Chapter 17

Spatial Organization of SubcellularSystems

Malte Schmick, Hernan E. Grecco and Philippe I.H. BastiaensDepartment of Systemic Cell Biology, Max Planck Institute of Molecular Physiology, Otto-Hahn-Str. 11, 44227 Dortmund, Germany

Ha

Co

Chapter Outline

Motivation 329

Dimensionality Effects in Biochemical Reactions 330

Towards a Systemic Understanding of Cellular Biology 330

Spatiotemporal Modeling of Cellular Processes 332

Spatiotemporal Quantification of Cellular Processes 334

ndbook of Systems Biology Concepts and Insights. http://dx.doi.org/10.1016/B978-0-12-38594

pyright � 2013 Elsevier Inc. All rights reserved.

Causality From Variation and Perturbation Analysis 336

Model-Driven Experimentation and Experimentally Driven

Modeling 337

Conclusions 339

References 340

In this chapter we describe how spatially organizedbiochemical networks give rise to biological function onthe cellular scale. We will first introduce self-organizedreactionediffusion systems, because many of them are usedby living systems as platforms on which functionality isadded. We then describe spatial patterning in biologicalsystems, focusing on how intracellular compartmentaliza-tion enables function. Finally, we discuss how new insightinto self-organization in reactionediffusion systems can beobtained by combining microscopy and computationalmethods [1].

MOTIVATION

Biological systems strive against entropy by consumingenergy and transforming it into order to reach a balancebetween influx of energy and the energy necessary tomaintain a certain level of organization. This balance, inwhich the system is apparently ‘resting,’ can be defined asthe state of the system. Take for example a maturemulticellular organism that does not grow or developalthough its cells keep dividing. A change in externalconditions disturbs the balance that the organism main-tains, so the organism needs to change as well. Thisadaptation requires the organism to sense and record theenvironmental and internal history, while computing andapplying changes to its own conditions to re-acquireproper balance, i.e., a new state. Sensing, recording,

computing and applying changes are therefore essentialfunctions of all living biological systems. On this time-scale, each cell encapsulates the biochemical reactionsthat evolved to perform these functions across the diffu-sively linked intracellular compartments.

In such a well-mixed reaction vessel, the functionalpossibilities are limited as all points perform the sameoperation simultaneously and in synchrony. Slowing downfor example the diffusion of only one part of a reactionnetwork constitutes a bridging of time and length scales,which introduces complexity to any system. Diffusion ofreactants and products transmits information about a local-ized reaction beyond the area in which the reaction itselfoccurred. While each point in space is equivalent to anyother, each senses a different environment and looks backto a different history. These reactions are limited only bythe supply of energy and reactants, and thus Angstrom-sized molecules can traverse meters (e.g., hormones such asadrenaline can travel large distances in an organism) andsub-second reactions can influence processes that occur atmuch longer timescales (e.g., seasonal cycles, such asmottling of fur). The richness of the involved reactionslimits the scope, flexibility and robustness of the higher-order functions, such as a ‘memory’ of environmentalchanges, and hence the success of the organism: simplesystems will be confined to simple functions, whereascomplex ones might be able to resolve the challengesimposed by the ever-changing environment.

4-0.00017-4 329

330 SECTION | III Dynamic and Logical Properties of Biological Systems

DIMENSIONALITY EFFECTS INBIOCHEMICAL REACTIONS

The term ‘cell’, from the Latin for ‘small room’, describesthe compartmentalization that enables life by confiningreactions and thereby shielding them from the entropiceffects of diffusion. The ‘wall’ of this ‘small room’ is theplasma membrane (PM),which in addition to defining theenclosed volume provides a reaction surface where localdensities of reactants and products are higher. The PMcomprises the organizational point of origin for bidirec-tional communication that integrates the intracellular statewith the extracellular context via networks of inter-connected interacting protein ensembles [2]. As a 2Dsurface, reactions and matter exchange function signifi-cantly differently from the enclosed cytosolic volume. Achemical example of this difference is the BeloussoveZhabotinski reaction (BZ reaction), the prototype ofa chemical oscillator, which consists of about 40 chemicalreaction steps. In a well-stirred beaker, the color of thesolution oscillates with a fixed period between two states(Figure 17.1). However, if ‘spread’ thin in a Petri dish, thereactants become an excitable medium [3]. Starting froma global excitable state, small hotspots of excitation (eithertriggered externally, or amplified from random fluctuationof the initial context) spread in concentric spiral waves,which can be reset by shaking the dish.

This example of self-organization in a lifeless/non-biological system has a striking impact on cellular biologyand the way we try experimentally and theoretically toapproach biological problems. The three main componentsof the BZ reaction, cerium sulfate, malonic acid andpotassium bromate dissolved in sulfuric acid, are interact-ing far from equilibrium at the expense of energy. Theinteraction is sufficiently complex that the chemistry,which occurs in each point of the dish at a given time e

time

x

y

z

Exp

FIGURE 17.1 BeloussoveZhabotinski reaction.

Left panel: Experimental snapshot of the BZ reaction.

Top row: color change signifying the cyclic reaction

over a period of 20 s. Middle row: Progression of

a spiral wave of the BZ reaction confined in a 2D dish as

seen from above. Lower row: Adding methanol, the

periodicity of the reaction becomes unstable and wave

progression chaotic. This cannot be derived from the

2D projection. However, a cut in z-direction reveals that

consecutive wave-fronts tilt increasingly, until the front

of the following wave interferes with the back of the

preceding one. This comprises an example for the type

of Turing instability that leads to Turing patterns. Right

panel: Cellular automaton implementation of the BZ

reaction. The center column shows the local building

blocks of the simulation and their connection. The

displayed simulations (left and right column) are discretized to 300� 300 of t

in a given cell is distributed among its neighbors. Depending on the local defin

small or larger neighborhoods lead to too-regular large-scale patterns. Botto

neighborhoods become warped to a varying degree (left: 10% variation; righ

even 60 years after its discovery e is not entirely under-stood. When this system is modeled, the large number ofparameters yields a parameter space which is simply toolarge to analyze systematically. However, sensible simpli-fications yield an easy set of reactions that are closelyrelated to the LotkaeVolterra equations, which governpredatoreprey systems and form a cornerstone ofbiophysics and theoretical biology. These equations can besolved numerically in 2D and yield results that match theexperiments closely with a manageable number of param-eters. To introduce another layer of complexity, perturbingthe system by adding methanol to the Petri dish hampersthe periodic structures in such a way that they becomefrazzled and unstable. This chaotic behavior cannot beunderstood simply by looking at the waves, as they appeartwo-dimensional when seen from above, and necessitatesexpanding the model to include more parameters about thewave’s 3D shape (Figure 17.1).

