Cellular and molecular structure as a unifying framework forwhole-cell modelingElijah Roberts

Available online at www.sciencedirect.com

ScienceDirect

Whole-cell modeling has the potential to play a major role in

revolutionizing our understanding of cellular biology over the

next few decades. A computational model of the entire cell

would allow cellular biologists to integrate data from many

disparate sources in a single consistent framework. Such a

comprehensive model would be useful both for hypothesis

testing and in the discovery of new behaviors that emerge from

complex biological networks. Cellular and molecular structure

can and should be a key organizing principle in a whole-cell

model, connecting models across time and length scales in a

multiscale approach. Here I present a summary of recent

research centered around using molecular and cellular

structure to model the behavior of cells.

Addresses

Department of Biophysics, Johns Hopkins University, Baltimore, MD

21218, USA

Corresponding author: Roberts, Elijah (eroberts@jhu.edu)

Current Opinion in Structural Biology 2014, 25:86–91

This review comes from a themed issue on Theory and simulation

Edited by Rommie E Amaro and Manju Bansal

S0959-440X/$ – see front matter, # 2014 Elsevier Ltd. All rights

reserved.

http://dx.doi.org/10.1016/j.sbi.2014.01.005

IntroductionIn a recent opinion [1], Geyer expressed a viewpoint

emerging among many computational biologists that

molecular and systems-level models of the cell must be

combined since ‘both the local details and the global

behavior are equally important.’ The most comprehen-

sive attempt to date at such a union has been that of Karr

et al. [2��], who presented a whole-cell model from a top-

down perspective. In an impressive feat of computational

biology, the authors showed that multiple independent

modeling methods can be combined into a coherent

simulation of cellular biochemistry. However, their

efforts stopped short of including molecular-scale fea-

tures in a detailed manner.

One, arguably the best, scaffolding upon which to base a

more complete molecular-systems fusion is the structure

of the cell. Biomolecular systems in the cell use its

structure to organize themselves into interacting units

at multiple scales [3]. From the compartmentation of the

Current Opinion in Structural Biology 2014, 25:86–91

cell into specialized subvolumes through the organization

of the cytoskeleton and down to the assembly of macro-

molecular complexes, structure is critical to the function

of the cell and can serve as a reference by which cellular

models can be integrated. As such, here I use the term

‘whole-cell modeling’ in a broader sense to also imply a

structural model of the cell. As a working definition of a

whole-cell model, I propose the following criteria:

– First, the model should account for the physical

structure and organization of the cell. While of obvious

importance in eukaryotic organisms, even in bacterial

systems many phenomena cannot be accurately

modeled without taking into account the three-

dimensional structure of the cell.

Models should account for changing structure and

organization during the cell cycle, including growth and

division of the cell. Included in this criterion is the

postulate the model should account for spatial localiz-

ation of macromolecules within the cell. Many cellular

processes require spatial gradients and cytoskeletal

organization within the cell for proper function.

– Second, the model should account for all known

cellular processes, even if not at the level of every

individual gene. Many models of individual bio-

chemical processes have been studied in the context

of a spatial model of the cell, but cannot be accurately

described as whole-cell models. Models of individual

pathways are useful for hypothesis testing of specific

biological questions, but lack the complexity to capture

emergent phenomena associated with a more discov-

ery-driven approach. From a modeling perspective, a

whole-cell model should be able to maintain cellular

homeostasis without resorting to arbitrary sources and

sinks of energy and mass.

– Third, the model should account for cellular time-

scales. Much of cellular biology happens on the length

scale of the cell cycle, typically measured in hours. A

whole-cell model should be able to model processes for

at least a cell cycle.

