Modeling non-genetic information dynamics in cells using reservoir computing

Virtually all cells use energy-driven, ion-specific membrane pumps to maintain large transmembrane gradients of Na+, K+, Cl-, Mg++, and Ca++, but the corresponding evolutionary benefit remains unclear. We propose that these gradients enable a dynamic and versatile biological system that acquires, analyzes, and responds to environmental information. We hypothesize that environmental signals are transmitted into the cell by ion fluxes along pre-existing gradients through gated ion-specific membrane channels. The consequent changes in cytoplasmic ion concentration can generate a local response or orchestrate global/regional cellular dynamics through wire-like ion fluxes along pre-existing and self-assembling cytoskeleton to engage the endoplasmic reticulum, mitochondria, and nucleus.

A Strategy Utilizing Protein-Protein Interaction Hubs for the Treatment of Cancer Diseases

We describe a strategy for the development of a rational approach of neoplastic disease therapy based on the demonstration that scale-free networks are susceptible to specific attacks directed against its connective hubs. This strategy involves the (i) selection of up-regulated hubs of connectivity in the tumors interactome, (ii) drug repurposing of these hubs, (iii) RNA silencing of non-druggable hubs, (iv) in vitro hub validation, (v) tumor-on-a-chip, (vi) in vivo validation, and (vii) clinical trial. Hubs are protein targets that are assessed as targets for rational therapy of cancer in the context of personalized oncology. We confirmed the existence of a negative correlation between malignant cell aggressivity and the target number needed for specific drugs or RNA interference (RNAi) to maximize the benefit to the patient's overall survival. Interestingly, we found that some additional proteins not generally targeted by drug treatments might justify the addition of inhibitors designed against them in order to improve therapeutic outcomes. However, many proteins are not druggable, or the available pharmacopeia for these targets is limited, which justifies a therapy based on encapsulated RNAi.

Computational Analysis and Experimental Testing of the Molecular Mode of Action of Gatastatin and Its Derivatives

Given its critical role in cell mitosis, the tubulin γ chain represents a viable chemotherapeutic target to solve the specificity issues associated with targeting α and β tubulin. Since γ tubulin is overexpressed in glioblastoma multiforme (GBM) and some breast lesions, the glaziovianin A derivative gatastatin, presented as a γ-tubulin-specific inhibitor, could yield a successful therapeutic strategy. The present work aims to identify the binding sites and modes of gatastatin and its derivatives through molecular-docking simulations. Computational binding free energy predictions were compared to experimental microscale thermophoresis assay results. The computational simulations did not reveal a strong preference toward γ tubulin, suggesting that further derivatization may be needed to increase its specificity.

Computational Prediction and Experimental Validation of the Unique Molecular Mode of Action of Scoulerine

Scoulerine is a natural compound that is known to bind to tubulin and has anti-mitotic properties demonstrated in various cancer cells. Its molecular mode of action has not been precisely known. In this work, we perform computational prediction and experimental validation of the mode of action of scoulerine. Based on the existing data in the Protein Data Bank (PDB) and using homology modeling, we create human tubulin structures corresponding to both free tubulin dimers and tubulin in a microtubule. We then perform docking of the optimized structure of scoulerine and find the highest affinity binding sites located in both the free tubulin and in a microtubule. We conclude that binding in the vicinity of the colchicine binding site and near the laulimalide binding site are the most likely locations for scoulerine interacting with tubulin. Thermophoresis assays using scoulerine and tubulin in both free and polymerized form confirm these computational predictions. We conclude that scoulerine exhibits a unique property of a dual mode of action with both microtubule stabilization and tubulin polymerization inhibition, both of which have similar affinity values.

