J. theor. Biol. (1977) 67, 2547
Hierarchical Modelling of Acclimatory
Processes
V. SITARAMAM~ Department
of Biochemistry
N. J. RAO School of Automation, Indian Institute of Science, Bangalore, India (Received 9 December 1975, and in revisedform
16 August 1976)
The term acclimation has been used with several connotations in the field of acclimatory physiology. An attempt has been made, in this paper, to define precisely the term “acclimation” for effective modelling of acclimatory processes. Acclimation is defined with respect to a specific variable, as cumulative experience gained by the organism when subjected to a step change in the environment. Experimental observations on a large number of variables in animals exposed to sustained stress, show that after initial deviation from the basal value (defined as “growth”), the variables tend to return to basal levels (defined as “decay”). This forms the basis for modelling biological responses in terms of their growth and decay. Hierarchical systems theory as presented by Mesarovic, Macko & Takahara (1970) facilitates modelling of complex and partially characterized systems. This theory, in conjunction with “growth-decay” analysis of biological variables, is used to model temperature regulating system in animals exposed to cold. This approach appears to be applicable at all levels of biological organization. Regulation of hormonal activity which forms a part of the temperature regulating system, and the relationship of the latter with the “energy” system of the animal of which it forms a part, are also effectively modelled by this approach. It is believed that this systematic approach would eliminate much of the current circular thinking in the area of acclimatory physiology. 1. Introduction Life and its environment constantly interact and the course of events in the life span of an organism is determined by the environment to a large extent. Survival of the organism as well as the survival of the species is based on this t Present address: Department of Pathology, Yale University, School of Medicine, 310 Cedar Street, New Haven, Conn. 06510, U.S.A. 2s
26
V.
SITARAMAM
AND
N.
J.
RAO
fundamental principle of flexibility of life processes in subsisting on as well as reacting to the environment, and which we refer to as the “adaptability” of life processes. This property manifests itself at all levels of evolution as well as at all levels of organization of every organism. Studies of this property of life over the last century have given rise to important concepts : the organic basis of evolution (Darwin, 1859), “milieu interieur” (Bernard, 1878) and “homeostasis” and “wisdom of body” (Cannon, 1935). An understanding of biological signals and information processing by neurohumoral mechanisms, which facilitate effective interaction of the organism with the changing environment, has developed. The concept of feedback as developed by engineers has greatly facilitated the understanding of the complex network of biochemical, physiological and behavioural pathways. Acclimatory responses to environmental stress have been shown to involve adjustments at all levels of organization, from molecular to behavioural levels (Bajusz, 1969; McC. Brooks, 1969; Prosser, 1964). Thus the composite action within and between various levels of organization are basic to acclimatory processes, and their study is of great potential importance. 2. Review of Literature Studies on acclimation by several workers reveal certain dominant lines of thinking and approaches towards the understanding of acclimatory processes, even though there has not been a rigorous formalization of the associated concepts. Prosser (1964) identifies acclimatory processes as complex inter-related regulatory events occurring in a co-ordinated fashion at various levels of organization. He discusses the goal-seeking nature of these processes and the feasibility of using the acclimatory responses as a tool in the study of biological regulation, even at the genetic level. The essential feedback nature of the acclimatory processes was recognized by Adolph (1964) and he visualized a “regulatory box” which regulates the response (output) characteristics and proposed that acclimation occurs in the regulatory box in the form of altered input-output (adaptagent-adaptate) relationships leading to increased survival efficiency. Selye (1950), whose pioneering work in the field of adaptive responses laid the foundations for the understanding of hormonal interactions in conditions of stress, distinguished three phases of adaptive responses which develop with time: (i) phase of alarm reaction-a non-specific phase, (ii) phase of compensation-wherein the animal adapts and improves its survival efficiency by bringing out suitable alterations specific to the type of stress imposed, and (iii) phase of decompensation-wherein, beyond certain limits of stress, the
MODELLING
OF
ACCLIMATORY
PROCESSES
27
