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arXiv2015

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation, and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.

q-bio.QM↗

arXiv2015

Theoretical analysis of transcription process with polymerase stalling

Experimental evidences show that in gene transcription, RNA polymerase has the possibility to be stalled at certain position of the transcription template. This may be due to the template damage, or protein barriers. Once stalled, polymerase may backtrack along the template to the previous nucleotide to wait for the repair of the damaged site, or simply bypass the barrier or damaged site and consequently synthesize an incorrect messenger RNA, or degrade and detach from the template. Thus, the {\it effective} transcription rate (the rate to synthesize correct product mRNA) and the transcription {\it effectiveness} (the ratio of the {\it effective} transcription rate to the {\it effective} transcription initiation rate) are both influenced by polymerase stalling events. This study shows that, Without backtracking, detachment of stalled polymerase can also help to increase the {\it effective} transcription rate and transcription {\it effectiveness}. Generally, the increase of bypass rate of the stalled polymerase will lead to the decrease of the {\it effective} transcription rate and transcription {\it effectiveness}. But when both detachment rate and backtracking rate of the stalled polymerase vanish, the {\it effective} transcription rate may also be increased by the bypass mechanism.

physics.bio-ph↗

arXiv2015

Translation with frameshifting of ribosome along mRNA transcript

Translation is an important process for prokaryotic and eukaryotic cells to produce necessary proteins for cell growth. Numerious experiments have been performed to explore the translational properties. Diverse models have also been developed to determine the biochemical mechanism of translation. However, to simplify the majority of the existing models, the frameshifting of ribosome along the mRNA transcript is neglected, which actually occurs in real cells and has been extensively experimentally studied. The frameshifting of ribosome evidently influences the efficiency and speed of translation, considering that the peptide chains synthesized by shifted ribosomes will not fold into functional proteins and will degrade rapidly. In this study, a theoretical model is presented to describe the translational process based on the model for totally asymmetric simple exclusion process. In this model, the frameshifting of the ribosome along the mRNA transcript and the attachment/detachment of the ribosome to/from the main body of mRNA codons during translation elongation process, are explicitly included. The results show that, with ribosome frameshifing, the speed of correctly synthesized peptide chains may increase first and then decrease with both the translation initiation rate $α$ and the ribosome detachment rate $ω_d$. This results indicates that regulating the translation process to reach maximal synthesized speed of proteins is theoretically feasible. Traffic-related problems of ribosome motion along the mRNA transcript are also addressed theoretically. Depending on parameter values, shock wave (or domain wall) may exist for ribosome probabilities along the mRNA.

physics.bio-ph↗

arXiv2015

Photostimulation activates restorable fragmentation of single mitochondrion by initiating oxide flashes

Mitochondrial research is important to ageing, apoptosis, and mitochondrial diseases. In previous works, mitochondria are usually stimulated indirectly by proapoptotic drugs to study mitochondrial development, which is in lack of controllability, or spatial and temporal resolution. These chemicals or even gene techniques regulating mitochondrial dynamics may also activate other inter- or intra-cellular processes simultaneously. Here we demonstrate a photostimulation method on single-mitochondrion level by tightly-focused femtosecond laser that can precisely activate restorable fragmentation of mitochondria which soon recover their original tubular structure after tens of seconds. In this process, series of mitochondrial reactive oxygen species (mROS) flashes are observed and found very critical to mitochondrial fragmentation. Meanwhile, transient openings of mitochondrial permeability transition pores (mPTP), suggested by oscillations of mitochondrial membrane potential, contribute to the scavenging of redundant mROS and recovery of fragmented mitochondria. Those results demonstrate photostimulation as an active, precise and controllable method for the study of mitochondrial oxidative and morphological dynamics or related fields.

q-bio.SC↗

arXiv2015

Mixed molecular motor traffic on nucleic acid tracks: models of transcriptional interference and regulation of gene expression