The Effect of the Protein Synthesis Entropy Reduction on the Cell Size Regulation and Division Size of Unicellular Organisms

The underlying mechanism determining the size of a particular cell is one of the fundamental unknowns in cell biology. Here, using a new approach that could be used for most of unicellular species, we show that the protein synthesis and cell size are interconnected biophysically and that protein synthesis may be the chief mechanism in establishing size limitations of unicellular organisms. This result is obtained based on the free energy balance equation of protein synthesis and the second law of thermodynamics. Our calculations show that protein synthesis involves a considerable amount of entropy reduction due to polymerization of amino acids depending on the cytoplasmic volume of the cell. The amount of entropy reduction will increase with cell growth and eventually makes the free energy variations of the protein synthesis positive (that is, forbidden thermodynamically). Within the limits of the second law of thermodynamics we propose a framework to estimate the optimal cell size at division.

Testing amino acid-codon affinity hypothesis using molecular docking

Genetic code refers to a set of rules that assign trinucleotides called codons to amino acids in the process of protein synthesis. Investigating the genetic code's logic and its evolutionary origin has always been both intriguing and challenging. While the correspondence rules between codons and amino acids in the genetic code are well-known, it is still unclear whether those assignments can be explained based on energetic or/and entropic arguments. As an attempt at deciphering basic thermodynamic rules governing DNA translation, we used molecular docking to investigate the ability of amino acids to bind to their corresponding anticodon compared to other codons. The total number of 1280 direct docking interactions have been performed for each amino acid-codon/anti-codon case to find whether the amino acids have a preference to bind to their cognate anticodons or codons. Based on docking scores which are expected to correlate with binding affinity, no correlation with genetic correspondence rules was observed suggesting a more subtle process, other than direct binding, to explain codon-amino-acid specificity.

A new method for protein characterization and classification using geometrical features for 3D face analysis: An example of tubulin structures

This article reports on the results of research aimed to translate biometric 3D face recognition concepts and algorithms into the field of protein biophysics in order to precisely and rapidly classify morphological features of protein surfaces. Both human faces and protein surfaces are free-forms and some descriptors used in differential geometry can be used to describe them applying the principles of feature extraction developed for computer vision and pattern recognition. The first part of this study focused on building the protein dataset using a simulation tool and performing feature extraction using novel geometrical descriptors. The second part tested the method on two examples, first involved a classification of tubulin isotypes and the second compared tubulin with the FtsZ protein, which is its bacterial analog. An additional test involved several unrelated proteins. Different classification methodologies have been used: a classic approach with a support vector machine (SVM) classifier and an unsupervised learning with a k-means approach. The best result was obtained with SVM and the radial basis function kernel. The results are significant and competitive with the state-of-the-art protein classification methods. This leads to a new methodological direction in protein structure analysis.

Dataset on interactions of membrane active agents with lipid bilayers

We address drug interactions with lipids using in silico simulations and in vitro experiments. The data article provides extended explanations on molecular mechanisms behind membrane action of membrane-active agents (MAAs): antimicrobial peptides and chemotherapy drugs. Complete interpretation of the data is found in the associated original article ‘charge-based interactions of antimicrobial peptides and general drugs with lipid bilayers’ [1]. Data on molecular dynamic simulations of the drug lipid complexes are provided. Additional data and information are provided here to explain the connectivity among various information and techniques used for understanding of the membrane action and/or binding of MAAs including aptamers. Brief explanation has been provided on the possibility of achieving a converted triangle from newly discovered quadrangle, sides of which explain four different phenomena: ‘membrane effects’, ‘detection and quantification’, ‘origin of energetics’ and ‘structure stability’ while drug effects occur. Triangle or quadrangle corners represent various techniques that were applied.

Signaling Complexity Measured by Shannon Entropy and Its Application in Personalized Medicine