animal cannot cope with the adjustments invoked in response to stress and progressively succumbs to stress. Hart (1971) suggests that “acclimation to cold can be described in terms of an exponential change in the physiological state from the initial to final level” and he distinguishes between responses observed (such as cold resistance) and the acclimatory process, per se. Most studies on the mechanisms underlying the responses are made in order to understand the processes involved in acclimation to a particular environmental stress. For example, Hochachka (1973) presents the biochemical strategies for studies on acclimatory processes invoked in the response to anoxia in animals. Given certain metabolic constraints for survival in anoxia, and alternate pathways to effect compensatory adjustments to anoxia, he discusses the experimental approach in unravelling the biochemical mechanisms underlying the physiological responses using the need-based logic. A critical review of literature in the field of acclimatory responses gives us only a limited qualitative understanding of the processes involved. The terms “acclimatory process/response”, “acclimation”, “acclimatization”, “accommodation”, “adaptation” and “adaptive process/response” have been used in some context or other, interchangeably. Several authors ascribed various shades of meaning to these terms, such as “normalization”, “optimization”, “fitness”, “survival efficiency”, “performance indices”, “goal seeking processes”, etc. Further, though the term acclimation has been used with reference to the entire organism, experimentally it has invariably been associated with the specific variable considered most relevant to the organism as a performance index for a given type of stress. For example, in cold exposed rats, much of the literature pertains to comparison of levels of variables in non-acclimated animals with acclimated animals, where “acclimated animals” refer to those exposed to cold for about three weeks, by which time the metabolic rate (oxygen consumption) apparently stabilizes. In spite of the differences in the formal definition of “acclimation” by several authors, general consensus of opinion prevails in that: (1) Acclimatory processes evolve with time, i.e., the processes develop as functions of time. (2) Acclimation is largely viewed with reference to specific variables, which have a bearing on the performance of the animal. (3) Within certain limits of stress, the animal tends to survive and perform the vital processes progressively more efficiently. (4) Specificity in response to a stress is considered to emerge with time. (5) It is an optimizing process as a result of co-ordinated events occurring at various levels of complexity.
28
V. SITARAMAM
AND
N. J. RAO
Thus we see that a rigorous formal definition of acclimation is needed to establish uniformity in these studies to understand the acclimatory processes. The present attempt addresses itself to the task of redefinition of acclimation and to the introduction of a certain measure of abstraction in a form amenable to mathematical analysis. 3. Acclimatory
Process: the Nature and the Problem
When an animal is exposed to stress, one can observe changes in several variables, which appear within seconds to several days. The time course of such variations is illustrated in Fig. 1. One may note from the figure that all 1
Time
FIG. 1. Biological
of exposure
(%I
responses to sustained exposure to stress.
variables tend either to stabilize at a different level, or more commonly, to return to the initial level. The variables may be grouped arbitrarily into a variety of classes such as enzymes, metabolites, hormonal levels, electrical activities etc. Even within the same class of variables, such as enzymes, variables with a wide range of time scale have been observed. Variables such as oxygen consumption and body insulation and norepinephrine secretion, which belong to different classes but are causally related vary in response to a step change in ambient temperature with the time scales as shown in Fig. 2 (Davis, Johnston, Bell & Cremer, 1960; Leduc, 1961; Precht, Christophersen, Hensel & Larcher, 1973). It is noteworthy that, whereas the increase in variables such as shivering can occur within seconds of exposure to cold stress, the suppression of shivering takes days to develop. In other words, the initial increase and subsequent fall need not necessarily be of the same time scale. Degree of stress (AT from body temperature in the case of cold exposure) is yet another determinant in subscribing the time course of the variables. In instances where the response is not an “all-or-none” type, proportionality may be observed with the degree of stress in the initial phase
MODELLING
OF
ACCLIMATORY
Days
PROCESSES
of exposure
FIG. 2. Changes in metabolic rate (MR), urinary excretion of norepinephrine insulation (INS) in response to sustained exposure to cold.
I
I I
I
I
2
3 Time
FIG. 3. Response of hepatic tryptophan rats.
(NE), and
( / )
pyrrolase to varying degrees of cold stress in
itself (Fig. 3) (Sitaramam & Ramasarma, 1975). However in other instances such as circulating levels of corticosteroids, growth hormone, TSH and shivering an increase in degree of stress considerably slows down the return to basal level (Fig. 4) (Itoh, Hiroshige, Koseki & Nakatsugawa, 1965). The stress-mediated alterations in the variables appear after a time delay, which may range from a fraction of a second (e.g., shivering) to days (e.g., insulation). Though such time delays may not be discerned due to experimental limitations, one may justifiably assume a finite time delay before the onset of any response, as shown in Fig. 5. The steady states that might be observed experimentally in the animal under sustained stress with regard to specific variables should be viewed with caution. Norepinephrine secretion, as measured by urinary output per day was considered to stabilize within 7-9 days after cold exposure (Sellers, Flattery, Shum & Johnson, 1971).