– Fourth, the model should allow for varying levels of

detail in model components. It is unreasonable to

require that detailed atomic or kinetic data are available

for every cellular component. At the same time, it is

also unreasonable to expect that every component must

be described using the lowest common denominator. A

whole-cell model must therefore allow components

where more information is known to be modeled at a

higher level of detail. This will allow whole-cell models

to be used in conjunction with common biological data

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Cellular and molecular structure in whole-cell modeling Roberts 87

Figure 1

Potential-based

Interactionenergies

MD

Conformationalsampling

BD

Nonspecificinteractions

Specificbinding

Potential-based

RDME

Particlediffusion

Probability-based

Reactionkinetics

Regulatory Model

Metabolic Model

Sim

ultan

eou

s Execu

tion

State E

xchan

ge

Serial ExecutionParameter Estimation

Data-drivennetwork inference

Metabolic flux

Directedcargo & vesicletransport

Cytoskeletaldynamics

Force-based

Cytoskeleton Model

Systems-level- Data-driven modeling- All cellular genes and pathways

Molecular-level- Physics-based modeling- Specific pathways and macromolecules

Mo

lecu

lar

Str

uctu

re

Cellular Structure

Current Opinion in Structural Biology

Schematic diagram showing a proposed hierarchical multiscale approach to a whole-cell model. Abbreviations: MD, molecular dynamics; BD,

Brownian dynamics; RDME, reaction–diffusion master equation.

sets, such as the results from mutation and knockout

experiments.

I would like to emphasize that in the foreseeable future,

any one computational method is unlikely to be able to

meet all of the above criteria. A multiscale approach will

be needed. Whether the most successful approach will be

that of the Covert lab in which all of the models are run in

parallel (simultaneous multiscale) or one in which differ-

ent layers are modeled serially, feeding parameters from

higher-to-lower resolution models (hierarchical multi-

scale; see Figure 1) is still a subject of debate.

Although no whole-cell models have yet been developed

that fit the above definition, many scientists who share

this vision are making progress toward such a goal. In this

minireview I focus on the first criterion enumerated above

and present a summary of some recent methods for

modeling the physical structure and organization of the

cell, along with biological studies using these methods,

that are pushing the envelope toward a comprehensive

model of the cell.

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Molecular models in a cellular contextStructural biologists have been producing exquisite

atomic scale structures of biological macromolecules for

more than 50 years. Computational biologists have been

using these structures for more than 30 years to study the

dynamics of proteins and other macromolecules. Whole-

cell modelers would do themselves a disservice if they

were unable to use the valuable data contained in mol-

ecular structures, and many researchers are looking for

ways to bring this wealth of data to bear on cellular

modeling. A primary difficulty is that extensive compu-

tational resources are needed to directly study cell-scale

phenomena using molecular models. Nevertheless, sev-

eral molecular approaches are potentially useful.

Molecular dynamics

Because molecular dynamics is well-known and covered

extensively in the literature, I mention it only briefly. For

a recent review see [4]. While there have been a few

efforts to simulate systems a substantial fraction of a cell

in size using molecular dynamics, the computational

resources necessary to reach cellular time scales are

Current Opinion in Structural Biology 2014, 25:86–91

88 Theory and simulation

beyond our current capabilities. For a recent example of a

large-scale molecular dynamics simulation, see the 64

million atom simulation of HIV-1 capsid [5]. Neverthe-

less, molecular dynamics modeling of the interactions of

molecules can provide valuable insight. Continual

improvements in computational power and also the de-

velopment of coarse-grained models will make these

methods critical to whole-cell modeling efforts, especially

in hierarchical multiscale approaches.

Brownian dynamics

Perhaps the most detailed simulation methods capable of

reaching to nearly cellular length and time scales are

Brownian and Stokesian dynamics. These methods in-

clude one or more inter-molecular potential terms along

with a random fluctuating force corresponding to the

solvent interactions. See [6] for a more thorough descrip-

tion and review. Such methods are notable because they

include to some degree the molecular details of the

biomolecules. To date, Brownian dynamics studies at

the upper limit of feasibility have provided valuable

insight into the diffusion of macromolecules in the cyto-

plasm, an understanding of which will be critical for

whole-cell modeling efforts. For example, it has recently

been shown that changes in the diffusivity of the protein

MEX-5 in different regions of the cytoplasm establish a

concentration gradient involved in cell-fate determi-

nation in Caenorhabditis elegans [7].