Traditional approaches to cancer therapy seek common molecular targets in tumors from different patients. However, molecular profiles differ between patients, and most tumors exhibit inherent heterogeneity. Hence, imprecise targeting commonly results in side effects, reduced efficacy, and drug resistance. By contrast, personalized medicine aims to establish a molecular diagnosis specific to each patient, which is currently feasible due to the progress achieved with high-throughput technologies. In this report, we explored data from human RNA-seq and protein–protein interaction (PPI) networks using bioinformatics to investigate the relationship between tumor entropy and aggressiveness. To compare PPI subnetworks of different sizes, we calculated the Shannon entropy associated with vertex connections of differentially expressed genes comparing tumor samples with their paired control tissues. We found that the inhibition of up-regulated connectivity hubs led to a higher reduction of subnetwork entropy compared to that obtained with the inhibition of targets selected at random. Furthermore, these hubs were described to be participating in tumor processes. We also found a significant negative correlation between subnetwork entropies of tumors and the respective 5-year survival rates of the corresponding cancer types. This correlation was also observed considering patients with lung squamous cell carcinoma (LUSC) and lung adenocarcinoma (LUAD) based on the clinical data from The Cancer Genome Atlas database (TCGA). Thus, network entropy increases in parallel with tumor aggressiveness but does not correlate with PPI subnetwork size. This correlation is consistent with previous reports and allowed us to assess the number of hubs to be inhibited for therapy to be effective, in the context of precision medicine, by reference to the 100% patient survival rate 5 years after diagnosis. Large standard deviations of subnetwork entropies and variations in target numbers per patient among tumor types characterize tumor heterogeneity.

Theorizing how the brain encodes consciousness based on negentropic entanglement

The physicality of subjectivity is explained through a theoretical conceptualization of guidance waves informing meaning in negentropically entangled non-electrolytic brain regions. Subjectivity manifests its influence at the microscopic scale of matter originating from de Broglie 'hidden' thermodynamics as action of guidance waves. The preconscious experienceability of subjectivity is associated with a nested hierarchy of microprocesses, which are actualized as a continuum of patterns of discrete atomic microfeels (or "qualia"). The mechanism is suggested to be through negentropic entanglement of hierarchical thermodynamic transfer of information as thermo-qubits originating from nonpolarized regions of actin-binding proteinaceous structures of nonsynaptic spines. The resultant continuous stream of intrinsic information entails a negentropic action (or experiential flow of thermo-quantum internal energy that results in a negentropic force) which is encoded through the non-zero real component of the mean approximation of the negentropic force as a 'consciousness code'. Consciousness consisting of two major subprocesses: (1) preconscious experienceability and (2) conscious experience. Both are encapsulated by nonreductive physicalism and panexperiential materialism. The subprocess (1) governing "subjectivity" carries many microprocesses leading to the actualization of discrete atomic microfeels by the 'consciousness code'. These atomic microfeels constitute internal energy that results in the transfer intrinsic information in terms of thermo-qubits. These thermo-qubits are realized as thermal entropy and sensed by subprocess (2) governing "self-awareness" in conscious experience.

Abstract B43: Validation of a network-based strategy for the optimization of combinatorial target selection in breast cancer therapy

Network-based strategies provided by systems biology are attractive tools for cancer therapy. Modulation of cancer networks by anticancer drugs may alter the response of malignant cells and/or drive network reorganization into the inhibition of cancer progression. Previously, using systems biology approach and cancer signaling networks, we identified the top 5 highly expressed and connected proteins (HSP90AB1, CSNK2B, TK1, YWHAB, and VIM) in the invasive MDA-MB-231 breast cancer cell line. Here, we have knocked down the expression of these proteins, individually or together using siRNAs. The transfected cell lines were assessed for in vitro cell growth, colony formation, migration, and invasion relative to control transfected MDA-MB-231, the noninvasive MCF-7 breast carcinoma cell line, and the nontumoral mammary epithelial cell line MCF-10A. The knockdown of the top-5 upregulated connectivity hubs successfully inhibited the in vitro proliferation, colony formation, anchorage independence, migration, and invasion in MDA-MB-231 cells, with minimal effects in the control transfected MDA-MB-231 cells or MCF-7 and MCF-10A cells. The in vitro validation of bioinformatics predictions regarding optimized multitarget selection for therapy suggests that protein expression levels together with protein-protein interaction network analysis may provide an optimized combinatorial target selection for a highly effective antimetastatic precision therapy in triple-negative breast cancer. This approach increases the ability to identify not only druggable hubs as essential targets for cancer survival, but also interactions most susceptible to synergistic drug action. The data provided in this report constitute a preliminary step toward the personalized clinical application of our strategy to optimize the therapeutic use of anticancer drugs.

