SGER: Communications Theory & Multicellular Biology

Project Summary

The assertion that biological systems are collections of elements that communicate would draw no re-buke from biologists – the termssignaling, communication, andnetworkare deeply embedded partsof the biology parlance. However, the more profound quantifiable meanings of information and com-munication are often overlooked when considering biological systems. Information can be quantified,its flow can be measured and tight bounds exist for its conveyance between transmitters and receiversin a variety of settings. Furthermore, communications theory is aboutefficientcommunication whereenergy is at a premium. Similarly, energy and its efficient use almost always plays a pivotal role in thedescription of biological systems. One intention of this proposed exploratory study is to consider a widevariety of problems in modern biology that involve large collections of cells (“multicellular systems”)from a communications theory perspective and determine if and when the theory confers any specialanalytic or predictive benefit. In addition, we seek to applyalready known organizational principlesfrom multicellular systems to engineering problems which might share the same sorts of constraintsand optimization metrics – such as large multielement sensor networks.

The intellectual merit of this program lies incareful exploration of communications conceptsapplied to signaling within cells (cellular networks) and between cells (multicellular networks) wheremainly cursory application has previously been pursued. Since energy consumption is a key featurein both biological networking problems and in the formal specification of communications problems,we believe that a communications theory perspective may help guide biological research in specificareas such as tissue biology, cancer biology, the biology ofaging, and microbial ecosystems as wellas other areas where a formal network perspective may be appropriate. Likewise, we suspect that theexistence proof provided by living things, in combination with a communication-theoretic perspective,can provide new approaches to biological and non-biological engineering problems.

Thebroader impact of developing an effective communications framework for biological systemswhich can both explain and predict the general behavior of multicellular systems is hard to overesti-mate. The most obvious impact areas are aging and age-related diseases such as cancer in biology, anddistributed specification and assembly of robust structures in engineering. But, a multitude of otherapplications in biology and engineering are clearly possible. However, the immediate purpose of theproposedexploratoryresearch is to rigorously exercise the notion of communications theory in biol-ogy as a pivotal tool. Perhaps most importantly, we will alsoidentify and engage other researcherswhose work and perspectives will help drive the overall endeavor. Through meetings (and possibly aworkshop) we hope to articulate the important problems which lie at the interstices of biology and com-munications theory and facilitate the formation of an associated vibrant, cohesive and directed researchcommunity.

Christopher Rose I. Saira MianWireless Information Network Lab Life Sciences Division

Rutgers University E.O. Lawrence Berkeley National Laboratory

1 Introduction

The assertion that biological systems are collections of elements that communicate would draw no re-buke from biologists – the termssignaling, communication, andnetworkare deeply embedded parts ofthe biology parlance. However, the more profound quantifiable meanings of information and commu-nication are often overlooked when considering biologicalsystems. Information can be quantified, itsflow can be measured and tight bounds exist for its conveyancebetween transmitters and receivers in avariety of settings [1–3]. Furthermore, communications theory is aboutefficientcommunication whereenergy is at a premium. Similarly, energy and its efficient use almost always plays a pivotal role inthe description of biological systems. One intention of this proposed exploratory study is to consider awide variety of problems in modern biology that involve large collections of cells (“multicellular sys-tems”) from a communications theory perspective and determine if and when the theory confers anyspecial analytic or predictive benefit.

A particularly interesting and profoundly important biological problem is the development, main-tenance, regeneration, subversion, and decline of tissues– the primary interest of one of the investi-gators. Subtle intra- and intercellular signaling in tissues is demonstrably important in maintainingform and function in the face of stochastic fluctuations and noise, aberrant genomes and environmentalinsults [4–8]. If one imagines that organisms and their constituent cells have been nudged towardenergy-efficiency through the selective pressures which drive evolution, then the issue of energy us-age in signaling could be extremely important and might suggest specific signaling methods amongthe myriad ones possible between living cells with a complexgenome. That is, energy considera-tions related to the cost of fabricating, operating and disassembling/deconstructing different signalingmodalities may severely restrict the ways in which cells caninteract or arrange themselves, and canthus provide something of an organizing principle for biological systems.

Alternatively, one might view the multitude of structural and functional solutions evinced by bi-ology as indicative of good network engineering practice. Efficient design of sensor networks comesimmediately to mind since both biological and human-engineered sensor networks seek to convey en-vironmental information in a timely yet energy-efficient fashion over a substrate of many individualsensing elements (for overviews, see [9,10]). If a cell is equated with a “sensor”, then one can imaginesituations where selective pressures might drive a collection of cells toward energy-efficient sensing –of nutrients in the environment, for example. In this way, the signaling functions of a given cellularcommunity might be a solution for certain distibuted sensing problems.

Likewise, one could view the genome (base-pairand conformational information [11, 12]) andproteome as the solution to a specification problem. That is,the development of an organism proceedsfrom a set of instructions which constitute information – the genome and the proteome of a “germ”cell. From an information-theoretic standpoint, one can argue that “that’s all there is” – that all therelevant information for specifying structure and function are completely contained in such a cell.Such thoughts lead to an intriguing, even if somewhat vaguely posed, question: how much informationis necessary to specify a physical structure? As a fascinating inversion of the question, consider – howmuch information, in the information theoretic sense, is contained in a genome?

Equally interesting, development and tissue maintenance is remarkably stable even in the face ofstochastic environmental perturbations. Although adult stem cells play a key role in regenerating tis-sues after injury and can be thought of providing some of the information necessary to achieve this feat,it is also the case that the regenerative potential of tissues declines with age [13]. This observation begsthe question of how much information is necessary to maintain form and function, and how does de-

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velopment proceed so robustly and repeatably in such “noisyenvironments.” The biological questionsare clearly important, but the abstraction of how one specifies form and the information/energy flowsinherent in structure development and maintenance are intriguing in their own right – and could havemajor impact on how we build tomorrow’s networks and machinery both small and large.

1.1 Research Thrusts

Following these ideas, our proposed study will consist of three main thrusts:

• Identification and analysis of specific high-impact biological problems which can be cast in acommon communication-theoretic framework.

• Identification of experiments to test specific aspects of communications between cells at a suffi-cient level of detail to answer communication-theoretic questions.

• Abstraction of biological structural, developmental and functional information and flows in anattempt to develop robust synthetic mechanisms of assemblyand maintenance from myriad iden-tically programmed units.

The first two thrusts are in some ways attempts at modeling specific biological multicellular sys-tems, but with the purpose of placing biology in a communications theoryframeworkrather than amodeling exercise. That is, we seek to understand whether communications theory can offer a set ofparticularly effectiveorganizing principlesfor biological systems. Information theory in particular,with its heritage of placing mechanism-blind bounds on performance, may be especially effective inthis regard given the large number of already known (and potential) biological mechanisms. The thirdthrust turns the problem around and asks what lessons might be learned from known biology about theconstruction of arbitrary structures from identically programmed units similar to [14–17] but with aninformation-theoretic (as opposed to computational or algorithmic) twist.

