Multi-resolution simulations of intracellular processes

Coarse-graining (CG) is essential for molecular modeling to access time and length scales that are computationally beyond the reach of the conventional atomistic simulations. Despite numerous advances, coarse-graining often involves making several a priori assumptions, which are rarely systematically addressed.  Dr Zavadlav investigates a number of CG models that differ in the level of coarse-graining and in the model complexity. The group will deploy Classical and Hierarchical Bayesian to quantify and calibrate the uncertainty of the models and to perform the model selection using experimental data.

In this work it is found that compared to the single interaction site models the multiple sites models can be used at higher levels of coarse-graining. These models behave similarly in terms of reproducing the experimental data, however, they significantly differ in the computational cost. The group observed no significant improvement of models when going from rigid to flexible models, thus implying that one should use rigid geometries for efficiency reasons. Dr Zavadlav will present a data-informed rationale for the selection of CG water models and provide guidance for future water model designs.

All-atom models of soft matter systems promise realism and accuracy, at the price of intense computational effort and difficult parametrisation. Coarse-grained models offer faster sampling of larger systems for lighter computational effort, at the price of lower accuracy and -alas- difficult parametrisation. A deceptively simple way to take advantage of high- and low-resolution models is to make one in between - not so coarse, yet not too accurate; Such models are highly specialised, and might easily result in an unsatisfactory compromise. Alternatively, one can try to make a model that is both coarse and accurate, distributing the detail unevenly across the system. Multiple-resolution approaches combine in the same model two or more different representations, keeping the resolution high where chemical accuracy is necessary and employing a coarser description where possible. These methods have been developed for and applied to gases, liquids, solids, polymers, proteins, crystals and other systems. They are effective in reducing the computational cost of a simulation and useful to gain understanding of the system and its physico-chemical properties. Yet, the construction of multiple-resolution models is not free from conceptual and practical difficulties, and several open questions are in place when dealing with them.

The role of the tumour/host microenvironment mechano-biology and the mechanisms involved in the delivery of anti-cancer drugs is heavily investigated using in-vitro or/and in-vivo models. However, in-silico models offer a promising alternative to contemplate tumour progression, and the major factors affecting the transport of tumour-targeting molecules. Thus, Dr Vavourakis will present here a three-dimensional, cancer-specific, in-silico modelling framework of solid-tumour growth, angiogenesis and drug delivery. The model is novel in that it describes in a coupled and multiscale manner the drug transport in the vascular network and the tumour interstitial space, the interaction of the chemotherapeutic agent with the extracellular matrix, tumour regression as a function of the drug concentration, the remodelling of the tumour vasculature in response to the drug, and the biomechanics of the tumour and the host tissue.

To identify optimal delivery of a cancer-killing drug, the group carried out a parametric analysis of in-silico cancer development / drug delivery simulations with respect to the binding properties of the chemotherapeutic agent and the tumour blood vessels permeability. The simulations describe a single-dose bolus injection of either small-sized molecules (1 nm) or a drug-borne nanoparticle (150 nm). The in-silico results suggest that tumour response to treatment is strongly dependent on the drug binding properties rather than the permeability of the tumour vessels. Importantly, increasing the binding affinity of the drug, remodels the tumour vasculature to obtain a more normal structure, thus, improving its functionality. These findings also suggest that enhancing the binding rate, the range of bolus injection time-window during which the tumour vasculature can be normalized become wider; which can lead to higher levels of perfused tumour vessels that may allow the delivery of higher drug concentrations to the tumour interstitial space in follow-up injections.