30
V.
SITARAMAM
AND
Time
N.
of exposure
J.
RAO
( I)
FIG. 4. Changes in levels of plasma TSH in response to varying degrees of sustained cold stress.
Log
time
of exposure
FIG. 5. An illustration of time delays before the onset of response of (a, b, and c) variables to sustained cold stress.
However, Leduc (1961) has shown that norepinephrine secretion diminishes subsequently as shown in Fig. 6. Similarly the decline in metabolic rate was observed only in those critical experiments wherein exposure to cold was continued for an adequately long time (Davis et al., 1960). The understanding of acclimatory processes poses two types of problems, one due to limitations peculiar to the general nature of biological experimentation and the other due to conceptual limitations in the current understanding of acclimatory processes per se. Noise in measurement (due to measurement techniques, inter- and intra-species variations, etc.), and paucity
I
I IO Time
FIG. 6. Urinary
output of noreprinephrine
I 20 of exposure
I 30
I
(days)
on sustained exposure to cold. A, steady
state according to Sellers et al. (1971); B, steady state according to Leduc (1961).
MODELLING
OF
ACCLIMATORY
PROCESSES
31
of data due to technical limitations are hurdles in experimentation obvious to all biologists. Even conceptually, understanding of acclimatory processes in terms of simple feed-backs or goal-seeking systems [as suggested by Adolph (1964), Prosser (1964), etc.] has specific limitations. Much of the literature on biological regulations pertains to modelling these complex regulatory systems in terms of relatively simple feedback loops. So the problem of biologists is one of identifying the structure and dynamics of these (hypothetical) simple feedback loops, a difficult exercise that often proves very unsatisfactory. For example, the time dependent variations of a metabolite may be viewed by a biochemist in terms of end-product inhibition of a particular enzyme. But a demonstration of end-product inhibition in uitro does not necessarily mean that such a mechanism is operative in viuo, where the particular end-product may not accumulate in the same compartment or to the same extent as it did in vitro. Feedback loops, which are suggested to be operative at all levels of organization from molecular to behavioural, are innumerable. In any attempt to model the responses of an organism to a given stress, one encounters the problem of identifying the structure of the feedback loops, actually invoked by the organism to modulate the variables. Even if this were possible in isolated instances with reference to a specific variable, the attempt to explain a highly interactive process such as the acclimatory process in terms of simple feed-back loops is quite hazardous, For example, the regulation of shivering is better understood in terms of heat production to facilitate homeothermy in cold than in terms of feedback via the Renshaw cells on the motoneurones. But shivering in itself is a highly integrated response in terms of brain neurotransmitters, their metabolism and also general metabolism. Though a great deal is known of the components of all these sub-systems in isolation, we know very little of how they interact with each other in terms of an integrated response such as shivering. Thus there is not much advantage in modelling acclimatory processes as simple feedback loops interconnected with each other since we know little of the nature of their interconnections and much less about their dynamics. The attempt to understand the acclimatory processes as goal-seeking processes also presents numerous difficulties. Though the gross goals of acclimation, in terms of survival efficiency and fitness, are intuitively obvious, a translation of these goals to microlevels of organization such as hormone and metabolite levels is rather d&cult. Similarly, goals at these microlevels, even if well appreciated may prove to be hazardous, if extrapolated. For example, cortisol treatment causes negative nitrogen balance in the body (Forsham & Melmon, 1968), but leads to an elevation of specific enzyme protein synthesis in the rat liver (Kenney, 1970). The problem in modelling any complex process such as acclimatory
32
V.
SITARAMAM
AND
N.
J.