McGuffee and Elcock [8] presented the first modern

treatment of the cytoplasm in a Brownian dynamics

simulation. Their model excluded hydrodynamic inter-

actions, but they were able to recover the trend of

decreasing long-time diffusion rates in the cytoplasm that

have been experimentally observed. The authors made

the case that nonspecific energetic interactions between

proteins in the cytoplasm indeed play an important role in

the molecules’ dynamics. Shortly thereafter, Ando and

Skolnick [9] performed a study of macromolecular diffu-

sion in a simulated cytoplasm using a Stokesian dynamics

method accounting for hydrodynamic interactions. Their

work showed that in the crowded cytoplasm intermole-

cular interactions through solvent fluid were of substantial

importance. More recently, Mereghetti and Wade [10�]investigated a mean-field approach to hydrodynamic

interactions that was able to recover the change in diffu-

sion due to hydrodynamic interactions, if not the local

correlations, while using atomic structures and being

substantially more efficient to calculate. While not an

explicitly heterogeneous cytoplasm, their model of a

concentrated protein solution likely represents a reason-

able approximation to the conditions inside a cell.

The Brownian dynamics simulations described above

typically account for a volume of �100 nm3 and time

of �50 ms, so they are still relatively small scale compared

to a full cell. Also, these studies assumed a random

Current Opinion in Structural Biology 2014, 25:86–91

distribution in the cytoplasm and did not study the effect

of local structure of complexes or assemblies which are

known to be prevalent in the cell. Future work will

hopefully see Brownian dynamics simulations that are

accurately able to capture specific and non-specific inter-

actions from molecular structures scaling up to a signifi-

cant volume of cytoplasm for biologically interesting

timescales.

Whole-cell reaction–diffusion modelsIn addition to methods for determining macromolecular

structure, there are also new methods being developed for

determining cellular structure. Primary examples are

cryo-electron tomography [11,12] and soft X-ray tomogra-

phy [13] of whole cells. It is also important to emphasize

that structural information is also becoming available of

subcellular structures, such as the nuclear pore complex

[14,15]. These data all need to be integrated into whole

cell models.

With these new types of data, simulation methods must

be used that can take advantage of experimentally deter-

mined cellular organization. Reaction–diffusion models

represent a further simplification from molecular-scale

models. They sacrifice molecular structure and inter-

action potentials and represent macromolecules as either

dimensionless points or hard spheres. By abandoning

molecular details reaction–diffusion methods can

simulate time scales relevant for cells using a random

walk model of Brownian motion and a Smoluchowski

description of reactions. Several classes of reaction–diffu-

sion models are in widespread use.

PDE methods

Reaction–diffusion partial differential equation (PDE)

methods use continuous and deterministic equations to

calculate concentration flux due to diffusion and reaction

processes. They provide spatial resolution and can

account for compartments and other cellular organization.

PDE models are very popular for modeling cellular

systems, as exemplified by the wide use of the Virtual

Cell project [16�]. Since they are inherently continuous,

they have difficulty dealing with macromolecules present

in small copy numbers inside the cell and the inherent

cell-to-cell variability that goes with small number fluctu-

ations. Many gene regulatory interactions within the cell

are likely to involve such features and it is unclear if PDE

models by themselves can be adapted to such situations.

However, they are computationally efficient and could

prove especially useful in a multiscale approach to a

whole-cell model [17].

Particle-based methods

The next class of methods considered is generically

known as particle-based. Molecules are treated as diffus-

ing particles, usually as either a hard sphere or a dimen-

sionless point. Reactions occur when two particles that

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Cellular and molecular structure in whole-cell modeling Roberts 89

can undergo a reaction approach each other. The exact

details vary from method to method but generally base

their approach on the Smoluchowski equation. Particle-

based methods forgo the idea of continuous deterministic

equations in favor of a discrete view of the biomolecules

in the cell. This allows the investigation of stochastic

phenomena and particularly, the ability to characterize

cell-to-cell variability.