1.2 Potential Impacts

From an engineering perspective, the potential impacts of understanding biological systems in a formalcommunications theory context range from the practically important to the futuristic:

• Discovery of energy-efficient biological communications methods developed through evolutionand appropriate application to engineering problems such as distributed sensor networks, or ro-bust network design.

• Biologically-inspired solutions to some network information theory problems

• Network-inspired treatements for injury, disease and aging

• Understanding how genomes are translated into organisms

• Object manufacture via collaboration of myriad identically programmed units

Needless to say, we do not propose to directly tackle (much less solve) these problems ourselvesin an exploratory research program. Rather, we intend to explore biological multicellular systems ascommunication systems in apreciseway –carefully formulating problems, exercising existing collab-orations and attending meetings (e.g., [18]) to form new ones which extend our collective expertise. Inthis way, we hope to help develop a vibrant, cohesive and directed research community which seeksbreakthroughs in what might be called “Biological Communications Theory”.

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2 Signaling in Biological Systems

Any biological system composed of more than one cell is by definition a communications network.Such networks span the range of complexity from microbial ecosystems such as biofilms, microbiomesand bacterial mats to complex tissues and organisms. One caneven argue that an animal can be con-sidered “a superorganism with an extended genome that includes not only its own cells but also thefluctuating microbial genome set of bacteria and viruses that share that body space.” [19].

Signaling within and between cells is accomplished througha variety of chemical, electrical andmechanical means so that individual cells can sense their cellular and non-cellular environment andbehave in an appropriate manner. Signals can be conveyed using a variety of methods including chem-icals (hormones, cytokines, growth factors, ions, drugs, small molecules, neurotransmitters, peptides,proteins, lipids, carbohydrates), mechanical forces, pressure, temperature, light, electrical potentialsand magnetic fluxetcetera. Stimuli may trigger a variety of responses occurring over different timescales such as an alteration in cell metabolism, a change in cell membrane voltage, activation of geneexpression (transcription in the nucleus) and cell locomotion, to name a few. Often such signal trans-duction involves a sequence of biochemical or other reactions whereby one species is converted toanother which in turn constitutes the input for the next reaction. This sequence of events is often calleda signaling pathwayand the intersection of pathways results insignaling networks. The behavior of agiven signaling pathway and hence signaling networks may bemodulated by a variety of stimuli.

As a useful abstraction, we will consider a signal to be somestimuluswhich causes someresponse– a general term which we will be careful to quantify in a communications theory sense. As a fur-ther abstraction, a stimulus may cause multiple responses,or a given response may be modulated bymultiple stimuli. The complex interplay of stimulus and response within and between the cells in amulticellular system constitutes a network.

We note that this basic network analogy can be pursued at a variety of levels, from organismsto tissues to cells to molecules to atoms. Our approach here,at least initially, will use cells as theunit of organization. There are a variety of reasons for thischoice with perhaps the most obviousbeing that cells are discrete entities with clearly definable boundaries, and cells can send and receivesignals. Furthermore, cells are specialized, self-contained, self-powered, sensing and communicationplatforms that can be assembled to create a cornucopia of complex systems of myriad functions. Froma practical perspective, whereas the molecular componentsof cells have been investigated extensively(see for example [20]), the form and function of tissues comprised by cells has received considerablyless attention.

2.1 Mechanics of Intercell Signaling

The cell membrane is a natural boundary which separates “inside” from “outside” and is a conduit forinformation transfer between the interior and exterior of acell. Intercellular communication can occurthrough a variety of mechanisms and structures mediated by the cell membrane. Agap junctionis anarea of apposed cell membranes containingconnexons, proteins that bridge the extracellular space be-tween two cells and allow the cytoplasm of one cell to communicate directly with that of the other viachemical and/or electrical means. Some categories of chemical signals such as steroids and nitric oxidesimply diffuse across the cell membrane through the cytoplasm and embedded organelles (cytosol),and into the nucleus where they effect a response. In receptor-mediated signaling – perhaps the mostimportant form of communication between cells or tissues – chemical signals, oftenhormones, bind to

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a specific protein located in the cell membrane and this resultant chemical signal-receptor complex me-diates the transmission of extracellular signals to the interior of a cell. The reverse process (sometimesusing the same structures, sometimes not) conveys intracellular signals to the exterior.

Receptor-mediated signaling involving hormones can be divided into the following types:

• endocrine signaling: a cell sends a chemical signal which travels through some extracellularmedium and is received by distant cells (in other parts of a colony or body);

• paracrine signaling: a cell sends a chemical signal which is received by cells only in its vicinity;

• autocrine signaling: a cell sends a chemical signal which is received by cells of the same type orthe sender cell itself;

• juxtacrine signaling: a cell sends a chemical signal which travels along the cell membrane andis received by the sender cell itself or a physically adjacent cell.

A cell interacts dynamically and reciprocally with its cellular and non-cellular environments at a va-riety of levels. Locally within its niche, a cell responds toneighboring cells, the extracellular matrix,paracrine factors and juxtacrine factors. In the tissue, the cell/niche are influenced by endocrine andautocrine signals. The systemic milieu affects the tissue and this in turn is affected by external environ-mental influences. Overall, endocrine, paracrine, autocrine and juxtacrine signals are chemical signalsthat play critical roles in communication within and between layers of this organizational hierarchy.Also, as might be expected in biological systems where evolution parsimoniously reuses and adaptsbasic themes to fit different purposes, communications methods can also be assemblages or cascades ofmore basic methods – such as auditory signal transduction inhair cells which incorporates mechanical,chemical and electrical means to relay sound stimuli to nerve fibers.

Our main point in enumerating biological signaling modalities is to convey the fact that biologicalsystems have already “discovered” a wide range ofchannel modelsused in standard communicationstheory; i.e., private channels, broadcast channels, multiple access channels, relay channels and thelike [1, 3]. One of our tasks is to look more closely at the communications physics of biologicalsystems to see how precise the communications analogy can bemade.

2.2 Metabolism & Communication

As previously mentioned, energy usage is at the core of biological systems and telecommunicationnetworks. It is thus useful to note that biological signal transmission between cells or tissues requiresenergy consumption:

• Biosynthesis, storage, and secretion (exocytosis, membrane transport) of the chemical signal bythe sender cell;

• Active or passive transport of the chemical signal to its destination;

• Recognition of the chemical signal by cells, relay and amplification of the signal within the cell,generation of a response, and removal or inactivation of thesignal;

• Maintenance of membrane potential in electrically excitable cells.

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Energy usage and ways of calculating it for biological systems will be considered more carefullyin Section 3, but the basic point is that anything which can besensed by another cell can be a signal.However, to convey useful information, a signaling cell must use energy to impose spatial and temporalstructure on the signal and thereby convey a message [21,22].

