind of internal quantum measurement process in the brain. In this paper we discuss the ideas of Hameroff-Penrose and Tegmark and their calculation for an estimate of decoherence time. We criticize the Hameroff-Penrose model in the context of a quantum brain model by gravitational collapse orchestrated objective reduction (OOR), assumed by Penrose, and we propose instead that the decoherence process is caused by interaction with the environment. We consider it useful to exploit this possibility because of the growing importance of the decoherence theory in quantum measurement, and also because quantum mechanics can be applied to brain study independently of the Hameroff-Penrose model for mind and consciousness. Our conclusion is that the Hameroff-Penrose model is not compatible with decoherence, but nevertheless the quantum brain can still be considered if we replace gravitational collapse OOR with decoherence. However, our result does not agree with Tegmark's conclusion of refuting not only the Hameroff-Penrose gravitational collapse but also the quantum brain, based on decoherence time calculations in specific cases in the brain. In spite of this fact we also disagree with some points of the response to Tegmark's article given by Hagan, Hameroff, and Tuszynski.

Quantum computation in brain microtubules: decoherence and biological feasibility

The Penrose-Hameroff orchestrated objective reduction (orch. OR) model assigns a cognitive role to quantum computations in microtubules within the neurons of the brain. Despite an apparently "warm, wet, and noisy" intracellular milieu, the proposal suggests that microtubules avoid environmental decoherence long enough to reach threshold for "self-collapse" (objective reduction) by a quantum gravity mechanism put forth by Penrose. The model has been criticized as regards the issue of environmental decoherence, and a recent report by Tegmark finds that microtubules can maintain quantum coherence for only 10(-13) s, far too short to be neurophysiologically relevant. Here, we critically examine the decoherence mechanisms likely to dominate in a biological setting and find that (1) Tegmark's commentary is not aimed at an existing model in the literature but rather at a hybrid that replaces the superposed protein conformations of the orch. OR theory with a soliton in superposition along the microtubule; (2) recalculation after correcting for differences between the model on which Tegmark bases his calculations and the orch. OR model (superposition separation, charge vs dipole, dielectric constant) lengthens the decoherence time to 10(-5)-10(-4) s; (3) decoherence times on this order invalidate the assumptions of the derivation and determine the approximation regime considered by Tegmark to be inappropriate to the orch. OR superposition; (4) Tegmark's formulation yields decoherence times that increase with temperature contrary to well-established physical intuitions and the observed behavior of quantum coherent states; (5) incoherent metabolic energy supplied to the collective dynamics ordering water in the vicinity of microtubules at a rate exceeding that of decoherence can counter decoherence effects (in the same way that lasers avoid decoherence at room temperature); (6) microtubules are surrounded by a Debye layer of counterions, which can screen thermal fluctuations, and by an actin gel that might enhance the ordering of water in bundles of microtubules, further increasing the decoherence-free zone by an order of magnitude and, if the dependence on the distance between environmental ion and superposed state is accurately reflected in Tegmark's calculation, extending decoherence times by three orders of magnitude; (7) topological quantum computation in microtubules may be error correcting, resistant to decoherence; and (8) the decohering effect of radiative scatterers on microtubule quantum states is negligible. These considerations bring microtubule decoherence into a regime in which quantum gravity could interact with neurophysiology.