Citation Format: Tatiana Martins Tilli, Nicolas Carels, Jack Adam Tuszynski, Manijeh Pasdar. Validation of a network-based strategy for the optimization of combinatorial target selection in breast cancer therapy [abstract]. In: Proceedings of the AACR International Conference held in cooperation with the Latin American Cooperative Oncology Group (LACOG) on Translational Cancer Medicine; May 4-6, 2017; São Paulo, Brazil. Philadelphia (PA): AACR; Clin Cancer Res 2018;24(1_Suppl):Abstract nr B43.

Computer-aided design of magnetic molecularly imprinted polymer nanoparticles for solid-phase extraction and determination of levetiracetam in human plasma

Analytical methods should be accurate and specific to measure plasma drug concentration. Nevertheless, current sample preparation techniques suffer from limitations, including matrix interference and intensive sample preparation. In this study, a novel technique was proposed for the synthesis of a molecularly imprinted polymer (MIP) on magnetic Fe₃O₄ nanoparticles (NPs) with uniform core–shell structure. The Fe₃O₄@MIPs NPs were then applied to separate and enrich an antiepileptic drug, levetiracetam, from human plasma. A computational approach was developed to screen the functional monomers and polymerization solvents to provide a suitable design for the synthesized MIP. Different analysis techniques and re-binding experiments were performed to characterize the Fe₃O₄@MIP NPs, as well as to identify optimal conditions for the extraction process. Adsorption isotherms were best fitted to the Langmuir model and adsorption kinetics were modeled with pseudo-second-order kinetics. The Fe₃O₄@MIP NPs showed reasonable adsorption capacity and improved imprinting efficiency. A validated colorimetric assay was introduced as a comparable method to a validated HPLC assay for the quantitation of levetiracetam in plasma in the range of 10–80 μg mL⁻¹ after extraction. The results from the HPLC and colorimetric assays showed good precision (between 1.08% and 9.87%) and recoveries (between 94% and 106%) using the Fe₃O₄@MIP NPs. The limit of detection and limit of quantification were estimated to be 2.58 μg mL⁻¹ and 7.81 μg mL⁻¹, respectively for HPLC assay and 2.32 μg mL⁻¹ and 7.02 μg mL⁻¹, respectively for colorimetric assay. It is believed that synthesized Fe₃O₄@MIP NPs as a sample clean-up technique combined with the proposed assays can be used for determination of levetiracetam in plasma.

A novel molecularly imprinted polymer on Fe₃O₄ nanoparticles was applied to extract antiepileptic drug; levetiracetam from plasma for TDM purposes.

Explaining the Microtubule Energy Balance: Contributions Due to Dipole Moments, Charges, van der Waals and Solvation Energy

Microtubules are the main components of mitotic spindles, and are the pillars of the cellular cytoskeleton. They perform most of their cellular functions by virtue of their unique dynamic instability processes which alternate between polymerization and depolymerization phases. This in turn is driven by a precise balance between attraction and repulsion forces between the constituents of microtubules (MTs)—tubulin dimers. Therefore, it is critically important to know what contributions result in a balance of the interaction energy among tubulin dimers that make up microtubules and what interactions may tip this balance toward or away from a stable polymerized state of tubulin. In this paper, we calculate the dipole–dipole interaction energy between tubulin dimers in a microtubule as part of the various contributions to the energy balance. We also compare the remaining contributions to the interaction energies between tubulin dimers and establish a balance between stabilizing and destabilizing components, including the van der Waals, electrostatic, and solvent-accessible surface area energies. The energy balance shows that the GTP-capped tip of the seam at the plus end of microtubules is stabilized only by −9 kcal/mol, which can be completely reversed by the hydrolysis of a single GTP molecule, which releases +14 kcal/mol and destabilizes the seam by an excess of +5 kcal/mol. This triggers the breakdown of microtubules and initiates a disassembly phase which is aptly called a catastrophe.