2.3 Cellular Community Examples

Most experimental studies of human health and disease have probed the intrinsic properties of cells suchas molecular mechanisms and cellular pathways using procedures that typically involve plating cellsas monolayers on flat surfaces (2D culture). Although such investigations have yielded innumerableinsights, cells cultured in such a manner experience a crudefacsimile of a real-life microenvironmentsince they are isolated from the complex milieu they would experience in a tissuein vivo.

Despite long-standing evidence that cells should be studied in the context of an environment whichattempts to recreate the kind of intercellular communication present in tissues, the three-dimensional or-ganization and mechanochemistry of cellular and non-cellular entities remains a largely under-exploredarea (see, for example, [7,23–26]). Thirty years ago, it wasdemonstrated that highly malignant mouseteratoma cells could be induced to develop all normal tissues of the mouse if placed in an early em-bryonic environment [27]. Since then, studies have shown that tumor cells can be “normalized” bycontact with normal cells and that tumorigenicity can be suppressed by recreating an appropriate three-dimensional (3D) tissue structure [4–6]. Elsewhere, cellular senescence, the loss of the ability of acell to divide, has been postulated to contribute to the age-related rise in cancer because senescent fi-broblasts secrete molecules that disrupt the integrity of the tissue stroma in which they reside therebycreating a more permissive tissue environment for the development of cancer [7,28–30].

As with tissues, experimental microbiology has begun to recognize that the insights gained fromclassical studies of microbial cells in laboratory (2D culture) settings provide an incomplete pictureof the form and function of natural microbial ecosystems where cellular and non-cellular entities cre-ate an intricately organized three-dimensional community[31–40]. For example, microbial mats aremillimeter-scale aquatic floor (benthic) ecosystems composed of microbial cells attached to extracellu-lar polymeric material and mineralized scaffolds and fueled by light energy. Ancient and modern matshave influenced the composition of the atmosphere and functional properties such as which wavelengthof light can penetrate the mat depend upon how the complex community of different species is strat-ified and structured. The majority of bacteria in natural ecosystems grow in matrix-encoded biofilmsadherent to surfaces and form integrated multicellular communities. Complex structures have beendiscovered in matrices of biofilms that contribute to the protection of sessile cells and that can transmitenergy from one location to another.

3 Communications Theory & Multicellular Systems

The rich tapestry of signaling methods and example multicellular systems discussed in Section 2 leadnaturally to a variety of potential network models. Extant studies tend to focus on understandingcellular processes in terms of gene networks that occur within a cell [41–44]. One of our proposedtasks is to develop useful models for networks between cellsin multicellular systems which can beexercised analytically or through simulation and which also suggest definitive experiments forin vitroor in vivo preparations.

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A variety of gene and biochemical networks have been examined experimentally and computation-ally (e.g., [45–49]). However, we note that existing modelsare almost exclusively graph-theoretic asopposed to information-theoretic in that they do not explicitly consider the flow ofinformation in aformal sense. A notable exception to this rule is [21] which explicitly considers the information theoryof molecular channels and as such explicitly considers energy consumption and specific molecular con-formation state information. Likewise, [22] seeks to cast information flow in (primarily sensorineural)biological networks in clear information-theoretic terms. In the following sections we more carefullyexplore the communications metaphor for cellular systems,and by so doing raise questions we hope toconsider as part of the proposed work.

3.1 Signal Representation

One of the most important concepts in communication theory is the notion of asignal spacein whichall signals can be represented, usually by a linear superposition of basis functions. The beauty of thisdecomposition is its generality and the way it casts almost every communications problem in terms ofa set of independentchannels.

As a specific example, consider a typical telecommunications systems with a signaling interval(0, T ) and a bandwidth constraintW . We can find2WT mutually orthogonal basis functions withwhich to represent time-limited and almost-band-limited signals [50–52]. That is, any bandlimitedsignal on such an interval can be simplyprojectedonto these basis functions and represented as a setof coefficients. Note that the specific constraints (bandlimited, time-limited) on basis set functions arenot really the point, but rather that signals can be decomposed in a convenient way.

The ability to decompose signals renders the information-theoretic treatment of real communica-tions channels simple and opens the door to fundamental results which state that for certain types ofchannels where signals are corrupted by random noise (i.e.,white, or “whitened” Gaussian channels),only the energy contained in the signal matters,not its detailed shape. This result is the basis for thepowerful and well-known figure of merit used in communications systems – signal to noise ratio (SNR)– which appears in the famous Shannon channel capacity expression,

C = W log2 (SNR+ 1) (1)

whereC is the channel capacity in bits per second [1,2].In communications problems, this signal space approach allows us to treat all signals in a common

and convenient way by determining thedegrees of freedomof a communications channel and represent-ing signals in a geometric space. The signal space concept isapplicable to any degree of freedom suchas spatial signal structure which has been recently exploited in multiple antenna systems which explic-itly use spatial structure to convey information [53, 54]. One could also imagine using other physicalproperties of channels as degrees of freedom – polarization, electric field, magnetic field, temperature,chemical species or any other measurable property of the transmission medium.

The signal space concept also allows us to more easily consider the effects of multiple transmittedsignals impinging on receivers in a common framework – even if the transmitters are mutually unawareof the signaling methods used. Signal space decomposition explicitly enables the derivation of a varietyof strong information-theoretic results for suchmultiusersystems [1, 3, 55] which bound informationflow from transmitters to receivers. Such mutual interference is particularly relevant for endocrine,paracrine, autocrine, juxtacrine and other types of biological signaling where many transmitting andreceiving cells share a transmission medium.

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This utility of a common signal representation in communications theory suggests we seek a similarcommon representation for the wide variety of signals and stimuli found in multicellular biologicalsystems. To this end we ask, “Is there an appropriate signal space description of biological signals?”We suspect the answer (as might be expected) is non-obvious and therefore interesting.

A possible first objection that signaling using electromagnetic signals is somehow different thanthat using chemical/mechanical methods is specious. In fact, transmission of information coded asmatter – of which chemical signaling is an instance – can be treated similarly and is oftenmuchmoreefficient than transmitting the same information electromagnetically over scales both small and large– so long as message delivery latency requirements are not too stringent [56–58]. The main problemwith a signal space approach in biological networks is linearity versus nonlinearity of the transmissionchannels.

For “dilute” chemo/mechano/other transmission methods, one can imaginelinear superposition ofsignals at cell membrane receptors which would support the notion of a signal space in the standardcommunications theory context. That is, signalss(t,x) with temporal (t) and spatial/chemical (x)dependence might be represented as

s(t,x) =∑

j

∑k

sjkφjk(t,x) (2)

where the{φjk(t,x)} are basis functions indexed inj over time and ink over space and where theprojectionssik are

sjk =

∫dt

∫s(t,x)φjk(t,x)dx (3)

Thus, any signals(t,x) would have a geometric interpretation

s = [s11, · · · , s1K , s21, · · · , sJK ]⊤ (4)

and the superposition of signalssℓ at receiverru would follow

ru =∑

ℓ

gℓusℓ (5)

wheregℓu is some gain/attenuation factor related to, for instance, diminution in chemical messengerconcentration with distance for a diffusive delivery system. In systems where signals are corrupted byadditive stochastic processes, a Gaussian channel assumption holds and in a signal space setting thisleads to simple and powerful euclidean measures of communications quality.