TOWARDS A SYSTEMIC UNDERSTANDINGOF CELLULAR BIOLOGY

As humans, we are limited in our ability to fully understandany system in its totality without intense study. As a foun-dation of science we typically apply three fundamentaltechniques: reductionism, abstraction and generalization.Compartmentalization is an example of reductionism: wedivide a problem into subsets with few critical componentsin each subset. For the critical components of a givensubset, we collect experimental observations to formulateabstract rules that allow us to generalize the behavior ofthat subset to include the behavior of a different subsetfollowing similar rules. Herein lies the strength of thescientific principle and its danger: it allows us to deal withcomplicated systems by narrowing our focus until we lose

eriment Simulationhe small square cells depicted in the center column. The value of excitation

ition of the neighborhood, varying spiral patterns result. Top row: Regular

m row: Adding a stochastic position to the centers of each square, local

t: 50% variation).

331Chapter | 17 Spatial Organization of Subcellular Systems

track of the bigger picture. In ethoecology, animal behaviorat the single individual level is studied to deduce generalprinciples of evolution that are also used to obtain insightsinto population dynamics. As a more pertinent example,although the amino acid sequences of many proteins andthe interaction rules of amino acids are known, we are stillunable to compute the folded structure of a protein from itsamino acid sequence. The problem needs to be studied at itsproper scale, hence the main tool in structural biology ismeasuring the structure of a folded protein with crystal-lography or NMR. From this structure we can deriveputative interaction partners or correlate the structuraldifferences of isomers with their respective functionaldifferences. Conversely, complete knowledge of structureand functionality of, for example, a small G protein ona molecular level will never be sufficient to explain its rolein the cellular context. To resolve this, additional layers ofinformation, for example intracellular localization, the roleof this protein in the different signaling networks, and theirimpact on inter- and intracellular communication, must beintegrated. In this respect, systems biology is not supposedto be a new tool to gather detailed information on an iso-lated facet of biology. Instead, it strives to holisticallycollect data and paradigms from different disciplines intoa more complete representation of the investigated problemat the correct scale. From this, the rules that govern systemsbehavior at different scales can then be extracted.

In cellular systems biology we are trying to piecetogether complex networks of protein interactions, which atfirst glance might be reduced to a few components thatnonetheless yield an extraordinarily large diversity. This isinextricably linked to pattern formation, as can be seenfrom the fact that in vitro experiments rarely reproduce orquantify the in vivo functionality of proteins. The reasonfor this is the trivial seeming difference between a cell anda beaker: the beaker is well mixed, isotropic and large,while a cell is viscous, structured with shifting compart-mentalization, but at least still large in comparison to thenanometer-size of a protein. In a real sense, cell biologyboils down to pattern formation, because in its constantstriving against entropy a cell must be continuously andconsistently rebuilt. In this way, a cell depends on robustmechanisms of self-organization and thus poses the idealplatform to adapt these mechanisms to new functionality.On a larger organism scale, pattern formation is wellestablished. In the 1960s the coloration of animals waslinked to the action of so-called morphogens [4]. Theinterplay of apoptotic and proliferative networks via tissuespanning morphogenetic cues can result in embryonicchanges. This is how tissue determines where to grow thefingers of a hand, and how to ‘retract’ a tadpole’s tail. Andthe ability to differentiate tissue into veins on cue isessential for wound healing, and detrimental in case oftumor angiogenesis factor-induced tumor vascularization.

Similarly, the coupling of electrical and chemical stimuliacross nerve cells with the intracellular protein stategenerates long-term memory in the brain. Furthermore,chemical synchronization by cyclic adenosine mono-phosphate (cAMP) waves analogous to the BZ reactiongenerates spatial organization in one stage of the lifecycleof Dictyostelium discoideum. When the resources of theirenvironment diminish, single Dictyostelium cells exudecAMP. Neighboring cells not only can hydrolyze cAMP bya membrane-bound phosphodiesterase, but have receptorsthat are part of a system to sense shallow cAMP gradientswith high precision and trigger a delayed but amplifiedcAMP release [5]. In close analogy with the BZ reaction,excitation centers are self-organized by spiral waves ofcAMP. Dictyostelium uses this to organize a chemotacticgradient that leads to a multicellular organism. In reactingto this gradient, single Dictyostelium cells generate motiveforce by a very complex network of extracellular adhesionsand intracellular cytoskeletal interactions. This last type ofnetwork is especially challenging, because correlationbetween spatial, temporal and compositional structure ofthe extracellular contacts is not clear. Does the contextdefine the network motifs that organize the contacts, or viceversa?