RAO
process, may be simply stated in the words of Mesarovic (1970) “A truly complex system, by definition evades complete description. We need a logic that explains all the events in relation to overall co-ordinated behaviour in simple terms-simplicity being the essential prerequisite for understanding. And yet we need to account for all the complexities of dynamic interactions. Hierarchical approach offers a resolution to this dilemma.” In the ensuing discussion, we suggest that acclimatory processes are best understood in terms of hierarchical theory of organization. An application of hierarchical system theoretic approach can lead to modelling of these responses both qualitatively and quantitatively. To do so, it is essential to define precisely the various terms that have been encountered. 4. Definitions
Acclimatory processes, different from adaptive processes which refer to changes on an evolutionary time scale, refer to responses to stress during the life span of an organism. “Acclimation” has relevance only with respect to a specific variable. Acclimation represents the cumulative experience and this experience may be characterized by a suitable performance index. Therefore we can dispense with the need to identify a finite interval of time at which the organism as a whole would be considered acclimated. Acclimation of a system variable, X, at a given instant of time is the cumulative experience gained till then and may be characterized by the value of the performance index, A,, where X,
i Ix,- x,lds
A,(t)= 2 pss- x,/ds
(1)
is the value of the state variable X, at time t = S, in response to step change in environment (stress) and x,, is the apparent steady-state value of the same. (The choice of the steady state value should be made with caution as pointed out earlier). Other similar performance indices may be defined to characterize acclimation. Acclimation is specific to each state variable, and to both type and degree of stress and as defined above, it can take any value between 0 and 1.0. Acclimation time, a parameter that can be associated with each state variable of acclimatory processes, and which indicates how long a variable takes to reach the (apparent) steady state, can be defined as follows: = o-95 i.e. the time taken at which the acclimation of the variable is O-95.
tA,
A&“)
MODELLING
OF
ACCLIMATORY
PROCESSES
33
It has been observed that, for a large number of responses, the acclimation, A,(t) can be approximated by an exponential curve of the type [l -exp (-t/r)]. It may be noted that in such cases, tA and r are related in a very simple manner (fA = 37). As acclimation is specific with reference to the variable and the type and degree of stress, the acclimation time f,,, should also be qualified accordingly. For example, tA (cortisol, cold, A 25°C) = 10 h. Acclimation time, fA, can be used as an index to fix the time sequence of events and acclimation, A,(t), to determine the bias of the organism in terms of its past history (e.g., age, drug treatment, previous exposure, etc.). Survival efficiency itself can now be interpreted in terms of acclimation and acclimation time. It must be cautioned that these quantities as defined here, have limited utility in understanding the regulatory mechanisms and do not directly represent any physiological process. 5. Hierarchical
Basis of Acclimatory
Process: Growth-decay Analysis
Modelling of a biological system with reference to acclimatory processes would involve the identification of the mathematical relationships of a large number of subsystems (stimulus-responses) and their interconnections. In view of all the difficulties stated earlier, the framework in which the problem of modelling is undertaken, should be able to explain the partially available structural and (noisy) quantitative information and should also indicate ways of improving the model through further (and better) experimentation. An attempt is made in the following section to identify such a framework to understand the acclimatory processes better. In a biological system, any variable is a complex function of all the system variables and the inputs. In literature, this relationship has been assumed, rather implicitly, to be either a simple algebraic one or a dynamic one . . . at least at the experimental level. The algebraic relationships can at best relate the steady state values of the system variables under very specific conditions. Some of the system responses shown in Fig. 1, may be modelled as those of simple feedback loops. It is obvious that the other responses (c, d, e . . . ) shown in Fig. 1, cannot be modelled as those of simple feedback loops. A multi-input, multi-output model, having a number of interactive feedback loops may be satisfactory to represent any biological situation, but the exact identification of the structure and dynamics of the system will be very hard, if not an impossible task. Guyton’s model of the cardiovascular system is an example of such interactive feedback loops (Guyton, Coleman & Granger, 3 T.8.
34
V. SITARAMAM
AND
N. J. RAO
1972). But the only analytical tool that could be used for the study of such models is simulation. Based on the general observation that stress leads to deviations in state variables from their normal vaiues and that sustained stress leads to those variables attaining steady states which may be above, below or at the basal values, one may express each response in terms of “growth” and “decay”. “Growth” refers to the initial deviation from the basal value and “decay” refers to the subsequent return to the normal. Any biological response may now be analyzed in terms of its growth and decay and time delays.? The example given below would serve to illustrate this growth-decay approach. The behaviour of hormones such as growth hormone and TSH in response to stress has been observed to be as shown in Fig. 7 (Itoh et al., 1965). The
FICA 7. Growth-decay
analysis of an experimentally observed response.
