A.2. Background and Significance

 

Major challenges of the post-genomic era include a detailed understanding of structure/function relationships and complex interactions for proteins and their assemblies at various scales. Computational and mathematical models and simulations become increasingly important to delineate not just the average behavior of biological systems, but also the systems' variability and propensity to switch operating modes and/or to fail.

 

The range of spatial and temporal scales over which molecular and cellular processes vary is enormous (Table A.1). A variety of theoretical and computational methods have been developed for problems at various scales (Table A.2), and arguably the most mature algorithms underlie software at the lower and upper extremes. At the lower level are molecular dynamics (MD) simulations, which can provide detailed information at the atomic scale. In practice, however, their high computational cost precludes space and time scales beyond a few hundreds of residues and nanoseconds. The accuracy of the results is limited by that of the adopted force field, and the simulations usually suffer from incomplete sampling of conformation space. At the higher level of cellular/multicellular processes, on the other hand, are methods based largely on empirical conjugate forces and flows, and involving the simultaneous solution of coupled ordinary or partial differential equations (ODEs or PDEs). In space-free or (relatively) simple compartmental models of biochemical networks, neuronal excitation, hemodynamics, or membrane transport, these methods can address biological processes on the time-scale of minutes to hours. Spatial information can be incorporated therein, but at the cost of dramatically increased computation time, because the space must be subdivided into finite elements and the coupled PDEs must be solved for each. Additionally, stochastic effects, which in vivo may contribute to the robust nature of the organism, but may also account for switching into disease states, are usually lacking at this level.

 

Most of functional cell physiology lies in between the two spatio-temporal extremes outlined above, i.e., a finite group of molecules subject to complex structural and spatial arrangements are coupled via stochastic and/or directed interactions driving cellular machinery. The central tenet of the proposed Center is that new, integrated models and methods are required at these intermediate levels to understand cell function, and therefore cell pathology and fate. As outlined below and summarized in Table A.2, work has already begun in several groups specializing in different methods, and thus there is a unique opportunity to build previously impracticable models, bridge the gap between molecular and cellular approaches, and answer biomedical questions of previously unassailable complexity. Accordingly, we aim to develop new models and methods at optimal levels of spatial, temporal, and stochastic realism (Aim 1) for the studied problems, integrate the information from different hierarchical levels (Aim 2), and provide new data/output storage, visualization and internet accessibility tools (Aim 3).

 

 

Table A.2. Summary of Existing Molecular & Cellular Modeling and Simulation Methods

Problem/

Method

Typical

Application

 

Software

Examples

Resolution (Scale)

Spatial

Realism

Stochastic

Realism

Time

Step

Time-

Scale

Comp

Time Cost

Pre-NPEBC member

Networks of reactions/

Sets of ODEs

Metabolic or

signaling

pathways

E-cell (1),

Gepasi (2;3), VCell (4-6), XPPAUT(a)(7)

N/A

(cell)

N/A

none

ms

ms - hrs

minimal

Ermentrout

(7-11)

Chow(12)

Taasan,

Stiles (16-20)

Excitation/

Compartmental Circuit

Neural modeling, signaling networks

GENESIS/ Kinetikit (13, 13a)

NEURON (14),

NEOSIM (b)

mm mm

(cell-multicell)

low-to-

medium

 

none

 

ms

 

ms - hrs

usually

low

Reaction

kinetics/ Stochastics

Gene

Regulation, cell cycle regulation

BioSpice(15), MCell (16-20); StochSim (21;22), XPPAUT (7)

N/A

(cell)

N/A

high

ms

ms - hrs

low

3-D Reaction Diffusion/Finite Elements

Flow models,

Calcium

dynamics

FIDAP (23),

Kaskade (24),

VCell (4-6)

< mm

(cell)

medium-to-high

none

ms-ms

ms - sec

low-to-

high

Stiles(16-20)

 

3-D Reaction Diffusion/

Monte Carlo (MC)

Micro-

physiological processes

MCell(16-20)

nm mm

(Subcell-cell)

high

high

ps

ms

ms - sec

low-to-

high

Diffusion in potential field/ Poisson-Boltzmann, Poisson Nernst-Planck

Electrostatic interactions,

ion channels

UHBD (25-27)

Delphi (28), See also (29;30)

1 - 100 nm

(proteins, membranes)

High

(implicit solvent)

N/A

N/A

ns 0.1 ms

low-to-medium

Madura(25) Coalson (29;30)

Macromolecular machinery/ elastic network model

Collective dynamics

(structural)

GNM (31),

ANM (32)

-100 nm

(multimers, complexes)

High (no solvent)

N/A

N/A

ps

10 ns

minimal

Bahar(31) (32)

Dynamic Monte Carlo (MC) -Metropolis

Coarse-grained simulations

See for example (33)

5-100 nm

(proteins, complexes)

Medium, on- or off-lattice

low

N/A

ps

10 ns

low-to-medium

Bahar(34;35), Coalson (129)

Conformational motions/Brownian Dynamics (BD)

Dynamics in solution or other fields

UHBD (25-27)

 

40 nm

(proteins + environment)

High

(implicit solvent)

high

2-10 fs

10 fs-

20 ns

medium

Madura

(25-27;36)

Bahar (37;38)

MD + Principal Component Analysis (PCA)

Normal modes, essential dynamics

CHARMM(39;40)

See also EDA(41)

nm

(macro-molecules)

High

(explicit solvent)

 

exact

 

1-5 fs

 

fs

10 ns

 

medium-to-high

Evanseck (42)

molecular mechanics / MD

Local motions,

free energies

AMBER (43),

CHARMM (39), GROMOS (44)

nm

(small proteins)

Exact (explicit solvent)

exact

 

1-2 fs

fs ns

high

Rosenberg

(45-47)

Deerfield

(48;49),

Meirovitch

(50), Jordan

Quantum chemistry/Ab initio

simulations

transition state, solution of Schrodinger eq

Gaussian98 (51)

 

<

(electrons-atoms)

exact

exact

-

N/A

highest

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(a) Bard Ermentrout; http://www.math.pitt.edu/~bard/xpp/xpp.html ; (b) http://www.dcs.ed.ac.uk/home/fwh/neosim/