Optomechanical proposal for monitoring microtubule mechanical vibrations

Microtubules provide the mechanical force required for chromosome separation during mitosis. However, little is known about the dynamic (high-frequency) mechanical properties of microtubules. Here, we theoretically propose to control the vibrations of a doubly clamped microtubule by tip electrodes and to detect its motion via the optomechanical coupling between the vibrational modes of the microtubule and an optical cavity. In the presence of a red-detuned strong pump laser, this coupling leads to optomechanical-induced transparency of an optical probe field, which can be detected with state-of-the art technology. The center frequency and line width of the transparency peak give the resonance frequency and damping rate of the microtubule, respectively, while the height of the peak reveals information about the microtubule-cavity field coupling. Our method opens the new possibilities to gain information about the physical properties of microtubules, which will enhance our capability to design physical cancer treatment protocols as alternatives to chemotherapeutic drugs.

Toward precision medicine of breast cancer

In this review, we report on breast cancer's molecular features and on how high throughput technologies are helping in understanding the dynamics of tumorigenesis and cancer progression with the aim of developing precision medicine methods. We first address the current state of the art in breast cancer therapies and challenges in order to progress towards its cure. Then, we show how the interaction of high-throughput technologies with in silico modeling has led to set up useful inferences for promising strategies of target-specific therapies with low secondary effect incidence for patients. Finally, we discuss the challenge of pharmacogenetics in the clinical practice of cancer therapy. All these issues are explored within the context of precision medicine.

On the classical vibrational coherence of carbonyl groups in the selectivity filter backbone of the KcsA ion channel

It has been suggested that quantum coherence in the selectivity filter of ion channel may play a key role in fast conduction and selectivity of ions. However, it has not been clearly elucidated yet why classical coherence is not sufficient for this purpose. In this paper, we investigate the classical vibrational coherence between carbonyl groups oscillations in the selectivity filter of KcsA ion channels based on the data obtained from molecular dynamics simulations. Our results show that classical coherence plays no effective role in fast ionic conduction.

Regulation of channel function due to physical energetic coupling with a lipid bilayer

Regulation of membrane protein functions due to hydrophobic coupling with a lipid bilayer has been investigated. An energy formula describing interactions between lipid bilayer and integral ion channels with different structures, which is based on the screened Coulomb interaction approximation, has been developed. Here the interaction energy is represented as being due to charge-based interactions between channel and lipid bilayer. The hydrophobic bilayer thickness channel length mismatch is found to induce channel destabilization exponentially while negative lipid curvature linearly. Experimental parameters related to channel dynamics are consistent with theoretical predictions. To measure comparable energy parameters directly in the system and to elucidate the mechanism at an atomistic level we performed molecular dynamics (MD) simulations of the ion channel forming peptide-lipid complexes. MD simulations indicate that peptides and lipids experience electrostatic and van der Waals interactions for short period of time when found within each other's proximity. The energies from these two interactions are found to be similar to the energies derived theoretically using the screened Coulomb and the van der Waals interactions between peptides (in ion channel) and lipids (in lipid bilayer) due to mainly their charge properties. The results of in silico MD studies taken together with experimental observable parameters and theoretical energetic predictions suggest that the peptides induce ion channels inside lipid membranes due to peptide-lipid physical interactions. This study provides a new insight helping better understand of the underlying mechanisms of membrane protein functions in cell membrane leading to important biological implications.

Nonlinear dynamics of microtubules: biophysical implications

A recently developed model of nonlinear dynamics for microtubules is further expanded based on the biophysical arguments involving the secondary structure of the constitutive protein tubulin and on the ferroelectric properties of microtubules. It is demonstrated that kink excitations arise due to GTP hydrolysis that causes a dynamical transition in the structure of tubulin. The presence of an intrinsic electric field associated with the structure of a microtubule leads to unidirectional propagation of the kink excitation along the microtubule axis. This mechanism offers an explanation of the dynamic instability phenomenon in terms of the electric field effects. Moreover, a possible elucidation of the unidirectional transport of cargo via motor proteins such as kinesin and dynein is proposed within the model developed in this paper.