For cell motility in tissue patterning the direction ofcause and effect is unclear, which makes it an example ofself-organization. With simultaneous upward and down-ward causation the large-scale patterns modulate the samelocal interactions from which they emerge. While theformation of the Dictyostelium slug on a larger scaleobviously represents a self-organizational process, on thetissue level this type of intracellular pattern formation hasbeen poorly represented in the literature, although itfollows some similar principles, such as the emergence ofpatterning by coupling an autocatalytic amplification witha negative feedback. For example, these principles of self-organization are easily understood for cell polarity in theyeast Saccharomyces cerevisiae as a related phenomenon[6]. The essential component to establish cell polarity isCDC42, a membrane-bound small G protein of the Rhosubfamily. Translocation of CDC42 to a subcellular spottriggers downstream cytoskeletal reorganization. Considerthe interconnecting levels: a symmetric cell establishes anasymmetric protein distribution to derive an asymmetriccell shape. But how to spontaneously establish the neces-sary CDC42 localization from otherwise symmetric initialconditions? In contrast to the analogy of a parked carwaiting to be started, proteins in cells are perpetuallysynthesized, modified, degraded and e most importantly ein motion. This refers to diffusion as well as a protein’s‘state’, as defined by its binding partners and post-trans-lational modifications. In the case of the CDC42protein these are different but interlinked processes: as a Gprotein it can exist in a GTP- or GDP-bound state, and as

332 SECTION | III Dynamic and Logical Properties of Biological Systems

a protein with a hydrophobic part it exists in a steady statewith a membrane-bound and a cytosolic fraction. It isimportant to stress that both kind of state are caused bydynamic and often cyclic processes, which are mediated byfurther binding partners. Guanine nucleotide binding isregulated by guanine nucleotide exchange factors (GEFs)and GTPase-activating proteins (GAPs), while scaffoldssuch as BEM1 increase the proximity of CDC42 and itsGEF CDC24. Under ‘normal’ cellular circumstances thesereactions are balanced out to remain stable. However, sinceBEM1-binding is CDC42-GTP dependent and theCDC42eBEM1eCDC24 complex favors CDC42-GTPbinding, this positive feedback carries the potential toswitch CDC42 activity and recruitment to a different mode.As Turing described for coupled reaction-diffusion systems[7], a shift in a parameter (e.g., expression level of CDC42)can destabilize a system, akin to a running car being shiftedinto gear. If the cell operates in this mode, a random fluc-tuation of CDC42-GTP can amplify into a sharp localiza-tion and can in the process deplete the cell of cytosolicCDC24 via diffusion. This is a method of communication,because it stops distant, less-pronounced spikes in CDC42-GTP concentration from growing further, delivering the‘message’ that there exists a more successful competitor inthe neighborhood. The result again is a stable dynamiccyclic process of binding/unbinding, albeit with a differentlocalization pattern. The cytosol in this example serves twofunctions: in the inactive mode it smoothes the randomfluctuations because of its rapid exchange of material. Inthe active mode its role is a medium for fast informationtransfer to suppress other sites of CDC42 localization if thefastest-growing site can, via CDC24 depletion, ‘commu-nicate’ its success faster than the growth rate of itscompetitors. However, the cytosol can only achieve this inthe presence of its complement: the plasma membrane withits reduced dimensionality which acts as a template forprocesses on a different timescale than in the cytosol.Another example for this principle is the generation ofa cell-spanning gradient by anchoring the point source ofactivity at a specific site as in Fus3-phosphorylation inyeast, or pheromonally activated transmembrane receptorsin the PM that diffuse at a timescale different from thespreading of their activity signal. In both cases perturba-tions of the steady state occur at the smallest relevantscale e post-translational modification in the form of, forexample, phosphorylation of an amino-acidic residue.Furthermore, in both examples these minute changes can beresponsible for a change in the cell’s fate, be it differenti-ation, proliferation or death. Mitosis is an example wherethe spatially homogeneous nucleus of eukaryotic cellsundergoes dramatic organization, which starts with mitoticspindle assembly and chromosome separation and leads tocytokinesis. In each of these processes multiple interactionnetworks govern the spatial restructuring, while at the same

time the spatial organization triggers new downstreamcomponents. Specifically, the formation of microtubulesinto the mitotic spindle is a necessary step before micro-tubule-binding proteins can separate chromosomes, buttiming does not imply causality, because the underlyingprocesses can be interlinked. In all these examples thescientific goal to determine the exact configuration of theprocess, be it a snapshot (in time) or a zoom-in (in space)needs to be tempered with knowledge of the bigger pictureto avoid postulating a standalone cause for a situationemerging from a complex interplay of spatiotemporaldynamics.

SPATIOTEMPORAL MODELINGOF CELLULAR PROCESSES

Abstraction of a biological phenomenon means that itsobservation must be quantified and transferred into thecommon language of mathematics, independent ofobserver or instrument. With an equation that describesa hypothesis of the process and a set of numbers thatdescribe a context, the outcome of a new experiment can bepredicted and the actual results compared. This functions asa test of whether the abstraction of a process was valid. Amisconception has long been perpetuated that completeknowledge of the parts of the process at its smallest scalecan be extrapolated to the end result. In case of a simplechemical reaction it is impractical to consider the collisionfrequency of single molecules and their electrostaticinteraction forces to derive the stoichiometry and speed ofthis reaction because of Avogadro’s number of molecules.But the large number of interacting molecules in a smallvolume also saves the day, as an abstract value for theprobability of a reaction to occur and the initial concen-trations adequately describe the outcome of the reaction.

Thus, in understanding a dynamic process we choosea level of abstraction and formulate partial differentialequations (PDEs), which describe the dynamics of thesystem at this level. Mathematically, a differential equationassumes that by dividing space and time into infinitesimallysmall elements, realistic behavior can be predicted if thecurrent state is known. As is usually the case, if there are noanalytical solutions numerical methods are employed.Here, the elements of time and space are chosen smallenough to guarantee accuracy, but large enough so that thefuture state of the system to be modeled can be calculatedin a reasonable timeframe. Non-linear dynamics and chaostheory (as used to describe turbulent flow, weather, etc.),however, have illustrated the limitation of this approach. Ifthe system is sufficiently interconnected and has enoughcomponents, small computational errors propagate andaccumulate so that the system may end up in different statesdepending on the initial conditions. In other words, local

333Chapter | 17 Spatial Organization of Subcellular Systems

effects determine the global pattern. Unfortunately, bio-logical systems tend to exhibit complex network motifs anda large number of components, making this kind ofmodeling extremely challenging.

