[Sohail 2011] Sohail, Ayesha, Julia M. Rees, and William B. Zimmerman. "Analysis of capillary-gravity waves using the discrete periodic inverse scattering ...
Cytoskeleton Structure & Function
Microscopic view of cells
Cell Organelles
Hypothesis: Motor proteins and MT’s * Vesicles and other organelles have receptor proteins, * To which motor proteins attach and then walk an organelle to its destination. * The network of MT’s extends throughout the cytoplasm.
MT’s help in transport
Knowledge of Dynamic instability (DI) and its applications ``DI’’ is basically the study of the rapid growth and
shrinking of the globular protein ``Tubulin’’ and its applications includes: Intracellular transport. Cancer research. Separation of chromosomes during mitosis. Remodelling of cytoskeleton during mitosis.
A diffusion based model Random diffusional processes can generate regular
microtubule organizations under specified kinetic conditions which are found to be compatible with the known properties of tubulin polymers. The kinetic requirements for self organization might ultimately be responsible for such extraordinary in vivo microtubule dynamics, as the rapid turnover and “dynamic instability” of the interphase network.
What is self organization of microtubules
Microtubules have just formed from the tubulin solution. They are still in a growing phase and have an isotropic arrangement.
Microtubule disassembly has started to occur. This produces trails of high tubulin concentration from the shrinking ends of the microtubules.
microtubules are growing and forming preferentially into these tubulin trails. Once started, the process mutually reinforces itself with time and leads to self- organization[Glade et’al 2002].
Coupled mechano-chemical modeling It has remained a great challenge to reduce the critical discrepancies, which exist between the experimental observations and modeling results. Recently, we have studied the small scaling parameter of the nonlocal Euler Bernoulli Beam Theory and have demonstrated the free vibration problem of
microtubules [Motemedi & Sohail (under review)]. During this research each tubulin was considered as a single sphere with 55 KDa weight, that connects to another tubulin with a nonlinear spring. A mechanical model for the microtubule was used and the finite element method was used to calculate natural frequencies of microtubules. The values of scale parameter for microtubules were recorded to be about e0 = 40 to 50 nm. The technique may prove to be helpful to explore the microtubules dynamics at the laboratory level.
We used the MD toolkit simulations to obtain the potential energy between four monomers category. GROMACS 4.5.3 software [Pronk et al., 2013] with the GRO142 MOS96 43a1 force field was used to perform the simulation using the methods of molecular dynamics and energy minimization.
Stochastic effects Recently, a considerable number of studies in different biochemical
processes such as: expression of single genes, gene networks and multi-step regulated pathways allow illustrating the stochastic nature of many metabolic self-organized activities.
There have been many stochastic models of motor driven transport at
multiple spatial and temporal scales, ranging from Brownian ratchet models to random walk models to reaction-hyperbolic equations. However, many of these treatments neglect the fact that the goal of such transport is to deliver molecular cargo to specific sites. This then naturally leads to a connection with random intermittent search processes.
Challenges in modeling and simulations One major challenge in stochastic simulations is how to
efficiently couple stochastic chemical reactions with diffusion in complex environments [Bressloff, and Newby 2013]. Because of dynamic instability, a microtubule population can, in principle, grow infinitely (ignoring tubulin depletion) or reach a finite size distribution. This can be predicted mathematically, as the fraction of microtubules in the shrinking and growing states can be computed from the frequencies of catastrophe and rescue, When details about individual microtubule are needed, stochastic models or simulations should be used[Karsenti 2006].
Challenges in modeling and simulations The development of a SDE and initial verification using
the EM numerical solver[Sohail et’al 2016]. The stochastic dynamics associated with transitions between different internal states can be studied with the help of a system of PDE’s describing the evolution of the probability density (with motor complex as the internal state). The discrete continuum and hybrid mathematical modeling of the problem will help to run Insilco experiments[Sohail et’al 2017].
Schematic of virtual cell ([Tuan 2006])
How agents demonstrate the dynamics agent-based model of intracellular transport and pattern
formation, is suitable for both, directed motion and fusion processes. A Brownian agent approach can be used which is described by a set of state variables. It allows to formalize the agent dynamics using methods established in statistical physics. The agent’s motion is influenced by two different forces, a deterministic one which results from the gradient of the effective potential, and a stochastic one, which is assumed to be Gaussian white noise. Comparing the pattern formation in the perturbed cell with the one in the control cell.
AGB-dynamical analysis of MT’s ([Klann 2011])
References [Vicker 2002] Vicker, Michael G. "Eukaryotic cell locomotion depends on the propagation of self-organized reaction– diffusion waves and oscillations of actin filament assembly." Experimental cell research 275.1 (2002): 54-66. [Gomez et al., 2016] Gomez, J. M., Chumakova, L., Bulgakova, N. A., and Brown, N. H. (2016). Microtubuleorganization is determined by the shape of epithelial cells. Nature communications, 7:13172. [Sohail 2011] Sohail, Ayesha, Julia M. Rees, and William B. Zimmerman. "Analysis of capillary-gravity waves using the discrete periodic inverse scattering transform." Colloids and Surfaces A: Physicochemical and Engineering Aspects 391.1 (2011): 42-50. [ Sohail 2017] Agent based modelling of tumour induced angiogenesis (under review Springer). [Motemedi & Sohail (under review)] Computational Approach to explore Nonlocal Beam Theory of Microtubules (Evise Computational Biology and Chemistry). [Bressloff, and Newby 2013] Bressloff, Paul C., and Jay M. Newby. "Stochastic models of intracellular transport." Reviews of Modern Physics 85.1 (2013): 135. [Tuan 2006]Dinh, Anh-Tuan, et al. "Theory of spatial patterns of intracellular organelles." Biophysical journal 90.10 (2006): L67-L69. [Klann 2011] Klann, Michael T., Alexei Lapin, and Matthias Reuss. "Agent-based simulation of reactions in the crowded and structured intracellular environment: Influence of mobility and location of the reactants." BMC systems biology 5.1 (2011): 71. [Karsenti 2006] Karsenti, Eric, François Nédélec, and Thomas Surrey. "Modelling microtubule patterns." Nature cell biology 8.11 (2006): 1204. [Glade et’al 2002]Glade, Nicolas, Jacques Demongeot, and James Tabony. "Comparison of reaction–diffusion simulations with experiment in self-organised microtubule solutions." Comptes rendus biologies 325.4 (2002): 283-294.