response, v(t) may now be expressed in terms of growth and decay in the following form O
Hierarchical Modelling of Acclimatory
Processes
V. SITARAMAM~ Department
of Biochemistry
N. J. RAO School of Automation, Indian Institute of Science, Bangalore, India (Received 9 December 1975, and in revisedform
16 August 1976)
The term acclimation has been used with several connotations in the field of acclimatory physiology. An attempt has been made, in this paper, to define precisely the term “acclimation” for effective modelling of acclimatory processes. Acclimation is defined with respect to a specific variable, as cumulative experience gained by the organism when subjected to a step change in the environment. Experimental observations on a large number of variables in animals exposed to sustained stress, show that after initial deviation from the basal value (defined as “growth”), the variables tend to return to basal levels (defined as “decay”). This forms the basis for modelling biological responses in terms of their growth and decay. Hierarchical systems theory as presented by Mesarovic, Macko & Takahara (1970) facilitates modelling of complex and partially characterized systems. This theory, in conjunction with “growth-decay” analysis of biological variables, is used to model temperature regulating system in animals exposed to cold. This approach appears to be applicable at all levels of biological organization. Regulation of hormonal activity which forms a part of the temperature regulating system, and the relationship of the latter with the “energy” system of the animal of which it forms a part, are also effectively modelled by this approach. It is believed that this systematic approach would eliminate much of the current circular thinking in the area of acclimatory physiology. 1. Introduction Life and its environment constantly interact and the course of events in the life span of an organism is determined by the environment to a large extent. Survival of the organism as well as the survival of the species is based on this t Present address: Department of Pathology, Yale University, School of Medicine, 310 Cedar Street, New Haven, Conn. 06510, U.S.A. 2s
26
V.
SITARAMAM
AND
N.
J.
RAO
fundamental principle of flexibility of life processes in subsisting on as well as reacting to the environment, and which we refer to as the “adaptability” of life processes. This property manifests itself at all levels of evolution as well as at all levels of organization of every organism. Studies of this property of life over the last century have given rise to important concepts : the organic basis of evolution (Darwin, 1859), “milieu interieur” (Bernard, 1878) and “homeostasis” and “wisdom of body” (Cannon, 1935). An understanding of biological signals and information processing by neurohumoral mechanisms, which facilitate effective interaction of the organism with the changing environment, has developed. The concept of feedback as developed by engineers has greatly facilitated the understanding of the complex network of biochemical, physiological and behavioural pathways. Acclimatory responses to environmental stress have been shown to involve adjustments at all levels of organization, from molecular to behavioural levels (Bajusz, 1969; McC. Brooks, 1969; Prosser, 1964). Thus the composite action within and between various levels of organization are basic to acclimatory processes, and their study is of great potential importance. 2. Review of Literature Studies on acclimation by several workers reveal certain dominant lines of thinking and approaches towards the understanding of acclimatory processes, even though there has not been a rigorous formalization of the associated concepts. Prosser (1964) identifies acclimatory processes as complex inter-related regulatory events occurring in a co-ordinated fashion at various levels of organization. He discusses the goal-seeking nature of these processes and the feasibility of using the acclimatory responses as a tool in the study of biological regulation, even at the genetic level. The essential feedback nature of the acclimatory processes was recognized by Adolph (1964) and he visualized a “regulatory box” which regulates the response (output) characteristics and proposed that acclimation occurs in the regulatory box in the form of altered input-output (adaptagent-adaptate) relationships leading to increased survival efficiency. Selye (1950), whose pioneering work in the field of adaptive responses laid the foundations for the understanding of hormonal interactions in conditions of stress, distinguished three phases of adaptive responses which develop with time: (i) phase of alarm reaction-a non-specific phase, (ii) phase of compensation-wherein the animal adapts and improves its survival efficiency by bringing out suitable alterations specific to the type of stress imposed, and (iii) phase of decompensation-wherein, beyond certain limits of stress, the
MODELLING
OF
ACCLIMATORY
PROCESSES
27