At the most microscopic level is the Green’s function

reaction dynamics (GFRD) method [18]. This method

decomposes each pair of reacting particles into a two-

body formulation of the Smoluchowski equation that can

be solved analytically using Green’s functions. Because of

the exact solution of the Smoluchowski equation, GFRD

is quite accurate, but can become slow for dense systems.

It was recently used to study processivity during multisite

phosphorylation in MAPK signaling [19]. Smoldyn [20]

also solves the Smoluchowski equation but using a time

step approach. Notably it pays particular attention to

correctly calculating particle–surface interactions. Smol-

dyn has been used to investigate cellular scale models,

including the effect of Bar1 on yeast mating response [20],

the role of morphology on kinase dynamics in neural

dendritic spines [21], and asymmetrical cell division in

yeast [22]. MCell [23] was one of the first particle-based

reaction–diffusion simulation methods and has been used

by numerous researchers, many in the study of neuro-

transmitter release [24]. Particle-based simulation

methods have proven to be a successful method for

studying reaction–diffusion dynamics in a crowded cel-

lular environment [25]. Researchers studying particle-

based methods are still making progress toward faster

and more accurate simulation methods, e.g., as in a recent

study from Klann and Koeppl [26�] describing a new

method for dealing with geminate recombination. With

such improvement, particle-based methods may achieve

the speed-ups necessary to play a central role in whole-

cell models.

Reaction–diffusion master equation methods

Demanding that a simulation model millions of particles

for times on the order of the cell cycle presently requires

further simplification. Especially, for very dense systems

with many nearby players, particle-based methods can-

not simulate out to the necessary time scales of cellular

dynamics (hours). Instead, a further approximation of

well-stirred local subvolumes can be made, with particles

jumping between subvolumes and reacting freely with

any other particle in its subvolume. This assumption

greatly simplifies the calculations and the resultant

model is known as the reaction–diffusion master

equation (RDME). The first simulation code to use

the RDME for cell scale simulation was MesoRD

[27�]. Initial work showed that complex dynamical pro-

cesses, such as the oscillations of the Min division system

in Escherichia coli, could be recovered even with a coarse

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spatial discretization [28]. Recently, new theoretical

developments from the Elf lab have shown that the

RDME can be corrected for error introduced by spatial

discretization [29], opening the possibility for the cell to

be discretized at finer length scales.

Roberts, Stone, and Luthey-Schulten introduced the idea

of an in vivo version of the RDME, in which the reaction

and diffusion propensities with the subvolumes could be

controlled to reconstruct a particular cellular organization

[30]. By including a static representation of the crowded

cytoplasm, the authors were able to study deviations in

the diffusion and reaction rates of particles and investi-

gate the effects on gene expression for times on the order

of the cell cycle [31�]. Additionally, using cryo-electron

tomograms of a single E. coli cell, the authors studied for

the first time the effect of including experimentally

determined cell geometry and organization on the

dynamics of biochemical processes.

Recently, the RDME has been used extensively to study

cell-scale processes. Sturrock et al. applied the RDME to

gene expression circuits in eukaryotic cells, reproducing

stochastic variability in oscillations of Hes1 [32]. Flegg

et al. recently [33] developed a hybrid method where

particles in certain regions of interest are treated using a

particle-based method while particles in the surrounding

volumes are treated using the RDME. The authors show

an example of the method’s utility for simulating large

volumes studying the release of calcium from the endo-

plasmic reticulum [34].

Lawson et al. [35�] recently published a study using the

RDME to model how yeast track and respond to a

pheromone gradient. In their stochastic simulations the

authors recovered a much more tightly localized response

than in their deterministic counterparts. Additionally,

they were able to recover a mutant phenotype only with

the stochastic simulations. This is likely to be a general

principle in biology, where positive feedback loops can

create bistable spatial systems with stochastic noise driv-

ing the populations to multiple states.