One could then seek a set of “basis functions” based on transmitter/receptor chemical composi-tion, position or whatever degrees of freedom were available in a manner perhaps analogous to Gram-Schmidt orthogonalization [59], and use them to represent all known signals – and perhaps to predictsome as yet unseen ones. Such a common framework would obviously be a boon for signal represen-tation in biological systems, and certainly we will pursue this line of inquiry.

Unfortunately (from a signal space perspective) signals inbiological systems often interact withone another in distinctly nonlinear ways. In fact, even signaling using single chemical species is oftennonlinear. Although there are methods for dealing with non-linearities in communications systems,nonlinearity and the implicit nonlinear interaction of signals from multiple sources lessens or evennullifies the utility of the standard signal space approach.

However, the multiplicity andspecificityof some biological signaling mechanisms suggests that at

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least in some cases, a signal space analogy might be appropriate. That is, nature seems to have gone toa lot of trouble to devise independent channels between cells using a variety of different physical struc-tures at the cellular level (gap junctions, nanowires and the like) and signaling chemicals or even in-frastructures (neural signaling) for exquisitely specificand generally non-interfering communications.If one imagines the evolution of such structures as an iterative process under conditions where efficientand non-interfering cellular communication conferred a selective advantage, one might expect the endresult to be a multiplicity of non-interfering signaling methods. Curiously, this is exactly analogousto what one sees with mutually interfering “cognitive radios” which can adapt signal transmissions toshare the same wireless spectrum [60–64]. In fact, this sortof iterative “interference avoidance” notionwhere competing signals “spread out” in the available signal space is common in multiuser communi-cations theory [55, 65–67]. So carefully investigating signal space analogies in biological signaling is,at the very least, interesting.

Of course, the multicellular network truth is certainly a mixture of linear and nonlinear methods.However, even if it proves impossible to develop a general signal space framework for biological sig-naling, the overarching information-theoretic ideas still hold since they are in many ways independentof the specific mechanisms for delivering information. Thatis, almost any given mechanism for in-formation delivery can be couched in information-theoretic terms. Thus, though having a signal spacedescription of biological signals would be extremely helpful, not having one will not invalidate aninformation-theoretic approach. We consider information-theoretic models of communication in a bitmore detail in the following section.

3.2 An Information-Theoretic Framework

In the simplest terms, information theory provides a means to quantify how muchinformationcan betransferred fromsourcesof information to receivers over some medium which constitutes achannel.

3.2.1 Source Characterization

Source information, quantified in bits, can be thought of as ameasure of how much is unknown aboutthe source. For instance, designation of one of eight (23) equally probable messages would require3

bits. Likewise an infinite set of messages{mk}, k = 1, 2, ... each having probability(0.5)k wouldrequire2 bits on average to designate using a code1, 01, 001, .... This concept of information contentin messages is obviously related to the amount of disorder (also calledentropy) in the source. If asource is completely predictable and can provide us with nothing we do not already know, its entropyis identically zero. Likewise, if a source can produce at anygiven time one ofN possible messagesequi-probably, its entropy islog2 N bits. In short, information is what we do not know but want toknow – a measure of observer/receiver ignorance about the possible source messages.

Formally the entropy of a sourceX is defined as

H(X) =∑

x

fX(x) log21

fX(x)(6)

wherefX() is the probability distribution representing our ignorance about the source messagex. Asimilar integral expression is used for continuousx, but we will consider only discrete sources here.The entropy is a measure of how compactly the source can be represented by symbols. In fact, thesource coding theorem[1–3] underbounds the minimum average source description length (the number

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of bits on average to represent source messages) by the source entropy. For the two examples givenabove (23 uniformly probable messages and messages with a geometric distribution(0.5)k), the numberof bits required is exactly the entropy of the message distribution.

In our consideration of multicellular systems, the source is any information a cell conveys to othercells. This could be comprised of some operation on signals received by the cell, the state of the cellitself or any combination of received signals and cell state(including stochastic processes active withinthe cell). Implicit in a source description is that a source sends out messages at some rate – that themessage is not static. This temporal variation leads to the analytical (and engineering) contrivance ofa “transmission interval” but general source descriptionsneed not be so restrictive and can be couchedin terms ofentropy rateson continuous time processes rather than rigid transmission intervals.

3.2.2 Channel Characterization

In the simplest case, the channel is interposed between source and receiver and in some sense obscuresthe source, requiring the receiver to guess what message wassent. If the source sends a random variableX and random variableY is received, we define the mutual information betweenX andY as

I(X;Y ) =∑xy

fY |X(y|x)fX(x) log2

fY |X(y|x)

fY (y)(7)

in units of bits perchannel use. The key element in an information-theoretic analysis (besides specifi-cation/description of the sourceX) is specification of the channel. The basic idea is thaty representsa “noisy” version of the message componentx. This relationship is distilled into the conditional prob-ability distributionfY |X(y|x). (We ignore complications such as channel memory, feedbackand thelike here for simplicity.)

Information theory tells us that equation (7) provides anabsolute upper boundon the averageamount of error-free information that can be transfered from source to receiver over a channel specifiedby conditional probability functionfY |X(y|x) and input distributionfX(x). Furthermore, if we canadjust the channel input distributionfX() (via source coding – another important area of informationtheory) we can form the following maximization

C = maxfX()

I(X;Y ) (8)

which is defined as thechannel capacity[1–3]. Information theory also tells us that there exist methodsfor coding the sequence of transmissions so that the transfer rate achieved is as close to the bound ofequation (8) as desired. These two results comprise the Channel Coding Theorem, certainly the mostpowerful early achievement of information theory. It is important to note that no constraints are put onhow the capacity bound might be achieved – the result is in some sensemechanism-blind.

If communications channel (also calledlink) descriptions can be had, an assemblage of communi-cating entities is readily represented as agraph– a group ofnodes(communicators) connected byedges(links). Such a representation is intuitively pleasing in that it reflects a variety of real-world scenariosfor intercommunicating elements [68] – the Internet, neural networks, metabolic reaction networks,ecological and food webs, citations networks in scientific papers, sexual contact networks and a hostof others. The attractiveness of graph representations of interactions has resulted in an increasinglylarge body of biological knowledge being cast in such network terms [41–49, 69–76]. Given a graphlevel of abstraction with known link properties it is relatively simple (using what amount to fluid flow

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models) to specify information flow bounds and/or to engineer optima using a variety of mathematicalmethods [77].

However, for most of the multicellular network settings we wish to consider, graph representa-tions could lead to a false sense of security for a variety of reasons. The properties of the link areusually not specified in information-theoretic terms, the notion of independent links between commu-nicating entities becomes increasingly untenable in environments where senders’ signals interfere withunintended receivers’ reception, and the information processing capabilities of network nodes is oftenpoorly understood. Fortunately, even in the absence of crisp models, theinformation processing theo-rem[1–3] can be used to provide bounds on the maximum amount of information a cell can provide toits neighbors given the information it receives.

