DESCRIBING CRYPTOBIOSIS AS A TIME BASED

PROTECTION SYSTEM USING PETRI NETS

Bengt Carlsson

, K. Ingemar Jönsson

and Keith Clark

School of Engineering Blekinge Institute of Technology Soft Center S-37225 Ronneby

Department of Mathematics and Science, Kristianstad University,S-291 88 Kristianstad, Sweden

Department of Computing, Imperial College, London

Keywords: Cryptobiosis, Petri net, Time based security model.

Abstract: Cryptobiosis represents the state of a living organism when it sh

ows no visible signs of metabolic life, but

maintains a capacity to return to an active, metabolic state. This peculiar state, although known from a wide

variety of organisms, has received little attention from a theoretically biological perspective. A description

based on a Petri net setting and a time based security model is proposed. In order to protect against a

prolonged exposure time, the pathways for chemical reactions involved must fulfil their actions during a

limited detection and response time to fulfil the protected state of entering/leaving cryptobiosis.

1 INTRODUCTION

Within biology the term cryptobiosis, or hidden life,

represents the state of an organism when it shows no

metabolic signs of life, while still maintaining a

capacity to return to normal metabolic activity

(Keilin 1959, Clegg 2001). Organisms with a

capacity to enter cryptobiosis are found in a variety

of prokaryote, plant, and animal taxa, and has

evolved as an adaptation to survive under temporally

hostile conditions, e.g., in very dry or cold

environments (Alpert 2005). One of the most

common environmental agents inducing cryptobiosis

is desiccation, leading to a variant of cryptobiosis

called anhydrobiosis. The cryptobiotic state is

characterised by temporally arrested metabolism,

growth, reproduction and senescence (Keilin 1959,

Crowe 1971). The lack of metabolism during

cryptobiosis can be described as temporary “death”

representing a unique biological state between life

and death, a potentially reversible death (Neuman

2006).

The biochemical and physiological mechanisms

allo

wing cryptobiotic organisms to survive in an

ametabolic and (in the case of anhydrobiosis) more

or less completely dry state remain poorly

understood (Schill et al. 2004, Watanabe et. al. 2002,

Guppy 2004). Also, the problems connected with

extreme desiccation and a complete shut-down of

the metabolic machinery have rarely been analysed

theoretically. However, some criteria are necessary

to fulfil for successful cryptobiosis to take place. For

instance, the organism must either prevent cellular

damage at the entrance of cryptobiosis and during

the cryptobiotic state, or be able to repair the

damage that is potentially expressed when

reactivated. It must also be able to respond to one or

more triggering signals connected with the

cryptobiotic period. We will here describe a possible

approach to a protection system during an induction

phase, a dormancy phase and a reactivating phase of

cryptobiosis.

In order to return to an active life, an organism in

cryp

tobiosis needs to interpret signals from the

environment including reactivating itself from the

ametabolic state, i.e. recovering original biological

functions despite the lack of basic metabolic

machinery. The organism must be “raised from the

dead”, by responding to an environmental signal

announcing favourable life conditions, e.g. a drop of

water for a dehydrated organism. It has been

suggested that cryptobiosis entails reversible

computation with a bootstrapping involving a

recursive hierarchy (Neuman 2006). This is similar

to models within computer science including

creating more complex tools from simple tools

(bootstrapping), sub and superclasses within object

oriented programming (hierarchies), and logic

programming using recursive functions. We will

here use a Petri net as a tool for describing the

reversible processes of cryptobiosis, without going

into the details of the metabolic pathways involved.

Biological systems modelled by Petri nets

were i

ntroduced by Reddy et al (1993). By using

281

Carlsson B., Ingemar Jönsson K. and Clark K. (2008).

DESCRIBING CRYPTOBIOSIS AS A TIME BASED PROTECTION SYSTEM USING PETRI NETS.

In Proceedings of the First International Conference on Bio-inspired Systems and Signal Processing, pages 281-285

DOI: 10.5220/0001068002810285

 SciTePress

Petri net it was possible to dynamically model the

intrinsic behaviour of e.g. metabolic pathways

within a cell. In Heiner et al (2004) the metabolic

pathways conducting an apoptosis (genetically

programmed cell death) is modelled using a

qualitative Petri net.