RNA polymerase (RNAP) is molecular machine that polymerizes a RNA molecule, a linear heteropolymer, using a single stranded DNA (ssDNA) as the corresponding template; the sequence of monomers of the RNA is dictated by that of monomers on the ssDNA template. While polymerizing a RNA, the RNAP walks step-by-step on the ssDNA template in a specific direction. Thus, a RNAP can be regarded also as a molecular motor and the sites of start and stop of its walk on the DNA mark the two ends of the genetic message that it transcribes into RNA. Interference of transcription of two overlapping genes is believed to regulate the levels of their expression, i.e., the overall rate of the corresponding RNA synthesis, through suppressive effect of one on the other. Here we model this process as a mixed traffic of two groups of RNAP motors that are characterized by two distinct pairs of start and stop sites. Each group polymerizes identical copies of a RNA while the RNAs polymerized by the two groups are different. These models, which may also be viewed as two interfering totally asymmetric simple exclusion processes, account for all modes of transcriptional interference in spite of their extreme simplicity. A combination of mean-field theory and computer simulation of these models demonstrate the physical origin of the switch-like regulation of the two interfering genes in both co-directional and contra-directional traffic of the two groups of RNAP motors.

physics.bio-ph↗

arXiv2015

libRoadRunner: A High Performance SBML Simulation and Analysis Library

This paper presents libRoadRunner, an extensible, high-performance, cross-platform, open-source software library for the simulation and analysis of models \ expressed using Systems Biology Markup Language (SBML). SBML is the most widely used standard for representing dynamic networks, especially biochemical networks. libRoadRunner supports solution of both large models and multiple replicas of a single model on desktop, mobile and cluster computers. libRoadRunner is a self-contained library, able to run both as a component inside other tools via its C++ and C bindings andnteractively through its Python interface. The Python Application Programming Interface (API) is similar to the APIs of Matlab and SciPy, making it fast and easy to learn, even for new users. libRoadRunner uses a custom Just-In-Time (JIT) compiler built on the widely-used LLVM JIT compiler framework to compile SBML-specified models directly into very fast native machine code for a variety of processors, making it appropriate for solving very large models or multiple replicas of smaller models. libRoadRunner is flexible, supporting the bulk of the SBML specification (except for delay and nonlinear algebraic equations) and several of its extensions. It offers multiple deterministic and stochastic integrators, as well as tools for steady-state, stability analyses and flux balance analysis. We regularly update libRoadRunner binary distributions for Mac OS X, Linux and Windows and license them under Apache License Version 2.0. http://www.libroadrunner.org provides online documentation, full build instructions, binaries and a git source repository.

q-bio.SC↗

arXiv2015

Mean-field analysis of two-species TASEP with attachment and detachment

In cells, most of cargos are transported by motor proteins along microtubule. Biophysically, unidirectional motion of large number of motor proteins along a single track can be described by totally asymmetric simple exclusion process (TASEP). From which many meaningful properties, such as the appearance of domain wall (defined as the borderline of high density and low density of motor protein along motion track) and boundary layers, can be obtained. However, it is biologically obvious that a single track may be occupied by different motor species. So previous studies based on TASEP of one particle species are not reasonable enough to find more detailed properties of the motion of motors along a single track. To address this problem, TASEP with two particle species is discussed in this study. Theoretical methods to get densities of each particle species are provided. Using these methods, phase transition related properties of particle densities are obtained. Our analysis show that domain wall and boundary layer of single species densities always appear simultaneously with those of the total particle density. The height of domain wall of total particle density is equal to the summation of those of single species. Phase diagrams for typical model parameters are also presented. The methods presented in this study can be generalized to analyze TASEP with more particle species.

q-bio.SC↗

arXiv2015

Contributions to the Theory of Thermostated Systems II: Least Dissipation of Helmholtz Free Energy in Nano-Biology

In this paper, we develop further the theory of thermostated systems along the lines of our earlier paper. Two results are highlighted: 1) in the Markov limit of the contracted description, a least dissipation of Helmholtz free energy principle is established; and 2) a detailed account of the appropriateness of this principle for nano-biology, including the evolution of life, is presented.

q-bio.SC↗

arXiv2015

Dynamics of p53 and Wnt cross talk

We present the mechanism of interaction of Wnt network module, which is responsible for periodic sometogenesis, with p53 regulatory network, which is one of the main regulators of various cellular functions, and switching of various oscillating states by investigating p53-Wnt model. The variation in Nutlin concentration in p53 regulating network drives the Wnt network module to different states, stabilized, damped and sustain oscillation states, and even to cycle arrest. Similarly, the change in Axin concentration in Wnt could able to modulate the p53 dynamics at these states. We then solve the set of coupled ordinary differential equations of the model using quasi steady state approximation. We, further, demonstrate the change of p53 and Gsk3 interaction rate, due to hypothetical catalytic reaction or external stimuli, can able to regulate the dynamics of the two network modules, and even can control their dynamics to protect the system from cycle arrest (apoptosis).