animal cannot cope with the adjustments invoked in response to stress and progressively succumbs to stress. Hart (1971) suggests that “acclimation to cold can be described in terms of an exponential change in the physiological state from the initial to final level” and he distinguishes between responses observed (such as cold resistance) and the acclimatory process, per se. Most studies on the mechanisms underlying the responses are made in order to understand the processes involved in acclimation to a particular environmental stress. For example, Hochachka (1973) presents the biochemical strategies for studies on acclimatory processes invoked in the response to anoxia in animals. Given certain metabolic constraints for survival in anoxia, and alternate pathways to effect compensatory adjustments to anoxia, he discusses the experimental approach in unravelling the biochemical mechanisms underlying the physiological responses using the need-based logic. A critical review of literature in the field of acclimatory responses gives us only a limited qualitative understanding of the processes involved. The terms “acclimatory process/response”, “acclimation”, “acclimatization”, “accommodation”, “adaptation” and “adaptive process/response” have been used in some context or other, interchangeably. Several authors ascribed various shades of meaning to these terms, such as “normalization”, “optimization”, “fitness”, “survival efficiency”, “performance indices”, “goal seeking processes”, etc. Further, though the term acclimation has been used with reference to the entire organism, experimentally it has invariably been associated with the specific variable considered most relevant to the organism as a performance index for a given type of stress. For example, in cold exposed rats, much of the literature pertains to comparison of levels of variables in non-acclimated animals with acclimated animals, where “acclimated animals” refer to those exposed to cold for about three weeks, by which time the metabolic rate (oxygen consumption) apparently stabilizes. In spite of the differences in the formal definition of “acclimation” by several authors, general consensus of opinion prevails in that: (1) Acclimatory processes evolve with time, i.e., the processes develop as functions of time. (2) Acclimation is largely viewed with reference to specific variables, which have a bearing on the performance of the animal. (3) Within certain limits of stress, the animal tends to survive and perform the vital processes progressively more efficiently. (4) Specificity in response to a stress is considered to emerge with time. (5) It is an optimizing process as a result of co-ordinated events occurring at various levels of complexity.
28
V. SITARAMAM
AND
N. J. RAO
Thus we see that a rigorous formal definition of acclimation is needed to establish uniformity in these studies to understand the acclimatory processes. The present attempt addresses itself to the task of redefinition of acclimation and to the introduction of a certain measure of abstraction in a form amenable to mathematical analysis. 3. Acclimatory
Process: the Nature and the Problem
When an animal is exposed to stress, one can observe changes in several variables, which appear within seconds to several days. The time course of such variations is illustrated in Fig. 1. One may note from the figure that all 1
Time
FIG. 1. Biological
of exposure
(%I
responses to sustained exposure to stress.
variables tend either to stabilize at a different level, or more commonly, to return to the initial level. The variables may be grouped arbitrarily into a variety of classes such as enzymes, metabolites, hormonal levels, electrical activities etc. Even within the same class of variables, such as enzymes, variables with a wide range of time scale have been observed. Variables such as oxygen consumption and body insulation and norepinephrine secretion, which belong to different classes but are causally related vary in response to a step change in ambient temperature with the time scales as shown in Fig. 2 (Davis, Johnston, Bell & Cremer, 1960; Leduc, 1961; Precht, Christophersen, Hensel & Larcher, 1973). It is noteworthy that, whereas the increase in variables such as shivering can occur within seconds of exposure to cold stress, the suppression of shivering takes days to develop. In other words, the initial increase and subsequent fall need not necessarily be of the same time scale. Degree of stress (AT from body temperature in the case of cold exposure) is yet another determinant in subscribing the time course of the variables. In instances where the response is not an “all-or-none” type, proportionality may be observed with the degree of stress in the initial phase
MODELLING
OF
ACCLIMATORY
Days
PROCESSES
of exposure
FIG. 2. Changes in metabolic rate (MR), urinary excretion of norepinephrine insulation (INS) in response to sustained exposure to cold.
I
I I
I
I
2
3 Time
FIG. 3. Response of hepatic tryptophan rats.
(NE), and
( / )
pyrrolase to varying degrees of cold stress in
itself (Fig. 3) (Sitaramam & Ramasarma, 1975). However in other instances such as circulating levels of corticosteroids, growth hormone, TSH and shivering an increase in degree of stress considerably slows down the return to basal level (Fig. 4) (Itoh, Hiroshige, Koseki & Nakatsugawa, 1965). The stress-mediated alterations in the variables appear after a time delay, which may range from a fraction of a second (e.g., shivering) to days (e.g., insulation). Though such time delays may not be discerned due to experimental limitations, one may justifiably assume a finite time delay before the onset of any response, as shown in Fig. 5. The steady states that might be observed experimentally in the animal under sustained stress with regard to specific variables should be viewed with caution. Norepinephrine secretion, as measured by urinary output per day was considered to stabilize within 7-9 days after cold exposure (Sellers, Flattery, Shum & Johnson, 1971).