In section 2 the different phases of

cryptobiosis are outlined followed by a description

of a time based protection system. Next, a Petri net

is introduced for modelling metabolic protection and

finally a discussion and concluding part sum up the

proposed description.

2 CRYPTOBIOSIS

Cryptobiosis may be induced by several

environmental factors e.g. low temperature

(cryobiosis), lack of oxygen (anoxybiosis) or lack of

water (anhydrobiosis). All of these factors may force

the organism to an arrested metabolism. Here, we

will use anhydrobiosis as an example to describe

cryptobiosis within a Petri net setting using a time

based security model.

Figure 1: An idealized figure of changes in metabolism

during the induction, dormancy, and reactivating phases of

cryptobiosis. A more realistic curve would likely involve

non-linear patterns of metabolic changes during induction

and reactivation.

Figure 1 shows the three general phases

connected with cryptobiosis, where the induction

phase prepares the organism for an ametabolic state

as a result of e.g. desiccation. Note that the factor

inducing changes in metabolic rate, e.g. reduced

hydration level, is not shown in Figure 1. During the

dormancy phase the organism is inactive due to a

lack of metabolic activity, but continued desiccation

may occur because metabolism will stop well before

the animal is completely dehydrated. The

reactivating phase involves both the reverse

processes of the induction phase and a repair process

depending on damages arisen during the induction

and dormant phases.

The pattern of water loss at the induction of

cryptobiosis as a result of dehydration

(anhydrobiosis) has been well documented (Wright

1989, Wharton 1996). Initially the evaporation of

water is high, but at some point the organism has

mobilised a first protection mechanism (mainly

based on morphological changes) which

dramatically reduces the rate of further dehydration.

Wright (1989) termed this point the “permeability

slump”. After this point, the rate of dehydration is

much reduced. The remaining time, until the

organism has lost so much of its water that

metabolism is arrested, is decisive of whether the

organism will enter a cryptobiotic state or die.

During this time, the organism must mobilise the

mechanisms that should protect it as it approaches

the dry anhydrobiotic state. Figure 2 describes the

temporal change in hydration level of an

anhydrobiotic organism exposed to a desiccating

agent.

Figure 2: Patterns of water loss over time in an

anhydrobiotic organism exposed to a desiccating agent,

with phases of detection (D) and responses (R

), creating a

state of cryptobiotic protection (P).

In both computer science and in cryptobiotic

organisms, a detection mechanism must recognize

the attack or stress input, after which different

response mechanisms must be activated (R1 and R2

in Figure 2). In cryptobiotic organisms these

preventing mechanisms together form the protection

system which must be activated before the

metabolism disappears.

3 A TIME BASED PROTECTION

SYSTEM

To describe, in general terms, a cryptobiotic

protection system, a time based security model

(Schwartau 1999) may be used, where a protection

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282

mechanism is successful only as long as the sum of

the time needed by the detection mechanism and the

response mechanism does not exceed the time limit

of the protection.

In this model the amount of exposure time E,

which may be positive or negative, determines the

outcome of an external attack. The exposure time

defines a time period under which the organism is

exposed to the environmental stress without a

mobilized protection system. The exposure time is

determined by three factors; a protection system P, a

detection mechanism D, and a response mechanism

R, see Figure 2. The purpose of a protection system,

independent of being within computer science or life

science, is to protect involved assets. This is valid

for a certain amount of time, i.e. the involved assets

lose their values or an organism loses the

opportunity to enter a cryptobiotic state. If detection

and response time is short enough, depending on the

current attack strength, the protection system will

not be invaded or exposed. So a negative exposure

time means that the protection mechanism manages

to keep the system secured during the time when

detection and responses are established.