Models of the collective behavior of proteins in cells: tubulin, actin and motor proteins

One of the most important issues of molecular biophysics is the complex and multifunctional behavior of the cell's cytoskeleton. Interiors of living cells are structurally organized by the cytoskeleton networks of filamentous protein polymers: microtubules, actin and intermediate filaments with motor proteins providing force and directionality needed for transport processes. Microtubules (MT's) take active part in material transport within the cell, constitute the most rigid elements of the cell and hence found many uses in cell motility (e.g. flagella andcilia). At present there is, however, no quantitatively predictable explanation of how these important phenomena are orchestrated at a molecular level. Moreover, microtubules have been demonstrated to self-organize leading to pattern formation. We discuss here several models which attempt to shed light on the assembly of microtubules and their interactions with motor proteins. Subsequently, an overview of actin filaments and their properties isgiven with particular emphasis on actin assembly processes. The lengths of actin filaments have been reported that were formed by spontaneous polymerization of highly purified actin monomers after labeling with rhodamine-phalloidin. The length distributions are exponential with a mean of about 7 μm. This length is independent of the initial concentration of actin monomer, an observation inconsistent with a simple nucleation-elongation mechanism. However, with the addition of physically reasonable rates of filament annealing and fragmenting, a nucleation-elongation mechanism can reproduce the observed average length of filaments in two types of experiments: (1) filaments formed from a wide range of highly purified actin monomer concentrations, and (2) filaments formed from 24 mM actin over a range of CapZ concentrations. In the final part of the paper we briefly review the stochastic models used to describe the motion of motor proteins on protein filaments. The vast majority of these models are based on ratchet potentials with the presence of thermal noise and forcing due to ATP binding and a subsequent hydrolysis. Many outstanding questions remain to be quantitatively addressed on a molecular level in order to explain the structure-to-function relationship for the key elements of the cytoskeleton discussed in this review.

Emergence of intrinsic representations of images by feedforward and feedback processes and bioluminescent photons in early retinotopic areas

Recently, we put forward a redox molecular hypothesis involving the natural biophysical substrate of visual perception and imagery. Here, we explicitly propose that the feedback and feedforward iterative operation processes can be interpreted in terms of a homunculus looking at the biophysical picture in our brain during visual imagery. We further propose that the brain can use both picture-like and language-like representation processes. In our interpretation, visualization (imagery) is a special kind of representation i.e., visual imagery requires a peculiar inherent biophysical (picture-like) mechanism. We also conjecture that the evolution of higher levels of complexity made the biophysical picture representation of the external visual world possible by controlled redox and bioluminescent nonlinear (iterative) biochemical reactions in the V1 and V2 areas during visual imagery. Our proposal deals only with the primary level of visual representation (i.e. perceived "scene").

Nonlinear ionic pulses along microtubules

Microtubules are cylindrically shaped cytoskeletal biopolymers that are essential for cell motility, cell division and intracellular trafficking. Here, we investigate their polyelectrolyte character that plays a very important role in ionic transport throughout the intra-cellular environment. The model we propose demonstrates an essentially nonlinear behavior of ionic currents which are guided by microtubules. These features are primarily due to the dynamics of tubulin C-terminal tails which are extended out of the surface of the microtubule cylinder. We also demonstrate that the origin of nonlinearity stems from the nonlinear capacitance of each tubulin dimer. This brings about conditions required for the creation and propagation of solitonic ionic waves along the microtubule axis. We conclude that a microtubule plays the role of a biological nonlinear transmission line for ionic currents. These currents might be of particular significance in cell division and possibly also in cognitive processes taking place in nerve cells.