30
V.
SITARAMAM
AND
Time
N.
of exposure
J.
RAO
( I)
FIG. 4. Changes in levels of plasma TSH in response to varying degrees of sustained cold stress.
Log
time
of exposure
FIG. 5. An illustration of time delays before the onset of response of (a, b, and c) variables to sustained cold stress.
However, Leduc (1961) has shown that norepinephrine secretion diminishes subsequently as shown in Fig. 6. Similarly the decline in metabolic rate was observed only in those critical experiments wherein exposure to cold was continued for an adequately long time (Davis et al., 1960). The understanding of acclimatory processes poses two types of problems, one due to limitations peculiar to the general nature of biological experimentation and the other due to conceptual limitations in the current understanding of acclimatory processes per se. Noise in measurement (due to measurement techniques, inter- and intra-species variations, etc.), and paucity
I
I IO Time
FIG. 6. Urinary
output of noreprinephrine
I 20 of exposure
I 30
I
(days)
on sustained exposure to cold. A, steady
state according to Sellers et al. (1971); B, steady state according to Leduc (1961).
MODELLING
OF
ACCLIMATORY
PROCESSES
31
of data due to technical limitations are hurdles in experimentation obvious to all biologists. Even conceptually, understanding of acclimatory processes in terms of simple feed-backs or goal-seeking systems [as suggested by Adolph (1964), Prosser (1964), etc.] has specific limitations. Much of the literature on biological regulations pertains to modelling these complex regulatory systems in terms of relatively simple feedback loops. So the problem of biologists is one of identifying the structure and dynamics of these (hypothetical) simple feedback loops, a difficult exercise that often proves very unsatisfactory. For example, the time dependent variations of a metabolite may be viewed by a biochemist in terms of end-product inhibition of a particular enzyme. But a demonstration of end-product inhibition in uitro does not necessarily mean that such a mechanism is operative in viuo, where the particular end-product may not accumulate in the same compartment or to the same extent as it did in vitro. Feedback loops, which are suggested to be operative at all levels of organization from molecular to behavioural, are innumerable. In any attempt to model the responses of an organism to a given stress, one encounters the problem of identifying the structure of the feedback loops, actually invoked by the organism to modulate the variables. Even if this were possible in isolated instances with reference to a specific variable, the attempt to explain a highly interactive process such as the acclimatory process in terms of simple feed-back loops is quite hazardous, For example, the regulation of shivering is better understood in terms of heat production to facilitate homeothermy in cold than in terms of feedback via the Renshaw cells on the motoneurones. But shivering in itself is a highly integrated response in terms of brain neurotransmitters, their metabolism and also general metabolism. Though a great deal is known of the components of all these sub-systems in isolation, we know very little of how they interact with each other in terms of an integrated response such as shivering. Thus there is not much advantage in modelling acclimatory processes as simple feedback loops interconnected with each other since we know little of the nature of their interconnections and much less about their dynamics. The attempt to understand the acclimatory processes as goal-seeking processes also presents numerous difficulties. Though the gross goals of acclimation, in terms of survival efficiency and fitness, are intuitively obvious, a translation of these goals to microlevels of organization such as hormone and metabolite levels is rather d&cult. Similarly, goals at these microlevels, even if well appreciated may prove to be hazardous, if extrapolated. For example, cortisol treatment causes negative nitrogen balance in the body (Forsham & Melmon, 1968), but leads to an elevation of specific enzyme protein synthesis in the rat liver (Kenney, 1970). The problem in modelling any complex process such as acclimatory
32
V.
SITARAMAM
AND
N.
J.