Let ∆P denote the duration of protection of a

system caused by an attack with strength a starting

at time t

and with protection strength s. Let ∆D

denote the time it takes to detect an attack with

strength a under given circumstances. Finally, let ∆R

denote the time it takes to implement sufficient

measures to eliminate the negative consequences of

the attack with strength a after the signal has been

detected. Then

),,,(),,,(),,,(),,,(

0000

ttsaPttsaRttsaDttsaE Δ−Δ+Δ=Δ

(1)

Equation (1) captures exposure time ∆E(a,s,t

,t)

as a relation between the three mechanisms above

and the time intervals t

and t where t>t

. The

system will be safe if and only if

, i.e., if the

system is not exposed to an attack without a

protection system.

0<ΔE

As already pointed out in Figure 2, a protection

system consisting of detection, responses and

protection are outlined for the induction phase.

During the first period of time (t

to t

) the organism

has not yet started to lose its internal water, but a

detection mechanism (D) recognizes the presence of

a stress signal. This may be, e.g., the evaporation of

surrounding water. In the next interval (t

to t

), the

organism starts to lose its body water and a first

response mechanism (R

) is mobilised. When the

establishment of this mechanism is completed (at t

the rate of dehydration is much reduced, but

continues until the organism has reached a level of

hydration at which metabolism stops. Since

metabolism is arrested well before the organism is

completely dry (Clegg 1986), the loss of water may

continue also after the cryptobiotic state has been

reached. In the interval between t

and t

the second

response (R

), representing the biochemical

preparations for the dry cryptobiotic state, takes

place. If these preparations are successful, i.e., if the

second protection system has been established

properly, the organism enters cryptobiosis. The time

available for the necessary actions (detection +

responses) will be determined by the rate of

desiccation from t

to t

, influenced in part by the

strength of the desiccation agent, and in part by the

ability of the organism to reduce the effect of this

agent. If detection or response is delayed the

protection system will not be ready, and the

organism will die or be damaged before reaching a

state of cryptobiosis. Equation (2) formalizes this

organism system:

),,,(),,,(),,,(),,,(),,,(

303222111030

ttsaPttsaRttsaRttsaDttsaE Δ−Δ+

(2)

The organism will enter a state of cryptobiosis if

∆E is negative, i.e. if the time needed to establish the

protection mechanism ∆P exceeds the sum of the

time for the detection ∆D and response mechanism

∆R

. The main difference in the interpretation of Eq.

(1) (representing a computer science model) and Eq.

(2) (representing a biological model) is that in the

former model the protection system is present

already at the beginning, with an expected time of

function. In the biological model, the protection

system is not described as present from the start, but

is established only after the stress agent is detected,

with an expected time of establishment (∆P).

However, from the perspective of P, the responses

leads to an intermediate protection system

(activated at the “permeability slump”) that

conceptually resembles that of computer systems,

since its location in Figure 2 defines a remaining

time within which the R

responses must take place.

Processes during the reactivating part must

include both activating the reversible processes of

the induction phase, and repairing of damage caused

by positive exposure time during induction and

dormancy phases.

4 USING A PETRI NET FOR

MODELLING METABOLIC

PROTECTION

A Petri net consists of nodes and arcs where nodes

are of two types; places p

and transitions t

. Tokens

DESCRIBING CRYPTOBIOSIS AS A TIME BASED PROTECTION SYSTEM USING PETRI NETS

283

represent activity of the sequence of transitions.

Places, represented by circles, are passive system

elements while transitions represented by boxes are

active system elements, e.g. in a metabolic setting

chemical compounds and chemical reactions. Arcs

connect nodes of different type. The activity of a

Petri net is a flow of tokens over the pathways of the

net

To start with, the organism must detect the state

of stress, or cryptobiosis stimuli, which in the case

of anhydrobiosis is represented by the initiation of

desiccation (loss of water), and the intensity of the

stress factor. If the humidity surrounding the

organism is very low the process towards a dry and

cryptobiotic state will be more rapid, and the

organism then has less time to prepare itself before

metabolism ceases. Preparations for the dry state

therefore often involve morphological changes that

reduce the rate of water loss (e.g., Wright 2001).