With the increase in available computational power,Monte Carlo methods have gained in importance. Here,many stochastic snapshots of the system are evaluated toderive dynamic information. While this is robust to errorpropagation, the needed computational power is large inrelation to the derived results. Even more computationallyexhaustive is the method of molecular dynamics. Here,every component molecule and the forces acting upon it aretracked. This can give exceptional insight into the behaviorof a small number of particles for short periods, but is verydependent on the assumptions and simplifications used formolecular shape, behavior and interaction.

As a phenomenological approach, based on the expe-riences with Turing patterns at a time when computationalpower was limited, the so-called cellular-automatonapproach was developed. Similar to PDE, in this approachspace and time are coarsely discretized, but so is the vari-able in question (e.g., concentration of protein). It thusbecomes a state, in the most fundamental case binary (0sand 1s). The state at a certain position x at a later time-steptþ1 is then determined by the state of x and its neighbors attime t by a fixed set of rules that are loosely related to theunderlying PDEs. The Wolfram automaton is a simple 1Dcellular automaton where time-evolution can be visualizedas the second dimension in a 2D plot. Different rules lead todifferent behaviors that can, for example, be mapped topigmentation patterns of mollusc shells [8].

As described previously, biological systems tend toexist in a steady state that is ‘waiting’ to be perturbed andthus to switch to a different mode of activity. This resem-bles a loose description of so-called excitable media, whichare one example that has given prominence to the cellularautomaton. All excitable media share a common ‘rule set’that generates global patterns from extremely localizedinteractions. It can be reduced to the following for oneobservable substance:

1. Every point in space (called cell) is either in an excit-able state with an excitation value of 0, or in the excitedstate with a value between 1 and n.

2. Excitation spreads via ‘diffusion’, i.e., the value of eachcell is distributed among the cells in its neighborhood ofa certain radius.

3. If a cell has state 0 and ‘receives’ excitation via diffu-sion, it becomes excited and its value is set to n;otherwise, its excitation value decays by 1 (a loss percell additional to the redistribution by diffusion).

This phenomenological description of an excitable mediumis the algorithm, which can be translated to a cellularautomaton and renders BZ-like 2D patterns [9]. Here, rule 3

is an oversimplification of the complicated auto-catalyticprocess on a fast timescale, which is visible as a change ofcolor in the system and can be triggered by the presence ofminute traces of the activating component, but once thisconversion is locally done, the system needs some time torecuperate (refractive time) before it again becomesexcitable. This refractive time (e.g., the specific value of n)combined with the decay strength implemented in rule 3and the diffusion coefficients determines the spatialdistance between the spiral wave fronts.

The interaction can be extremely localized (here: acti-vation within each cell and diffusion to its four neighboringcells) and still affect a global pattern. We can use thissimple system to illustrate the effect of small differences inlocality of this rule set being reflected in the global pattern.By changing the size of the diffusion radius or randomizingthe shape of this neighborhood, the shape of the resultinglarge-scale spirals is determined (see Figure 17.1).

In this example, we minimize the system to oneobservable, which hides an interaction network of multipleagents. Expanding the above rule 3, one realizes that thetopology of this kind of interaction network between theinvolved agents can also be a determining factor of a globalpattern. By including a second substance that depends onthe concentration of the first and at the same time influencesit, one arrives at the classic activatoreinhibitor type ofsystem. As an example, two morphogens that act as acti-vator and inhibitor of undifferentiated cells of a homoge-neous tissue can form a spatially distinct pattern(fingerprint, retinal blood vessel network) of differentiatedcells. These patterns are generated by the network topologyof interacting substances. However, on the one hand itsspecific implementation follows stochastic fluctuations,which is why identical twins have distinct fingerprints andretinal patterns. On the other hand, global parameters (e.g.,temperature, foreign substances or overlying gradients) canalso affect the pattern formation and result, for example, indeformations in embryonal development, or can determinepatterns of revascularization that are essential in woundhealing but disastrous when initiated by tumors.

Similar pattern formation processes are also present atan intracellular scale. For example, a receptor tyrosinekinase (RTK) with a transmembrane domain to sense thepresence of its extracellular growth factor ligand can beactivated by ligand-induced di- or oligomerization, whichresults in autophosphorylation of the receptor by itsintrinsic tyrosine kinase activity. As a balancing reaction tothis activation, cytosolic protein tyrosine phosphatases(PTPs) inhibit this RTK activity by dephosphorylation ofthe receptors. RTK oligomerization and phosphorylation-induced increases in activity can be described as a positivefeedback of RTK activity; this activity can also influencethe inhibiting strength of PTPs either by inactivating PTPsvia reactive oxygen species (ROS) or by translocating PTPs

334 SECTION | III Dynamic and Logical Properties of Biological Systems

to the PM via adaptor modules that bind phosphorylatedactive receptors to in turn enhance the activity of the boundPTPs by phosphorylation. The system of RTKs interactingwith different PTPs is an example where the inversion of aninteraction from activating to inhibiting changes the globalactivity pattern from silenced but excitable to local activityhotspots. If, however, we track the localization of a PTP inresponse to its recruitment to the PM, the activity patternbecomes a time-dependent transient phenomenon(Figure 17.2). Before ligand binding, the system remainsstable and activatable. Weak random activity fluctuations ofthe RTKs are countered by the cytosolic PTPs. Ligandbinding constitutes a strong fluctuation as it continuouslyactivates those RTKs to which the ligand is bound. As thesystem is a balance waiting to be tipped, this perturbationspreads more rapidly than diffusion of activated RTKs fromthis point of origin would allow. This is mediated by theinactivation of PTPs in close proximity to the PM via short-ranged action of ROS. The diffusion-limited translocationof a PTP to the PM by RTK activity-triggered binding tophosphotyrosines via an adaptor module again increasesthe strength of PTP activity in the globally activated state ofRTK. As a result, in regions where fluctuations reduce RTKactivity slightly, PTP activity further reduces RTK activityand hence ROS production. The system is still able tomaintain hotspots of activity because the PM now hasa pool of inactive, diffusing RTKs that can be locallyreactivated. To test this hypothetical system and to putconstraints on the physicochemical parameters of themodeling, experimental observations of the involvedcomponents are obviously crucial. However, reasonable,simple considerations about the biochemical properties ofRTKs and PTPs and the interdependence of their activities