"Memory bytes" - molecular match for CaMKII phosphorylation encoding of microtubule lattices

Learning, memory and long-term potentiation (LTP) are supported by factors including post-synaptic calcium ion flux activating and transforming the hexagonal calcium-calmodulin kinase II (CaMKII) holoenzyme. Upon calcium-induced activation, up to six kinase domains extend upward, and up to six kinase domains extend downward from the CaMKII association domain, the fully activated holoenzyme resembling a robotic insect 20 nanometers in length. Each extended kinase domain can be phosphorylated, and able to phosphorylate other proteins, thus potentially further encoding synaptic information at intraneuronal molecular sites for memory storage, processing and distribution. Candidate sites for phosphorylation-encoded molecular memory include microtubules, cylindrical lattice polymers of the protein tubulin. Using molecular modeling, we find spatial dimensions and geometry of the six extended CaMKII kinase domains can precisely match those of microtubule hexagonal lattice neighborhoods (both A- and B-lattices), and show two feasible phosphorylation mechanisms. In one, phosphorylation sites (e.g., valine 208) on a CaMKII extended kinase domain interact with serine 444 on a C-terminal "tail" of tubulin. In the second, the CaMKII kinase domain unfurls, enabling phosphorylation sites to contact threonine and serine sites on the tubulin surface. We suggest sets of six CaMKII kinase domains phosphorylate hexagonal microtubule lattice neighborhoods collectively, e.g., conveying synaptic information as ordered arrays of six "bits", and thus a "byte", with (minimally) 2⁶ (64) possible bit states per CaMKII-microtubule interaction. We model two levels of interaction between CaMKII and microtubules, suggesting a testable framework for molecular memory encoding.

Quantum metabolism explains the allometric scaling of metabolic rates

A general model explaining the origin of allometric laws of physiology is proposed based on coupled energy-transducing oscillator networks embedded in a physical d-dimensional space (d = 1, 2, 3). This approach integrates Mitchell's theory of chemi-osmosis with the Debye model of the thermal properties of solids. We derive a scaling rule that relates the energy generated by redox reactions in cells, the dimensionality of the physical space and the mean cycle time. Two major regimes are found corresponding to classical and quantum behaviour. The classical behaviour leads to allometric isometry while the quantum regime leads to scaling laws relating metabolic rate and body size that cover a broad range of exponents that depend on dimensionality and specific parameter values. The regimes are consistent with a range of behaviours encountered in micelles, plants and animals and provide a conceptual framework for a theory of the metabolic function of living systems.

A nonlinear model of ionic wave propagation along microtubules

Microtubules (MTs) are important cytoskeletal polymers engaged in a number of specific cellular activities including the traffic of organelles using motor proteins, cellular architecture and motility, cell division and a possible participation in information processing within neuronal functioning. How MTs operate and process electrical information is still largely unknown. In this paper we investigate the conditions enabling MTs to act as electrical transmission lines for ion flows along their lengths. We introduce a model in which each tubulin dimer is viewed as an electric element with a capacitive, inductive and resistive characteristics arising due to polyelectrolyte nature of MTs. Based on Kirchhoff's laws taken in the continuum limit, a nonlinear partial differential equation is derived and analyzed. We demonstrate that it can be used to describe the electrostatic potential coupled to the propagating localized ionic waves.

Gravitational symmetry breaking leads to a polar liquid crystal phase of microtubules in vitro

Recent space-flight experiments performed by Tabony's team provided further evidence that a microgravity environment strongly affects the spatio-temporal organization of microtubule assemblies. Characteristic time and length scales were found that govern the organization of oriented bundles under Earth's gravitational field (GF). No such organization has been observed in a microgravity environment. This paper discusses physical mechanisms resulting in pattern formation under gravity and its disappearance in microgravity. The subtle interplay between chemical kinetics, diffusion, gravitational drift, thermal fluctuations, electrostatic interactions and liquid crystalline characteristics provides a plausible scenario.

