Factores de riesgo cardiovascular

From a microbial perspective, a substrate with a higher free energy state (ΔG0) enables a faster growth rate (Servizi & Bogan, 1963). Oxidising a substrate with oxygen yields the most energy and consequently the highest growth rates. 1 mole of glucose using oxygen as an electron acceptor will produce 38 mol of ATP, while in the absence of oxygen, alcohol and CO2 are produced yielding only 2 mol of ATP (Gliński & Stępniewski, 1985). In the

absence of oxygen, other electron acceptors are utilised (Cho, Burton, & Chang, 1997; Dassonville et al., 2004; Mayberry et al., 1967) and growth proceeds, albeit at a slower pace.

It is the need to model the microbial process which has given rise to the concept of a rate constant. This is based on a phenomenological law of a mass of microbial activity, not an actual microbial parameter (substrate ΔG0

is the useful microbial parameter). From the microbial perspective, some microbes would utilize oxygen as it becomes available, while their neighbours continued with other electron acceptors – a diverse range of electron acceptors could be utilised at any one time in the composting mosaic. The measured rate constant would tend towards reflecting the rate of the dominant electron acceptor, but would remain affected by all the others. However, oxygen exhibits strong concentration gradients in a composting particle and, when present in sufficient concentration, is a dominant electron acceptor.

A second form of variability exists in the microbial world. This arises from the difficulty in utilizing the available substrates. Substrates able to be absorbed directly by cells, for example, soluble sugars and cellular contents from dead micro-organisms, will result in higher growth rates, and higher composting rates, than high molecular weight substrates, for example cellulose, which must be broken down by cellulosomes before being able to be utilised by cells. See Atkey & Wood (1983) for an electron micrograph study of the burst of microbial activity when a cell wall is breached and micro-organisms invade the cell contents. Some substrates, especially lignin can only be broken down by specific micro- organisms (Tuomela, Hatakka, Raiskila, Vikman, & Itavaara, 2001; Tuomela, Vikman, Hatakka, & Itavaara, 2000).

Kaiser (1996) incorporated this variability (his first trophic level) by allocating each substrate to its component microflora and modelled it as a microbial ecosystem. These

substrates, and their associated microflora, in his model are then converted via upper trophic level micro-organisms into humus.

Within the framework proposed in this thesis, the phenomenological rate constants associated with this variability, are placed on two axes, a substrate axis and an electron acceptor axis (Table 3-2). Within this framework the „humification‟ process appears as a fraction, that is the part of the composting time course not explainable by the fast or slow fractions.

Table 3-2 – Possible phenomenological rate constants from three substrates and three electron acceptors. SUBSTRATE FAST (Soluble) SLOW (Insoluble) HUMIFICATION Electron acceptor (Redox Potential)

Oxygen kO2(f) kO2(s) kO2(h)

Nitrate kNi(f) kNi(s) kNi(h)

Anaerobic kan(f) kan(s) kan(h)

The non steady-state condition arising from the change in oxygen concentrations as substrate is degraded, can be accommodated within steady-state diffusion law solutions by limiting analysis to an appropriately short time interval (discussed above in section

3.2.1.3). This accommodation can be extended to multiple substrates as utilisation of the different substrates is not sequential. In general, utilisation of the slow fraction continues while the fast fraction is still present, however, the utilisation of some substrates has been shown to be inhibited by the presence of others (Haag et al., 2005; Lemus, Lau, Branion, & Lo, 2004; Vavilin & Lokshina, 1996). The fast fraction is degraded faster than the slow fraction over time, it follows therefore that there will be a gradual transition from

composting being dominated by a fast fraction substrate to being dominated by a more refractory substrate. This gradual transition can be accommodated in the steady-state conditions of diffusion law solutions because over any particular period of analysis it can be considered to be constant.

Indeed, the parameter needed for diffusion law solutions is volumetric oxygen uptake rate (rO2 of Equation 3-3). How this is determined is of no consequence. Considerable

computational complexity can exist in determining oxygen uptake rate without impacting on the diffusion law solutions. Different substrates and their attendant different rate constants are only one form of the possible computational complexity.

In a similar manner, the many phases identified in microbial kinetics (Luedeking, 1967) can be reduced to two for application in micro-environment analysis (Figure 3-2):

 A growth phase, attributed to the composting rate increasing as the biomass builds up.

 A decline phase, where substrate limits the composting rate (the composting rate declines as substrate is degraded).

Time Com po stin g rate Gr ow th Decline

Figure 3-2 - A typical composting profile, under assumed conditions.