active RTK

active PTP

active RTKin basal PM

FIGURE 17.2 Cellular automaton simulation of an

RTK-PTP-interaction in a 3D virtual cell, depicted in

the simplified reaction schemes on top. Time progresses

from left to right column, with a coloring table for indi-

vidual pictures as last column. Top row: vertical section of

the cell; normalized RTK activity; Middle row: top view of

the basal membrane; Both: darke no activity, brighte high

activity. Bottom row: vertical section of the cell; normal-

ized PTP concentration; dark e no concentration, bright e

high concentration. Continuous PTP activity suppresses

RTK activity, which remains below an activation threshold.

A ligand-binding event perturbs the system above activa-

tion threshold. High RTK activity lowers PTP activity

proximal to the PM, allowing the autocatalytic RTK acti-

vation to spread. Although initially localized, activation

signal promptly spans the whole PM. High RTK activation

also triggers PM binding of PTP via adaptor protein (lower

row). This increases PTP concentration by sequestering PTP activity in clo

translocation transforms the double-negative feedback of RTKePTP interacti

slightly lower RTK activity is suppressed by the faster-diffusing PTP tethered

This is seen most easily in the middle row, where the RTK activity declines ev

RTK activity is sufficiently high to maintain its activity state, because the au

allow the exploration of the possible manifestations of thesystem on the micrometer scale.

SPATIOTEMPORAL QUANTIFICATIONOF CELLULAR PROCESSES

The macroscopic activity and localization patterns that giverise to cellular function emerge from the interaction andmobility of nanometer-sized molecules. These localmolecular properties are themselvesmodulated by the globalcellular patterns that they generate. Such simultaneousupward and downward causation is typical for self-organizedsystems. To understand the principles and mechanisms bywhich a cell operates, it is therefore necessary to quantify theprogression of processes starting from a certain state withspatial and temporal resolution at the molecular levelwithout losing sight of the cellular context.

Owing to its ability to resolve micrometer-sized struc-tures, biological microscopy has been instrumental in thediscovery and understanding of living systems. Microscopyas an extension of our eyes has quickly become a windowinto the subcellular world. At the dawn of microscopy,Robert Hooke, in 1665, published the first observation ofthe basic unit of life: the cell. One of the oldest preserveddrawings is from the prolific microscopist Antonie vanLeeuwenhoek (1632e1723), who observed a lumen in thered blood cells of salmon. The discovery of the nucleusshowed that compartmentalization does not end at thecellular level but is a pattern that repeats within itself.

As staining agents with better contrast became availablemore than a century later, chromosomes, which stronglyadsorbed basophilic dyes, were identified inside the nucleusby Walther Flemming and named by von Waldeyer-Hartz.

time

RTK

PTP

RTK

PTPco

nc.

a

ctiv

ity

max

0

se proximity to the RTK that raises RTK activation threshold. The PTP

on to an activatoreinhibitor topology. There, RTK activity in regions with

to the membrane. A stable Turing pattern forms from this lateral inhibition.

erywhere (white to yellow to blue) apart from the local hotspots. Here local

tocatalytic activation outperforms deactivation by PTP.

335Chapter | 17 Spatial Organization of Subcellular Systems

The term chromosome (colored body) that we still usetoday reveals that cellular structures were first discoveredand named according to their appearance (phenotype), andonly later were their functions studied and understood,mostly by other means. Such a merely descriptive usage ofmicroscopy evolved to be the quantitative tool that it istoday, suitable to understand the operation of spatiallyorganized intracellular communication [10].

Fluorescence microscopy provides an unsurpassed wayto observe the dynamics of molecules inside living systemsand has therefore become a cornerstone of cell biology. Inthis technique molecules are specifically labeled withagents that absorb energy as photons of a given wavelengthand re-emit it as photons of a different, usually red-shiftedwavelength. In immunofluorescence and related methods,labeling is accomplished by using specific biomoleculessuch as antibodies to target fluorescent dyes to a protein ofinterest. As an excess of labeled material needs to beapplied to the sample to ensure saturation of binding sites,washing of unbound material is essential to obtain contrast.While recent developments in chemical genomics haveprovided ways of accomplishing such labeling in livingcells, most labeling methods are not suitable for live cells.Discovery and tooling of the green fluorescent protein (FP)was therefore a breakthrough in fluorescence microscopy.FPs can be fused to a protein of interest by geneticmanipulation of cells to create a fluorescent chimericversion that can be expressed and imaged in livingorganisms.

With the ability to visualize molecules in living cells,the challenge then is to derive from the acquired fluores-cence images information about molecular mobility, suchas diffusion and transport, and molecular state such asinteraction, conformation or post-translational modifica-tions, to understand how biological patterns arise. Interac-tions, for example, could be investigated by simultaneousimaging of two or more labeled species. However, co-localization of different molecular species in the samespatially resolvable volume does not mean that interactionis occurring. A standard microscope is an optical low-passfilter that removes the fine details of an object, preventingthe observation of sub-wavelength structures (Abbediffraction limit). A point-like light source in the sample isreconstructed by a microscope into a larger image calledpoint spread function (PSF), and its dimensions are relatedto the optics of the microscope and the wavelength of thelight. For standard wide-field microscopy, the PSF is 250nm in the lateral dimension (perpendicular to the beampropagation), and in the longitudinal dimension spans theheight of a typical cell, resulting in a volume of about 5 fL.Such dimensions are much larger than the size of a typicalprotein (80 kDA equivalent to 10e7 fL), and therefore twoapparently perfect co-localizing objects in an image can befar apart on the molecular scale.