A potentially more disturbing problem is that even in situations where the channel physics is com-pletely understood, the resultingnetwork information theoryproblem may only be partially under-stood [1, 3]. That is, network information theory is an active area of modern telecommunicationstheory research.

Thus, for the biological systems we hope to study, the establishment of a graph model whose linkproperties are carefully defined in terms of capacity is agoal as opposed to a starting point. In fact, wemay even find that graph models of multicellular systems withcells as nodes are not particularly usefulrepresentations. So, what we seek is to understand what might be called “the physics of communica-tion” in various multicellular settings so that appropriate information flow models can be developed.Likewise, as implied in [22], we can expect to find examples inbiological systems where information-theoretic limits are nearly achieved using simple methods.Such discoveries could have implicationsfor the design of human-engineered networks.

4 Research Plan

We have painted a picture of multicellular systems as networks through which formally-defined in-formation flows. This abstraction cannot itself be challenged since any physical system composed ofmore than one particle must by definition have communicatingparts. However, though the abstractionis interesting for any of the number of reasons discussed in previous sections, the question of utilityremains. Determining the utility of information flow modelsfor multicelluar systems, and determiningwhether this abstraction can shed light on engineering problems which consist of coordinating largenumbers of similar elements is the purpose of the proposed exploratory research.

In this section we consider what must be done to arrive at reasonable models of intercell interactionsin a multicellular system. We also suggest questions one might ask about cellular organization in tissuesand show how an information flow model might be used to probe tissue behavior both theoretically andexperimentally. We then turn the problem around and ask whether we can intuit design principles forsuch tissuede novofrom a functional description using information flow models. That is, if we weregiven a high level description of the structure and function, can we design efficient communicationsmethods which render that structure and function.

4.1 Noise, Energy and the Channel

With the definition of the channel transition probability function fY |X(y|x) we have indirectly intro-duced the notion ofnoisein a communications channel – anything which serves to obscure the sourcemessage and which we cannot predict well enough to ignore. Noise is ever-present – in the random

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fluctuations of molecules which comprise the operation of any cell or medium and energy must be ex-pended to convey useful information [21,22]. However, in both biological systems and in telecommu-nication networks, energy is often limited and such limitations constrain the rate at which informationcan be delivered in ways similar to that seen in equation (1).Thus, the fundamental tension of com-munications theory comes into play – how does one convey information necessary for some task withtolerable energy requirements at tolerable delay?

Energy considerations in multicellular networks arise at avariety of levels, some of which are al-ready being considered in molecular channel work [21] and sensorineural studies [22]. The cost ofgenerating the protein components of signaling networks can be decomposed into the costs of express-ing the gene encoding the protein into a message (transcription) and producing the protein from thismessage (translation). Recent studies have attempted to estimate a lower bound on the cost of transcrib-ing a gene in the genome of a yeast at experimentally observedlevels using knowledge of the energyneeded to synthesize the nucleotides and amino acids that constitute the building blocks of the messageand protein respectively [78]. We intend to undertake both retrospective literature studies of signal-ing to establish energy-use tables for many forms of intercellular (and perhaps implicitly intracellular)signaling methods.

We will also need to characterize sources of noise and build reasonable models of what amount totransition probabilitiesfY|X() where the boldface subscripts indicate vectors of joint random variablesassociated with channel inputs and outputs. These could be simple, as in the case where noise is gener-ated by the addition of many stochastic effects and is approximately Gaussian, or much more complex.Again building on [21, 22] as well as the direct and/or indirect biological studies of signaling energyrequirements, we hope to frame intercellular communication in terms of available signal energy andchannel characterizations which should allow quantification of possible information transfer rates be-tween cells. Such results might be cullable from retrospective studies of previously described signalingpathways.

Noise levels and available energy are important, but their interaction is what determines channelcapacity. Additive models of signal and noise are easiest toanalyze and are often applicable (as insummation of receptor potentials in excitable tissues), but one must also recognize that biologicalsystems often employ strongly nonlinear methods of signal combination; e.g., [79]. Thus, we mustconsider general models of signal and noise interactions based first on previous biological studies. Forinstance, some knowledge exists regarding “transfer functions” associated with intra- and intercellularsignaling networks in multicellular systems. The transmission of signals through synthetic geneticcircuits (transcription cascades) in noisy cellular environments has been examined and estimates ofthe input-output relationship between protein regulatorsand their targets in the genome determined(reviewed in [80]) but clearly more needs to be done, especially for our proposed information flowapproach.

As a specific for instance, consider (quoted from [42])

The Notch Signaling Pathway (NSP) is a well-known highly conserved pathway for cell-cell communication. NSP is involved in the regulation of cellular differentiation, prolifer-ation, and specification. For example, it is utilized by continually renewing adult tissuessuch as blood, skin, and gut epithelium not only to maintain stem cells in a proliferative,pluripotent, and undifferentiated state but also to directthe cellular progeny to adopt dif-ferent developmental cell fates. Analogously, it is used during embryonic development tocreate fine-grained patterns of differentiated cells, notably during neurogenesis where theNSP controls patches such as that of the vertebrate inner earwhere individual hair cells

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are surrounded by supporting cells. This process is known aslateral inhibition: a molecu-lar mechanism whereby individual cells within a field are stochastically selected to adoptparticular cell fates and the NSP inhibits their direct neighbours from doing the same. TheNSP has been adopted by several other biological systems forbinary cell fate choice. Inaddition, the NSP is also used during vertebrate segmentation to divide the growing em-bryo into regular blocks called somites which eventually form the vertebrae. The coreof this process relies on regular pulses of Notch signaling generated from a molecularoscillator in the presomatic mesoderm. The Notch receptor is synthesized in the rough en-doplasmic reticulum as a single polypeptide precursor. Newly synthesized Notch receptoris proteolytically cleaved in the trans-golgi network, creating a heterodimeric mature re-ceptor comprising of non-covalently associated extracellular and transmembrane subunits.This assembly travels to the cell surface ready to interact with specific ligands. Followingligand activation and further proteolytic cleavage, an intracellular domain is released andtranslocates to the nucleus where it regulates gene expression.

Though very detailed in specification and ubiquitous enoughto be interesting from a general mul-ticellular perspective, obtaining information flow from the detailed molecular biology of the NotchSignaling Pathway will require significant effort or could even be impossible. Thus, we must also beopen to the possibility that not enough indirect information exists to allow any reasonable cobbling ofprevious results into energy, noise and channel models. It would then be necessary to identify experi-mental means for measurement of intercellular channel characteristics. Recent technology [81] whichallows isolation of cells and spatially selective application of various stimuli will be carefully exploredfor application to a future more directed approach to intercellular channel estimation.