Directed Binding: A Novel Physical Mechanism That Describes the Directional Motion of Two-Headed Kinesin Motor Proteins

We propose a novel physical mechanism to describe the mode of processive propagation of two-headed kinesin motor proteins along microtubule (MT) filaments. Binding and unbinding of the kinesin heads to and from the MT filament play a crucial role in producing movement. The chemical energy of adenosine triphosphate hydrolysis is used in large part for the unbinding process of kinesin from the MT filament. Importantly, in our model, the binding of each head is to be directionally oriented to the MT filament. Therefore, we treat the two motor domains (heads) as extended objects that are connected with each other by a neck region that contains the kinesin dimerization domain. The head domains recognize tubulin binding sites by feeling the two-dimensional periodic potential from the MT surface and are also subjected to thermal noise. Using experimentally determined results regarding physical parameters of the walk, we develop a simple mathematical and mechanical model in which directed binding of the heads to tubulin results in a directed twist of the molecule, probably in the neck linker region, away from its relaxed state. Unbinding of the head from the filament relaxes the twist and defines the propagation direction. We showed that there must be at least two torsional springs (one for every head) involved that can store elastic energy. Consequently, in our model, it is the internal structure both of the relaxed and tensed-up state and the transition mode between them that define the walking direction of kinesin. We present calculations based on the model that are in good quantitative agreement with experimental observations for kinesin.

Models of spatial and orientational self-organization of microtubules under the influence of gravitational fields

Tabony and co-workers [C. Papaseit, N. Pochon, and J. Tabony, Proc. Natl. Acad. Sci. U.S.A. 97, 8364 (2000)] showed that the self-organization of microtubules from purified tubulin solutions is sensitive to gravitational conditions. In this paper, we propose two models of spatial and orientational self-organization of microtubules in a gravitational field. First, the spatial model is based on the dominant chemical kinetics. The pattern formation of microtubule concentration is obtained (1) in terms of a moving kink in the limit when the disassembly rate is negligible, and (2) for the case of no free tubulin and only assembled microtubules present. Second, the orientational pattern of striped microtubule domains is consistent with predictions from a phenomenological Landau-Ginzburg free energy expansion in terms of an orientational order parameter.

Reassessing models of hepatic extraction

The aim of this investigation is to compare different mathematical models of the liver in the context of in vitro-in vivo correlation. We reanalyze drugs from the Houston reviews [1, 2], and compare the mathematical models. For the well-stirred model, a particular form of the distributed tubes model, and the dispersion model, fits are done to in vitro and in vivo intrinsic clearance data from microsomal and hepatocyte experiments. The distributed and dispersion models have decreased residuals as compared to the well-stirred model, but neither is to be clearly preferred over theother. It seems likely that drug-specific factors have a major impact on the quality of IVIVC correlations. While new experiments are needed to validate IVIVC models, our results indicate that improved correlation of in vitroand in vivo data is possible for high clearance drugs by using either a dispersion or distributed tube model rather than a well-stirred model.

Analysis of the migration behaviour of single microtubules in electric fields

By video contrast microscopy, individual microtubules formed from pure tubulin in the presence of taxol were studied in constant electric fields. At nearly physiological conditions, i.e., in a buffer at pH 6.8 and 120 mM ionic strength, suspended microtubules moved towards the anode with an electrophoretic mobility of approximately 2.6 x 10(-4) cm(2)/V s, corresponding to an unbalanced negative charge of 0.19 electron charges per tubulin dimer. Strikingly, this value is lower by a factor of at least 50 than that calculated from crystallographic data for the non-assembled tubulin dimer. Moreover, the taxol-stabilized microtubules had an isoelectric point of about pH 4.2 which is significantly lower than that known for the tubulin monomers. This indicates that microtubule formation is accompanied by substantial changes of charge distribution within the tubulin subunits. Constant electric fields were shown to affect also the orientation of microtubules gliding across a kinesin-coated surface at pH 6.8.

A chemical kinetics model for microtubule oscillations

A model for microtubule oscillations is presented based on a set of chemical reaction equations. The rate constants for these reactions are largely determined from experimental data. The plots of assembled tubulin and the phase diagram for assembly are compared with the experimental findings and are found to agree quite well. Copyright 1999 Academic Press.