Using a pinhole to reject out-of-focus light, confocalmicroscopy reduces the longitudinal dimension to <1 mm,enabling optical section of a typical cell into several slices.In spite of this achievement, the size of a typical confocalvolume (1 fL) is still seven orders of magnitude larger thanthe size of a typical protein. Novel super-resolution tech-niques such as PALM/STORM or STED can routinely godown to a resolution of 20 nm. In PALM/STORM theability to localize single fluorophores with nanometeraccuracy is exploited to reconstruct a high-density super-resolution picture from a series of images of sparselyexcited fluorophores [11,12]. In STED, the PSF ofa confocal laser scanning microscope is sharpened bystimulated emission depletion of the fluorophores far awayfrom the center of the PSF [13,14]. To identify and localizesingle molecules, both imaging methods benefit if thedensity of molecules to be detected is low. Longer acqui-sition times are required to attain the resolution needed todistinguish between interacting and nearby molecules (ora protein conformational change), thereby precluding itsuse to monitor fast cellular dynamics.

Although most of the aforementioned techniques havepushed the resolution well below the diffraction limit,a different subfamily of methods has been developed todirectly assess functional observables such as diffusion,conformation and interacting populations of molecules. Ina first group of functional techniques, the macroscopicfluorescent steady state is locally perturbed by photo-chemical means while monitoring its re-equilibration overthe cell. Such recirculation of fluorescent species isa macroscopic reporter of the mediating intracellularprocesses: transport, binding and diffusion. The oldest andmost common of these techniques is fluorescence recoveryafter photobleaching (FRAP), in which a region of the cellis first bleached using a strong laser beam for a short time;the recovery of the fluorescence intensity is monitoredafterwards [15,16].

In a second group of functional techniques the macro-scopic fluorescent steady state is dissected in space andtime into the microscopic fluctuating parts that are aver-aged out on a larger scale. Such fluctuations are a productof the discrete molecular composition of the observedsystem and can be harvested for information about theunderlying physicochemical processes that give rise tothem. In an ergodic system, the observation in a limitedregion of space of a sufficient large number of events isequivalent to observing a statistical sample of all theensemble’s possible events. This principle is used in fluo-rescence correlation spectroscopy (FCS) to obtain absoluteconcentrations and diffusion times by measuring themotion of individual fluorescent species through a small(~ 0.5 fL) confocal volume [17,18]. With two-color FCS,the co-diffusion of proteins through the confocal volumewill become coincidences in the intensity time traces [19].

336 SECTION | III Dynamic and Logical Properties of Biological Systems

Interaction (direct or mediated via a third protein) can beinferred from a high coincidence rate, as the co-diffusion ofindependent proteins is statistically rare.

While FRAP and FCS aim to obtain molecular infor-mation by observing the ensemble, they still cannotobserve different conformational states directly, ordistinguish between direct interactions and those mediatedvia a large protein complex. Foerster resonance energytransfer (FRET) measures molecular proximity by moni-toring the far-field photophysical effects of the near-fielddipoleedipole coupling between two fluorophores(usually called donor and acceptor). Such effects includethe quenching of the donor fluorescence [20], the sensi-tized emission of the acceptor and the reduction in thedonor fluorescence lifetime [21], and others [22]. Asenergy transfer only occurs when the distance betweenfluorophores is in the order of a few nanometers, FRETeffectively senses proximity in a volume (10e5 fL) rele-vant to uncover interactions between proteins. In addition,FRET has been used as a basis for sensors that useconformational changes to relay information aboutactivity, pH or concentration of molecular species [23].

In summary, functional fluorescence microscopy allowsa cellular dynamic topographic map of proteins to beoverlaid with topological information on the causality thatdetermines protein state [24]. Such a state consists ofmobility and population evolution of the different inter-acting or modified proteins. Altogether, this state is themolecular basis of the cell-spanning patterns that generatefunctionality on the micrometer scale [25].

CAUSALITY FROM VARIATIONAND PERTURBATION ANALYSIS

Each cell is an individual entity that may respond to a signaldifferently from its neighbors, even in a clonal populationexposed to the same environmental conditions. One of thesources of such variation are the stochastic properties ofchemical reactions at low concentrations [26]. Many of thecomponents involved in signaling are in such low numbersthat actual reaction speeds can differ significantly from theaverage. The other source of variation arises from extrinsicfactors such as its microenvironment. The accumulation ofsmall differences in a series of events leads to an overallcell-to-cell variation in the internal state determining theirresponse properties [27]. Cellular heterogeneity has beenobserved in a variety of cell types, ranging from bacteria tomammalian cells.

For example, in gene expression the process by whichmRNAs and proteins are synthesized is inherentlystochastic. This stochastic nature introduces fluctuationsaround the mean level of mRNA, causing identical copiesof a given gene to express at different levels. This noise in

gene expression is a substantial factor of populationheterogeneity and a cause of variability in the cellularphenotype. Interestingly, the noise in the allele transcrip-tion in diploid cells is gene specific and not dependent onthe regulatory pathway or absolute rate of expression.Moreover, mutations can alter the noise in gene expression,suggesting that it is an evolvable trait that can be optimizedto balance fidelity and diversity in eukaryotic geneexpression [28,29].

Methods that rely on the measurement of cell pop-ulation averages provide a weighted summation over allpossible states. In contrast, single cell techniques such asmicroscopy, flow cytometry and recently developed masscytometry can assess such variation by providing cellularand, in the case of microscopy, subcellular information.The first clear advantage is that multimodal populations canbe properly characterized. More importantly, single cellobservations of the state of a set of intracellular compo-nents can provide information about the network connec-tivity between them.