q-bio.SC↗

arXiv2015

Liquids that form due to dynamics of the molecules that depend on the local density

RNA molecules in living cells form what look like liquid droplets formed by liquid/liquid phase separation. But unlike the molecules in conventional phase separating mixtures, RNA molecules are transported by molecular motors that consume energy and so are out of equilibrium. Motivated by this we consider what sort of simple rules for the dynamics of model mRNA molecules lead to liquid/liquid phase separation. We find that dynamics that slow as the local density of molecules increases, drive the formation of liquids. We also look at the analogous separation of the two blocks of a block copolymer, in which the monomers of one block have dynamics that depend on the local density of monomers of that block. We find that this block condenses and separates from the monomers of the other block. This is a simple model of the out-of-equilibrium domain formation found in the chromatin in the nucleus of cells.

cond-mat.soft↗

arXiv2015

Phase transition in p53 states induced by glucose

We present p53-MDM2-Glucose model to study spatio-temporal properties of the system induced by glucose. The variation in glucose concentration level triggers the system at different states, namely, oscillation death (stabilized), sustain and damped oscillations which correspond to various cellular states. The transition of these states induced by glucose is phase transition like behaviour. We also found that the intrinsic noise in stochastic system helps the system to stabilize more effectively. Further, the amplitude of $p53$ dynamics with the variation of glucose concentration level follows power law behaviour, $A_s(k)\sim k^γ$, where, $γ$ is a constant.

q-bio.SC↗

arXiv2015

Synchronization efficiency in coupled stochastic oscillators: The role of connection topology

We study the efficiency of synchronization in ensembles of identical coupled stochastic oscillator systems. By deriving a chemical Langevin equation, we measure the rate at which the systems synchronize. The rate at which the difference in the Hilbert phases of the systems evolve provides a suitable order parameter, and a 2--dimensional recurrence plot further facilitates the analysis of stochastic synchrony. We find that a global mean--field coupling effects the most rapid approach to global synchrony, and that when the number of "information carrying" molecular species increases, the rate of synchrony increases. The Langevin analysis is complemented by numerical simulations.

q-bio.SC↗

arXiv2015

Phase-separation transitions in asymmetric lipid bilayers

Morphological transitions of phase separation associated with the asymmetry of lipid composition were investigated using micrometer-sized vesicles of lipid bilayers made from a lipid mixture. The complete macro-phase-separated morphology undergoes a transition to a micro-phase-separation-like morphology via a lorate morphology as a metastable state. The transition leads to the emergence of monodisperse nanosized domains through repeated domain scission events. Moreover, we have numerically confirmed the transitions using the time-dependent Ginzburg-Landau model describing phase separation and the bending elastic membrane, which is quantitatively consistent with experimental results by fixing one free parameter. Our findings suggest that the local spontaneous curvature due to the asymmetric composition plays an essential role in the thermodynamic stabilization of micro-phase separation in lipid bilayers.

physics.bio-ph↗

arXiv2015

Interplay of receptor memory and ligand rebinding

Rapid rebinding of molecular interaction partners that are in close proximity after dissociation leads to a dissociation and association kinetics that can profoundly differ from predictions based on bulk reaction models. The cause of this effect can be traced back to the non-Markovian character of the ligand's rebinding time probability density function, reflecting the fact that, for a certain time span, the ligand still 'remembers' the receptor it was bound to previously. In this manuscript, we explore the consequences of the hypothesis that initial binding and consecutive rebinding give rise to a bond lifetime density that is non-Markovian as well. We study the combined effect of the two non-Markovian waiting time probability densities and show that even for very short times the decay of the fraction of occupied receptors deviates from an exponential. For long times, dissociation is slower than an exponential and the fate of the the steady-state bound receptor fraction critically depends on the extent of the deviation, relative to the rebinding time density, from the Markovian limit: The population of occupied receptors may either decay completely or assume a non-vanishing value for small and strong deviations, respectively. Furthermore, we point out the important role played by fractional calculus and demonstrate that the short- and long-time dynamics of the occupied receptors can be naturally expressed as well as easily obtained in terms of fractional differential equations involving the Riemann-Liouville derivative. Our analysis shows that cells may exploit receptor memory as mechanism to dynamically widen the range of potential response-patterns to a given signal.