4.2 Connectivity Inference

The previous section considered, essentially, devising information-theoretic channel models for already-identified single channels. Such work is clearly important in that it could lead to organizing principlesfor intercellular signaling. However, a direct approach tointercellular signaling which might iden-tify important but previously unknown or under-studied ways in which cells affect one another is alsonecessary.

Transcription can be viewed as the process of converting theinformation encoded in a genome intoa physical message in the form of messenger RNA (mRNA). Recent studies of transcription in individ-ual cells isolated from mouse heart have shown that for the same gene, the amount of mRNA producedvaries from one cell to another [8]. Furthermore, the extentof cell-to-cell variability differs in cellstaken from young mice compared to old mice. These studies raise a number of interesting questions.First, only a small number (tens) of genes were examined so automated, high throughput technologiescapable of assaying all the genes in a genome in a large numbers of cells are required to determine thegenerality of this phenomenon not only in cardiomyocytes, but also cells from other tissues. Second,the components of signal transduction in multicellular systems are proteins and not genes so it remainto be determined whether the fluctuations in amount of mRNA for a given gene is reflected in similarfluctuations in the amount of protein that is produced from translation of the mRNA. These and similarquestions could be addressed by a device that would take as input a biological sample of interest, sep-arate the cells in the sample, and for each cell, perform genome wide measurements of transcript andcorresponding protein levels. The single cell gene expression and other data could be used to recon-struct transcriptional regulatory subnetworks (see for example [82]). The data would indicate which

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cell surface receptors (proteins) and chemical signals (hormones, cytokines and so on) are produced byindividual cells and how this might vary. Whilst such studies would discard all knowledge of the tem-poral and spatial location of proteins involved in intra- and intercellular communication, they wouldidentify specific molecules that can be investigated in multicellular systems using live cell imagingtechniques.

4.3 What Do Cells Talk About? What Can Cells Tell Us?

Suppose we have a reasonable understanding of signaling between cells in a multicellular community.For the case where each cell carries the same genetic code (asin a tissue) a number of simple struc-tural/functional questions come immediately to mind. For instance, in mammary epithelium, how doesa given cell know it is part of an alveolus and to secrete milk only through the lumen side of its mem-brane? How do cells in the developing breast know how to form alveoli and ducts? Recent work [4–8].asks how breast cells with malignant tendencies know to behave themselves when placed in a matrix ofhealthy tissue. These sorts of questions, taken to their logical extremes form the heart of developmentalbiology inquiry – how does a “complex” organism grow from a single germ cell?

A great deal of effort has been devoted to answering questions related pattern formation in biology(reviewed in [83] and for a recent experimental and computational study of tissues see [16,17]). We ofcourse intend to review and incorporate this work where useful, but our proposed contribution lies inanother direction. We ask what rate ofinformation input do cells need to perform their functions andwhat signaling infrastructure is needed to support these rates.

To this end, consider the simplest possible abstraction. Assume that specifying a given cell’s expres-sion requiresB bits. Equally simplistically, assume that a cell can changeits expression at some maxi-mum rateR in response to signaling . Such an assumption is consonant with observations that isolatedcells express themselves differently than when they are part of a community and over time [4–7,23–27].Thus, to a first order, the rate of information flow into such a cell necessary to maintain a given ex-pression is thenRB bits per second per cell. How is such information delivered efficiently giventhe available signaling modalities? Does the communications problem suggest heretofore unexploredsignaling methods? How is information coded in both the genome and the structure?

One can also askpredictivequestions about the model. If information flow is selectively disrupted,a good model should predict cell fate. Experiments where signal paths in the signal space are disrupted,or structural insults inflicted might be conducted with cellular communities eitherin vivo, in situ, oreven retrospectively through literature searches on the effects of different sorts of disruption. Suchstudies are needed to vet our models against physical reality.

Questions about information flow can also be asked in a variety of ways, in a variety of settings andat a variety of scales, from simple cellular communities of thousands to organisms with billions of cells.Do cellular systems have “communications standards” – a kind of ISO protocol stack for biology? Howis information actually coded for transmission between cells? What spatial characteristics of signalingdetermine form and function?

The answers to these sorts of questions might be suggested byturning the problem completelyaround. Suppose we wish to construct items from identicallyspecified units whose task is to commu-nicate and differentiate themselves appropriately. What information flow is necessary to support such afeat and what signaling structures do it energy-efficiently? Our question is almost identical to that askedin “amorphous computing” and pattern formation studies [14–17] but with an information-theoretic asopposed to computational bent.

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In short, carefully applying communications theory to biological multicellular systems seems apotentially rich area of research. The reverse – applying biological systems principles to engineer-ing design problems – seems rich as well. Our goal with this preliminary work is to determine theoverall geography of such a grand inquiry and suggest topicsand programmatic thrusts aimed at usingcommunications theory to help explain what cellular communities talk about and what they can say tous.

5 Research Agenda and Impact

• Develop and vet appropriate information flow models from literature on inter/intra-cell signalingand (measured or inferred) knowledge of chemical pathway energetics for a variety of multicel-lular systems.

• Design experiments to measure appropriate channel properties directly.

• Study object assembly as an information flow problem and search for low-energy solutions tothe implicit communications problem.

• Study energy-efficient sensor networks from a tissue biology perspective.

We suspect that these research directions will prove compelling, and if so, it is immediately apparentthat the range of expertise and the amount of effort necessary to fully develop the ideas is well beyondthe capacities of any single team of researchers. In fact, perhaps even the problem specification andelaboration is beyond the range of a small group. Thus, as part of the process we will engage a variety ofinvestigators in our explorations, attend meetings, conduct many small meetings and seminars, perhapsculminating in a workshop which draws interested investigators together with the express purpose ofdeveloping a programmatic effort in what might be calledThe Science of Interaction.

The broader impact of developing an effective communications framework for biological systemswhich can both explain and predict general multicellular network behavior is hard to overestimate.Certainly such a framework, if successful, would be pivotalin quantifying the process by which ge-netic codes are translated into organisms or understandingdisease and aging as information networkdisorders. Likewise, distributed specification and assembly of robust structures in engineering and amultitude of other applications in biology and engineeringare clearly possible.

6 Management Plan

The PI (Rose) will coordinate this effort though web-based and other telecommunications tools, butalso through numerous face-to-face meetings with Mian, theLBL-based investigator. Travel fundshave specifically been requested toward this end. Rose’s principal expertise is communications, but hehas a strong graduate background in biological systems. Mian’s primary areas are physical chemistryand computational biology which afford enough overlap to allow more careful and detailed technicalexchange than were a communications theorist vaguely interested in biology paired with a biologistvaguely interested in communication theory.

We expect that preliminary results from this one-year studyshould be available by Spring 2007Detailed recommendations for a potential larger programmatic effort will be one of the “deliverables”of this project. The previously discussed “capstone” workshop might also constitute a deliverable.