However, the transition from one electron acceptor to another is not so easily

accommodated in diffusion law solutions. While two different rate constants can be accommodated within steady-state conditions if the transition from one to the other is gradual and they both consume oxygen, the relationship would only apply to a new

electron acceptor if it did not significantly impact on the composting rate, as the oxygen based electron acceptor would need to continue to dominate the composting rate, however low its concentration may get. This is clearly not the case because non-oxygen based electron acceptors do occur, and while they may not contribute much to the composting rate, they can make their presence known in other ways: e.g. odour, low pH.

For example, nitrate as an electron acceptor generates 19 mole ATP mole-1 glucose (Dassonville et al., 2004) while oxygen as an electron acceptor generates 38 ATP mole-1 (Gliński & Stępniewski, 1985). Nitrate as an electron acceptor would be expected to compost at 50% of the rate of oxygen as an electron acceptor, if the appropriate microbes were not limiting the rate and the concentrations were the same. However, the electron acceptor relationship is more complex than this. For example, there is suppression of nitrification at high oxygen concentrations because heterotrophs outcompete the autotrophs

for the available oxygen (Zhang et al., 1994). By contrast, the denitrifiers which can utilise nitrates as an electron acceptor, do not begin activity until very low oxygen levels (Cho et al., 1997). As many of the micro-organisms capable of utilising these different electron acceptors will need to grow when the environmental conditions become suitable, it becomes apparent that the electron acceptor transitions will be impacted by many more factors than oxygen concentration.

3.3.1 The Anaerobic – Aerobic Transition

The effect of time on the oxygen concentration profile of the fast fraction in compost can be seen in Figure 3-3. Under these assumed conditions (k = 10 W MJ-1, E = 0.002 MJ cm-

3

) the oxygen penetration depth increases from 0.018 cm to 0.020 cm over the 6 hour period. The compost between these two depths undergoes a transition in rate constant from anaerobic to aerobic. The two rate constants are sequential.

Figure 3-3 shows that the position of the second graph relative to the first is a function of the time interval. A very short interval would cause them to merge; yet a longer time interval would see them diverge. Thus, the oxygen front moves continuously in composting space over time; it has a velocity (Figure 3-4).

0.000 0.002 0.004 0.006 0.008 0.010 0.001 0.003 0.005 0.007 0.009 0.011 0.013 0.015 0.017 0.019 0.021 0.023 Depth (cm) Ox y g e n c o n c e n tr a tio n ( g /L ) T_0 T_1 (6 hours later) Anaerobic Aerobic Anaerobic - aerobic Transition

Movement of oxygen front over time

Figure 3-3 – Oxygen concentration profiles with a 6-hour separation, assuming only the fast fraction is composting. Data using Bouldin’s (1968) model II with k=10 W MJ-1 & E = 0.002 MJ cm-3.

In addition, it was argued in Section 3.2.1.4 that with a fast rate constant of 10 W MJ-1 some 2% of the substrate is degraded in 30 minutes. Considering that a micro-

environment is formed using parameter states at the end of the interval, and that these are taken to represent the „average‟ of the states in the micro-environment, then the shorter the interval the better the parameter states at the end of the interval will represent the average state; and the less variation in substrate concentration that will occur between the outer and inner boundaries. It follows that the shorter the interval the better the model output will represent the actual time course. The effect on calculated oxygen velocity in Figure 3-4 is a result of this effect.

0.0082 0.0083 0.0084 0.0085 0.0086 0.0087 0.0088 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 Interval (Minutes) O x y g e n p e n e tr a tio n V e lo c it y ( c m /d a y )

Figure 3-4 – The influence of length of analysis interval on determination of the oxygen penetration velocity (cm/day) of Figure 3-3. The 0.0087 cm/day velocity at the 6 hour interval in Figure 3-3. reduces to 0.00825 cm/day as the interval → 0.

The steady movement of the oxygen front has been measured at the macro-scale in leaf composting (Strom, Morris, & Finstein, 1980), and at the micro-scale using

microelectrodes in a soil-manure system over a 21 day period (Petersen et al., 1993 Figure 5c).

3.3.2 Aerobic Composting Start-time

It is aerobic composting which is being modelled in this thesis. It was shown in the previous section that, over time, the oxygen front moves into previously anaerobic parts of a particle. For the case of oxygen penetrating into previously anaerobic/anoxic compost, the rate constant changes from kanaerobic/anoxic to kaerobic. The kinetic model requires the rate

constant to be constant, therefore there are two sequential kinetic functions with a start- time t(0) for each rate constant (k). Oxygen reaching new substrate causes the transition

from anaerobic/anoxic to aerobic, therefore this transition determines start-time t(0) of the aerobic composting kinetic, and the end of the anaerobic composting kinetic.

As this transition occurs within the macro-scale time frame of the composting pile, it is only the outer layer of the particle for which the pile start-time = micro-environment start-