Previous research has shown that this is a critical

phase, where the cell must be able to mobilize the

necessary metabolic changes that allow it to

maintain structural integrity and enter a dry state

without lethal damage. These changes, or set of

places p

and transitions t

in a Petri net setting, are

represented as different pathways in Figure 3.

Figure 3: Induction phases of cryptobiosis. The dotted

circles and squares indicate examples of metabolic

pathways.

The dynamics of a Petri net allows transitions to

split between multiple places or places requires more

than one transition to enter a state. The number of

places and transitions are not known nor are the

structures of the pathways. When two arcs arrive at a

place it is a synchronisation step - only when the

tokens from the converging pathways have both

arrived at the place, does the transition on the

outgoing arc fire.

Examples of pathways are molecules (e.g.,

sugars, Crowe 2002) that replace structural water in

cell membranes, and molecular chaperones (stress

proteins) that prevent aggregation of proteins (Goyal

et al. 2005). All the details involved are outside the

scope of this work, but several pathways that slow

down or disappear during transforming from R1 to

R2 are involved.

Thus, the protection system allowing

cryptobiotic survival includes several protection

parameters, the induction of which relies on

metabolic activity. Note that this has to be done

before entering the cryptobiotic state, i.e. the

protection system must act proactively.

Compared to the induction phase and the

reactivating phase, which normally amounts to

minutes or hours, the dormancy phase may be much

more extended in time and may last for weeks,

months or years (Guidetti and Jönsson 2002,

Watanabe 2006).

The reactivation from the anhydrobiotic state

also provides a challenge for the organism, the

physiological details of which has yet to be

described. At some point in time the metabolism

must restart as a reaction to changed conditions, e.g.,

to rehydration. In principle this is the reverse

function of the induction phase restarting the

protection system. All the necessary biochemical

components for starting up the system are present,

and some of the protection components may be used

for energy production or for repairing DNA and

other parts of the cell.

In principle the protection system needs to be

restored to its pre-conditions with one major

addition, damaged parts or processes must be

repaired. This is part of the existing pathways

added as new pathways enlarging the Petri net. The

protection system will not be restored without

successful repair facilities and, in order to have a

functioning repair mechanism, some restored

protection mechanisms must be present. Meanwhile

there should be a replacement process where water

is tied to the organism again. Finally, when the

metabolism is restored to 100 percent, we are back

to a fully active organism.

5 DISCUSSION AND

CONCLUSION

As pointed out by Neuman (2004), cryptobiosis

involves reversible computation with a suggested

bootstrapping involving a recursive hierarchy. As a

model for analysing the behaviour of cryptobiotic

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systems, we propose using a Petri net, initiated by

one or more input signals, computing a number of

pathways for the induction and reactivating phases.

In computer science bootstrapping refers to a

process where an initial system activates a more

constant system maintaining fundamental skill. The

initial process may be simple, activating a complex

system step by step. Activating metabolism in a

cryptobiotic organism may cause a chain reaction

that step by step brings back the organism to its

initial conditions. To model cryptobiosis both a Petri

net setting and a time based security model is used,

i.e. the chemical reactions involved and time for

accomplishing the involved tasks.

The input stress to which cryptobiotic organisms

are exposed could be seen as an “attack” against a

system. The organism must first detect the attack

and then respond to it in order to protect the system.

Organisms with a fast enough detection and

response will fulfil the protection mechanism’s

conditions. In a dynamic environment, where

varying environmental conditions are presupposed,

the robustness of the protection system may be

modelled. This robustness is dependent of the

strength of stress factor, possible threshold functions

connected Petri net pathways, detection time and the

success of all responses during a limited amount of

time.

Currently the biological phenomenon of

cryptobiosis lacks comprehensive models for

describing involved processes, both at a general

level and within more specific system. Such models

may be found within computer science. Petri net

settings may describe the different biological aspects

and processes connected with cryptobiosis, and

allow simulation of them. By putting more realism

into the models, a future progress of both models

and simulation tools may result in a better

understanding of resource control within protection

systems, an important issue both within life science

as within computer science.

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