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7 Promoting Diversity

The PI (Rose) is an African American male, the co-PI/subcontractor (Mian) is female. Both have ahistory of actively seeking minority talent. Rose has been most effective in supporting undergraduateprojects for minority students and in moving promising students along to top graduate schools. Mianis a member of the External Advisory Committee of the Arkansas IDeA Network for Biomedical Re-search Excellence (http://brin.uams.edu/), a program established by the NIH to broaden thegeographic distribution of NIH funding for biomedical and behavioral research. Finally, a large por-tion of the proposed research should be especially accessible to undergraduates and therefore under-represented minorities whose proportion is usually greater in undergraduate populations.

8 Research and Education

Both PI’s have substantial experience guiding graduate andundergraduate students and feel that sup-porting graduate students on exploratory research funds isrisky. Master’s level students generally donot have sufficient theory/bench expertise to complete thissort of project within a year. Good doctoralstudents might be effective, but the possible short term nature and uncertainty of the project constitutesa penalty. Thus, this request for support is more “PI-heavy”and “travel-heavy” than usual.

Nonetheless, funds have been solicited for substantial hourly student support with the expectationthat good communications theory and biology doctoral students can be supported part time while stillpursuing their primary degree objectives. Should our research bear fruit and help initiate programmaticsupport, interested students could opt to pursue the topicsfull time.

We suspect that the overarching “grand design” aspect of theproject will be especially attractiveto undergraduates, and thus anticipate significant undergraduate student participation in some of thesimpler tasks such as collecting existing genome sequence data from public databases and some pro-gramming tasks.

9 Results from Prior NSF Support

Christopher Rose has served as PI and co-PI on a number of previous NSF grants; (PI) NCR-9206148[84], CCR-98-14104 [85] and CCR-99-73012 [86]; (co-PI) NCR-9506505 [87], NCR-97-29863 [88],ITR/CCR-00-85986 [89], ITR/CCR 02-05362 [90], NeTS-0434854 [91] and NeTS-0435370 [92]. Thework completed on these grants has addressed a broad range ofproblems associated with optimizingthe use of radio resources in wireless communications systems. Call admission for wireless systemswas studied in [93–96]. Fundamental algorithms for paging and registration of mobile nodes wereestablished in [97–109]. Recent work has been focused on understanding the U-NII [85, 110, 111],opportunistic transmission methods and associated delivery protocols [112–114], and developing inter-ference avoidance methods for a variety of communications problems [60, 63, 66, 115–142] as well asnon-standard communications models [56–58,143,144]. Thework described in [56] is featured on theNSFDiscoveriesweb page.

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[84] C. Rose and R. Yates. Searching for Good Call Admission Policies in Communications Net-works. NSF grant NCRI 92-06148, $416,000.

[85] C. Rose, A.T. Ogielski, and D. Goodman. WINLAB FOCUS’98: A Workshop to Study PeacefulCoexistence in the Unlicensed National Information Infrastructure. NSF grant CCR 98-14104.

[86] C. Rose and R. Yates. Interference Avoidance in Wireless Systems. NSF grant CCR 99-73012,$430,000.

[87] R. Yates and C. Rose. Power Control for Packet Radio Networks. NSF grant NCRI 95-06505,$469,897.

[88] D. Goodman, N. Mandayam, A. Ogielski, C. Rose, and R. Yates. Parallel computing for wirelessnetworking research. NSF CISE Instrumentation grant NCR 97-29863. 11/1/97.

[89] R. D. Yates, N. B. Mandayam, and C. Rose. “Free” Bits: TheChallenge of the Wireless Internet.NSF grant ITR 00-85986, $860,000.

[90] R. Yates, N. Mandayam, D. Raychaudhuri, C. Rose, and P. Spasojevic. ITR: CollaborativeResearch: Achieving Innovative and Reliable Services in Unlicensed Spectrum. NSF grantCCR-0205362 ($866,411), in collaboration with Michigan State (CCR-0205362) and Cornell(CCR-0205431).

[91] N. Mandayam (PI), C. Rose, P. Spasojevic, and R. Yates. NeTS-ProWin: Cognitive Radios forOpen Access to Spectrum. National Science Foundation NeTS-0434854, $670k.

[92] B. Ackland (PI), M. Bushnell, D. Raychaudhuri, C. Rose,and T. Sizer. NeTs-ProWin: High Performance Cognitive Radio Platform with Integrated Physical and Net-work Layer Capabilities. National Science Foundation NeTS-0435370, $1.2M. available athttp://www.winlab.rutgers.edu/pub/docs/NeTS-ProWiN1.pdf.

[93] A. Yener and C. Rose. Genetic Algorithms Applied to the Cellular Call Admission Problem:Local Policies.IEEE Transactions on Vehicular Technology, 46(1), February 1997.

[94] C. Rose and R. Yates. Genetic Algorithms and Call Admission to Telecommunications Net-works. Computers and Operations Research, 23(5):485–499, May 1996.

[95] A. Yener and C. Rose. Near-Optimal Call Admission Policies for Cellular Networks UsingGenetic Algorithms.IEEE Wireless’94, July 1994. Calgary.

[96] R. Yates, S. Gupta, C. Rose, and S. Sohn. Soft dropping power control. InProceedings of TheIEEE Vehicular Technology Conference VTC 97, May 1997.

[97] C. Rose and R. Yates. Minimizing the average cost of paging under delay constraints.ACMWireless Networks, 1(2):211–219, 1995.

[98] C. Rose. Minimizing the average cost of paging and registration: A timer-based method.ACMWireless Networks, 2(2):109–116, June 1996.

[99] C. Rose and R. Yates. Ensemble polling strategies for increased paging capacity in mobilecommunications networks.ACM Wireless Networks, 3(2):159–167, 1997.

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[100] C. Rose and R. Yates. Location uncertainty in mobile networks: a theoretical framework.IEEECommunications Magazine, 35(2):94–101, February 1997.

[101] C. Rose. A Greedy Method of State-Based Registration.In IEEE International Conference onCommunications ICC’96, June 1996. Dallas, TX.

[102] C. Rose. State-based paging/registration: A greedy approach.IEEE Transactions on VehicularTechnology, 48(1):166–173, January 1999.

[103] R. Yates, C. Rose, S. Rajagopalan, and B. Badrinath. Analysis of a mobile-assisted adaptivelocation management strategy.ACM Mobile Networks and Applications (MONET), 1(2):105–112, 1996.

[104] C. Rose and A. Yener. Highly mobile users and paging: optimal polling strategies. IEEETransactions on Vehicular Technology, 47(4):1251–1257, 1998.

[105] C.U. Saraydar. Selection of good location areas from population and traffic data. Master’s thesis,Rutgers University, May 1997.

[106] C. U. Saraydar and C. Rose. Minimizing the paging channel bandwidth for cellular traffic. InICUPC’96, Boston, pages 941–945, October 1996.

[107] Z. Lei and C. Rose.Wireless Subscriber Mobility Management using Adaptive Individual Loca-tion Areas for PCS Systems. ICC’98, 1998.

[108] Z. Lei and C. Rose. A Probability Criterion Based Location Tracking Method.Proceedings ofGlobecom 97, 2:977–981, Nov. 1997. Phoenix, AZ.