Whole-cell modeling of the activecytoskeletonAs a final example of the types of cellular organization

that will need to be included in whole-cell models,

consider the problem of modeling the dynamics of the

cytoskeleton. A cytoskeletal model was missing from

each of the models considered above, and yet is critical

for many cellular functions. In a recent study using the

Virtual Cell software, Ditlev et al. [36] modeled actin

dynamics in response to the Nck protein, which

induces actin polymerization. The authors quantitat-

ively studied the dependence of actin polymerization

on the local density of Nck, combining computation

and experiment.

Current Opinion in Structural Biology 2014, 25:86–91

90 Theory and simulation

Modeling the cytoskeleton involves the assembly and

disassembly of long filaments and also the use of these

cellular highways by motor proteins transporting various

cargo. An important aspect of the cytoskeleton for whole-

cell modeling is the transport of vesicles. For instance,

recent continuum modeling of yeast polarization has

investigated the role of directed exocytosis and endocy-

tosis of Cdc42 in the maintenance of a polarized cell state

[37–39]. To integrate both reaction–diffusion and

directed transport along discrete cytoskeletal filaments,

Klann et al. introduced an agent-based modeling method

for vesicle dynamics in which they walk along static

cytoskeletal filaments [40�]. The method is able to model

vesicle budding, transport along cytoskeletal filaments,

and fusion. The authors used the model to investigate

receptor-mediated endocytosis, correctly recovering the

polarization of the cell due to cytoskeletal asymmetry.

Although the model lacks active remodeling of the cytos-

keleton, it represents an important first step in creating a

multiscale model of vesicle dynamics.

Another possible approach to directed transport has been

explored by Alberts [41]. The author introduced a model

in which cytoskeletal filaments are modeled as a series of

rigid rods linked with translational and torsional springs.

By tuning the parameters one can achieve biophysically

realistic filament properties. The introduction of filament

assembly and disassembly along with the modeling of

force application by motor proteins carrying cargo would

make this approach highly suitable for modeling active

cytoskeleton in a whole-cell model.

Finally, transport in eukaryotic cells must also account for

subcellular structures, such as the nuclear pore complex.

A biophysical model of discrete filaments was recently

used in a study of transport through the nuclear pore

complex based on known structural features [42]. The

combination of a gradient of RanGTP (a GTPase

involved in cargo binding) and binding of FG filaments

to localization sequences on the cargo provided a starting

point for a comparison with experimental measurements,

including single molecule experiments where molecular

distributions can be used.

ConclusionsIn this minireview I presented some recent examples of

the sorts of structure-based modeling methods that will

be useful in a whole-cell model. Molecular and cellular

structure can create a framework for simulating multiscale

models of cellular processes. Several efforts are now

beginning to be directed toward integrating different

resolution methods into a multiscale approach.

In my opinion, RDME methods are a leading candidate for

a core method upon which to base a whole-cell model. It

has become apparent that cell-to-cell variability is an

important phenomena that must be an integral component

Current Opinion in Structural Biology 2014, 25:86–91

of any whole-cell model. Particularly, predicting how

cellular fluctuations move individual cells between phe-

notypic states is key to understanding cellular decision

making. RDME methods are probabilistic to capture

such cell-to-cell variation, can calculate hours of simu-

lation to capture dynamics on the time scales of the cell

cycle, and can capture at a coarse-grained level cellular

and subcellular structure. In Figure 1, I present a

schematic diagram for a whole-cell modeling approach

centered around the RDME. However, regardless of the

actual approach that ultimately proves most successful,

whole-cell modeling that integrates scales from the

molecular to the system stands poised to help us quan-

titatively approach biological problems in new and

exciting ways.

AcknowledgementThe author would like to acknowledge Zan Luthey-Schulten for manyinsightful conversations regarding most of the topics discussed in thisreview.

References and recommended readingPapers of particular interest, published within the period of review,have been highlighted as:

� of special interest�� of outstanding interest

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26.�

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27.�

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35.�

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Current Opinion in Structural Biology 2014, 25:86–91