A common feature of almost all signaling networks isthe presence of feedback loops, and these are the basis forany regulated response [30,31]. An aspect of this networkmotif is that the response of any given protein withina feedback loop contains information about the dynamicsof the network as a whole. Each protein can be consideredas an embedded probe that relays the coherent response ofthe network. If the state of two proteins is monitored ina single cell, their relationship will be dictated by theconnectivity in the network to which they belong. Thepaired observations in multiple cells will therefore repre-sent a statistical sample of the landscape of possible rela-tions compatible with the underlying network. While causalinformation cannot be derived from such correlations(correlation does not imply causation), the number ofpossible networks that can describe the system can besignificantly reduced.

To obtain causal connections from observational data,extra information is needed. A priori knowledge, such aspartial causal connectivity (or lack of), can be used to derivetopological motifs. This has proved useful to detect positivefeedback loops in tyrosine phosphorylation networks evenin the case of the elusive autocatalytic loops [32]. Othermeans of deriving causality are by acquiring and analyzingricher datasets in which the time evolution of the system isfollowed [33]. In such time-dependent datasets the obser-vation of subsequent events allows the analysis of flow ofinformation and therefore enables the reconstruction ofcausality that is missing from static data.

While causality can be derived from correlative data incertain restricted cases, in general it must be derived fromdata after perturbation of the system. Here, one or moreparameters of individual elements in a signaling networkare perturbed, such as the activity level or concentration of

337Chapter | 17 Spatial Organization of Subcellular Systems

a protein [34,35]. The effects of such interventions on thenetwork components reflect the causal connectivity amongthem. A perturbation in a single node propagatesthroughout the network following its topology. Bymeasuring the response of other nodes, this propagator canbe determined. In perturbation analysis, the networkcomponents (or a linearly independent set of components)are sequentially perturbed to probe the network. Bycombining the propagators obtained from independentperturbations, the intrinsic structure of the system can beused to predict the system response to different input data.

Whereas in correlative studies the size of the datasetscales linearly with the network size, in perturbation studiesthis relationship is quadratic, as the number of possibleconnections scales in this way. Effective implementation ofnetwork reverse engineering methods to resolve networkstructure therefore demands a high-throughput automatedsystem for data acquisition. Recently developed fluores-cence lifetime imaging microscopy on cell arrays(CA-FLIM) is one such method [32]. Cells are plated onmicroscopy-compatible chambers where chemical (inhibi-tors) or genetic (siRNA, cDNA) perturbations have beenspotted in a high-density grid (up to 25 spots/mm2). Cellstake up the material locally from the spot, creating anaddressable array of perturbed samples. Fully automatedfrequency domain FLIM is used to traverse the arrayaccurately determining in each spot the post-translationalmodification state with subcellular resolution. As wasshown for the epidermal growth factor tyrosine phosphor-ylation network, CA-FLIM can provide correlative data onsignal propagation. As FLIM measures the post-trans-lational modification extent with spatial resolution,CA-FLIM is the basis to resolve the local structure ofsignaling networks in spatially regulated cellular processes.The current ability to measure 104 samples per dayprovides a way to derive causality in large networks (102

components) by perturbation analysis.

MODEL-DRIVEN EXPERIMENTATION ANDEXPERIMENTALLY DRIVEN MODELING

From the causality maps, further insight into the spatio-temporal dynamics of biological processes can be obtainedby iteratively integrating experiments with simulations.Partial information about the reactions involved in a bio-logical process is used to simulate the biological process ofinterest and the resulting insights inspire new experimentalobservations. Biological parameters are obtained by fittingthe data to hypothetical models, and new experiments thatresolve the uncertainties/degeneracy of the models can bethen performed.

As described earlier, information about causation andthe agents involved can be extracted from the measurement

of large populations and their variation. If the underlyingagents and their interaction are known, a cellular automatonoffers a rapid approach to recreate the observed behavior insilico on a single cell level. However, the prime challenge iscurrently the inverse process. This means, can we computethe network’s causality if we know the topography of thesystems and the players involved, even from single cellmeasurements? This would mean exploring the potentialbehaviors of all possible network motifs in simulation andthen looking for distinguishing features that allow theexclusion of certain motifs. For the example of an RTKinteracting with PTPs given above, that would meandeducing a double-negative feedback from an observedglobal activation pattern and excluding that for an observedformation of activity hotspots.

As a further example of deducing a network architecturefrom observed patterns, let us consider cell division inEscherichia coli. To measure the size of the cell and at thesame time provide a spatial cue onwhere to divide, theMinD,MinC and MinE proteins self-organize into a cell-spanningoscillation of aMinDwave frompole to pole. A reconstitutedsystem ofMinD,MinE andATP proved sufficient to generate2D-patterns in vitro [36]. This biological example is akin tothe BZ reaction and can be solved similarly to demonstratethe power of modeling in deriving a network topology fromscant experimental knowledge. The reconstituted system invitro exhibits waves of membrane-bound MinD/MinE withthe following simplified characteristics:

l MinD can bind to the membrane, slowing its diffusion.l MinD density increases slowly to a peak and drops more

steeply as seen from the direction of the traveling wave.l MinE density increases almost linearly towards the

trailing edge of the wave and drops off very sharply atthe end.

In this system we have two observables (MinD and MinE)in two states (free and bound). In trying to model thissystem, let us consider these two species in two states (free,bound; in case of MinD to the membrane, in case of MinEto MinD). This simple network therefore has four nodespairwise-linked by binding reactions, resulting in fourreaction rate constants, where each reaction rate can beinfluenced by each node in a positive or negative way(Figure 17.3). As long as no node influences its attachedreaction rate, this system comprises linearly coupleddifferential equations, and a systematic check of thesepossibilities shows that no combination leads to travelingwaves. Knowledge of the system further limits the amountof sensible connections: e.g., the ATPase MinD is known tobind to the PM in ATP-bound form and MinE mediates theMinD-ATPase activity, thereby increasing MinD-PMdissociation, and favorably binds to PM-bound MinDdimers. By this reasoning, MinE can be considered anantagonist to MinD-PM binding.

