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/