q-bio.QM↗

arXiv2015

Traffic Dynamic Instability

Here we study a driven lattice gas model for microtubule depolymerizing molecular motors, where traffic jams of motors induce stochastic switching between microtubule growth and shrinkage. We term this phenomenon \enquote{traffic dynamic instability} because it is reminiscent of microtubule dynamic instability [T. Mitchison and M. Kirschner, Nature 312, 237 (1984)]. The intermittent dynamics of growth and shrinking emerges from the interplay between the arrival of motors at the microtubule tip, motor induced depolymerization, and motor detachment from the tip. The switching dynamics correlates with low and high motor density on the lattice. This leads to an effectively bistable particle density in the system. A refined domain wall theory predicts this transient appearance of different phases in the system. The theoretical results are supported by stochastic simulations.

cond-mat.stat-mech↗

arXiv2015

Time Until Neuron Death After Initial Puncture From an Amyloid-Beta Oligomer

Hardy and Higgins first proposed the amyloid cascade hypothesis in 1992, stating that the decrease in neuronal function observed in Alzheimer's Disease (AD) is due to a process initiated by the oligomerization of amyloid-beta peptides. One hypothesis states that toxicity arises from the aggregation of amyloid-beta into a pore structure, which can then puncture the brain cell membrane; this allow toxic calcium ions to flood through the opening, causing eventual cell death. In 2007, neurobiologist Ruth Nussinov calculated the three pore sizes most likely to occur within the brain. Based on her findings, we constructed a method to determine the time it takes for a cell to die after the cell is punctured by the pore. Our findings have shown that cell death occurs within one second after the oligomer makes contact with the cell. We believe this is important because instant cell death has been one criticism of Nussinov's model, and we have calculated a concrete time value for that criticism. We identify two potential deficiencies with our model that could be improved: first, we treat the calcium as an ideal gas, which it is not; second, we assume that the pores are static (i.e. constantly open), while recent developments suggest that they may open and close dynamically.

physics.bio-ph↗

arXiv2015

Poisson-Nernst-Planck equations in a ball

The Poisson Nernst-Planck equations for charge concentration and electric potential in a ball is a model of electro-diffusion of ions in the head of a neuronal dendritic spine. We study the relaxation and the steady state when an initial charge of ions is injected into the ball. The steady state equation is similar to the Liouville-Gelfand-Bratu-type equation with the difference that the boundary condition is Neumann, not Dirichlet and there a minus sign in the exponent of the exponential term. The entire boundary is impermeable to the ions and the electric field satisfies the compatibility condition of Poisson's equation. We construct a steady radial solution and find that the potential is maximal in the center and decreases toward the boundary. We study the limit of large charge in dimension 1,2 and 3. For the case of a small absorbing window in the sphere, we find the escape rate of an ion from the steady density.

physics.class-ph↗

arXiv2015

Identification of the Zeo1 Protein as a Candidate Structural Homolog of α-Synuclein in Budding Yeast

Human α-synuclein (SNCA) is a 140-amino-acid protein belonging to the three-member synuclein family. It has been extensively studied due to its misfolding/aggregation in and genetic linkage to neurodegenerative diseases, especially Parkinson's disease (PD). To better understand its biology, models of SNCA toxicity have been developed in budding yeast over the past decade, which have yielded insights into the protein's modes of action in specific pathways and potential therapeutic targets. Given that the synuclein gene family is not present in yeast, an extensive homology search was undertaken to determine if any yeast protein may possess structural homology to SNCA and whose native biology may shed more light on SNCA's pathomechanism in eukaryotes. We identified Zeo1, a membrane-associated protein involved in the cell wall integrity (CWI) pathway, as a candidate structural homolog. We show that Zeo1 overexpression is toxic in yeast and, similar to SNCA, localizes to lipid membranes. A number of biochemical similarities between Zeo1 and SNCA also become apparent in light of this potential structural connection. Moreover, the yeast PKC1 gene, a kinase acting as a downstream signaling hub in the CWI pathway, rescues both SNCA- and Zeo1-induced toxicities. Using the same homology search methods that identified Zeo1, we show that Pkc1 has a hybrid structural similarity to PINK1 and PARIS, two mitochondrial PD-implicated proteins not generally linked directly to synuclein-specific pathobiology. Overall, this proof-of-concept study shows the potential utility of hitherto uncharacterized cross-species structural homologs, identified using comparative proteome-wide structure prediction algorithms, in shedding light on abstruse connections among disease-relevant proteins.

q-bio.QM↗