RAO
process, may be simply stated in the words of Mesarovic (1970) “A truly complex system, by definition evades complete description. We need a logic that explains all the events in relation to overall co-ordinated behaviour in simple terms-simplicity being the essential prerequisite for understanding. And yet we need to account for all the complexities of dynamic interactions. Hierarchical approach offers a resolution to this dilemma.” In the ensuing discussion, we suggest that acclimatory processes are best understood in terms of hierarchical theory of organization. An application of hierarchical system theoretic approach can lead to modelling of these responses both qualitatively and quantitatively. To do so, it is essential to define precisely the various terms that have been encountered. 4. Definitions
Acclimatory processes, different from adaptive processes which refer to changes on an evolutionary time scale, refer to responses to stress during the life span of an organism. “Acclimation” has relevance only with respect to a specific variable. Acclimation represents the cumulative experience and this experience may be characterized by a suitable performance index. Therefore we can dispense with the need to identify a finite interval of time at which the organism as a whole would be considered acclimated. Acclimation of a system variable, X, at a given instant of time is the cumulative experience gained till then and may be characterized by the value of the performance index, A,, where X,
i Ix,- x,lds
A,(t)= 2 pss- x,/ds
(1)
is the value of the state variable X, at time t = S, in response to step change in environment (stress) and x,, is the apparent steady-state value of the same. (The choice of the steady state value should be made with caution as pointed out earlier). Other similar performance indices may be defined to characterize acclimation. Acclimation is specific to each state variable, and to both type and degree of stress and as defined above, it can take any value between 0 and 1.0. Acclimation time, a parameter that can be associated with each state variable of acclimatory processes, and which indicates how long a variable takes to reach the (apparent) steady state, can be defined as follows: = o-95 i.e. the time taken at which the acclimation of the variable is O-95.
tA,
A&“)
MODELLING
OF
ACCLIMATORY
PROCESSES
33
It has been observed that, for a large number of responses, the acclimation, A,(t) can be approximated by an exponential curve of the type [l -exp (-t/r)]. It may be noted that in such cases, tA and r are related in a very simple manner (fA = 37). As acclimation is specific with reference to the variable and the type and degree of stress, the acclimation time f,,, should also be qualified accordingly. For example, tA (cortisol, cold, A 25°C) = 10 h. Acclimation time, fA, can be used as an index to fix the time sequence of events and acclimation, A,(t), to determine the bias of the organism in terms of its past history (e.g., age, drug treatment, previous exposure, etc.). Survival efficiency itself can now be interpreted in terms of acclimation and acclimation time. It must be cautioned that these quantities as defined here, have limited utility in understanding the regulatory mechanisms and do not directly represent any physiological process. 5. Hierarchical
Basis of Acclimatory
Process: Growth-decay Analysis
Modelling of a biological system with reference to acclimatory processes would involve the identification of the mathematical relationships of a large number of subsystems (stimulus-responses) and their interconnections. In view of all the difficulties stated earlier, the framework in which the problem of modelling is undertaken, should be able to explain the partially available structural and (noisy) quantitative information and should also indicate ways of improving the model through further (and better) experimentation. An attempt is made in the following section to identify such a framework to understand the acclimatory processes better. In a biological system, any variable is a complex function of all the system variables and the inputs. In literature, this relationship has been assumed, rather implicitly, to be either a simple algebraic one or a dynamic one . . . at least at the experimental level. The algebraic relationships can at best relate the steady state values of the system variables under very specific conditions. Some of the system responses shown in Fig. 1, may be modelled as those of simple feedback loops. It is obvious that the other responses (c, d, e . . . ) shown in Fig. 1, cannot be modelled as those of simple feedback loops. A multi-input, multi-output model, having a number of interactive feedback loops may be satisfactory to represent any biological situation, but the exact identification of the structure and dynamics of the system will be very hard, if not an impossible task. Guyton’s model of the cardiovascular system is an example of such interactive feedback loops (Guyton, Coleman & Granger, 3 T.8.
34
V. SITARAMAM
AND
N. J. RAO
1972). But the only analytical tool that could be used for the study of such models is simulation. Based on the general observation that stress leads to deviations in state variables from their normal vaiues and that sustained stress leads to those variables attaining steady states which may be above, below or at the basal values, one may express each response in terms of “growth” and “decay”. “Growth” refers to the initial deviation from the basal value and “decay” refers to the subsequent return to the normal. Any biological response may now be analyzed in terms of its growth and decay and time delays.? The example given below would serve to illustrate this growth-decay approach. The behaviour of hormones such as growth hormone and TSH in response to stress has been observed to be as shown in Fig. 7 (Itoh et al., 1965). The
FICA 7. Growth-decay
analysis of an experimentally observed response.
response, v(t) may now be expressed in terms of growth and decay in the following form O