FIGURE 17.3 Modeling the MinD/MinE system. Experiments and trial-and-error by simulation refine a four-node network of unknown causality to putative network that reproduces key features of

the experiments. Main feature of the causality network are the red arrows: a positive feedback of MinD-dependent MinD recruitment to the PM and more than linear increase of MinDePM release

dependent on MinEeMinD binding. Gray arrows depict the coupling of MinE activity to MinDePM binding (mainly PM-bound MinD is activated by M E, and MinE is released fromMinD when not at

PM). The network exhibits oscillations in ‘0D’ of well-mixed reaction vessels, and wave progression in 1D that does not quite match the experimentall measured profiles. However, in 2D spiral waves

and Turing patterns can be observed, and in a restricted 1D simulation the size of the cell sharply influences the time-average of MinDE peak concen ation. Only in the case of medium size does the

maximum of MinE coincide with a minimum of MinD. This can result in downstream activation of cell division localization in space and time.

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339Chapter | 17 Spatial Organization of Subcellular Systems

To achieve a spontaneous increase in membrane bindingof MinD in the presence of its antagonist, MinD bindingmust be self-referencing. This means that the presence ofbound MinD favors further MinD binding, which can becaused by, for example, dimerization of MinD in the boundform. This introduces a first non-linearity in the reactionnetwork. However, this needs to be balanced by a similarnon-linearity on the antagonistic side, otherwise only highlevels of membrane-bound MinD will be a stable solution.As postulated in the above paper, rapid rebinding of freeMinE to MinD at high MinE concentrations is likely. Thise partly by experimental knowledge, partly by exclusionvia trial and error in simulations e reconstituted system iscapable of oscillatory behavior in ‘0D’ of a well-mixedreaction vessel and standing or travelling waves in 1D(Figure 17.3). When extended to 2D, these waves will self-propagate comparably to the reconstituted systemdescribed earlier [36]. Furthermore, a decrease in the MinEfeedback strength results in localized Turing patterns.When restricting the 1D system to finite lengths, we realizethat below a critical length wave propagation is impossible,whereas above a certain length multiple waves can form.Only at a certain length does the time-averaged maximumof MinE coincide with a minimum of MinD at the center ofthe cell, which could provide the spatial cue on where todivide, coincidentally with a cue on when the cell hasgrown large enough. This network operating with nm-sizedmolecules and reactions at microsecond timescalesdecides the fate of micrometer-sized bacteria after hoursof growing. The above simulation hinges on the collisionof scales in two instances: diffusion is about an order ofmagnitude slower in the membrane than in the cytosol, andrecruitment of MinE to MinD is an order of magnitudeslower than recruitment of MinD to the PM. The first letsa local reaction deplete a cytosolic pool fast enough to staylocal, and the second is responsible for the delay of theMinE-peak in the wave with respect to the progressingMinD peak. These two assumptions need to be experi-mentally verified to validate the simulation. However, whenconsidering the profile of the 1D travelling wave, a cleardiscrepancy with the experiment is obvious. The simplifiedmodel generates an almost symmetrical MinE profile of the1D wave, whereas the experiment showed a linearly risingfrontal edge with an abruptly decreasing tail edge. Eventhough the MinD profile is more similar, the MinE profile’sonly reproduced feature is its delay in respect to the MinDpeak.

This points to the necessity for further experimentscoupled with more detailed simulations to narrow down thereason for this discrepancy. For example, one could intro-duce further states to detail the order of MinDeMinEcomplex dissociation with regard to the state of PM bindingand the ADP/ATP switch of MinD recently detachedfrom the PM. Increasing the complexity of the model

without increasing the number of observables at the sametime runs not only the risk of over-fitting, but creates a falsesense of security if the model can account for all previouslyobserved experimental aspects. A more detailed model willcreate testable new features that need to be checked againstexperiments. In this way experiments and modeling mustimprove upon each other, and need to be interwoven morecompletely. The search for interaction partners of proteins(via screening or FRET approaches), their localization andtransient translocation, the physicochemical properties thatgovern interaction and translocation timescales (reactionand association rates, diffusion coefficients) and theiractivity needs to continue. Equally essential are modelingapproaches which can build on the existing experimentaldata to validate hypotheses and at the same time predict themissing experiments to complement current paradigms.

CONCLUSIONS

Biological systems manage to increase their own organi-zation and maintain it at the expense of the order takenfrom the environment. Energy is consumed and disorder(entropy) is exported. It has been suggested that fora sufficiently complex network of chemical reactions, self-organization into autocatalytic loops will necessarily occur[37]. Such loops, as a form of closure, are a necessarytopology for any system that needs to maintain itself, andhence are a prerequisite for life. Evolution shapes the pathby favoring those structures adapted to the environment. Insuch self-organized systems, global coherence spontane-ously emerges out of local interactions. This effect cannotbe understood without the effect of simultaneous upwardand downward causation of the involved scales. Closure isagain present wrapping up the global and local scale.

Systems biology tries to describe living organismsbeyond reductionism to create a coherent view of theiroperational principles and mechanisms. Our descriptionstarts at the scale which is most appropriate for thephenomenon that we are studying, being able to reach outto other levels when understanding increases. In the wordsof Sydney Brenner, we describe the system neither bottom-up nor top-down, but middle-out. Closure of biologicalsystems makes the starting point logically irrelevant:‘There is no privileged level in biology that dictates therest’ [38]. And understanding how closure is achieved aidsour understanding of living matter.

In cellular systems biology we work towards under-standing how nanometer-sized molecules generate cell-spanning patterns from which biological function emerges.As we have described in this chapter, this requires bridgingconceptually, theoretically and experimentally scales inspace and time. A causal description of the molecularecology that runs the cellular operation can aid in bridgingthe scale gap. Deriving such a causality map requires a tight

340 SECTION | III Dynamic and Logical Properties of Biological Systems

iteration between experiments and simulations, directingthe efforts of the former and increasing the predictiveability of the latter.

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