[109] C. Rose. Paging and Registration in Mobile Networks. In Wiley Encyclopedia of Telecommuni-cations, 2003. to appear.

[110] C. Rose and A.T. Ogielski. WINLAB Focus’98 on the U-NII. ACM,MC2R, 2(4):20, October1998. 6/98 in Long Branch NJ (also seewww.winlab.rutgers.edu/Focus98).

[111] C. Rose and A.T. Ogielski. WINLAB Focus’99 on Radio Networks for Every-thing. ACM, MC2R, 3(3):24–25, July 1999. 5/99 in New Brunswick NJ (also seewww.winlab.rutgers.edu/Focus99).

[112] A. Iacono and C. Rose. Bounds on file delivery delay in aninfostations system. InVehicularTechnology Conference, pages 6.11–3, May 2000. Tokyo.

[113] A. Iacono and C. Rose. Infostations: New PerspectivesOn Wireless Data Networks. InNextGeneration Wireless Networks. Kluwer Academic, May 2000. Editor: S. Tekinay.

[114] A. Iacono and C. Rose. MINE MINE MINE: Information Theory, Infostation Networks andResource Sharing. InWCNC 2000, September 2000. Chicago, IL.

[115] S. Ulukus and R. D. Yates. Iterative signature adaptation for capacity maximization of cdmasystems. InAllerton Conf. on Comm., Control and Computing, September 1998.

[116] S. Ulukus and R. Yates. Iterative construction of optimum signature sequence sets in syn-chronous CDMA systems.IEEE Trans. Info. Theory, 47(5):1989 –1998, July 2001.

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[117] S. Ulukus and R. Yates. Iterative construction of optimum signature sequence sets in asyn-chronous CDMA systems. InProceedings of the 38th Allerton Conference on Communications,Control, and Computing, Oct. 2000. (invited).

[118] S. Ulukus and R. Yates. User Capacity of Asynchronous CDMA Systems with Matched FilterReceivers and Optimum Signature Sequences.IEEE Trans. Info. Theory, 50(5):903–909, May2004.

[119] D. C. Popescu and C. Rose. Interference Avoidance and Dispersive Channels. A New Look atMulticarrier Modulation. InProc. 37th Allerton Conf. on Communication, Control, and Com-puting, pages 505–514, Monticello, IL, September 1999.

[120] C. Rose. Cdma codeword optimization: interference avoidance and convergence via class war-fare. IEEE Transactions on Information Theory, 47(7):2368–2382, September 2001.

[121] C. Rose. Sum capacity and interference avoidance: convergence via class warfare. InCISS 2000,March 2000. Princeton.

[122] D. Popescu and C. Rose. Codeword Optimization for Asynchronous CDMA Sys-tems Through Interference Avoidance. InCISS 2002, March 2002. (available athttp://www.winlab.rutgers.edu/∼crose/papers/async4.ps.

[123] D. C. Popescu and C. Rose. Codeword Quantization for Interference Avoidance. InProc. 2000Int. Conf. on Acoustics, Speech, and Signal Processing - ICASSP 2000, volume 6, pages 3670–3673, June 2000. Istanbul.

[124] C. Rose, S. Ulukus, and R. Yates. Interference avoidance for wireless systems. InVehicularTechnology Conference, pages 2.05–3, May 2000. Tokyo.

[125] D. C. Popescu and C. Rose. Interference Avoidance for Multiaccess Vector Channels. In2002IEEE International Symposium on Information Theory - ISIT’02, Lausanne, Switzerland, July2002.

[126] D. C. Popescu and C. Rose. Interference avoidance and multiaccess dispersive channels. In35thAnnual Asilomar Conference on Signals, Systems, and Computers, Nov 4-7 2001. Pacific Grove,CA.

[127] O. Popescu and C. Rose. Minimizing total square correlation with multiple receivers. In39thAllerton Conference on Communication, Control, and Computing, pages 1063–1072, October3-5 2001. Monticello, Illinois.

[128] O. Popescu and C. Rose. Interference avoidance and sumcapacity for multibase systems. In39thAllerton Conference on Communication, Control, and Computing, pages 1036–1035, October 3-5 2001. Monticello, IL.

[129] D.C Popescu and C. Rose. A new approach to multiple antenna systems. InCISS’01, March2001. Baltimore, MD.

[130] D. C. Popescu and C. Rose. Fading Channels and Interference Avoidance. InProc. 39th AllertonConf. on Communication, Control, and Computing, pages 1073–1074, Monticello, IL, Septem-ber 2001. (available athttp://www.winlab.rutgers.edu/∼cripop/papers).

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[131] D Popescu, O. Popescu, and C. Rose. Codeword Optimization for Uplink CDMA DispersiveChannels.IEEE Transactions on Wireless Communications, 4(4):1563–1574, July 2005.

[132] D. C. Popescu and C. Rose. Interference Avoidance and Multiuser MIMO Systems.Interna-tional Journal of Satellite Communications, 15(1):1–19, January 2003.

[133] D. C. Popescu and C. Rose. Interference Avoidance. InWiley Encyclopedia of Telecommunica-tions, 2003. to appear.

[134] O. Popescu, C. Rose, and D. C. Popescu. Maximizing the Determinant for a Special Class ofBlock-Partitioned Matrices.Mathematical Problems in Engineering, 1:49–61, 2004.

[135] J. Singh and C. Rose. Distributed Incremental Interference Avoidance. InIEEE Globecom 2003,San Francisco, December 2003.

[136] O. Popescu and C. Rose. Waterfilling May Not Good Neighbors Make. InGlobecom 2003,December 2003. San Francisco.

[137] C. Popescu and C. Rose. Interference Avoidance and Power Control for Uplink CDMA Systems.In IEEE Vehicular Technology Conference, October 2003. Orlando.

[138] D. C. Popescu and C. Rose.Interference Avoidance Methods for Wireless Systems. KluwerAcademic Publishers, New York, NY, 2004.

[139] O. Popescu and C. Rose. Greedy SINR Maximization in Collaborative Multi-Base WirelessSystems.EARASIP Journal on Wireless Communications and Networking, 2:201–209, 2004.

[140] O. Popescu and C. Rose. Sum Capacity and TSC Bounds in Collaborative Multi-Base WirelessSystems.IEEE Transactions on Information Theory, 50(10):2433–2438, October 2004.

[141] O. Popescu, D. Popescu, and C. Rose. Simultaneous Water Filling in Mutually Interfering Sys-tems.IEEE Transactions on Wireless Communications, 2005. (submitted).

[142] J. Singh and C. Rose. Channel Probing Under a Power Budget. In CISS’06, Princeton, March2006.

[143] F. Atay and C. Rose. Exploiting Mobility in Multi-hop Infostation Networks to Decrease Trans-mit Power. InIEEE WCNC’04, Atlanta, GA, March 2004.

[144] F. Atay and C. Rose. Threshold Based Policies in Infostations Networks. InCISS’04, Princeton,NJ, March 2004.

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