One of the key unsolved challenges at the interface of physical and life sciences is to formulate comprehensive computational modeling of the whole eukaryotic cell, at a single molecule resolution, which would deeply integrate reaction-diffusion, mechanical-structural and transport processes of cell's salient mechanochemical modules. Towards addressing this problem, the group has developed a unique reactive mechanochemical force-field and software, called MEDYAN (Mechanochemical Dynamics of Active Networks: http://medyan.org). MEDYAN integrates dynamics of multiple mutually interacting phases: 1) a spatially resolved solution phase is treated using a reaction-diffusion master equation; 2) a polymeric gel phase is both chemically reactive and also undergoes complex mechanical deformations; 3) flexible membrane boundaries interact mechanically and chemically with both solution and gel phases. The above-mentioned computational components constitute the fundamental ingredients for minimal modeling of eukaryotic cells at a single molecule resolution. In this talk, Professor Papoian will outline our recent progress in simulating multi-micron scale cytosolic/cytoskeletal dynamics at 1000 seconds timescale, and also highlight the outstanding challenges in bringing about the capability for routine molecular modeling of eukaryotic cells.

Simulations have become an important complement to experimental structural biological approaches since they provide a molecular-level view on structural ensembles and dynamics of conformational transitions or aggregation processes on ns to ms timescales. In recent years, multiscale simulation methods that combine classical atomistic and coarse grained levels of resolution have gained popularity in the biomolecular simulation community. While the coarse grained level extends the accessible length and timescales compared to an all-atom model, a systematic link to an atomistic level of resolution allows to maintain information from a more accurate representation.

In the talk, Professor Peter will present an example of how such a multiresolution approach in combination with advanced analysis methods can be used to investigate and characterize the structural variability of multidomain proteins and protein conjugates. Professor Peter will show how dimensionality reduction can be employed to characterize the sampling of free energy landscapes of such multidomain systems and to assess the consistency of the sampling in models at different levels of resolution. These methods are optimally suited to identify, compare, and classify relevant conformational states and to guide the interpretation of the simulations with respect to experimental data.

Recent experimental and computational advances allow investigations of liquid biomolecular solutions at spatial and temporal scales (nanometers, nanoseconds) where two representations are equally valid and necessary: atomistic and continuous (fluid dynamics). Examples of the former include MD simulations of systems composed of tens of millions of atoms or cryo-EM measurements of complete viruses and cell organelles with atomistic resolution. The latter is represented, for example, by the multitude of nano- and micro-fluidic devices including, among others, non-contact liquid atomic force microscopy capable of measuring flows of liquids at atomistic scales. Despite comparable quality of theoretical predictions using both atomistic and continuum representations, the physics behind them is fundamentally different, from the basic concepts (discrete atoms vs continuum of matter) to the equations of motion describing the system’s structure and dynamics. This disparity becomes particularly obvious if the problem at hand requires transition between the scales or the description of the same system at different scales simultaneously.

Dr Nerukh will present the recent attempts to develop a unified description of liquid systems such that they are described by the same equations of motion throughout multiple scales, from atomistic to macroscopic hydrodynamic. Two different frameworks will be described each having a set of equations that are valid equations of motion at both limiting scales, MD and hydrodynamic, and at all scales between these extremes. The frameworks are physically consistent, obeying fundamental conservation laws (of mass, momentum, and energy) at all scales. Examples of applying these frameworks to the complete virus in aqueous solution and flows in nanofluidic channel will also be given.

Obtaining predictive dynamical equations from data lies at the heart of science and engineering modeling, and is the linchpin of our technology. In mathematical modeling one typically progresses from observations of the world (and some serious thinking!) first to equations for a model, and then to the analysis of the model to make predictions. Good mathematical models give good predictions (and inaccurate ones do not) - but the computational tools for analyzing them are the same: algorithms that are typically based on closed form equations.

While the skeleton of the process remains the same, today we witness the development of mathematical techniques that operate directly on observations -data-, and appear to circumvent the serious thinking that goes into selecting variables and parameters and deriving accurate equations. The process then may appear to the user a little like making predictions by "looking in a crystal ball". Yet the "serious thinking" is still there and uses the same -and some new- mathematics: it goes into building algorithms that jump directly from data to the analysis of the model (which is now not available in closed form) so as to make predictions. This work here presents a couple of efforts that illustrate this "new” path from data to predictions. It really is the same old path, but it is travelled by new means.